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http://crypto.stackexchange.com/tags/modes-of-operation/hot?filter=year
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# Tag Info
16
CBC does not perform authentication This property makes it less suitable for places where authentication is required, basically any transport protocol. TLS uses CBC, but by default performs authentication over the plain text instead of the ciphertext, which opened up a host of attacks. CBC can be used here, but it is error prone and may require an ...
13
Contrary to what Stephen says, you absolutely can compute the tag in parallel. Here's how it works; the tag computation is essentially "assemble the AAD, data, the length field and $Encr(Nonce)$ into a series of values $x_n, x_{n-1}, x_{n-2}, ..., x_0$", and then "compute the polynomial $x_nh^n + x_{n-1}h^{n-1} + x_{n-2}h^{n-2} + ... + x_0h^0$ This ...
9
It is not secure, because an attacker can "mix and match" the output blocks from different authentication tags on different input messages, or repeat output blocks for repeated input blocks. For example, if the attacker knows the tag $F_k(m)$ for a one-block message $m$, then it can forge the correct tag $F_k(m) \mid F_k(m)$ for the two-block message $m ... 8 I would like to ask if that is true for every AES CTR mode implementation?, Doesn't have to be. You can store the nonce anywhere. You could even send it to the recipient via a different channel (e.g., email the ciphertext and use SMS to transmit the nonce). Storing it at the beginning has its advantages. For example, if streaming the data, you can ... 8 One obvious thing that it is vulnerable to a known plaintext attack that truncates the known message. This attack is quite simple; suppose the attacker knows a message$(P_1, P_2, ..., P_n)$and the corresponding ciphertext$(C_1, C_2, ..., C_n, T)$(using some IV; we don't care what it is). Here is how the attacker can generate a ciphertext that would ... 8 The modern trend for encryption-only modes is clearly CTR, which has a number of advantages over other modes: no padding is needed (contrary to CBC); the computationally-intensive part can be efficiently performed with the IV (and key) only, before the plaintext or ciphertext is available (contrary to CBC, CFB); the computationally-intensive part can be ... 8 There are several scenarios where you wouldn’t want to use AES in CBC mode. In CBC mode, each block is dependent on a previous one. As @fgrieu nicely hinted at in his comment, using CBC means that if you have a large, encrypted file and you only want to update/change/modify a tiny fraction of it, you would have to follow the decrypt-modify-encrypt path each ... 7 The other answer is correct in general. However, if your messages are all exactly one block long (or all one block after padding), ECB is a secure MAC. A PRP looks like a PRF up to half its bit length, i.e. up to$2^{64}$blocks for AES. A secure PRF is a secure MAC of the same size. Thus, AES ECB used on 128-bit messages is a secure MAC as long as you use ... 7 First, the fact that the data is "easy" to guess (in the sense that an attacker has a one-in-2^32 or a one-in-2^64 chance of guessing correctly) doesn't mean much if the attacker has no way of checking if his guess is correct. Or at least, it's not a problem with the cryptography. Second, even if he does have that ability, the problem of protecting your ... 7 There are probably quite a few good reasons for this, although I don't expect that a scientific answer can be composed (as you would need to use a survey, and I've never heard of such a thing for modes of operation). Let me list a few possible reasons: Developers don't know about CTR mode of operation; most questions on StackOverflow are about ECB and CBC ... 5 I know that some of them are pretty hard to crack, but since they are so commonly known is it even practical to consider using something like that as an encryption method considering the algorithms for encryption and decryption are commonly known (from a security perspective)? In fact, this is exactly what we want. Schneier's law Anyone, from the ... 5 If you want strict indistinguishability, then yes, you need to store the IV (initial counter) somewhere. However, there are some relaxed modes that are used in practice for things like disk encryption, where it is often very useful to decrypt things "in the middle" like you say. For instance, XEX uses a counter which is derived from the sector and offset ... 5 The GCM flowchart on Wikipedia and my intuition support the notion that some of the GCM work can be done in parallel. At the very least you can do each$E_k(ctr)$operation in parallel, but it doesn't look like you should be able to parallelize the authentication, as each$mult_H$requires the output of a previous call as its input. Edit: poncho explains why ... 4 Well,$\operatorname{GHASH}$might be better understood as the polynomial: $$\operatorname{GHASH}_H(X_1, X_2, ... , X_{m-1}, X_m) = X_1 H^{m} + X_2 H^{m-1} + ... + X_{m-1} H^2 + X_m H^1$$ where addition, multiplication and exponentiation are in the field$GF(2^{128})$. These addition, multiplication and exponentiation operations act algebraically quite a ... 4 Encrypting big amounts of data is no problem for block cipher - if you remember a few important things. You can't encrypt plaintext which is bigger than the block size. You need to do some addition work. Most cipher operation modes first divide the plaintext into blocks of the size of the cipher. Now you can do different things: How about just encrypting ... 4 Actually, s is in CFB mode to handle transmission channels for the encrypted data that can add or drop individual bytes. In the olden times (say, the 70's), it was common to transmit data over serial channels, for example, RS-232. These channels were not perfect, and one common error we see is that if the transmitter sent 7 bytes, the receiver might get ... 4 Like the other answers say, it does not always have to be the case. One other case where it is often not stored is when you have a single use key, for example as part of some hybrid encryption scheme. Then there is no need to use a nonce at all and it is usually taken to have zero value. 4 There are two well-known Encryption modes, that can construct a$mn$-bit tweakable blockciphers from a$n$-bit blockcipher ($n=64$for DES) with$1\le m\le n\$. The older one is CMC, being not parallelizable. It was superseeded by Encrypt-Mix-Encrypt (EME), which is parallelizable. The basic idea of the two algorithms is to encrypt each block of input data ...
4
What is this method/algorithm/construction called? Dunno; this is a new one on me. Is it as secure as CBC implemented the normal way? Should be. Modeled as an abstract 'take plaintext, output ciphertext' model, this method (with a random last ciphertext bits) has precisely the same ciphertext output distribution as CBC mode (with a random IV), ...
3
Yes, it is correct. Just follow the bits in the decryption pictures on the Wikipedia page about modes of operation. Modes of operation don't have to have a meaning compared to other modes of operation. I don't see CFB or OFB used too much anymore. OFB with partial feedback has been shown to be less secure, so that shouldn't be used anymore. Currently the ...
3
The standard for full-disk encryption (FDE) is XTS mode or ESSIV-AES-CBC. XTS tweaks each block within each sector differently (and hence avoids ECB's problems) and is considered the best choice available at the moment. ESSIV-AES-CBC works by using AES-CBC with the IV being the hash of the sector index. The problem with this mode is that you can flip bits ...
3
Better is a subjective term. However for the choice between ECB and CBC, the choice should be CBC for almost all situations. Although ECB and CBC are modes of operation of a block cipher, you could also turn this way of thinking around and see the block cipher as a configuration option for the mode of operation. The mode of operation has a big influence on ...
3
It is certainly wrong to state that "MAC can only be produced with AES in CBC and CFB mode", but there seems to be a simple reason that people were inspired by these modes when thinking up possible MAC constructions: They carry along some state that incorporates information from the message while traversing the input blocks. In both modes, encrypting a block ...
3
No, usually you are required to use hybrid cryptography. ECB, CBC etc. are defined for block ciphers. Although you could possibly apply them to asymmetric cryptosystems, it would make little sense: performing sequential asymmetric cryptography is not efficient, block ciphers are much more efficient in general there will be a lot of overhead per block, ...
3
In addition to the tweakable enciphering schemes in the comments, I'll leave this reference here: https://eprint.iacr.org/2009/356.pdf It essentially shows (in the ideal cipher model) that using an n-bit block cipher in a three-round Feistel construction gives you a 2n-bit block cipher.
3
Forget OFB mode. You should use CTR (counter) mode. It has the best bounds, and is parallelizable. This means that when you are using the AES-NI instruction set, encrypt with CTR is about 7 times faster than CBC, OFB etc. If you encrypt in OpenSSL you will get this performance. For a good thorough analysis and comparison of modes of operation, see ...
3
Your mode is essentially equivalent to CFB mode, except that: you've reversed the order of the blocks in the message, and you're using the block cipher in the opposite direction than usual. Neither of those differences should have any direct security implications (since all standard block ciphers have the same security properties in both directions), ...
2
In general we nowadays use fixed paddings or a stream mode of operation such as CTR. Authentication tags are usually used to validate integrity/authenticity. Examples of authentication tags are those created by calculating a MAC or HMAC over the ciphertext and additional data such as the IV. In general known plaintext - including the padding - should not ...
2
Dmitry's suggestion to use AES in counter mode sounds good to me, assuming that you only need confidentiality, and not integrity protection. (Counter mode, like most stream ciphers, is very malleable.) One trick you can use to save a bit of space is to use the current time as part of the nonce. (Of course, this only works if your devices have fairly well ...
2
A self-made modification to CBC is a bad idea, since your "IV" will not be random enough, whereas it must be truly random for CBC. Stream cipher is a good idea. You may use AES in the Counter mode, or you could use Salsa20, or any other eStream portfolio cipher (software and hardware implementations are available for all of them). Ensure that you have ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2015-08-31 21:55:16
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https://www150.statcan.gc.ca/n1/pub/11f0019m/11f0019m2019021-eng.htm
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# Analytical Studies Branch Research Paper Series The Long-term Economic Outcomes of Refugee Private Sponsorship
by Lisa Kaida, Feng Hou and Max Stick
11F0019M No. 433
Release date: January 13, 2020
## Abstract
An important policy initiative implemented for the past 40 years in Canada, refugee private sponsorship has attracted international attention as Europe continues to grapple with an influx of refugees. However, no research has systematically evaluated the long-term economic outcomes of private sponsorship and whether such outcomes vary by refugees’ human capital. This study compared the economic outcomes of privately sponsored refugees (PSRs) and government-assisted refugees (GARs) using the Longitudinal Immigration Database, an administrative database that contains information on virtually all immigrants and refugees who have arrived in Canada since 1980. The results show that PSRs had higher employment rates and earnings than GARs, particularly during the initial settlement period, even after taking into account differences in education, official language ability, and other observed socio-demographic characteristics, although the differences diminished over time. The PSR advantage was particularly noticeable among less-educated refugees.
Keywords: refugees, private sponsorship, employment, earnings
## Executive summary
Canada was the first country to introduce private sponsorship, and the program has played a key role in the country’s responses to international refugee crises over the last four decades. Private sponsorship has been regarded as a promising policy option for other major Western countries in their commitments to refugee resettlement.
However, empirical evidence regarding the economic outcomes of refugee private sponsorship is notably limited. To fill this gap, this paper examined the long-term economic outcomes of privately sponsored refugees (PSRs) with various human capital levels in Canada. It addressed two questions. First, how do the economic outcomes of PSRs compare with those of government-assisted refugees (GARs) in the initial resettlement period and over the longer term? Second, do the economic outcomes of PSRs vary by the refugees’ initial levels of human capital (official language skills and education)?
Based on the Longitudinal Immigration Database, this study found that PSRs and GARs differed in some key socio-demographic characteristics. Over the 1980-to-2009 period, more PSRs came from Eastern Europe than GARs, whereas more GARs came from South and Central America and the Caribbean than PSRs. PSRs had a higher level of education and were more concentrated in Toronto than GARs. This study takes into account of these observed differences in comparing their labour market outcomes, while recognizing that other possible unmeasured differences between the two groups of refugees, such as exposure to violence, duration of displacement, physical and mental health, and ethnic and family networks could impact their economic outcomes.
PSRs had higher employment rates and earnings than GARs in the initial years after arrival, even after taking into account differences in education, official language ability, and other observed socio-demographic characteristics, but these differences diminished over time with GARs steadily catching up. The study further found that the employment and earnings advantage of PSRs over GARs was greater among refugees with less than a high school education than among refugees with higher educational levels. The majority of refugees (51% and 61% for men and women in the study sample, respectively) had less than a high school education.
The study showed that refugees with poor official language skills benefited from private sponsorship as much as refugees with good official language skills. This is likely related to the fact that refugees with poor official language skills can take government-financed language training, regardless of whether they are in private sponsorship or government assistance programs.
## 1 Introduction
Timely economic integration of refugees has become a pressing policy issue for Western democracies as refugees have arrived at their national borders from the Middle East, West Asia, and Africa in large numbers in recent years. For most receiving countries, refugees are admitted for humanitarian rather than economic reasons. As a result, many refugees are not equipped with postsecondary education or host-country language skills, and they face greater challenges in economic and social integration than other immigrants (Beiser 2003; McKeary and Newbold 2010; Simich, Este and Hamilton 2010).
To fill this gap, this paper evaluated the economic outcomes of PSRs with various levels of human capital. Two research questions were addressed. First, how do the economic outcomes of PSRs compare with those of government-assisted refugees (GARs) in the initial resettlement period and over the longer term? Second, do the economic outcomes of PSRs relative to GARs vary by initial levels of human capital (i.e., official language skills and education)? These questions were answered using the Longitudinal Immigration Database (IMDB)—an administrative database that contains the landing and annual tax records of immigrants and refugees who arrived in Canada from 1980 onward.
This paper makes three research contributions. First, by using multivariate analysis, the economic outcomes of PSRs were compared with those of GARs while controlling for differences in observed demographic, socioeconomic and contextual characteristics. This provides a more robust assessment of the differences between these groups than previous research, much of which used simple descriptive techniques.
Second, this study provides new evidence on the interaction effects between refugee admission categories (PSR versus GAR) and refugee human capital upon arrival in Canada. This interaction effect considers the fact that refugees are a heterogeneous population with varying degrees of educational attainment and host-country language skills at their time of arrival.
Third, this study provides empirical evidence on the long-term economic outcomes of PSRs. These results are relevant to refugee integration policies not only for Canada, but also for Western nations that are responding to refugee inflows.
## 2 The economic integration of refugees and private sponsorship
It is widely acknowledged that refugees tend to do less well in the host country’s labour market than those who immigrated through other streams (e.g., economic immigrants) (Constant and Zimmermann 2005; Bevelander 2016). While some of the factors that contribute to the refugees’ poorer labour market outcomes also apply to other immigrants (e.g., limited host-country language skills, lack of host-country work experience, non-recognition of foreign credentials), other factors are specific to refugees—such as physical and mental health issues related to traumatic experiences, a lack of legal documents, and long-term disruption of education and careers (Bruno 2011; Hynie, Korn and Tao 2016; Krahn et al. 2000; Neupane 2012; van Selm 2003).
In Canada, the main findings about refugee economic integration were threefold. First, refugees’ economic outcomes during the initial settlement period were generally comparable with those of family-class immigrants, but were less favourable than those of economic immigrants (Aydemir 2011; Bevelander and Pendakur 2014; Hiebert 2009; Hyndman, Payne and Jimenez 2017; Wilkinson and Garcea 2017; Yu and Dempsey 2004). Second, despite their initial disadvantage, refugees narrowed the gap vis-à-vis other immigrants over subsequent years. Abbot and Beach (2011) reported that refugees achieved increases of 7% to 12% annually in median earnings over their first 10 years in Canada—a rate of increase that was higher than that of all other immigrant entry groups. That said, refugees’ initial disadvantage was so large that it would take them 12 to 18 years to reach the median earnings of all immigrants. Third, the employment outcomes documented among refugees varied considerably depending on the metrics and groups (i.e., men or women) being compared (Hiebert 2009; Picot, Zhang and Hou 2019; Wilkinson and Garcea 2017).
GARs and PSRs hold the same legal status: they are granted permanent resident status upon arrival and are eligible for the government support available to other permanent residents. Moreover, the motivation and pre-migration circumstances of GARs and PSRs are similar; they are often forced out of their home country because of war, political persecution or violence, and are seeking protection and a safe place to rebuild their lives in Canada.
However, PSRs and GARs also differ in many ways. GARs tend to settle in smaller cities and often have lower education and limited official language skills than PSRs (Jedwab 2018). Differences in pre-migration circumstances (e.g., experience in refugee camps, length of dislocation), selection processes (e.g., measurement of “vulnerability” in selecting GARs), and local receptivity (e.g., welcoming community) may partially account for the divergent trajectories of economic integration between the two refugee groups. In particular, because of local sponsor support, PSRs may be received more favourably in their host community compared with GARs. Even though the sponsor’s initial support ends one year after arrival, some refugees may maintain ties with sponsors (Aylesworth and Ossorio 1983; Neuwirth and Clark 1981). In addition, some ethnic communities may selectively sponsor co-ethnic refugees, and the sponsored refugees may take advantage of the pre-existing ethnic networks and receive culturally sensitive resettlement support (Portes and Rumbaut 2001). These favourable environments may help PSRs find jobs and achieve economic independence quickly.
Although limited in scope, existing empirical evidence on the economic integration of PSRs suggests that they achieve “slightly quicker self-sufficiency” than GARs; they find employment more quickly and garner higher earnings during their first 10 years in Canada (Picot, Zhang and Hou 2019; Wilkinson and Garcea 2017). PSR employment rates are higher, especially during the initial settlement stage. An analysis of refugees who were admitted to Canada between 2002 and 2012 showed that 70% of PSRs were employed one year after landing, compared with only 40% of GARs (IRCC 2016). However, by the 10th year in Canada, the employment rates of PSRs and GARs had almost converged.
Other studies show that PSRs have higher earnings or incomes than GARs during their initial years in Canada (Beiser 2003; Bevelander and Pendakur 2014; DeVoretz, Pivnenko and Beiser 2004; Mata and Pendakur 2017; Sweetman and Warman 2013; Yu and Dempsey 2004). However, findings about whether this advantage persists in the longer term are mixed. In her analysis of refugees who arrived in 1991, Dhital (2015) found that female and male PSRs had annual median earnings that were $5,000 and$12,000 higher than their respective GAR counterparts 10 years after landing, with a PSR advantage observed even up to 18 years after arrival. By contrast, Immigration, Refugees and Citizenship Canada’s IMDB analysis found that the gaps in employment earnings between the PSRs and GARs who arrived between 2002 and 2012 diminished after the 10-year mark (IRCC 2016).
Despite such positive evidence and Canada’s international reputation for community-based refugee resettlement, to date there has been no systematic evaluation using rigorous statistical techniques of the long-term economic outcomes of private sponsorship (Fratzke 2017; Treviranus and Casasola 2003). Most of the existing assessments did not fully consider the differences in human capital and other demographic and contextual characteristics between PSRs and GARs (Jedwab 2018). One exception was the study by Picot, Zhang and Hou (2019) that compared earnings of refugees by admission program up to 15 years after immigration, although it did not examine employment rates. Meanwhile, studies on PSRs have been done mostly on a smaller scale and have focused on specific ethnic or country-of-origin groups who settled in certain cities, or on the private sponsorship program itself (Beiser 2003; Denton 2003; Hyndman, Payne and Jimenez 2017; Labman 2016; Lenard 2016; Neuwirth and Clark 1981; Treviranus and Casasola 2003; Woon 1987). As a result, little is known about whether the results observed from a specific refugee group that arrived in a specific historical context can be generalized to other refugee groups, or whether PSRs’ initial advantage over GARs can be attributed solely to their landing characteristics (e.g., human capital, country of origin, place of settlement) or to other factors, such as settlement programs themselves.
To address these gaps, the IMDB was used to examine the employment and earnings of PSRs and GARs who landed in Canada between 1980 and 2009. Using multivariate analysis, the analysis adjusted for the differences in characteristics at landing and post-migration between GARs and PSRs. PSRs were expected to have better labour market outcomes than GARs, especially in the initial resettlement period, given the sponsors’ legal responsibility to provide financial and social support to the PSRs in the first 12 months. After the end of the sponsorship commitment, such differences were expected to diminish over time. However, studies have shown that many refugees maintain contact or friendship with their sponsors, which may help their long-term economic integration (Beiser 2003; Woon 1987). Therefore, the first hypothesis was as follows:
Hypothesis 1: PSRs are more likely to be employed and to earn more than GARs both over the short term (less than 5 years) and over the longer term (15 years) when their demographic, socioeconomic and contextual characteristics are taken into account.
This study also considered the possibility of interaction effects of refugees’ admission categories and human capital, given that refugees are a socioeconomically diverse group (IRCC 2016; Jedwab 2018). Refugees with high human capital (e.g., highly educated, proficient in English or French) may be more self-sufficient and could achieve economic success without much sponsor support (Nakhaie 2018). By contrast, refugees with limited human capital may benefit more from private sponsorship since sponsor support could compensate for their human capital deficit. Thus, the second and third hypotheses were as follows:
Hypothesis 2: The employment and earnings advantage of private sponsorship over government assistance is greater for less-educated refugees (e.g., less than high school) than for highly educated refugees (e.g., bachelor’s degree or above).
Hypothesis 3: The employment and earnings advantage of PSRs over GARs is greater among refugees with limited host-country language skills than those with higher host-country language skills.
## 3 Data and methods
### 3.1 Data
The data were drawn from the IMDB, which contains landing records and annual tax records of immigrants, including refugees, who arrived in Canada from 1980 onward and filed taxes at least once (Hou and Bonikowska 2016). Those who filed taxes at least once since 1982 are included in the database.
The sample consists of individuals who landed in Canada as PSRs or GARs at ages 20 to 54 between 1980 and 2009. Other refugee categories (e.g., in-Canada asylum seekers, refugee dependants, blended visa office-referred [BVOR] refugees) are not included in the analysis because of small population sizes (e.g., refugee dependants, BVOR refugees) and stark differences in characteristics compared with PSRs that would make the comparison difficult. Moreover, PSRs and GARs from the United States, Northern and Western Europe, Australia and New Zealand, and stateless individuals were dropped from the analysis because of their small sample sizes.
### 3.2 Measures
Two dependent variables were used to measure refugee economic integration: employment (the presence of positive annual employment incomes) and employment earnings among those with positive annual earnings in a specific year since landing. The presence of positive annual employment income is a proxy of employment status. Employment is an indicator of self-sufficiency and is a critical factor in shaping other aspects of refugee integration, such as finding housing, expanding social networks, improving host-country language skills, improving mental health and gaining a greater sense of belonging (Beiser 2003; Hynie, Korn and Tao 2016). The employment variable is coded “1” if a refugee reports a positive annual employment income for a specific tax year, and “0” otherwise.Note
Employment income (including wages and salaries) reflects the combined effect of hourly wages and total hours of work in a particular year (Hou and Bonikowska 2016). Better-paying employment may allow refugees to participate more fully in the host society (Hynie, Korn and Tao 2016). This is a continuous variable (adjusted to the 2015 value using the Consumer Price Index), but it is top coded at $300,000 to keep the higher income values from skewing the distribution. For multivariate analysis, logged-earnings values were used. Refugee admission categories were central in the analysis and were categorized as PSRs and GARs (the reference group). In addition, years since landing (YSL) was also a key factor. In this study, the first two years were coded as dummy variables, and the third year and onward were coded as a continuous variable. This was because the differences in labour market outcomes between PSRs and GARs were likely the largest in the first year—the period when sponsors were formally committed to providing financial and social support. The effect of that direct support may linger in the second year. Descriptive statistics (Charts 1 and 2) confirmed that the employment and earnings differences between PSRs and GARs were notably large in the first year, dropped drastically in the second year and remained stable or gradually decreased afterward. Treating the YSL variable as a linear (and quadratic) term did not adequately reflect the observed employment and earnings trajectories of refugees. This was confirmed in an F-test between a model where the YSL was treated as a continuous variable from year 1 onward and Model 1 (see next section), which controlled for refugee class, year 1 and year 2 dummies, a linear YSL term (for year 3 and onward), and its quadratic term. The regression models controlled for demographic and socioeconomic characteristics at the time of landing that were expected to influence subsequent economic outcomes: the highest level of education obtained before landing, knowledge of official languages, age at landing, region of origin, and entry cohort. The models further controlled for three time-varying variables: place of residence, unemployment rates (for men aged 25 to 64) in the refugee’s province of residence in a specific tax year, and the number of months in school during a specific year as a full-time student. The values of these variables could vary in each year. ### 3.3 Analytical technique Ordinary least squares (OLS) regression models were used to examine whether the differences in economic outcomes of PSRs and GARs persisted after controlling for the duration of residence in Canada. To test Hypothesis 1 (the assessment of the advantage of private sponsorship over time), the following model was estimated: Model 1: Y signifies the dependent variable, employment or earnings. YSL indicates years since landing (including year 1 and 2 dummies, and a linear term for year 3 and onward). The TYPEj variable represents the refugee admission category, and HC refers to the human capital variables (highest level of education and knowledge of official languages). One of the control variables, period of landing in Canada (COHORT), interacted with years since landing, considering that refugees’ economic outcomes may vary by entry cohort (Picot, Zhang and Hou 2019). This is a common approach in regression models that predict immigrants’ economic outcomes. X represents other individual-level control variables (e.g., age at landing, region of origin, place of residence), and Uy represents the time-varying variables of regional unemployment, number of months in full-time schooling and place of residence. To test Hypotheses 2 and 3 (evaluating the advantages of private sponsorship by different levels of human capital), three-way interactions among refugee admission categories, YSL, and the highest level of education (for Hypothesis 2) and among refugee admission categories, YSL, and the knowledge of official languages (for Hypothesis 3) were added to the regression model. Model 2: All the models were run separately for female and male refugees. Also, cluster-robust standard errors were estimated to consider the clustering of data at the province (for the unemployment rate variable) and year (for refugee person-year data) levels. The person-year data contained 3,345,239 cases (men) and 2,468,735 cases (women) for the employment analysis. The comparable numbers for the earnings analysis were 2,676,928 and 1,608,467 for men and women, respectively. ## 4 Results ### 4.1 A first look To begin, Chart 1 shows the incidence of employment for male and female PSRs and GARs across years since landing. PSR employment rates in the first year after landing were high, at 90% and 71% among men and women, respectively. These incidences were 17 and 24 percentage points higher than those among male and female GARs. These were the largest differences observed over the refugees’ first 15 years in Canada. After their first year in Canada, PSR employment rates dropped in the next two years. Male PSRs’ employment rates remained around 85% over the next 13 years, whereas female PSRs’ employment rates first dropped to 66%, then rose and stabilized at around 70%. The decrease in the employment rate after the first year was the opposite of the general pattern among immigrants whose employment rates tend to increase during the initial settlement period (Chui and Tran 2005). This decrease may reflect several possibilities: some jobs they found with the sponsor’s help were short term and disappeared when the sponsor’s formal commitment ended; some PSRs might take jobs that they did not like if the sponsor made them self-sufficient as quickly as possible. Over time in Canada, the gap in employment rates between female GARs and PSRs narrowed. Among men, the gap decreased to around 5 percentage points by the 10th year and 3 percentage points by the 15th year after arrival. Overall, PSRs had a higher employment rate than GARs over many years. Data table for Chart 1 Data table for Chart 1 Table summary This table displays the results of Data table for Chart 1. The information is grouped by Entry class (appearing as row headers), Years since landing in Canada and percent, calculated using 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 units of measure (appearing as column headers). Entry class Years since landing percent 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Male GAR 73.2 78.7 80.3 80.8 80.7 80.7 80.7 80.6 80.5 80.3 80.2 79.8 79.7 80.1 80.2 Male PSR 90.4 85.9 84.8 84.8 84.5 84.9 85.4 85.6 85.6 85.3 84.5 84.3 83.9 83.8 83.6 Female GAR 47.7 54.7 57.9 59.9 61.0 61.5 62.3 63.2 63.9 64.8 65.3 66.4 67.0 68.1 68.7 Female PSR 71.3 67.6 66.4 66.2 66.1 66.7 67.5 68.2 68.9 69.4 69.5 69.9 69.9 70.1 70.6 Data table for Chart 2 Data table for Chart 2 Table summary This table displays the results of Data table for Chart 2. The information is grouped by Entry class (appearing as row headers), Years since landing and dollars, calculated using 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 units of measure (appearing as column headers). Entry class Years since landing dollars 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Male GAR 17,800 23,900 26,300 28,300 30,100 31,800 33,400 34,800 36,300 37,400 38,800 39,900 41,300 42,300 43,300 Male PSR 22,800 26,100 28,200 30,000 32,000 33,800 35,700 37,800 39,400 40,600 41,600 42,600 43,600 44,600 45,500 Female GAR 10,700 15,000 17,100 19,100 20,700 22,300 23,700 25,100 26,300 27,500 28,600 29,400 30,400 31,300 32,200 Female PSR 14,400 17,200 18,800 20,200 21,700 23,100 24,700 26,000 27,300 28,500 29,500 30,700 31,600 32,700 33,700 Observed earnings rose steadily for both PSRs and GARs each year (Chart 2). The PSR lead was again noticeable in the first year ($5,000 and $3,700 more than male and female GARs, respectively). The PSR earnings advantage narrowed after the second year, stabilizing at around$2,500 and \$1,000 for men and women, respectively.
The above results did not consider the differences in the observed characteristics between PSRs and GARs. As Table 1 demonstrates, PSRs and GARs have some different characteristics. Refugees from Eastern Europe (especially Poland) were overrepresented among PSRs (43% and 39% of male and female PSRs, respectively), whereas the percentage of refugees from South and Central America and the Caribbean was notably higher among GARs (over 10%). Moreover, refugees with less than a high school education were overrepresented among GARs (53% and 65% for male and female GARs, respectively). Further, PSRs were concentrated particularly in the 1985-to-1994 cohorts (comprising 62% and 57% of all male and female PSRs), whereas the arrival periods of GARs were evenly distributed. Finally, 4 in 10 PSRs initially settled in Toronto, whereas comparable percentages of GARs lived in smaller metropolitan areas (e.g., Ottawa, Calgary). These group differences in demographic and socioeconomic characteristics may partially explain PSRs’ employment and earnings advantage over GARs. The next section examines whether the PSR advantage remained when these group differences were taken into account using multivariate analysis.
Table 1
Descriptive statistics of government-assisted refugees and privately sponsored refugees, characteristics in year 1, by sex
Table summary
This table displays the results of Descriptive statistics of government-assisted refugees and privately sponsored refugees. The information is grouped by Variables (appearing as row headers), Government-assisted refugees, Privately sponsored refugees, Men and Women, calculated using percent units of measure (appearing as column headers).
Variables Government-assisted refugees Privately sponsored refugees
Men Women Men Women
percent
World region
South and Central America, Caribbean 13.7 16.9 1.8 2.6
Eastern Europe 23.7 23.5 43.1 38.9
Southern Europe 6.1 8.2 1.7 2.3
Africa 14.9 13.5 15.0 13.9
Middle East, West Central Asia 17.2 16.8 15.0 17.5
Southeast Asia 22.5 19.7 22.1 23.8
Other Asia 1.9 1.4 1.2 1.1
Highest level of education at landing
Less than high school 53.0 63.3 48.3 58.3
High school diploma or trades certificate 26.8 19.4 29.7 22.4
Some postsecondary education 6.8 7.0 8.6 8.2
Bachelor's degree or above 13.4 10.2 13.4 11.1
Knowledge of official language
English and/or French 30.9 22.0 29.9 23.5
Neither English nor French 69.1 78.0 70.1 76.5
Age at arrival
20 to 29 50.3 49.1 49.8 50.7
30 to 39 34.7 34.9 35.3 33.0
40 to 49 12.8 13.3 12.3 12.9
50 to 54 2.2 2.7 2.6 3.4
Year of landing
1980 to 1984 23.2 19.9 16.1 17.2
1985 to 1989 28.3 22.8 29.1 26.3
1990 to 1994 15.6 15.3 33.1 30.5
1995 to 1999 12.9 14.6 5.9 7.3
2000 to 2004 11.2 14.3 7.1 8.6
2005 to 2009 8.8 12.9 8.7 10.1
Place of residence at tax filing time, year 1
Montréal 8.5 8.6 6.9 7.5
Toronto 26.6 24.0 41.2 39.1
Vancouver 9.7 10.3 6.4 6.7
Second-tier metropolitan areas 28.1 28.9 23.6 24.1
Other small census metropolitan areas 15.8 17.3 12.5 12.8
Small urban or rural areas 8.6 8.7 8.0 7.8
No information on place of residence 2.6 2.2 1.3 2.1
### 4.2 The short- and long-term economic outcomes of government-assisted refugees and privately sponsored refugees
OLS regression models were used to predict the probability of employment and earnings after adjusting for group differences in characteristics at the time of landing, including age at arrival, region of birth, period of landing, level of education and knowledge of official languages, as well as characteristics after arrival—including unemployment rates of the province of residence, the number of months in full-time schooling and the geographic location of residence in a specific year.
To make the regression results easy to interpret, the probabilities of employment and earnings were estimated for PSRs and GARs from years 1 to 15 when the control variable values were held constant (using the sample means for continuous variables and proportional distributions for categorical variables). Furthermore, the differences in the estimated outcome values (probability of employment and logged earnings) between PSRs and GARs were calculated. Charts 3 and 4 display these estimated differences for male and female employment and earnings results from years 1 to 15.
Chart 3 shows that PSRs’ employment advantage over GARs persisted over the long term among both male and female refugees. The PSR advantage was particularly sizeable in the first year, which was reflective of the fact that PSRs’ employment rates over the 15-year reference period were highest in year 1, while the employment rate among GARs was lowest in year 1.
Data table for Chart 3
Years since landing probability 1 2 3 4 5 6 7 8 9 10 11 12 13 0.172 0.092 0.065 0.062 0.058 0.055 0.051 0.048 0.045 0.042 0.039 0.037 0.034 0.032 0.029 0.236 0.150 0.107 0.098 0.089 0.080 0.072 0.064 0.056 0.049 0.043 0.037 0.031 0.026 0.021 Source: Statistics Canada, Longitudinal Immigration Database, 1980 to 2015.
However, PSRs’ employment advantage diminished over the first three years. By year 15, the PSR employment rates were only 2 to 3 percentage points higher than those of GARs, with this difference remaining statistically significant.
Similar patterns held for PSR estimated earnings in comparison with their GAR counterparts. As Chart 4 demonstrates, the earnings advantage of PSRs over GARs was substantial in the first year (over 0.40 log points for both women and men) and diminished markedly after that year. Nevertheless, PSRs continued to earn more than GARs up to their 15th year in Canada, earning 0.06 (or 6%) and 0.02 (or 2%) log points more among men and women, respectively.
Data table for Chart 4
Years since landing log points 1 2 3 4 5 6 7 8 9 10 11 12 13 0.407 0.190 0.149 0.139 0.129 0.121 0.112 0.104 0.096 0.089 0.082 0.076 0.070 0.064 0.059 0.448 0.236 0.133 0.119 0.106 0.094 0.082 0.072 0.062 0.053 0.045 0.038 0.032 0.026 0.021 Source: Statistics Canada, Longitudinal Immigration Database, 1980 to 2015.
The following analysis examined whether the economic advantage of private sponsorship varied by refugees’ initial human capital—measured by level of education and knowledge of official languages. The model added two-way interaction terms between refugee admission categories and human capital, and human capital and YSL. It also added three-way interaction terms among refugee admission categories, human capital and YSL. The results were reported using the graphs that show the estimated advantage (disadvantage) of PSRs over GARs by education levels (Charts 5 to 8), knowledge of official languages and YSL.
The results showed that male refugees with a lower level of education benefited more from private sponsorship than those with bachelor’s degrees or above. In the first year after landing, the estimated probability of employment of PSRs with less than a high school education was 19 percentage points higher than that of their GAR counterparts (Chart 5). Although this employment advantage of less-educated male PSRs shrank by half (8 percentage points) by year 3, their advantage remained statistically significant throughout the first 15 years. In year 15, their estimated probability of employment was still 3 percentage points higher than that of their GAR counterparts. By contrast, the employment advantage of PSRs was much smaller and lasted a shorter time for those with bachelor’s degrees or above. By the 12th year, their advantage was below 2 percentage points—virtually the same (estimated) employment probability as GARs. The results for refugee women were similar to men overall (women with less education benefited more from private sponsorship in employment), which supported Hypothesis 2 (Chart 6).
Data table for Chart 5
Data table for Chart 5
Table summary
This table displays the results of Data table for Chart 5. The information is grouped by Initital level of education (appearing as row headers), Years since landing and probality, calculated using 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 units of measure (appearing as column headers).
Initital level of education Years since landing
probability
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Less than high school 0.189 0.102 0.075 0.071 0.068 0.064 0.060 0.056 0.053 0.049 0.046 0.042 0.039 0.036 0.032
High school diploma or trades certificate 0.150 0.079 0.054 0.052 0.049 0.047 0.044 0.042 0.040 0.038 0.036 0.034 0.033 0.031 0.029
Some postsecondary education 0.181 0.084 0.046 0.044 0.043 0.041 0.039 0.038 0.036 0.035 0.033 0.032 0.031 0.030 0.029
Bachelor's degree or above 0.179 0.091 0.059 0.053 0.048 0.043 0.038 0.033 0.029 0.025 0.022 0.019 0.016 0.014 0.012
Data table for Chart 6
Data table for Chart 6
Table summary
This table displays the results of Data table for Chart 6. The information is grouped by Initial level of education (appearing as row headers), Years since landing and probality, calculated using 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 units of measure (appearing as column headers).
Initial level of education Years since landing
probability
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Less than high school 0.262 0.172 0.130 0.120 0.110 0.100 0.091 0.082 0.073 0.065 0.058 0.051 0.044 0.038 0.032
High school diploma or trades certificate 0.209 0.115 0.070 0.062 0.055 0.048 0.042 0.036 0.030 0.025 0.020 0.016 0.012 0.008 0.005
Some postsecondary education 0.209 0.117 0.070 0.062 0.054 0.047 0.041 0.035 0.029 0.024 0.019 0.015 0.011 0.008 0.005
Bachelor's degree or above 0.191 0.119 0.063 0.055 0.046 0.039 0.032 0.025 0.020 0.014 0.010 0.006 0.002 -0.001 -0.003
When the earnings of refugees with different levels of initial education were estimated, the overall results were the same as those for employment. PSRs without a high school education had the greatest advantage over their GAR counterparts throughout their first 15 years in Canada, and less-educated female PSRs’ relative advantage was far greater than their more-educated counterparts (Charts 7 and 8).
The effect of private sponsorship on refugee employment varied little by official language ability when the refugees’ demographic and socioeconomic characteristics at landing and post-migration characteristics were held constant (figures not shown). PSRs were more likely to be employed than GARs, and their employment advantage persisted in the long term (up to 15 years) whether or not they knew English or French at arrival. For male refugees, the advantages of PSRs for those with and without official language knowledge converged in year 3 and onward. For female refugees, those without knowledge of English or French had a slightly greater advantage over GARs than those who knew English or French at arrival (24- and 22-percentage-point advantage, respectively).
When the refugees’ earnings were estimated (figures not shown), men and women followed fairly similar patterns of PSR–GAR differences. For both female and male PSRs, their earnings advantage over their GAR counterparts was 0.1 log points greater than those who knew English or French at arrival. However, their advantage quickly diminished. In the longer-term resettlement, the PSRs with knowledge of English or French benefited more from private sponsorship in earnings.
Data table for Chart 7
Data table for Chart 7
Table summary
This table displays the results of Data table for Chart 7. The information is grouped by Initial level of education (appearing as row headers), Years since landing and log points, calculated using 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 units of measure (appearing as column headers).
Initial level of education Years since landing
log points
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Less than high school 0.478 0.238 0.184 0.173 0.162 0.151 0.141 0.131 0.121 0.112 0.103 0.095 0.087 0.079 0.072
High school diploma or trades certificate 0.337 0.114 0.106 0.102 0.098 0.094 0.091 0.088 0.084 0.081 0.079 0.076 0.073 0.071 0.069
Some postsecondary education 0.411 0.162 0.123 0.113 0.104 0.096 0.088 0.081 0.074 0.067 0.062 0.057 0.052 0.048 0.044
Bachelor's degree or above 0.390 0.183 0.098 0.085 0.074 0.062 0.052 0.042 0.034 0.025 0.018 0.011 0.005 0.000 -0.004
Data table for Chart 8
Data table for Chart 8
Table summary
This table displays the results of Data table for Chart 8. The information is grouped by Initial level of education (appearing as row headers), Years since landing and log points, calculated using 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 units of measure (appearing as column headers).
Initial level of education Years since landing
log points
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Less than high school 0.530 0.293 0.192 0.176 0.160 0.146 0.132 0.118 0.106 0.094 0.082 0.072 0.062 0.053 0.044
High school diploma or trades certificate 0.350 0.166 0.069 0.056 0.044 0.033 0.023 0.014 0.006 -0.001 -0.007 -0.012 -0.015 -0.018 -0.020
Some postsecondary education 0.405 0.152 0.048 0.042 0.036 0.032 0.027 0.023 0.020 0.018 0.016 0.014 0.013 0.013 0.013
Bachelor's degree or above 0.391 0.130 0.022 0.015 0.009 0.004 -0.001 -0.005 -0.008 -0.010 -0.012 -0.013 -0.013 -0.012 -0.011
## 5 Conclusion and discussion
This study compared the short- and long-term employment and earnings outcomes between privately sponsored refugees (PSRs) and government-assisted refugees (GARs) who were admitted to Canada between 1980 and 2009. Using the Longitudinal Immigration Database, this study estimated refugees’ employment rates and earnings up to 15 years after landing, while controlling for the group differences in demographic and socioeconomic characteristics at the time of landing, and some post-migration characteristics.
The multivariate analysis demonstrated that PSRs had higher employment rates and earnings than GARs even after taking into account differences in education, official language ability, and other observed socio-demographic characteristics. The differences were particularly large in the initial two years after arrival, and narrowed over time. The better labour market outcomes of PSRs may be related to other unmeasured pre-migration characteristics, selection processes, and host country reception factors. For example, unmeasured pre-migration characteristics (e.g., health, experience of refugee camps, duration of displacement) of refugees may be associated with the selection criteria of government-assisted refugee program (e.g., vulnerability), while welcoming reception may be reflective of the private sponsorship program which settles refugees in the community where sponsors are located (IRCC 2016; Oda et al. 2018).
This study also found that the employment and earnings advantage of private sponsorship compared with government assistance was greater among refugees with less education than among highly educated refugees. While this finding applies to both male and female refugees, the employment advantage of female PSRs without a high school education over their GAR counterparts was particularly high compared with more-educated female PSRs. Three to eight years after landing, more-educated PSR women had the same employment rates as their GAR counterparts. As such, only the less-educated women benefited from private sponsorship in the long term. Since the majority of refugees (51% and 61% for male and female refugees, respectively, in the study sample) had less than a high school education, this finding implies that private sponsorship arguably has long-lasting benefits for a large segment of this disadvantaged group, especially women.
Finally, the study found that refugees with poor official language skills benefited from private sponsorship as much as those with good official language skills. This was likely related to the fact that refugees with poor official language skills could take government-financed language training, regardless of whether they were in the private sponsorship or government-assistance programs (Kaida 2013). If anything, GARs were more likely to take full advantage of the free language training because they had guaranteed government financial support for their first year of resettlement and their employment rate was lower than that of PSRs.
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## Algorithms – Removes the last x elements from an array and reinserts them before the y position
I am looking for an algorithm to move a sub-array before an element (which is not part of this sub-array) in the same array where the last element of the sub-array is the last element of the array with O (1) extra space and O (n) runtime.
for example. where * p1 = 5 and * p2 = 3:
1 2 5 6 7 3 4
bECOMES
1 2 3 4 5 6 7
That's what I have up to now (written in C programming language). Problems arise when p1 reaches p2.
``````void swap(long* p1, long* p2, long* array_end) {
long* p2_i = p2;
while (p1 < array_end) {
if (p2_i > array_end) {
p2_i = p2;
}
// swap *p1 and *p2_i
long* temp = p1;
*p1 = *p2_i;
*p2_i = temp;
++p1;
++p2_i;
}
}
``````
## algorithms – Application of the sub-problem technique to permutations with grouping
I try to apply overlapping subproblems and dynamic programming to permutations.
Say, we have a set of $$n$$ elements in a chain. Each of these elements could be a $$1$$ or one $$0$$.
Given some strings, I try to count the number of valid permutations, where a valid setting is defined as an order without $$1$$ which is different from others 1.
Example of input string: $$0101$$
Example of valid arrangements: $$1100, 0011, 0110$$
Not valid: $$0101, 1010, 1001$$
EXPECTED PRODUCTION: $$3$$
For example:
Suppose our input string contains four 1s and two 0s.
I guess my difficulty comes with defining the sub-problem. Initially, I thought I could create a channel with only the $$0$$ elements with slots / bins in between. $$[] 0 [] 0 []$$, then continue using the combinatory to calculate the number of possible extra arrangements with each added 1.
The first possibilities 1: 0 because it will never have a 1 to accompany it.
Added the second possibility 1: 3, because the pair can go in one or the other of the 3 boxes.
Added the 3rd possibility 1: 0, because it must go with the 2 others, wherever they are.
Added the 4th 1: We have enough to make 2 groups of $$1$$Now … here is where I'm starting to be uncertain. I would think it would be 3 additional possibilities. $$binom {3} {1} + binom {3} {2} = 6$$ total
Would anyone have an idea if I am on the wrong track, or if not, how to proceed? This approach does not seem to work for larger values. Thank you!
## algorithms – Check the sum of subsets for a special array
I was trying to solve the following problem.
We are given N and A (0)
``````N <= 5000
A(0) <= 10^6 and even
if i is odd then
A(i) >= 3 * A(i-1)
if i is even
A(i)= 2 * A(i-1) + 3 * A(i-2)
element at odd index must be odd and at even it must be even.
``````
We must minimize the sum of the table.
and we are given a number Q
`````` Q <= 1000
X<= 10^18
``````
We need to determine if it is possible to get the subset-sum = X from our array.
What I have tried,
Creating a minimum sum table is easy. Just follow the equations and the constraints.
The approach I know for subsets is dynamic programming that has the sum * sizeof (Array) time complexity, but since the sum can reach 10 ^ 18, this approach will not work.
Is there a relationship of equation that I miss?
## algorithms – Random isomorphism of rooted trees
I'm trying to solve the following problem on the random isomorphisms of trees – this comes from an old test that I found online. I state below the problem and my progress up to here. Any help is appreciated.
Problem:
A rooted tree is a tree in which a vertex is marked as root. Two rooted trees $$T_1$$ and $$T_2$$ they say to be isomorphic if there is one to one mapping (an isomorphism) $$f$$ summits of $$T_1$$ to those of $$T_2$$, such as $$f (root (T_1))$$ = $$Root (T_2)$$and for each vertex $$v$$ of $$T_1$$ with children $$v_1, ldots, v_k$$, children (in $$T_2$$) of $$f (v)$$ are exactly $$f (v_1), ldots, f (v_k)$$ (in any order).
In this problem, you will design an efficient random algorithm to check if two given rooted trees are isomorphic. Given a rooted tree $$T$$, define a polynomial $$P_v$$ for each summit $$v$$ of $$T$$ recursively as follows. For each sheet $$v$$, to define $$P_v equiv x_0$$. (Thus, all leaves have the same trivial polynomial.) For each non-leaf top $$v$$ height $$h$$ with children $$v_1, ldots, v_k$$, to define $$P_v equiv (x_h – P_ {v_1}) (x_h-P_ {v_2}) … (x_h-P_ {v_k})$$.
(a) For a tree $$T$$ height $$h$$ with $$m$$ leaves, how many variables are there in the $$P_ {Root (T)}$$, the polynomial at the root of $$T$$? And what is the degree of this polynomial?
(B) Show that if two trees rooted $$T_1$$ and $$T_2$$ are isomorphic, so $$P_ {Root (T_1)} equiv P_ {Root (T_2)}$$. (hint: Use induction on the height of the tree. You can assume that, if $$f$$ is an isomorphism of $$T_1$$ at $$T_2$$ and $$v$$ is a peak of $$T_1$$, then the sub-trees rooted in $$v$$ and $$f (v)$$ are also isomorphic.)
(vs) Show that if $$T_1$$ and $$T_2$$ are rooted trees and $$P_ {Root (T_1)} equiv P_ {Root (T_2)}$$then $$T_1$$ and $$T_2$$ are isomorphic. (hint: Again, use the induction on the height of the tree. You can assume that, if a polynomial $$Q equiv (x – alpha_1) ldots (x – alpha_k)$$, where the $$alpha$$does not depend on $$x$$Such a factorization is therefore unique, up to the order of the factors.)
(re) Give an efficient algorithm to test if two given rooted trees, $$T_1$$ and $$T_2$$ are isomorphic. If they are isomorphic, the result should be "yes"; if they are not, it should be "no" with at least one probability $$1/2$$.
Attempt:
(a): There is $$h$$ variables in $$P_ {Root (T)}$$ (one variable per level in the tree). The polynomial is degree $$m$$.
(b) and (c): I struggle with these two.
(d): With (b) and (c) we know that $$P_ {Root (T_1)} equiv P_ {Root (T_2)} iff T_1$$ and $$T_2$$ are isomorphic. This means that we can answer "yes" or "no" by asking $$P_ {Root (T_1)} equiv P_ {Root (T_2)}?$$. Of course, this means that we can perform polynomial identity tests to check whether the two polynomials match. It is an application of the Schwartz-Zippel lemma. The algorithm would work as well as the multivariate polynomial identity test algorithm that satisfies the requirements of the question.
## Algorithms – How to solve the following tree problem with a number assigned to each node and respond to queries?
I have a tree whose nodes have numbers that were originally assigned to them. A series of $$Q$$ questions are asked from $$n = 0$$ at $$n = Q-1$$ seconds. At the end of each second, the numbers of a node (which are not sheets) are deleted and are transferred to each direct child node. is possible that a new number be added to a node. How to solve this problem effectively?
Example: Suppose I have a tree 1 —– 2 —— 3 ——- 4 (1 is parent). Suppose at the beginning that the numbers on the nodes are 1,2,3,4 respectively.
At zero, the second end 5 is added to the zero node. At the end of 0 seconds, the number on the node is 5.1.2.3 (note 1 is not added to 5 because it is removed ).
At a second end, 1 is added to node 4, then the numbers are 0.5,1,3. The fourth node is number three since it has received 2 of the parent node and 1 is added.
Now, suppose that, two seconds from the end, I am asked to say the number on the second node?
I mean that in each query, a number can be added on a node or a question can be asked as – what is the number on $$ith$$ node?
How to solve this problem in less than $$O (nQ)$$. Or $$n$$ is the number of nodes and $$Q$$ is the number of requests?
## algorithms – How to encode accessibility in a graph with walls as SAT problem
Suppose we have a graph representing a grid of cells. We are given a cell to start and a cell that is the destination. There are cells in which we can not enter and we call them walls. Finally, we can only move in adjacent cells (diagonal movements are not allowed).
My question is: how to code this problem in CNF so that it is solved by a SAT solver?
For example, suppose the graph represents the following 2 x 3 grid:
``````0 1 0
0 0 0
``````
where 0 cells are cells in which we can be or move, and cells 1 are walls. Suppose we leave (0, 0) and want to go to (0, 2). Then there is a path.
On the contrary, consider another 2 x 3 grid with the same starting and destination positions:
``````0 1 0
0 1 0
``````
Then, this graphic has no path from the beginning to the destination.
Clearly, we can run BFS on the graph and if there is a path, we can code it as a trivially satisfying CNF file or, if there is not one, encode as a non-unsatisfactory CNF file. For example, $$A$$, or, $$A land neg A$$. However, the purpose of my exercise is to code the existence of the path in CNF.
This is actually part of my homework. I'm stuck for a while now. Help on this problem would be greatly appreciated.
## Algorithms – Improve the time of the next largest Next function with the same Javascript digits
I've created a function that gives a number n by taking its numbers and looking for the next larger number than the one that can be formed …
Examples:
1. n = 513 back to 531,
2. n = 9219 return 9912,
3. n = 123 back 213
not being able to form the number pq n = 5 (there are no numbers to form others), n = 321 .. the function returns -1 .. The problem is that this function simple is the brute force and does not pass the speed test because what he does is to increase the number of 1 until he finds a number that has the same numbers in that part he does numerous comparisons in which he transforms the number, passes it by orders, etc. How can you improve the part where you compare if the numbers of the number are the same as those of my number?
``````function nextBigger(n) {
const digitos = `\${n}`.split('').sort((a, b) => a - b).join('');
if (n <= 11 || n == mayorPosible) return -1
else {
do {
n++
} while (digitosNumero(n) != digitos)
}
return n
}
function mayorPosible(n) {
return Number(`\${n}`.split('').sort((a, b) => b - a).join(''))
}
function digitosNumero(n) {
return `\${n}`.split('').sort((a, b) => a - b).join('')
}
console.log(nextBigger(513));
console.log(nextBigger(2063));
console.log(nextBigger(1497));``````
## algorithms – Java Dictionary implementation
I'm doing a dictionary in java using a separate string. It uses a configuration of X and O and empty spaces on the table ex. "XXOOOX X" for a tic-tac-toe game that evaluates the board through a string related to the arrangement and records the score. I use an "ArrayList". A list of table lists. My problem is for the remove function and the functions get that a given configuration can hash to the same value, that is why a separate chaining obviously occurs, but when the get or remove functions only take param, c & e Is a String configuration, when I try to delete or get the value in this distinct string I struggle with there are several values associated with the unique value how can I identify the correct value in the string ??
## algorithms – find a pair of coprimes
we are given a table
Size of the array <= 10 ^ 4.
0 <= A [i] <= 15
We must divide it into 4 parts. Take xor from each game and add these xors.
find the maximum amount.
The approach is very expensive.
there are only 16 different values of xor, so for each value of xor = X one can search in array is it possible to partition the array so as to obtain xor = X.
## algorithms – Fuse 3D-Points in Bundel Adjustment?
I am setting up my own Pose-Estimate / – and-Refinement pipeline. To this end, I use a moving mono camera. Then I take the consecutive images to estimate the pose and triangulate the points (nothing special). In the last step, I fine-tune the poses and 3D dots with a beam-fitting approach.
The generation of 3D points with triangulation from consecutive image pairs will give me several estimates for a real 3D point. In fact, all estimates refer to the same point. For my understanding, these estimates of the same 3D points must be merged in one way or another. Otherwise, the poses were no longer linked by a common point (see also the picture below).
Do I understand this right or do I have to use a different set of 3D points for each camera view?
|
2019-10-14 04:36:50
|
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|
https://www.wyzant.com/resources/answers/646538/how-do-i-know-the-script-file-name-in-a-bash-script
|
# How do I know the script file name in a Bash script?
How can I determine the name of the Bash script file inside the script itself? Like if my script is in file runme.sh, then how would I make it to display "You are running runme.sh" message without hardcoding that?
By:
Tutor
4.9 (78)
|
2022-01-22 10:57:11
|
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|
https://datascience.stackexchange.com/questions/107278/in-ml-why-selecting-the-best-variables/107300
|
# In ML why selecting the best variables?
Almost all ML notebooks out there have a section where they select the best features to use in the model. Why is this step always there ? How bad can it be to keep a variable that is not correlated with the response variable ? If you are really unlucky then yes a feature that is positively correlated with your response in your training set could in fact be negatively correlated with it in the real world. But then, it's not even sure that one will be able to catch it with a feature selection routine.
My assumption is that it used to be a necessary step when computing resources were scarce, but with today's resources it is basically irrelevant.
What is your view ? Can you give a real world example where it would harm the model to keep all training features ?
• Objective usually is to maximize predictive accuracy against some benchmark (e.g. test data). Redundant variables often lead to lower predictive power. Thus, selecting or generating features with high predictive power is almost always a required step in predictive models. [For models which are estimated to do causal inference this is not true - in this case features are selected in a different way] Jan 20 at 16:43
• The more the variables, the more the dimensions your data has (the array). Hence its that much harder to operate on and visualise. So we try reduce the dimensions of the data (i.e. the variables) to make the whole data science process smooth both for the data scientist and the computer that's doing the ML (in terms of computation power). Jan 21 at 9:56
You are right. If someone is using regularization correctly and doing hyperparameter tuning to avoid overfitting, then it should not be a problem theoretically (ie multi-collinearity will not reduce model performance).
However, it may matter in a number of practical circumstances. Here are two examples:
1. You want to limit the amount of data you need to store in a database for a model that you are frequently running, and it can be expensive storage-wise, and computation-wise to keep variables that don't contribute to model performance. Therefore, I would argue that although computing resources are not 'scarce' they are still monetarily expensive, and using extra resources if there is a way to limit them is also a time sink.
2. For interpretation's sake, it is easier to understand the model if you limit the number of variables. Especially if you need to show stakeholders (if you work as a data scientist) and need to explain model performance.
• I would soften the first paragraph: surely in some cases, the regularization strength needed to prune out a purely-noise feature is to large a shrinkage in the other parameters, in which case removing the feature before tuning regularization strength would outperform? Feb 13 at 5:53
The feature selection step is there to guard against model overfitting. The feature selection step may decide that all the variables in the dataset are relevant, or it may decide to remove some. If no feature selection step is performed then no variables are removed and the resulting model may be well-fitted but may be (and likely is) overfitted.
The main concern with overfitted models is their poor performance on out-of-sample or validation data. That is the main reason given by Wikipedia and matches my experience. If you have extra variables in the model then irrelevant data will corrupt your models output and make its predictions less accurate.
You could take a more philosophical perspective and say that you want to base your modelling on some consistent and reasonable foundation of statistical reasoning. Whichever system you choose (classical, Bayesian, etc), it is likely to encode some form of Occam's razor and therefore have some mechanism of feature selection built in. That is it say, when comparing two models with the same quality of fit it will prefer the one with the fewest variables selected.
In some cases, the ability of humans to interpret the model is important, as fractalnature points out. Sometimes you want a model so simple that a human can apply it themselves with a calculator. The introduction to the paper Supersparse linear integer models for optimized medical scoring systems provides a nice example of this.
Generally I think we want to get rid of unnecessary/bad features to save ourselves from the curse of dimensionality -- the more features we use, the more data we need to make sure each part of the feature space has enough data to fit the model. On top of that there are concerns specific to our model choice, for example,
1. Random Forest / GBDT. If we have 30 features and set feature_bagging to 10, it takes >= 30C10 = 30,045,015 trees to go through all possibilities. Also, features that are highly linearly correlated with one another do not add extra value to the model but are more possible to be chosen during feature bagging.
2. Distance-based model like K-means can be volunerable to high dimensions.
My assumption is that it used to be a necessary step when computing resources were scarce, but with today's resources it is basically irrelevant.
You are entirely right. In the early days of computing, when resources were scarce, it was necessary just to keep important features and discard the rest.
However, with the current abundance of resources, that is no longer necessary. The model will not overfit more with "useless" features included. Indeed, there is a branch of Machine Learning called "reservoir computing" where you purposely generate random features in the hope that a subset of them are still useful for the model.
For instance, you can checkout the algorithm called "Rocket" for time series prediction.
|
2022-10-02 09:20:03
|
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|
https://chemistry.stackexchange.com/questions/16473/ring-strain-and-c-o-stretching-frequency
|
# Ring Strain and C=O Stretching Frequency
Why does $\ce{C=O}$ stretching frequency increase with ring strain?
Why does conjugation decrease $\ce{C=O}$ ring strain?
I am told that cyclopropanone exhibits a higher $\ce{C=O}$ stretching frequency than does cyclohexanone. I know that higher stretching frequencies are correlated with a shorter, stiffer, and stronger bond. What I can't see is why would the $\ce{C=O}$ bond have more of these characteristics in a strained ring system than in a less strained ring system.
Are there hyperconjugative effects going on?
Are there other rationalizations that we can make? I.e. would smaller $\ce{C-C-C}$ angles suggest higher $p$-character in the $\ce{C-C}$ bonds and therefore higher $s$-character in the $\ce{C=O}$ bond?
The carbonyl carbon prefers to be (more or less) $\ce{sp^2}$ hybridized. Imagine taking the two other bonds attached to the carbonyl carbon and bending them towards each other so that the R-C-R angle is forced from 120 to 90 degrees (the same thing as incorporating these bonds into a smaller and smaller ring). As we do this, the hybridization of the orbitals the carbonyl carbon uses to form these bonds changes from $\ce{sp^2}$ to $\ce{p}$. As these bonds use more p-character, more s-character remains for use in the C-O sigma bond. This would strengthen the CO bond and raise the energy required to stretch it (increase its ir stretching frequency).
An alternate explanation can be made based on resonance structures. Look back at the acylium ion resonance structure used in our earlier acid chloride discussion (resonance structure IV). As we strain the carbonyl by placing it in a small ring, the bonds between the carbonyl carbon and the adjacent carbons become weaker. This means that resonance structure IV, with a strong $\ce{C#O}$ triple bond, becomes more important. Here, in the present case, we would say that resonance structure IV involves carbon-carbon hyperconjugation.
|
2019-10-14 10:21:42
|
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|
https://asmedigitalcollection.asme.org/biomechanical/article/140/8/081013/425512/A-Surface-to-Surface-Finite-Element-Algorithm-for
|
This study formulates a finite element algorithm for frictional contact of solid materials, accommodating finite deformation and sliding. The algorithm uses a penalty method regularized with an augmented Lagrangian scheme to enforce contact constraints in a nonmortar surface-to-surface approach. Use of a novel kinematical approach to contact detection and enforcement of frictional constraints allows solution of complex problems previously requiring mortar methods or contact smoothing algorithms. Patch tests are satisfied to a high degree of accuracy with a single-pass penalty method, ensuring formulation errors do not affect the solution. The accuracy of the implementation is verified with Hertzian contact, and illustrations demonstrating the ability to handle large deformations and sliding are presented and validated against prior literature. A biomechanically relevant example addressing finger friction during grasping demonstrates the utility of the proposed algorithm. The algorithm is implemented in the open source software febio, and the source code is made available to the general public.
## Introduction
Frictional contact of biological tissues is fundamental in biomechanics, and consideration of friction is often necessary to fully describe relevant physical phenomena. Within the body friction plays an important role in the mechanics of tendons and ligaments, for example, in the flexor tendons of the finger [1,2], gliding resistance through the carpal tunnel [3,4], and between the cruciate ligaments and bone in the knee [5]. Externally, skin friction has been studied both to reduce workplace accidents [6] and to provide pleasing sensory feedback on commercial products [79]. Medical applications include friction between internal organs and surgical microdevices [10] and frictional resistance during prosthesis implantation [11]. Although some biological tissues may be treated with constitutive models involving fluid phases, this work is particularly concerned with finite element modeling of friction between solid, elastic, or inelastic materials. Other applications in biomechanics, such as friction between porous hydrated materials, e.g., articular cartilage in diarthrodial joints [12,13], will be addressed in a future study.
Due to the inherent complexity of general three-dimensional contact, finite element algorithms for frictional contact have been extensively studied over the past few decades. In contrast to early finite element efforts [14,15] which were restricted to specific discretizations, Laursen and Simo [16] provided a complete continuum formulation for contact that was independent of the numerical discretization, a framework later extended by Pietrzak and Curnier [17]. To resolve inequalities arising from contact constraints, the penalty method was widely adopted [18,19], permitting minor violations of constraints. Augmented Lagrangian schemes of first- [20] and second- [21] order were devised to avoid the ill-conditioning inherent in penalty formulations and provide more exact enforcement of contact constraints. These early efforts were generally formulated as variations of the node-to-segment or node-to-surface (NTS) approach, where contact constraints are imposed pointwise at a finite number of slave nodes [19,22], thus introducing an artificial asymmetry into the contact problem. This technique is unable to pass the patch test [23], where a constant contact pressure needs to be exactly transmitted between contacting surfaces [24]. It also suffers from geometrical difficulties related to contact detection [22]. Segment-to-segment algorithms [25,26], introduced to enforce constraints in an approximate sense in an effort to remedy errors associated with NTS algorithms, led to development of the mortar method [2735]. An alternative approach has been the development of contact smoothing algorithms [36,37], which attempt to provide tangent plane continuity between adjacent segments, thus mitigating the errors associated with discretization at the cost of computational efficiency. More recently, the concept of isogeometric contact was proposed by Hughes et al. [38], which adopts the shape functions of 3D modeling software for contact analyses to obtain a smoother description of the contact interface. A series of frictional algorithms has been developed based on this approach [3941].
In general, the finite element algorithms described above are implemented in custom codes and are thus unavailable to the majority of researchers. Furthermore, the simple and commonly used NTS algorithms exhibit severe convergence difficulties for complex problems, while the powerful and advanced methods (e.g., mortar methods, isogeometric analysis) are much more expensive computationally. To handle the wide variety of frictional contacts occurring in biomechanics, many of which involve finite deformation and large sliding within arbitrary geometries employing complex constitutive models, there exists a need for a simple, robust finite element algorithm for frictional contact, implemented in an open-source framework for the biomechanics community.
This study describes the formulation and implementation of a surface-to-surface finite element algorithm for frictional contact that retains the simplicity and physical interpretation of NTS methods, while robust enough to solve problems that otherwise typically require specialized contact smoothing, mortar methods, or higher order shape functions. To accomplish this objective, we propose a novel continuum approach and a new algorithmic formulation, extending our previous work on frictionless biphasic contact [42]. Here, frictional stick will be treated as a case of tied contact, with an exact return mapping to frictional slip which is independent of the single penalty parameter and based on a standard slip criterion. Unlike the traditional approach, no rate form for the frictional traction is prescribed, avoiding the need for complex numerical integration [43,44] or elastoplastic-type algorithms [18]. A main contribution of this work is the use of a contact detection algorithm that avoids many of the pitfalls of classical NTS schemes, allowing smooth results without specialized contact elements or computationally expensive smoothing algorithms [36]. Our frictional contact algorithm is formulated in the spatial frame, using a penalty method regularized with an augmented Lagrangian scheme to enforce contact constraints. To improve convergence rates, the linearization of the gap function used during contact slip is accomplished without the simplifying assumptions made in our earlier work [42], and the novel derivation of the frictional formulation utilizes a cleaner matrix notation (see Supplementary Materials, available under the “Supplemental Data” tab for this paper on the ASME Digital Collection). The implementation of this algorithm is incorporated into the free, open-source finite element software febio2 [45], which has been developed to address the needs of the biomechanics community. The validity of the presented formulation and algorithm is demonstrated with a series of benchmark problems that involve finite deformation and large sliding.
The paper is organized as follows: Sec. 2 describes the continuum formulation of the contact problem, for both penalty and augmented Lagrangian regularization schemes. Section 3 describes the finite element implementation and presents a series of numerical examples demonstrating the ability of the formulation to handle a wide variety of friction problems. A discussion of these results is presented in Sec. 4. The detailed linearization and discretization of the results in Sec. 2 may be found in the Supplementary Materials which are available under the “Supplemental Data” tab for this paper on the ASME Digital Collection, along with a description of the Gaussian quadrature integration scheme adopted for the present study.
## Continuum Formulation
### Notation.
The problem to be considered consists of two deformable bodies in contact. In a contact analysis, it is convenient to define one body as the contactor and the other as the target, typically referred to as the slave and master, respectively, in the literature. Each point on the slave can be assigned an intersection on the master. As this study uses a modification of the gap function and projection method described by Ateshian et al. [42], which differs from the conventional approach, the designation of surfaces as “slave” and “master” will not be employed, and surfaces will be referred to as primary and secondary. A subscripted or superscripted index (i), i = 1, 2, will be used to denote a quantity on either the primary or secondary surface, respectively. Greek indices refer to surface quantities and thus vary implicitly from 1 to 2, with repeated Greek indices implying summation. The standard derivation of the virtual work of contact forces is briefly summarized in the Appendix using the notation of this study.
### Contact Integral.
Following standard finite element contact procedures in the Appendix, the virtual work arising from contact may be written as an integral over the primary surface γ(1) only, yielding
$δGc=∫γ(1)(δv(1)−δv(2))·t(1) da(1)$
(2.1)
Equation (2.1) is commonly referred to as the contact integral.
To evaluate the directional derivatives of δGc along increments in the displacements $Δu(i)$ of γ(i), as required for an iterative technique such as Newton’s method, it is necessary to formulate the integration over an invariant domain so that the directional derivative may be brought inside the integral without concern for variations in the domain of integration. In our approach, the integral is formulated over the invariant parametric space of γ(1) [42,46].
Each surface γ(i) is expressed in parametric form using coordinates $η(i)α$, and material points X(i) are identified through their parametric coordinates. On each surface γ(i), covariant basis vectors are given by
$gα(i)=∂x(i)∂η(i)α$
(2.2)
Here, $x(i)(η(i)α,t)$ is the spatial representation of surface γ(i) as it deforms over time t, in terms of contravariant surface parametric coordinates $η(i)α$. These covariant basis vectors are tangent to γ(i), and it follows that the unit outward normal to γ(i) is
$n(i)=g1(i)×g2(i)|g1(i)×g2(i)|$
(2.3)
Furthermore, the elemental area on γ(i) is evaluated as
$da(i)=Jη(i) dη(i)1dη(i)2 , Jη(i)=|g1(i)×g2(i)|$
(2.4)
Therefore, the contact integral of Eq. (2.1) may be placed into matrix form and rewritten as
$δGc=∫Γη(1)[δv(1)δv(2)]·[t(1)−t(1)] Jη(1) dη(1)1dη(1)2$
(2.5)
where $Γη(1)$ represents the invariant parametric space of surface γ(1), and integration is performed over points X(1) with prescribed parametric coordinates $η(1)α$. Since $Γη(1)$ represents a material frame, it is possible to linearize δGc by applying the directional derivative operator directly to the integrand
$DδGc=∫Γη(1)D([δv(1)δv(2)]·[t(1)−t(1)] Jη(1))dη(1)1dη(1)2$
(2.6)
where it is understood that for any function f
$Df≡∑i=12Df[Δu(i)]$
(2.7)
To proceed with this linearization, it is necessary to formulate the kinematics of points on γ(i) and provide expressions for the contact traction t(1) that can differentiate between frictional stick and slip.
### Slip Kinematics.
During contact slip, γ(1) and γ(2) move relative to one another as their configurations evolve. Performing a contact analysis requires mapping points between these surfaces. For the spatial position $x(1)(η(1)α,t)$ of each material point on the primary surface, we define the intersection point $x(2)(η(2)α,t)$ on the secondary surface as the point intersected by a ray directed along the unit outward normal to the primary surface $n(1)(η(1)α,t)$
$x(2)=x(1)+gn(1)$
(2.8)
where the gap function g is defined to be positive when the surfaces γ(1) and γ(2) are separated, and negative when they penetrate
$g=(x(2)−x(1))·n(1)$
(2.9)
The ray intersects γ(2) at a spatial position x(2) through which different material points X(2) identified by parametric coordinates $η(2)α$ may convect. Computationally, this ray intersection and contact detection is performed with an Octree method [47].
The projection approach of Eq. (2.8), described in our previous studies [42,48] and commonly termed ray-tracing [49], can be characterized as an inverse projection relative to the classical contact mechanics approach used for NTS contact [18,19]. Although the definition of this projection and its associated gap function is not new, it has typically been employed mostly for mortar contact (e.g., as in Tur et al. [33]). The benefits associated with a projection method such as Eq. (2.8) for nonmortar contact have been developed in detail [49]. Here, it suffices to note that avoiding a reliance on secondary surface normal vectors eliminates many contact-searching difficulties that plague NTS algorithms [22] and also serves to greatly reduce the complexity of the linearizations and the resulting stiffness matrices.
### Stick Kinematics.
Equations (2.8) and (2.9) describe searching for evolving contact and are only valid during slip. In stick no relative motion occurs between contacting points, thus, the intersection point X(2) on γ(2) does not evolve during the iterative solution process, allowing the development of kinematics of sticking contact. Implicit in this condition is the assumption that the contact projection was previously resolved, and thus, contact searching is not performed again; rather, the contact point on γ(2) is given by the parametric coordinates of intersection $η(2)α$ found from the previous time point, which will be denoted as $η(2)pα$, with the subscripted p referring to the previous time. Thus, we write the spatial position of X(2) in stick as
$xs(2)=x(2)(η(2)pα,t)=x(1)(η(1)α,t)+gs$
(2.10)
where gs is a vectorial gap function
$gs=xs(2)−x(1)$
(2.11)
Here, gs is the vectorial distance, at the current time t, between material points which were in contact at the previous time-step; for perfect stick, we must have gs = 0. In a finite element implementation, however, it is important to note that the intersection point $xs(2)$ is not in general the point that would be found from a ray directed from $η(1)α$ along the unit outward normal n(1). This is because stick will not be enforced exactly, so the points x(1) and $xs(2)$ will separate slightly when using a penalty method for enforcing this constraint. How to minimize this separation and enforce perfect stick behavior is the subject of Sec 2.6.
### Velocities.
The kinematics developed above can be used to formulate velocities. The formulation for stick developed in Sec. 2.6 does not rely on velocity constraints; therefore, we are only concerned with velocities of opposing contact points in slip. The development of velocities presented below anticipates the need for a relative velocity as required by Coulomb’s law of kinetic friction, which aligns the friction force with this slip direction.
Since the parametric coordinates $η(1)α$ of integration points represent material points on γ(1), the velocity v(1) of these points on the primary surface is evaluated from the material time derivative in the material frame
$v(1)(η(1)α,t)=∂x(1)(η(1)α,t)∂t$
(2.12)
In contrast, since material may convect through the intersection point of the ray with γ(2), the total velocity v(2) at the intersection point on γ(2) needs to be evaluated using the material time derivative in the spatial frame
$v(2)(η(2)α,t)=∂x(2)(η(2)α,t)∂t+η˙(2)αgα(2)$
(2.13)
Here, $∂x(2)/∂t$ represents the velocity of the intersection point on γ(2), whereas $η˙(2)α$ are the contravariant components of the convective velocity of material passing through this intersection point. In effect, $η˙(2)αgα(2)$ represents the relative (slip) velocity between the material on γ(2) and that on γ(1). Importantly, as noted below when performing time discretization and linearization, by definition $∂x(2)/∂t$ is evaluated while keeping $η(2)α$ constant.
We now use these relations to produce a more practical formulation of the slip velocity for our frictional contact implementation. Taking the material time derivative of Eq. (2.8) and using the contact persistency condition $g˙=0$ [16] produces $v(2)=v(1)+gn˙(1)$. Substituting Eqs. (2.12)(2.13) into this expression yields a frame-invariant measure of relative velocity between γ(1) and γ(2) [49,50]
$vr≡η˙(2)αgα(2)=gn˙(1)+∂x(1)(η(1)α,t)∂t−∂x(2)(η(2)α,t)∂t$
(2.14)
where $n˙(1)$ is the material time derivative of n(1) in the parametric material frame of γ(1), evaluated from Eq. (2.3) as
$n˙(1)=PN·g˙1(1)×g2(1)+g1(1)×g˙2(1)Jη(1)$
(2.15)
Here, $g˙α(1)$ denotes the material time derivative of $gα(1)$ in the material frame
$g˙α(1)(η(1)β,t)=∂gα(1)(η(1)β,t)∂t$
(2.16)
and we define the tangential plane projection tensor PN as
$PN=I−n(1)⊗n(1)$
(2.17)
Previous authors have utilized $vr=η˙(2)αgα(2)$ directly instead of the right-hand-side of Eq. (2.14); this expression requires the evaluation of time derivatives of parametric coordinates [15,16,41], which necessitates special integration algorithms to handle crossing element boundaries [44]. The relative velocity measure on the right-hand-side of Eq. (2.14) obviates the need for any such special treatment. In particular, the choice of $∂x(2)/∂t$ ensures that element boundaries will never be crossed when calculating this velocity, since it is evaluated while keeping $η(2)α$ constant.
The tangential frictional traction in slip depends only on the tangential component of the relative velocity; therefore, we may define the slip direction s(1) as the unit vector of the projection $PN·vr$ of vr onto the tangent plane of γ(1)
$s(1)=PN·vr|PN·vr|$
(2.18)
These definitions of contact kinematics may now be used to formulate frictional contact.
### Coulomb Frictional Contact.
This work considers Coulomb frictional contact, with no distinction made between static and kinetic coefficients of friction. Although classical Coulomb friction is the most frequently adopted behavior, it should be noted that other constitutive equations, including micromechanically inspired formulations which consider local phenomena, have been proposed as well [15,19]. During frictional contact, the contact traction t(i) on the opposing surfaces is determined by the sticking or slipping behavior. For Coulomb friction, the relationship between sticking and slipping is described by a slip criterion Φ, where on the primary surface
$Φ=|tT(1)|−μ|tn|$
(2.19)
Here, $tn=t(1)·n(1)$ is the normal component of the contact traction (negative in compression), $tT(1)=t(1)−tnn(1)$ is the tangential component of the contact traction, and μ is the friction coefficient. The value of the slip criterion determines the stick–slip status
$Φ{< 0sticking=0slipping$
(2.20)
Algorithmically, stick and slip are typically based on a predictor–corrector approach derived from an analogy with elastoplasticity [43], leading to constitutive relations for the rate of the traction and thus requiring numerical integration [44]. Variations of this approach have been utilized in differing forms [15,16,41].
In contrast, this presentation proposes to treat stick and slip separately, controlled by an exact return mapping based on the slip criterion. The return mapping defines a rule for correcting a calculated traction which exceeds the slip limit and is thus not permissible. Stick will be treated as a special case of a tied interface, whereas in slip the traction will be directly prescribed. The formulation of Coulomb frictional contact is presented for both penalty and augmented Lagrangian regularization schemes.
#### Penalty Scheme.
During stick, no relative motion may occur between surfaces; thus, points on γ(1) and γ(2) that were in contact at the previous time must remain in contact. The stick traction may be obtained by penalizing any relative motion between such points
$t(1)=εgs$
(2.21)
where ε is the penalty parameter, and we have employed Eq. (2.11).
During slip, we first calculate the normal component of the contact traction by penalizing the normal gap of Eq. (2.9)
$tn=εg$
(2.22)
The total traction vector is then directly obtained as
$t(1)=tn(n(1)+μs(1))$
(2.23)
Here, we have achieved an exact expression for the tangential traction in slip and remark that since tn is strictly negative in contact, the frictional contact traction $μtns(1)$ acting on γ(1) is in the direction opposing the motion of γ(1) relative to γ(2). A trial state and return map, presented in Sec. 2.6.3, is employed to differentiate between stick and slip.
#### Augmented Lagrangian Scheme.
The augmented Lagrangian scheme employed in this study is first-order and utilizes Uzawa’s algorithm [51], where multipliers are updated outside of the Newton step, producing a double loop algorithm (see the texts by Laursen [18] and Wriggers [19] for a discussion of Uzawa’s algorithm applied to frictional contact problems). Such an approach preserves the quadratic convergence of Newton’s method near solution points. The presented scheme is a modification of the approach suggested by Simo and Laursen [20].
During stick, the traction is calculated by augmenting the vector gap gs,
$t(1)=λs+εgs ,$
(2.24)
where $λs$ is the vectorial Lagrange multiplier in stick. In slip, we first calculate the normal component of the contact traction by augmenting the normal gap g
$tn=λn+εg$
(2.25)
where λn is the normal Lagrange multiplier. The total traction vector in slip is then defined to be
$t(1)=tn(n(1)+μs(1))$
(2.26)
where tn is given by Eq. (2.25). In this approach, the Lagrange multiplier $λs$ augments the traction t(1) in stick, but in slip only the normal component of traction tn is augmented by λn, and the tangential traction is directly prescribed from the augmented normal component. This approach has the advantage of preserving an exact mapping to the proper tangential traction in slip, which is consistent with the augmented normal traction. As in the penalty case, a trial state and return map controlled by the slip criterion is employed to differentiate between stick and slip, presented in Sec. 2.6.3.
The Lagrange multipliers λn and $λs$ are held constant during each Newton step. Outside of the Newton loop, in this study, we propose a novel update scheme where one of these multipliers is considered active and is updated from the kinematic data (gs or g), and the other is considered passive and is derived from the active multiplier. The contact status is determined via Eq. (2.20). If the current status is stick (Φ < 0), we update $λs$ (active) and derive λn (passive)
$λs←λs+εgsλn=λs·n(1)$
(2.27)
Alternatively, if the current contact status is slip (Φ = 0), we update λn (active) and derive $λs$ (passive)
$λn←λn+εgλs=λn(n(1)+μs(1))$
(2.28)
An active-passive strategy for the multipliers ensures consistency when the contact status switches between stick and slip and is made possible due to this formulation’s use of a single penalty parameter ε, in conjunction with an exact return mapping for slip.
Augmentations proceed until a tolerance related to a convergence criterion is met. In this formulation, two separate convergence criteria and their associated tolerances are defined. The first criterion considers the relative change of the norms of the active Lagrange multipliers between successive iterations, where the associated unitless tolerance Ptol specifies the largest allowable change. Convergence is achieved when
$|Lr−Lr−1Lr|
(2.29)
where Lr represents the total norm of the active multipliers across the contact surface at augmentation step r, calculated by summing all the individual norms
$Lr=∑e=1ne(1)∑k=1nint(e)lk,er$
(2.30)
In this expression, $ne(1)$ is the number of element faces on $γ(1), nint(e)$ is the number of integration points on the eth element face, and $lk,er$ is the norm of the active Lagrange multiplier at the kth integration point on the eth element of γ(1) at augmentation step r, defined by
$lk,er={λsr·λsrΦ<0, sticking(λnr)2Φ=0, slipping$
(2.31)
The second criterion is a gap tolerance, where augmentations will continue until the magnitude of the gap is lower than the specified tolerance Gtol at every location. Convergence of the augmentations requires
$max (|gs|,|g|)
(2.32)
where $|gs|$ is associated with points currently sticking and $|g|$ with those in slip. The tolerance Gtol has units of length, allowing enforcement of the nonpenetration and stick constraints to arbitrarily small precision.
#### Stick–Slip Algorithm.
Determination of whether stick or slip is active which is accomplished by a trial state and return map and follows the same procedure for both penalty and augmented Lagrangian regularizations. We begin by calculating a trial traction $t̃(1)$ assuming stick, utilizing either Eq. (2.21) or (2.24). The trial normal and tangential components $t̃n$ and $t̃T(1)$ are evaluated from $t̃(1)$ and inserted into the slip criterion Φ
$Φ=|t̃T(1)|−μ|t̃n|$
(2.33)
Based on the slip criterion and trial traction vector, we perform a return mapping and obtain the traction vector as
$t(1)={t̃(1)Φ<0 , stickingtn(n(1)+μs(1))Φ=0 , slipping$
(2.34)
where tn is given by either Eq. (2.22) or (2.25). In the case of first contact, a trial stick traction cannot be calculated, as stick requires a previous intersection point. Consequently, first contact is treated as a case of slip in this framework. The alternative of treating first contact as frictionless is unsatisfying, as the lack of friction at the first iteration can lead to premature failure and thus precludes the modeling of certain problems that rely on frictional forces for stability (such as load-control analyses). After one iteration, the traction can be evaluated via the return map described above.
Computationally, care must be taken to ensure that augmentation does not unnecessarily change the stick–slip status. For normal contact, the update $λn←λn+εg$ will augment the normal traction until the nonpenetration contact constraint is adequately satisfied, with no adverse consequence if λn slightly overshoots the final target value during an intermediate augmentation. For tangential contact however, augmentation of the tangential traction that overshoots the final target value may cross the boundary between stick and slip, thus changing the nature of the solution. For example, at the first augmentation step, the stick traction is $t(1)=εgs$ and the multiplier $λs$ is augmented from its initial zero value to $λs=εgs$ according to Eq. (2.27). Thus, at the start of the next iteration, when gs has not yet changed, the traction is calculated as $t(1)=λs+εgs=2εgs$ according to Eq. (2.24), which essentially counts the gap function twice and can in some cases shift the contact from stick to slip. To circumvent potential error introduced by this step, our implementation freezes the stick–slip status until the completion of the first iteration following an augmentation step. After the first iteration, the gap function has been reduced by the augmentation, and the traction is split appropriately between the remaining gap and the multiplier. In this way, the double-counting of the gap function does not unnecessarily shift the contact status, but augmentation is able to modify the stick–slip status if accurate enforcement of the contact constraints requires it.
## Examples and Verifications
### Constitutive Relations.
Several finite deformation, large sliding examples are illustrated below to verify the accuracy of the implementation and demonstrate the ability of the algorithm to accurately handle complex contact problems with a conceptually simple framework. Unless otherwise noted, all presented examples use a compressible neo-Hookean constitutive model for the solid material [46], with the strain energy density given by
$Ψ=G2(I1−3)−GlnJ+λ2(lnJ)2$
(3.1)
where the constants G and λ are material coefficients, $J=det F$ is the Jacobian of the deformation, and $I1=tr C$, where C is the right Cauchy-Green tensor. For each example, the material properties given will be Young’s modulus E and Poisson’s ratio ν, where E = 2G(1 + ν) and λ = 2/(1 – 2ν). Unless otherwise noted, all benchmark problems utilize the augmented Lagrangian regularization scheme and a two-pass algorithm which enforces contact constraints twice, swapping the primary and secondary surfaces the second time and applying the same procedure [42]. All examples are quasi-static, thus references to time henceforth refer to increments in the load in quasi-static analyses.
### Finite Element Implementation.
The presented algorithm was implemented in the custom, open source finite element code febio [45] as “sliding-elastic” contact. All finite element analyses were performed using three-dimensional models and eight-node hexahedral isoparametric brick elements, unless specified otherwise. Consequently, contact surfaces generally consisted of four node quadrilateral isoparametric element faces. Gaussian quadrature was used, with four integration points per element face unless specified otherwise. For each contact pair, the penalty parameter ε was computed using
$ε=α1N∑i=1NEiAiVi$
(3.2)
where the summation is taken over all N element faces representing the contact surfaces in the contact pair, Vi is the volume of each element, Ai is the area of the element face on the contact surface, Ei is a measure of the average Young’s modulus, and α is a user-defined, nondimensional scale factor [42]. For all examples, the scale factor α is reported, along with augmented Lagrangian tolerances Gtol and Ptol presented in Sec. 2.6.2, when applicable.
In contrast to some algorithms that automatically detect surface contact pairs that evolve in real-time as a result of penetration or destructive tests [52], febio requires users to pre-identify potential contact pairs when prescribing boundary conditions on the finite element model. In displacement-control analyses, contacting bodies may be initially separated; however, in quasi-static load control analyses, an initial overlap of contacting surfaces must be prescribed so that force balance can be satisfied at the initial time-step.
### Patch Tests.
When a contact surface between two bodies is subjected to a spatially constant stress field, this stress field should be exactly transmitted from one body to another [24], as any variations in the stress at the interface are due to errors in the formulation employed. In this study, we perform the patch test proposed by Neto et al. [37]. Two cubes of identical geometry and material properties are pressed against each other under frictionless conditions (Fig. 1(a)). The cubes are 10 mm on each side, with material properties E = 100 MPa and ν = 0.3. The bottom surface of the lower cube is fixed, and displacements of the lateral surfaces of all cubes are constrained in the normal direction. A uniform pressure is prescribed by applying a vertical displacement uz = −1 mm to the top surface of the upper cube between t = 0 and t = 1 s, ramped up over ten uniform time steps.
Fig. 1
Fig. 1
Close modal
The distribution of the vertical Cauchy stress component Tzz at the final time is shown in Fig. 1, for different choices of the primary and secondary surface. A single-pass analysis was utilized without an augmented Lagrangian regularization scheme. The patch test fails when the coarser bottom surface is taken as the primary (α = 2000, Fig. 1(b)), yet the patch test is passed to five decimal places when the finer top surface is taken as the primary (α = 1 × 109, Fig. 1(c)). When keeping the top surface as the primary and utilizing an augmented Lagrangian regularization with Ptol = 1 × 10–6, the penalty scale factor can be reduced to α = 1000 while still retaining the same accuracy.
It has been well documented that classical single-pass NTS algorithms introduce artificial asymmetry into the contact interface and cannot pass the patch test [23], although extensions of the NTS framework have been attempted. Chen and Hisada [53] developed a modified NTS approach that can pass the patch test with a single-pass algorithm, although their formulation required a Lagrange multiplier approach. More recently, Zavarise and De Lorenzis [54] were able to modify a single-pass NTS algorithm to pass the patch test with a penalty method for two-dimensional contact. In the present formulation, a single-pass algorithm with the penalty method can pass the patch test for general three-dimensional contact problems. That the patch test can be passed to such high accuracy in a single-pass analysis demonstrates the strength of the proposed algorithm and offers a powerful advantage over classical NTS formulations.
With a two-pass algorithm, similar accuracy can be obtained with α = 1 × 108 with a penalty method and, with augmented Lagrangian regularization, α = 1 × 104 and Ptol = 1 × 10−4. Although a two-pass algorithm is not required to pass the patch test and ensure accurate transmission of contact tractions, in practice the use of a two-pass analysis often offers additional accuracy. Furthermore, augmented Lagrangian regularization allows for identical results with significantly reduced penalty factors, thus eliminating ill-conditioning associated with large penalties. However, if one contact surface is much coarser than the other, or if contact occurs between a rigid body and a deformable surface, a two-pass analysis may not be advised. Potential adverse consequences of an augmented Langrangian method will be treated in Sec 3.9. Consequently, although the following examples generally use a two-pass analysis with augmented Lagrangian regularization, certain problems may call for a different method of analysis and constraint enforcement. Fortunately, the results of the patch tests presented in this section demonstrate that the modeler has the freedom to choose between different methods without fear of compromising accuracy.
### Hertzian Contact.
Cylinder on plane Hertzian contact was used to verify the accuracy of the implementation, due to the availability of a closed form analytical solution [55] which can be compared to calculated stresses. A schematic of this problem is shown in Fig. 2, where we use L = 8 mm, R = 50 mm, and unit depth. An isotropic, linearly elastic material was used for both contacting bodies, with E = 115 GPa and ν = 0.32. The friction coefficient was specified to be μ = 0.7.
Fig. 2
Fig. 2
Close modal
In this plane strain analysis, a normal load P = 800 N is ramped up over 1 s and then held constant in time. Subsequently, a tangential load Q = 504 N is applied linearly between 1 s and 2 s. The choice of Q = 0.9μP created distinct stick and slip regions, allowing evaluation of the algorithm’s ability to switch between contact cases. Since frictional problems are history-dependent, this problem was solved in two time steps in order to match the assumptions made in deriving the analytical solution. Both coarse (Fig. 2(b)) and fine (not shown) meshes were employed. The coarse mesh utilized 7680 elements, whereas the fine mesh utilized 66,240 elements. Penalty and augmented Lagrangian parameters were taken to be α = 0.1 and Ptol = 0.05 for the coarse mesh and α = 1 and Ptol = 0.05 for the fine mesh. In each case, a minimum of six augmentations was enforced, regardless of whether the tolerance condition was met at a prior augmentation.
Tyy stress contours after the final time-step are displayed on the coarse mesh (Fig. 3). Both coarse and fine meshes display strong agreement with the analytical solution (Fig. 4). The coarse mesh fails to capture the contact width exactly, although that is likely related to the absence of an element at the exact contact radius. Upon refining the mesh, the exact contact width is captured to a high degree of accuracy. Interestingly, the spatial distribution of contact traction is not exactly symmetric, in opposition to the analytical solution, although the asymmetry is very minor. This is a consequence of employing a finite deformation code to replicate a problem solved under the assumption of infinitesimal deformation.
Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal
### Stacked Blocks in Contact.
This example presents the compression of four stacked blocks with dissimilar material properties and meshes, demonstrating the ability of the algorithm to handle problems involving loss of contact. Each block is a 2 mm cube (Fig. 5(a)). The first and third blocks from the top have material properties E = 10 MPa and ν = 0.1. The second and fourth blocks have E = 0.3 MPa and ν = 0.4. The friction coefficient and penalty scale factor between the third and fourth blocks are μ = 1 and α = 10, with μ = 0.05 and α = 1 at the other two interfaces. Ptol = 0.2 was selected for convergence of the augmented Lagrangian scheme. A prescribed displacement uz = –2 mm was applied to the top face of the top block in 10 time steps. The bottom face of the bottom block is constrained in all directions, but no other constraints are applied to the model.
Fig. 5
Fig. 5
Close modal
As a consequence of the friction coefficients employed, the bottom two blocks stick, while sliding develops at the other interfaces (Fig. 5). This problem is adapted from an illustration provided by Laursen et al. [29], who noted that the dissimilar meshes and the transverse gap developed on the top contact surface typically leads to failure of NTS algorithms. The contact detection strategy employed in this study encounters no difficulties with the overhanging blocks.
Next, this benchmark problem is extended by introducing finite rotations. We repeat the same analysis, but now also apply a rotation Rz = π/2 to the top surface of the top block simultaneously with uz. Due to the additional instability caused by the rotations, the friction coefficient at the top two interfaces was increased to μ = 0.08, while the penalty was decreased to α = 0.1. At the bottom interface, the penalty was decreased to α = 5. The resulting analysis involved finite deformation edge-to-face contact, with nodes and integration points coming into and out of contact. A series of snapshots of the twisting behavior is presented in Fig. 6.
Fig. 6
Fig. 6
Close modal
The bottom two blocks are still sticking at the end of the twisting analysis, despite the increased traction on the interface. The top three blocks are experiencing both edge-to-edge and edge-to-face contact, with large transverse gaps forming due to the twisting behavior. Despite the challenging nature of the benchmarks, the distribution of the contact traction is very clean for both examples presented here (Movies S1 and S2 and Figs. S1 and S2 are available under the “Supplemental Data” tab for this paper on the ASME Digital Collection).
### Twisting Contact Between Hemisphere and Box.
In this example described by Sauer and De Lorenzis [41], a thick-walled hollow hemisphere indents a deformable box and then rotates, developing large shear deformations and twisting contact between the hemisphere and box.
The mesh and geometry are shown in Fig. 7, where we have adopted L = 2 mm. The box is a cube, with material properties E = 10 MPa and ν = 0.3. The thick-walled hemisphere’s material properties are E = 50 MPa and ν = 0.3, and the friction coefficient between the hemisphere and box is taken to be μ = 0.5. Penalty and augmented Lagrangian parameters were taken to be α = 10 and Ptol = 0.05, respectively. A vertical ramp displacement uz = −1 mm is applied to the top surface of the hemisphere between t = 0 s and t = 1 s, and then held constant. A rotation Rz = π is subsequently applied to the top face of the hemisphere from t = 1 s to t = 10 s. This problem is solved with 100 evenly spaced time steps.
Fig. 7
Fig. 7
Close modal
During twisting, contact between the box and hemisphere transitions from predominantly sticking initially to predominantly slipping behavior by the end of the analysis (Fig. 7). Consequently, the applied torque required to rotate the hemisphere remains essentially constant beyond the transition to slip. Figure 8 displays the twisting torque as a function of prescribed rotation angle, for both this study and that of Sauer and De Lorenzis [41], demonstrating strong agreement. The slight oscillations observed in the mostly flat torque curve from 100 deg to the end of twisting are due to stick–slip instabilities in the motion. Visually, the box displays a type of slight chattering behavior during this time.
Fig. 8
Fig. 8
Close modal
### Compression of Concentric Spheres.
The next example has been used to motivate mortar formulations for contact [31] and thus represents a challenging benchmark. We consider compression of two thick-walled concentric spheres between rigid planes (Fig. 9). Frictional sliding contact is present between the faces of the two spheres, which are modeled in octant symmetry. The use of incompatible meshes forces gap discontinuities during both contact and sliding. This problem was originally presented by Puso and Laursen [31], who noted premature failure of NTS algorithms even in frictionless contact, and was later solved by Areias et al. [56] with friction, albeit to a smaller applied displacement.
Fig. 9
Fig. 9
Close modal
Both spheres have material properties E = 1 MPa and ν = 0.3. Sliding contact between the planes and the spheres is modeled as frictionless, with α = 10 and Ptol = 0.2. Since the planes are rigid, a single-pass analysis was used for these contacts, with the sphere selected as the primary surface. Frictional contact occurs between the two spheres, where we examined friction coefficients μ = 0, 0.5 and 2. As different friction coefficients introduced markedly different interfacial behaviors, the penalty and augmented Lagrangian parameters differed for each friction coefficient. For μ = {0, 0.5, 2}, we selected α = {1, 3, 8} and Ptol = {0.2, 0.2, 0.05}, respectively. The vertical displacement of the top plane is prescribed linearly, reaching a final displacement uz = −10 mm in 10 s. The problem is solved in 100 evenly spaced time steps for all three values of the friction coefficient.
Snapshots of the deformed mesh are presented in Fig. 9, for the case μ = 0. For μ = 0.5, the buckling of the inner sphere occurs slightly later, and in the μ = 2 case, not at all. This can be observed in plots of the vertical reaction force during compression (Fig. 10(a)), where the force is much larger in the μ = 2 case due to lack of this buckling behavior. As Areias et al. [56] only performed their analysis to uz = −9 mm, these results were also compared to those obtained with the commercial finite element software abaqus3 for all three values of friction coefficient (Figs. 10(b)10(d)); thus, this benchmark also served to evaluate the agreement between the present algorithm implemented in febio and proprietary commercial software. Notably, the data from Areias et al. display a much smaller reaction force for μ = 2, although agreement between febio and abaqus is quite good. Areias et al. do not present details on buckling of the inner sphere, but it is possible that the discrepancy may have emerged if their model showed buckling at μ = 2, which would have reduced the magnitude of the normal compression force.
Fig. 10
Fig. 10
Close modal
### Deep Indentation of Square Blocks.
This benchmark problem, originally proposed by Temizer [34] in a mortar framework, introduces sharp corners and edges into a three-dimensional finite deformation problem. In this example, a small stiff block is fully compressed into a larger, softer body (Fig. 11), developing contact between the sides of the small block and the surface of the larger block.
Fig. 11
Fig. 11
Close modal
The top block has material properties E = 100 MPa and ν = 0.3, whereas those of the bottom block are E = 1 MPa and ν = 0.3. A linearly increasing vertical displacement uz = −0.6 mm was applied to the top face of the top block over 1 s. This example was solved to a slightly larger final displacement, as Temizer begins with the blocks separated by 0.0375 mm [34]. Although the problem was initially presented as frictionless, we consider μ = 0.2 here to evaluate the performance of the proposed friction algorithm. The penalty scale factor was α = 150 and augmentation was performed on the gap, with Gtol = 0.0009 mm. Since the large indentation can cause the softer material to rise up against the indenting small block, and since the small block has a coarse mesh in the vertical direction, a single-pass analysis is employed for this benchmark, using the surface of the large block as the primary surface. 100 evenly spaced time steps were utilized in this analysis.
This example is challenging due to the sharp corners in the indenting block, which tend to introduce singularities in the contact pressure. Indeed, examples involving indentation (and sliding) with sharp corners have long been used to motivate mortar formulations for contact [32,35]. Our implementation in febio is able to complete this analysis without difficulty. Examination of the distribution of contact pressure (Fig. 12) displays a large peak in the corners and elevated values along the edges, as may be expected. Comparing the vertical reaction force to results obtained by Temizer [34] (scaled by the correct factor of 10), a reasonable agreement is seen (Fig. 13), although the slopes differ slightly. This may reflect differences between the mortar strategy employed by Temizer and the formulation of this study, differences in the constitutive model adopted for neo-Hookean behavior, errors in the febio solution introduced by the sharp corners in this example, or the effect of friction on the reaction force. To address the latter concern, an identical analysis with μ = 0 was performed (results not shown), and the vertical reaction force from the frictionless case was virtually indistinguishable from that of μ = 0.2. In an effort to understand the discrepancies between the results obtained Temizer et al. and those from febio, this problem was solved in abaqus as well, with μ = 0.2. The vertical reaction force obtained from abaqus (Fig. 13), although displaying the same trend as the other models, lies in between the two curves, suggesting that results from this problem may be influenced by differences in contact formulations or constitutive models.
Fig. 12
Fig. 12
Close modal
Fig. 13
Fig. 13
Close modal
### Shallow Ironing.
This example demonstrates shallow ironing of a rectangular block by a smaller indenter and represents a classic benchmark that can be used to evaluate contact smoothness. Various forms of this example have been presented by many authors, e.g., see Refs. [28], [33], [41], and [49]. For this study, we adopt the geometry of Neto et al. [37]. In this plane strain example, a stiff indenter with rounded corners is pressed vertically into a larger, soft block, and then displaced horizontally. The discretization employed for both surfaces has been noted to lead to chatter [28], or oscillations in the response, as contact shifts from one discretized facet to another with no tangent plane continuity. This example demonstrates the ability of the presented formulation to ameliorate discretization-induced noise in a framework that does not explicitly adopt smoothing techniques.
The geometry and mesh are given in Fig. 14. The material properties for the indenter are E = 1000 MPa and ν = 0.3, while those of the block are E = 100 MPa and ν = 0.3. The friction coefficient was taken to be μ = 0.3. A downward displacement uy = −10 mm is applied to the top surface of the indenter over 1 s and then held while a horizontal displacement ux = 250 mm is prescribed between t = 1 s and t = 2 s. As Neto et al. [37] do not provide information on the number of time steps utilized in their study, we performed simulations using 200, 400, 800, and 1600 uniformly spaced time steps. 200 time steps appeared to introduce artificial smoothing, but results obtained with 800 and 1600 time steps did not differ appreciably from results with 400 time steps. Therefore, for what follows, 400 uniformly spaced time steps were used. In keeping with the presentation of Neto et al., the surface of the block was selected as the primary surface and a single-pass analysis was employed. Contact constraints were enforced with both penalty (α = 5) and augmented Lagrangian (α = 2, Ptol = 0.2) methods. Snapshots of the deformed mesh at the end of indentation, halfway through sliding, and upon completion of sliding are presented in Fig. 15 for the augmented Lagrangian analysis.
Fig. 14
Fig. 14
Close modal
Fig. 15
Fig. 15
Close modal
The study of Neto et al. [37] examined the effect of contact smoothing with Nagata patches on the behavior of an NTS algorithm and compared results for faceted and smoothed surfaces. The evolution of the normal (FN) and tangential (FT) components of the contact force, for this study and that of Neto et al., is presented in Fig. 16 for both penalty and augmented Lagrangian regularizations. The results obtained by the penalty method, although generally in agreement with those of Neto et al., display weaker enforcement of sticking behavior during the indentation phase (indicated by the arrow in Fig. 16), necessitating the use of augmentations. Both normal and tangential contact forces predicted by febio with an augmented Lagrangian method are in excellent agreement with the smoothed results of Neto et al. (in that study, the faceted surface of the indenter caused the iterative procedure to diverge around ux = 85 mm if smoothing was not performed). If we calculate the friction coefficient from these data as $μ=FT/FN$, we find μ = 0.298 ± 0.002 for the penalty method and μ = 0.296 ± 0.001 for the augmented Lagrangian method between t = 1.2 s and t = 1.7 s, corresponding to the pure sliding regime. This result is in excellent agreement with the prescribed value μ = 0.3.
Fig. 16
Fig. 16
Close modal
A close-up of the tangential forces in Fig. 16 reveals substantial differences between schemes during sliding (Fig. 17). Oscillations in the tangential force during sliding are numerical and caused by the discretization. The faceted data from Neto et al. show large chatter, as elements on their master surface come into and out of contact. Their smoothing technique, employing Nagata patches to reduce discretization error on the master surface, is successful and greatly reduces the magnitude of the oscillations. In contrast, the present formulation, which employs no smoothing algorithms and relies on a wholly different contact detection approach, exhibits oscillations of much smaller magnitude. The present formulation is independent of the secondary surface normal, but the projection is still between two bilinearly interpolated surface facets and involves a degree of discretization error. The use of very small time steps amplifies the nonsmoothness of the gap function, which is due to the contact associated with a primary surface integration point intersecting a linearly discretized surface. Although the augmented Lagrangian scheme reduced the magnitude of the oscillations during the steady sliding regime, it created larger spikes in the response as sliding was initiated; these spikes were not present in the penalty method. Nearly identical spikes were observed regardless of the number of time steps. Although these larger spikes are still smaller than the magnitude of the oscillations in the smoothed data of Neto et al., and are quickly damped, it is instructive to consider their origin and whether they reveal flaws in the augmented Lagrangian scheme presented in Sec. 2.6.2.
Fig. 17
Fig. 17
Close modal
As we shall see, the origin of these spikes reveals potential pitfalls associated with employing augmented Lagrangian methods for contact of curved surfaces modeled with linear elements. Penalty and augmented Lagrangian methods are used to enforce contact constraints, chiefly the nonpenetration constraint for normal contact and the constraint of no relative motion during stick. For this benchmark, a theoretically perfect enforcement of these contact constraints is actually not desirable. Since we are approximating a smoothly curved surface with linear elements, a degree of discretization error is introduced in the secondary surface; additionally, although the rectangular primary surface suffers no discretization error relating to its geometry, deformations of this surface are limited by the linear elements employed. Thus, for this benchmark, a perfect enforcement of contact constraints would in fact correspond physically to sliding contact between a polygonal indenter and a surface comprised of straight links connected by flexible joints. The penalty method, as it enforces the constraints imperfectly, actually implicitly provides for a degree of smoothing and comes closer to replicating the physical scenario of interest. In contrast, augmented Lagrangian methods, though a powerful tool to reduce unphysical constraint violations, can dramatically increase discretization-induced errors under special circumstances. This mechanism is not purely a frictional phenomenon. Indeed, setting μ = 0 in the penalty and augmented Lagrangian models presented above shows a similar increase in oscillatory noise as augmentation tolerances are tightened (results not shown).
To evaluate this hypothesis more fully, the geometry of Fig. 14 was reproduced with 20-node quadratic hexahedral elements with eight integration points per surface (hex20), although the number of elements was halved along each side. Consequently, 200 evenly spaced time steps were utilized in order to obtain the same rate of crossing element boundaries seen in the linear case. For this analysis, α = 2 and Ptol = 0.2. As shown in Fig. 18, utilizing hex20 elements nearly entirely eliminates these initial spikes and ameliorates the oscillations during sliding, although they still remain present. The remaining oscillations occur because although quadratic elements allow for individual element faces to conform to one another smoothly, they still do not enforce tangent or normal continuity between elements. For the hex20 simulation, we find μ = 0.299±0.0005 between t = 1.2 s and t = 1.7 s, virtually identical to the prescribed μ = 0.3. As the number of elements was halved along each direction, the number of time steps was also halved, and a 20-node hexahedral variant with only eight integration points per surface was used, there was no extra computational cost associated with this analysis.
Fig. 18
Fig. 18
Close modal
### Pinching of a Hollow Ball.
This last example simulates compression of a hollow ball between two fingers, demonstrating the biomechanical relevance of incorporating frictional interactions into computational models (Fig. 19(a)). Two hollow tubes represent deformable fingers. Each tube has an outer radius of 1 cm, an inner radius of 0.5 cm, a length of 10 cm, and is capped by a hemisphere with outer radius 1 cm and inner radius 0.5 cm. To obtain a reasonable response for the soft pads of the fingers, material properties for each tube were taken to be E = 1 MPa and ν = 0.3, which may be considered average values for biological tissues [57]. To take into account the rigid bone underlying the soft tissue of the finger, a rigid body was attached to the inner surfaces of each tube, preventing deformation. A revolute joint connects the tubes at the intersection of their centerlines, enabling them to come together in an approximation of a pinching motion. A hollow sphere is placed initially between the two fingers, in grazing contact with the finger surfaces. The sphere has an outer radius of 2.5 cm and an inner radius of 2.25 cm, and is modeled as a nearly incompressible Mooney–Rivlin material where c1 = 1.25 MPa, c2 = 0, and the bulk modulus is k = 1250 MPa. Contact was defined separately between each finger and the sphere and a single-pass analysis was used, where the finger was the primary surface for each contact interface. Augmented Lagrangian parameters were α = 4 and Gtol = 0.01 cm, and the friction coefficient was taken to be μ = 0.9. A 15 degree rotation of the revolute joint comprised the pinching behavior and was applied in 20 uniformly spaced time steps over 1 s.
Fig. 19
Fig. 19
Close modal
This model displays several interesting behaviors. During compression, the ball sticks to the finger surfaces and deforms (Figs. 19(b) and 19(c)). Around t = 0.7 s, the sphere buckles inward and large sections lose contact with each finger. However, the finger has deformed, as it is sandwiched between the rigid material simulating bone on the inside and the ball surface on the outside, and this deformation increases the contact surface area and thus the friction force holding the ball in place. Such behavior cannot be observed in the absence of friction. In a frictionless simulation (results not shown), the model managed two time steps and failed at t = 0.06 s, when the ball lost contact with the fingers and jumped away. The inclusion of friction allows this model to develop deformation of the finger (Fig. 19(d)), which further traps the ball by adding a plowing component to the friction force, and demonstrates the necessity of including frictional interactions if one wants to model certain physically relevant behavior.
## Discussion
This paper has presented the formulation, implementation, and verification of a surface-to-surface finite element algorithm for frictional contact of solid materials that can accommodate large deformation and sliding within a conceptually simple framework. A distinguishing characteristic of the proposed formulation is the ability to solve challenging problems without recourse to mortar methods or contact smoothing, thus retaining the simple physical interpretation of classical NTS formulations and avoiding computational overhead associated with more complex algorithms. Consequently, special contact elements and large numbers of integration points are not required, and the contact algorithm functions efficiently on faces of standard linear elements, such as the eight-node hexahedral bricks used in the examples presented in Sec. 3. This formulation endows the presented algorithm with a robustness that allows solution of complex three-dimensional finite deformation problems without significantly increased computational demands, facilitating its incorporation into challenging contact problems typically encountered in biomechanics.
The numerical examples presented in Sec. 3 were selected to verify the accuracy of the formulation and validate it against common test problems in the literature. The results demonstrate the ability of the proposed algorithm to handle a wide variety of challenging frictional contact problems, and a robust mechanism to differentiate between areas of stick and slip. Patch tests were passed to five decimal places with a single-pass algorithm using only the penalty method (Fig. 1), and the use of two-pass algorithms and augmented Lagrangian regularization achieved the same accuracy with significantly reduced penalty values. The algorithm was verified with Hertzian contact, where analytical solutions were in excellent agreement with finite element results (Fig. 4). Additional examples demonstrated the ability to handle three-dimensional large-deformation contact problems (Figs. 7 and 9), including the biomechanically relevant problem of object pinching (Fig. 19). Importantly, the present approach was able to solve problems typically associated with failure of NTS algorithms (Figs. 5 and 11), and also provided results which could previously only be obtained with contact smoothing techniques (Fig. 17). The proposed augmented Lagrangian scheme of Sec. 2.6.2 was shown to be robust, generally needing two or fewer augmentations on average to meet the required tolerances. Exceptions include the patch tests where an extremely demanding tolerance was required and the Hertzian contact benchmark where we enforced a minimum of six augmentations. A full summary of the average number of augmentations required for convergence is available in Table S1 available under the “Supplemental Data” tab for this paper on the ASME Digital Collection, for all benchmarks presented in Sec. 3 utilizing an augmented Lagrangian scheme.
One weakness of the proposed algorithm derives from the formulation, which prioritized a robust, fast algorithm over the ability to solve the most demanding problems. To maintain speed and robustness, the contact algorithm was developed to provide excellent results with standard linear finite elements of the type most commonly adopted for complex problems. Consequently, although able to solve numerous problems typically used in the literature to motivate more complex algorithms, the proposed formulation did encounter difficulties with the problem of deep ironing with a square indenter (see, e.g., Ref. [35] for the problem description). The use of bilinear interpolation and linear finite elements led to difficulties in wrapping individual surface facets around the sharp corner of the indenter and produced convergence issues leading to failure at t = 1.6 s, although the problem could be solved if a slight radius was applied to the sharp corners of the indenting block (results not shown). Although the presented algorithm develops a powerful, robust method to solve a broad variety of challenging contact problems in a computationally efficient manner, it may not represent the most technically advanced or complex framework. For the purpose of advancing the capabilities of an open-source software tool, this type of general purpose algorithm is desirable, although the tradeoff is a lack of ability to solve certain highly specialized contact problems and may be considered a limitation.
This study addresses an important computational need in the biomechanics community. Importantly, the algorithm is implemented in the open source finite element code febio, which is available to the general public and contains specialized constitutive models and boundary conditions specific to biomechanics problems. Incorporation of a robust frictional contact algorithm within this framework provides a valuable computational tool to the biomechanics community and represents a necessary first step toward the development of a finite element algorithm for frictional contact of biphasic materials.
## Disclaimer
The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health or the National Science Foundation.
## Funding Data
• National Institute of General Medical Sciences (Grant No. GM083925).
• National Science Foundation Graduate Research Fellowship Program (DGE-11-44155).
### Appendix: Principle of Virtual Work
The weak form of the statement of conservation of linear momentum for quasistatic analyses may be written in the spatial frame as
$∫bδv·div T dv=0$
(A1)
where b is the domain of interest in the current configuration, T is the Cauchy stress, δv is a virtual velocity, and dv is an elemental volume [46]. By applying the divergence theorem, this expression may be rearranged as
$δW=∫bT:δD dv−∫∂bδv·t da=0$
(A2)
where $δD=(grad δv+grad Tδv)/2$ is the virtual rate of deformation tensor, $t=T·n$ is the traction on the surface ∂b, n represents the unit outward normal to ∂b, and da represents an elemental area of ∂b. For convenience, we split the virtual work into its internal and external parts, $δW=δWint−δWext$, where
$δWint=∫bT:δD dv$
(A3)
and
$δWext=∫∂bδv·t da$
(A4)
Since the system of equations in Eq. (A2) is generally nonlinear, an iterative scheme such as Newton’s method is required for solution. This scheme requires the linearization of δW at some trial solution for the motion $χ$, along an increment in displacement $Δu$ in $χ$
$δW+DδW[Δu]=0$
(A5)
where $Df[Δu]$ represents the directional derivative of f along $Δu$. The directional derivatives of the external virtual work depend on the type of boundary conditions present. Conditions relevant to contact analyses are discussed next.
Consider a domain b consisting of two bodies b(1) and b(2) with respective boundaries ∂b(1) and ∂b(2). The two bodies are in contact over portions of ∂b(1) and ∂b(2), respectively denoted γ(1) and γ(2). According to Eq. (A4), the contribution of contact to the external virtual work may be written as
$δGc=∑i=12∫γ(i)δv(i)·t(i) da(i)$
(A6)
where $δv(i)$ is a virtual velocity, t(i) represents the traction on γ(i), and da(i) is an elemental area of γ(i). In contact analyses, the tractions on γ(i) are equal and opposite, $t(1)=−t(2)$, and the contact surfaces are shared, hence we may select one surface to perform the integration over.
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https://www.hpmuseum.org/forum/thread-12540-page-6.html
|
emu48 now for android-OS
07-20-2019, 08:14 PM
Post: #101
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
Pinch zoom has no effect, the scratch is still there.
The original BMP is not the problem: if you off the calculator the LCD does not have the scratch any more... The scratch is caused by the emulation.
07-21-2019, 01:57 PM
Post: #102
Regis Cosnier Junior Member Posts: 26 Joined: Apr 2019
RE: emu48 now for android-OS
(07-20-2019 08:14 PM)Vincent Weber Wrote: Pinch zoom has no effect, the scratch is still there.
The original BMP is not the problem: if you off the calculator the LCD does not have the scratch any more... The scratch is caused by the emulation.
It is weird because the screen seems shift. But I guess you have just copy Eric's image "real28s.bmp" on Christoph's image "REAL28S.BMP" :-D
07-21-2019, 04:13 PM
Post: #103
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
(07-21-2019 01:57 PM)Regis Cosnier Wrote:
(07-20-2019 08:14 PM)Vincent Weber Wrote: Pinch zoom has no effect, the scratch is still there.
The original BMP is not the problem: if you off the calculator the LCD does not have the scratch any more... The scratch is caused by the emulation.
It is weird because the screen seems shift. But I guess you have just copy Eric's image "real28s.bmp" on Christoph's image "REAL28S.BMP" :-D
Heu...no.
None of the BMPs have the scratch when opened in a picture viewer.
And the scratch does not surface when the calculator is off, as I said. Only when it is on...
07-21-2019, 06:41 PM
Post: #104
cdmackay Senior Member Posts: 509 Joined: Sep 2018
RE: emu48 now for android-OS
Is there a Polywatch emulator app?
Cambridge, UK
41CL/DM41X 12/15C/16C DM15/16 71B 17B/BII/bII+ 28S 42S/DM42 32SII 48GX 50g 35s 30b/WP34S Prime G2
& Casios, Rockwell 18R :)
07-21-2019, 07:26 PM
Post: #105
Massimo Gnerucci Senior Member Posts: 2,049 Joined: Dec 2013
RE: emu48 now for android-OS
(07-21-2019 06:41 PM)cdmackay Wrote: Is there a Polywatch emulator app?
Greetings,
Massimo
-+×÷ ↔ left is right and right is wrong
07-21-2019, 08:41 PM
Post: #106
ijabbott Senior Member Posts: 893 Joined: Jul 2015
RE: emu48 now for android-OS
(07-21-2019 04:13 PM)Vincent Weber Wrote:
(07-21-2019 01:57 PM)Regis Cosnier Wrote: It is weird because the screen seems shift. But I guess you have just copy Eric's image "real28s.bmp" on Christoph's image "REAL28S.BMP" :-D
Heu...no.
None of the BMPs have the scratch when opened in a picture viewer.
And the scratch does not surface when the calculator is off, as I said. Only when it is on...
Does the same thing happen on the 19BII?
I don't see the problem on either my tablet or my phone, but they're both based on Android 7.1 (actually LineageOS 14.1), so they're a little bit out of date.
— Ian Abbott
07-22-2019, 08:48 AM
Post: #107
Regis Cosnier Junior Member Posts: 26 Joined: Apr 2019
RE: emu48 now for android-OS
(07-21-2019 08:41 PM)ijabbott Wrote:
(07-21-2019 04:13 PM)Vincent Weber Wrote: Heu...no.
None of the BMPs have the scratch when opened in a picture viewer.
And the scratch does not surface when the calculator is off, as I said. Only when it is on...
Does the same thing happen on the 19BII?
I don't see the problem on either my tablet or my phone, but they're both based on Android 7.1 (actually LineageOS 14.1), so they're a little bit out of date.
I'm pretty sure that you mix the Christoph and Eric KML/BMP because I'm able to reproduce your issue. Your HP28S is dark brown like the Eric image and not dark grey like the Christoph image! I cannot explain the scratch line, may be due to the mask combination.
Attached File(s) Thumbnail(s)
07-22-2019, 12:01 PM
Post: #108
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
Thanks Regis, you are actually right, replacing the BMP file with Christoph's actually solved the problem.
By the way, the emu48 clock issue (not in synch with Android's when the calc is turned on) is still there
Any news from Emu71 ?
Thanks a lot and cheers
07-29-2019, 05:29 PM (This post was last modified: 09-05-2019 10:02 PM by compsystems.)
Post: #109
compsystems Senior Member Posts: 1,257 Joined: Dec 2013
RE: emu48 now for android-OS
Hello,
The memory file (port 0, stack and others) is stored in *.e48/9, while the memory file (port2, ..., 32) is stored in *.bin
A feature that emu48 is missing is that from the kml script file you can read a working session, both port0 and port2, that is, all the memory, for this it is necessary that someone be able to improve the source code and add two new instructions
RAM (main memory)
RAMP2 (port 2 memory)
PHP Code:
Global Title "Eric's Real hp48gx for Emu48" Author "Eric Rechlin" ROM "ROMGx.48G" RAM "ram_01.e49" RAMP2 "port2_01.bin" Bitmap "Real48x.bmp" ...End
Another idea is to change the shape of the pixel, solid, with a grid (as seen in real calculators) and another style as shown in
custom pixel form
dot pixel
Real LCD emulation (grid)
The PocketPC was the missing link between the first mobile devices with touch screen and the ipad (current tabletPC and smartphones), the author of the emu48 CG improvements, developed the emu48 version for PocketPC, the KML has commands (Topbar, Menubar, Vertical) that would be useful on Android, that is to say that from the kml, the automatic form of visualization is controlled, without doing it from manual configuration. Please incorporate these commands in a future version
Topbar 0/1 # 0 -> Android: Hide the status bar, PC/PocketPC: Hide the title bar
Vertical 0/1 # 1 -> Android/PC/PocketPC: portrait on, 0 -> landscape on
Bottombar 0/1 # 0 -> Android: Hide the navigation bar
Quote:Topbar is a special command only for the Pocket-PC versions of Emu42 and Emu48 to enable/disable the top bar of the screen. Valid entries are 0 or 1. One is enabled and Zero is disabled.
Example:
Topbar 0
Menubar is a special command only for the Pocket PC versions of Emu42 and Emu48 to enable/disable the menu bar of the screen. If the menu bar is disabled you can get the menu over the context menu gesture on a display area isn’t covered by virtual key buttons. Valid entries are 0 or 1. One is enabled and Zero is disabled.
Example:
Vertical is a special command only for the Pocket PC versions of Emu42 and Emu48 to rotate the display drawing by 90° anti-clockwise.
Example:
Vertical 1
10-21-2019, 04:47 PM
Post: #110
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
Hi Regis,
I noticed that the new emu42 version now supports low-end pioneers (10b, 20s, 21s).
Any plan to support them on Android as well ? That would be awesome
And btw where are you with Emu71 ?
Thanks a lot and cheers,
Vincent
10-21-2019, 09:41 PM (This post was last modified: 10-21-2019 09:42 PM by Regis Cosnier.)
Post: #111
Regis Cosnier Junior Member Posts: 26 Joined: Apr 2019
RE: emu48 now for android-OS
(10-21-2019 04:47 PM)Vincent Weber Wrote: I noticed that the new emu42 version now supports low-end pioneers (10b, 20s, 21s).
Any plan to support them on Android as well ? That would be awesome
And btw where are you with Emu71 ?
At first shot, it seems to work quite well by updating the source code of Emu42. Thank you Christoph.
For Emu71, it is still a work in progress to add the ports configuration. The interface is ready but it misses some pipes ;-)
10-21-2019, 09:47 PM
Post: #112
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
Excellent, many thanks Regis !
When can we get emu42 1.2 ?
Thanks and cheers
10-22-2019, 12:59 AM
Post: #113
SammysHP Member Posts: 99 Joined: Jul 2018
RE: emu48 now for android-OS
Any progress with the 50g port 2 access? I was still not able to get any persistence of port 2, even when I use a copy of all files (as explained previously in this thread).
https://github.com/dgis/emu48android/issues/3
10-22-2019, 09:20 PM
Post: #114
Regis Cosnier Junior Member Posts: 26 Joined: Apr 2019
RE: emu48 now for android-OS
(10-21-2019 09:47 PM)Vincent Weber Wrote: When can we get emu42 1.2 ?
I just created a version 1.2 (which is actually a beta) here:
http://regis.cosnier.free.fr/soft/androi...Binary.zip
You may need to uninstall your previous install if it comes from Google Play Store because it is not the same signature,
and then select the folder where are the KML/ROMs to give the permission to access.
I added an experimental and still buggy "Overlapping LCD mode" (drag and pinch works on this very small screen too).
Tell me is everything is ok, else I can fix the bugs.
(10-22-2019 12:59 AM)SammysHP Wrote: Any progress with the 50g port 2 access? I was still not able to get any persistence of port 2, even when I use a copy of all files (as explained previously in this thread).
https://github.com/dgis/emu48android/issues/3
I hope when I will have the time to do it. I don't know yet how to do that, but may be saving the full ROM in another file...
10-22-2019, 09:24 PM (This post was last modified: 10-22-2019 09:42 PM by Regis Cosnier.)
Post: #115
Regis Cosnier Junior Member Posts: 26 Joined: Apr 2019
RE: emu48 now for android-OS
I just add it to the Google Play Store in beta, so, you don't have to uninstall your previous version:
I never use that functionality yet, so, I hope it will work for you!
The updated and fixed (case) KMLs coming from Christoph without the ROM are here:
http://regis.cosnier.free.fr/soft/androi...t-ROMs.zip
10-22-2019, 09:48 PM
Post: #116
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
Hi Regis,
Many thanks, but it does not work for me.
Whatever was working in 1.1 is still working.
But starting any of 10b,20s or 21s kmls crashes the app without even an error... Any clue ?
Cheers
10-24-2019, 02:53 PM
Post: #117
Regis Cosnier Junior Member Posts: 26 Joined: Apr 2019
RE: emu48 now for android-OS
(10-22-2019 09:48 PM)Vincent Weber Wrote: But starting any of 10b,20s or 21s kmls crashes the app without even an error... Any clue ?
I tried with different Android versions: 5.0, 7.1 and 9.0. It works each time for me!
Are you sure that your ROM and associated KML files work with Emu42 version 1.23 for Windows before trying with Emu42 version 1.2(beta) for Android?
10-24-2019, 02:58 PM
Post: #118
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
Hi Regis,
Indeed, I tried this with the very same KMLs and ROM files on Emu42 1.23 for Windows, which works fine on all 3 models: 10b, 20s, 21s.
On your version for Android (on my Galaxy S8 running Android 9.0), when I select the KML, the app stands still for quite a few seconds, before crashing with no warning whatsoever...
I used the version from your direct link, not from the store. Should I delete and re-install from the store ?
Many thanks and best regards,
Vincent Weber
10-24-2019, 03:03 PM
Post: #119
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
I just did that (install from store), and it does the same. A new 17bII is no problem, a new 20S crashes the app...
Don't know what to do...
10-24-2019, 03:15 PM
Post: #120
Vincent Weber Member Posts: 122 Joined: May 2015
RE: emu48 now for android-OS
I managed to get it to work !! You would'nt believe it.
My low-end pioneer ROM files names were in lower case, e.g. hp20s.rom.
I noticed the other ones (working ones) were in upper case, so I changed to e.g. HP20S.ROM and... it works ! seems that the case is still an issue...
Cheers
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2020-09-23 09:19:53
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http://digital.lib.usf.edu/SFS0050196/00015
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## A fortune at stake, or, A Wall Street messenger's deal
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## Material Information
Title:
A fortune at stake, or, A Wall Street messenger's deal
Series Title:
Fame and fortune weekly : stories of boys who make money
Creator:
A self-made man (J. Perkins Tracy)
Place of Publication:
New York
Publisher:
Frank Tousey
Publication Date:
Language:
English
Physical Description:
1 online resource (28 pages)
## Subjects
Subjects / Keywords:
Dime novels -- Periodicals ( lcsh )
Wealth ( lcsh )
Entrepreneurship -- Fiction ( lcsh )
Boys ( lcsh )
Genre:
serial ( sobekcm )
## Record Information
Source Institution:
University of South Florida
Holding Location:
University of South Florida
Rights Management:
The University of South Florida Libraries believes that the Item is in the Public Domain under the laws of the United States, but a determination was not made as to its copyright status under the copyright laws of other countries. The Item may not be in the Public Domain under the laws of other countries.
Resource Identifier:
F18-00015 ( USFLDC DOI )
f18.15 ( USFLDC Handle )
031444493 ( ALEPH )
840611527 ( OCLC )
## USFLDC Membership
Aggregations:
University of South Florida
Dime Novel Collection
Fame and Fortune Weekly
## Postcard Information
Format:
serial
Full Text
PAGE 1
.. ,;VE12a. The rascal sprang at Tom and seized him by the throat. Help! shouted the boy, realizing his disadvantage. His cry was heard. The door was flung open and Mr. Arnold dashed into the room and rushed to Tom's assistance.
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Fame and Fortune Weekly STORIES OF BOYS WHO MAKE MONEY l1111ed W e ekl11-B11 Subs cription l!l.60 p e r 11e ar. Entered according to A ct of in t he ttea r 1908, in the oJllce of the LibrarlM of Co11gr e111, W cuhing t on, D C ., b11 Frank Touse11, P ubl iaher, U Unio n S qua.-., Neio Y o r k . No. 1 28 NEW YORK, MARCH 13, 1908. PRICE 5 CEN TS. A FORTUNE AT STAKE DB, A WALL STREET MESSENGER ts DEAL By A SELF:..MADE MAN CHAPTER I. THE MAN WITH THE WHISKERS. "Hi, there, son!" Tom Sedgwick looked up from the market report he was studying and saw, fflfilled in the cashier's little window, a fac e that res e mbl e d an ourang-outang, so bewhi s kered and _ _, mahogany..,hued it was. Tom was employed as messenger by Frederick Carvel, a not over prosperous stock broker, who operated o n the Curb, a.t No. Wall Street, and his customar y pos t was a well"-' worn, leather covered chair by the window in the waiting room, if the limit e d s pace, divided from the little counting room by a wire f e nce, and fitted up wit h a few chairs, a t i cker, and framed docu ments on side wall col)l d be called by such a n ame. At the present moment Tom was i n charge of the office, th e l ord of all he surveyed. It was one o 'clock. The junior bookkeeper, who attended to o rders and called h imself the ma. rgin clerk because he thought it looked more important, was out at lunch, while the head bookkeeper, who was also the cashier, and g e neral boss when Mr. Carvel was out-which he was most of the t ime between ten and three--was up s tairs on business Alth9ugh Tom, from where he sat, coul d see a nybody w h o entered the office, he had not noticed the b ewhiskered visitor come in, so silently had he ma.de his appearance Tom was rather n ettled at this fact and at the familiar way the caller had a d dressed him B esides, he didn't like the ma.n's face, anyway. "Speaking to me?" he a sked, curtly. "Who else?" grinned the man "I thought ma ybe you were trying y()u.r voice, or calling to a man ac ross the street." The pair of little, round eyes, almost l ost i n the hairy countenance, snapped in a peculia.r way. "No; I was talking to you. "What do you want?" "Well, son-" "Cut the son out, please," r eplied Tom, impatiently "Well my laddybuck --" Oh, switch off! I'm neither son nor laddybuck, but the messenger of this office. W h at's y o u r business? Say i t quick, for I'm busy." "Is the boss in?" "If you mean M r. Carvel, he isn t in." "Where is he?" "He's out on the street "When will he be in ?" "Three o'clock if he doesn't return before." The vis itor cocked his eye<> up at the clock and then brought them back to Tom s face again. "Can I have a word with you, son?" "Say, what' s the matter with you, anyway?" The eyes peered around behind the boy to see if he was a lone. "I'd like to say something confidential." "Why don't you say it, then? "Want to do me a favor?" "I'm not dying for tihe privilege."
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A FORTUNE AT S'l'AKE. v lunch, and this he collected every morning before he went to business. Out of this princely sum the boy could save nothing, but he managed to have some spare change in his clothes just the same. He was chiefly brought into contact with the brokers who did business in the open air on Broad Street, that is, the Curb market, aml he often had a chance to do a favor for one of them in a rush, and was always rewa.rded with a quarter, if not a half-dollar when the broker had nothing smaller at hand. Tom didn't consider it necessary to tell his mother about these donations, for he had an idea if she knew that he had any money the daily stipend would cease till he was broke. One day a fellow messenger explaiEed to Tom how e11sy it was to make money out of 1a stock deal if he had a small capital to start with. \ I 'l'om was interested at once. He wanted to know more about the matter and his friend told him all he knew about the modus operandi. Tom learned that there was a little bank on Nassau Street that did a brokerage business in connection with its bank ing opera.tions. It made a specialty of taking in small deals from the junior clerks and office boys in the financial district. W11ile the average broker would hardly bother with an order for less than 100 shares of stock on a margin deal, the little ba11k would buy or sell as small a quantity as five shares. So Tom began to economize his spare change with a view of taking advantage of the opportunity to make easy money. While waiting for his funds to grow he began to study the stock market wit]1 a view of being in shape to do some-thing when the time came. Wha t would have been dull work to most boya soon be came a fascinating occupation for our hero. The more he learned about the stock market and Stock Exchange methods the more he wanted to know. The brokers seemed to be a jolly, free-handed lot of men, who dressed well and appeared to enjoy life, so Tom de cided that some day he would be a broker himself. It is true that his employer, Mr. Carvel, acted as if life was a serious proposition, and he often looked as if he had a grouch against fate, but Tom judged that that was his nature, and that there are exceptions to every rule. One morning !Tom, while on his way to the station, picked up a small pocketbook from the gutter and found $40 in it. As there was no clue to the owner Tom appropria.ted his :find and patted himself on the back. He had$15 saved up, and that gave him a capital of $55. At that time the stock market was on the rise and the public seemed especially excited over a stock ca.lled A. & C., which was booming. Tom lost no time in buying te:.n shares of it for 52 at the little bank, and a. few days later, after watching the market closely, he sold out at 66 7-8. He clearecl a profit of$1-, and was in the seventh heaven of delight Indeed he was so tickled that he told his mother all about the transaction. She immediately proceeded to lay a claim to the money. ----Tom protested. "It's my money, mother, and you ought to let me keep it. I'll need it, anyway, to invest again when I see anotl1er good chance. I've been saving up every cent I go t hold of in order to take advantage of such a. chance to make a stake. With $200 I expect to make$300 or $400 more shortly." His arguments were lost on his mother. She wanted the money, and what was more to the point, she was going to have it. The result was i Tom had to cough up, and he did it with mighty bad grace All his bright anticipations were nipped in the bud, and he went to business next day feeling as if he didn't care whether school kept or not. However, he did no t remain long depressed. He was full of animal spirits, and he resolved to save up again until he could make a fresh deal, the result o f wh i ch, one way or the other, he didn't intend to acquaint his mother with. Ha.cl his mother really needed that$200 he wouldn't have grudged it to her, but he knew she had no particular use for it, so he thought he sh<.mld have been allowed to keep it. He failed to realize that his mother could ha1dly be ex pected to look at the matter fr.om his po,int. of view. She had no confidence in his schemes to make more. Two hundred dollars in the hand, in her opinion, was worth more than $400 in the bush, as the expression is, and who s\a,ll say she was not right? So Tom's$200 went intd the Bronx Savings Bank, along with her own money. In the course of human events, if the boy lived, that $200, with the interest thereon, and all the rest of his mother's money, together with the house, would come to Tom; but the young messenger wasn't looking forward to such a thing as that. He loved and respected his mother as all good boys do, bfi.t he was ambitious to get ahead in the world through his own exertions, that's why he objected to losing that par ticular$200. In time Tom saved enough money to make another deal, and as he was successful he found himself in possession of another $200. This he hid in a corner of his trunk and said nothing about it to anybody. On the day this story opens was watching the stock market closely, for he thought he saw indications of a gen eral rise, and he was figuring on bringing his$200 downtown next morning to have it at hand in case the opportunity presented itself for him to make a promising deal. As we said at the close of the last chapter, Tom went to lunch. He patronized a quick-lunch house on Bro ad Street, where, for fifteen cents, he got a plate of stew and a glass of milk. As soon as he finished his lunch he returned to the office, where he found a message awaiting him to call on a Stock Exchange broker who had an office in the Johnson Build mg. He was out and in all the afternoon, and finally at ten minutes to three he cm: riecl the clay's depo s its to the bank.
PAGE 5
I I 4 A FORTUNE AT '"STAKE. ., When he got back he hande
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A FORfr'UNE AT STAKE. "' soou as lie 2aw that the conversation was taking !mch a pcrrnn al trend. l\J r. Carvel made no answer, but looked at the boy with mingled am:iety and doubt. "What did you understand from that conversation?" he asked, at length. "I'd rather not say, sir," replied the boy, slowly and in a hes itating way. '''I hen yon believe that man's story? "Wasn't it trne, sir?" "It \ras a tissue of falsehoods," said the broker, excitedly. "That fellow is a rascal. He has me in his--" He s topped abryptly, as if realizing the slip he had al-most made. "Tom, I wa.nt you to promise me to be silent about wha. t you heard-as silent as the grave IThe world is rea.dy to believe evil of any man, ho\\ ; ever great or respected he may be. In fact, the higher the pedestal on which he stands the more cager certain people are to drag him down therefrom at tl!e fir st of suspicion. I have enemies, Tom, who would be delighted at a chance to pick my bo1ies. You do noL wish to hann me, do you, boy?" "No, sir." "Then keep what you have learned to yomself. Do noL even t e ll your mother. I will make it all right. wages s hall be $10 a week after this, or$12, if that i s not enough, and besides I will make you a prescnt." He took a roll of bills from his pocket and pushed it into the boy's hand. "Keep or that as you choose. All I ask i s that yon will not go ba.ck on me." He spoke with feverish eagerness, and Tom felt sorry for him. "I'd rather not take this money, sir," he said "I don't want to be paid for keeping your secrets." "Boy, do yon mean to betray me, then?" "No, sir; but as long as I am in your employ it is my duty to do the right thing by you without extra pay." "But this is a present." "No, Mr. Carvel, it is not a present; it is a bribe, and I wish you to understand that I am not to be bought. Steve Johnson may have his price, but I have none." The broker stared at his messenger in wonder. "Do you mean to say that you reruse this money and yet '"ill keep silent?" "I mean to say that I regard your interests as 0 the first importance as long as my conscience tells me to stand by them,. I promise you never to breathe a word of what I overheard for t.he purpose of injuring you. But if the time ever should come when, in the interests of an innocent and wronged person, it would be necessary for me to speak, then I will know that my lip s are my own and not sea.led by a price. At any rate, you can trust me, sir, which I could not answer for if I accepted a bribe." The broker did not answer for some moments. '1'11en he took the boy's hand in his. "'I do trust you, Tom, and you shall not find me ungrate ful. I belie )'e your word is b etter than some people's bond I accept it ancl will rely on it." The rest of the journey uptown was passed in silence. II CHAPTER V. TOM MEETS THE llfAN WITH 'l'HE WHISKERS UNDER THRILLING CIHCUMSTANCES. Alter leaving Ml. Carvel safe ly at his residence on l\Iadi son Avenue, Torn hurried home himself, for he knew that his mother would be wondering why he so late in get1.ing back his work. He found her looking anxiously from the front window of their little parlor in the direction he usually came from the station. She wanted to know what had detained him, and he told her that his employer had been taken ill at the office and tha.t he had to go home with him in a cab. His supper was ready arnl waitin g, so he saL clown to it at once. Next morning he dug his $200 ont of the depths of his trunk and took it downtown with him. He had already decided to buy 30 sharoo of D. & L. at 60, and as business was _not rnry lively that day he easily found a chance to go to the littl e b ank on Nassau Street and put the deal through on a margin basis. 1\lr. Carvel did not appear at the office that day, and the cashier was in full charge of the establishment. Next da.y, however, the broker turned up ail a quarter of Len as usual, and things resumed their customary in the office. 'I'om wondered"' when Steve Joluison would show l;p again, for that he would do so soo n see med to his mind a foregone conclusinn. He had shown that he held a winning hand, ancl next move naturally wnuld be to re ac h out for the s take he was playing for. Although Tom was undoubt ed ly interested in the movements of the man with the whiskers, he was more interested in D. & L., vi1hich went up s lowly as the days slipped by until it reached 70 3-8. All the stocks on the Stock Exchange list had partici pated in the bull mark et and w e re more or less higher than they had been a fortnight b efo re. Tom d ecide d tha t$10 a sha re profit was good enough for him, so he ordered his thirty shares sold. When he got his check from the bank he found that he was worth just $500. He cashed the check, got five$100 bills, took them home and towed them away at the bottom of his tnmk again. IThat evening he went to call on a fri end of hi s namcd Dick Butterick, 'Yho was also a messenger in Wall Street. Dick lived about eight blocks away, and T'om stayed at his house ti11 ten o'clock. When he got up to go Dick said he"d walk part of the way back with him. When the boys had gone about four blocks Tom seized his friend by the arm all of a sudden and exclaimed: ''Look there! I believe that house i s afirr." "It is, for a fact!" agreed Dick, excitedly. lt was a three-story brick building, the ground floor L crng occupied as a store, and the blaze wa.s in a front room on the floor. As the boys looked up ai the window where they saw the
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I J A FORITUNE AT ST AKE. 9 ==========---At that moment a fire-engine, by a hose-cart,! whiskers, for they consisted of the forged check on which dashed up, while a second was seen coming up the next he had been railroaded to Sing Sing, and the sworn con street. fession of the real forger, which exonerated Johnson from A hook-and -1a. dder was humming along a block away, and the crime the toots of the engines and jangle of the bells had aroused Without these documents Steve could neither prove his the immediate neighborhood to a pitch of consi
PAGE 11
. -. 10 A FOR!T'UNE AT STAKE. It gave him something of a shock, too. Slme Johnson was likely to call on him to learn whether he lmew anything about the pa. pers he (Johnson) had had in his grasp when he was overcome by the smoke. Tom felt that he could not deny having them in his posSssion if the man with the whiskers pre$ed him fo.r a direct answer on the subject. "If he suspects that I have them he will a strong effort to get them back, and I don't know as I have any real right to refuse to give them up," thought Tom. "I wish to goodness that I didn't get hold of them. In any case, if Johnson should be arrested and taken back to Sing Sing I'd have to send them to him so that he could clear himself, -no matter wha.t effect their production had on 1\fr. Carvel." All thi s passed through Tom's mind in a twinkling while Dick was 1ooking at him. "Well, if the m!lJl chooses to hunt me up I can't prevent him doing so," he replied. After some further talk on the subject of the fire the boys parled. That afternoon when on an errand to the Mills Building, Tom hea:rcl a couple of brokers talking abot1t a syndicate that had been fo11necl to boom C. & A. stock. He heard enough to assure him that C. & A. would be a good thing to get next to as soon as possible. ; When he returned to the o.ff:ice he looh:!d the stock up on the daily market report and found that it was going at 17. "I'll be able to get 100 shares on. margin," he told him self. "With that amoilllt, if the syndicate doesi1't run against a snag, l ought to make over$1,000. Then I'll be worth at least $1,500, which is a whole lot of coin for a messenger boy to own in. these strenuous times." When he starled for home after his work was done tha t 1 day it was with the determination to bring his$500 do wn town in the morning and slap it into C. & A. He had just finished his supper and was reading the evening paper when a ring ca.me at the front door. Throwing down the pa.per he went to the door and opened it. The man with the whiskers stood there. He was clearly quite ta.ken a.back on seeing Tom, whom he recognized as Mr. Carvel's office boy. He had read the a....-ticle in the paper which stated that a boy named T6m Sedgwick, of No. Bo/ton Road, had rescued him from the burning building in an unconscious condition, but there was nothing in the story to connect Tom with Wall Street, so that Steve.Johnson did not dream that it was the san1e boy he had tried t'o bonow the dolla.r of the day he c;alled on Mr. Carvel. Although a bit staggered by the encounter, he quickly pu1led. himself together. "Well, son, we meet again," he began, with the same old chuckle. "Apparently so," replied the young messenger. "Do you wish to see me?" "If you are Tom Sedgwick, I do." "iThat's my name." "I came ai;ound to thank you for savin' me from becomin' a human torch last night," he said, slo.wly. "You needn't have put yourself to the trouble of coming here to thank m e for the service. I pulled you out of the house because I should have considered myself a coward had I left you all alone in the condition I found you. I was willing to take your thanks for graiited." "Well, son, I'm greatly ,obliged to you for what you did, and I'm sony that I'm fl.at broke and cant make you a suitable acknowledgment; but that ain't sayin' I'll never be in shape to make it all right with you." "You needn't worry about making it right with me. I'm glad I saved you, so we'll let it. go a.t that," replied Tom. "No," said the man with the wl1iskers, shaking his head, "you did me a good turn and you're entitled to some reward." "I'm not taking rewards for saving people's lives." "Well, son, we won't argue the matter. Now, I want to ask you a question. Where di cl you find me?" "On the floor in the corner of the room opposite the bed." "Jest so. I had somethin' in my hand, didn't I?" and Johnson looked fixedly a.t the boy. "Yoilr hand was under the end of the carpet, which was loose." -"Exactly,'' replied Steve, anxiously. "You pulled my hand out and you found I had a couple of papers in it, didn't you?" "You did ];ave some papers in your hand, but yo; u dropped thimi on the floor." "And didn t you pick them up? They were important to me, thats why I kept them hidden under the carpet. When I wok. e up half smothered I thought of th>?m first. I tried to them. I remember get.tin' hold of them, and that's all. Did you leave them behind when you dragged me out? I was up in the room this morn in' huntin' for them, but they wasn't there. If you didn't take them somebody else did, for that end o f the room wasn't burned. 'rhey must ha .ve been there somewheres if they wasn't ta.ken by someone." "You say they belonged to you and were very impor-tant?" 1 "Yes, yes," said the man with the whiskers, eagerly. "You name is Brown, William Brown, isn't it?" "'Dhat' s right." "I found two papers-one a check bea. ring a date of fo.ur years since, and purporting to bea. r the signa ture of. my employer, Frederick Carvel; the other a oonfession signed by a man named James Duggleby, and sworn to in the pres of a notary public and one witness, which stated that the check had been forged by Duggleby, under arrangement with Mr. Carvel for the purpose of sending Steve Johnson, Mr. Carvel's chief clerk, to State prison in order to get rid 0 him for reasons good and sufficient to the said J\fr. Car vel. The object of the paper was clearly to establish tl1e innocence of Steve Johnson, and the check was the evidence used against him a t his trial. Now, Mr. Brown, in what way do those papers concern you?" Tom's presentation of the matter quite staggered the man with the whiskers. For a moment or two he could only stare at the }'Ol\l.Ug messenger in a dazed way. Finally he seerq.ed. to come to a determination. "Son, can I trust you?" he asked, hoarsely. "Yes," replied Tom. t l
PAGE 12
A FORJTUNE AT STAKE. 11 "Then my name isn't William Brown. I gave that to tl1e cop la t night as a blind I am Steve Johnson." "I know you are," replied Tom, coolly. \ CHAPTER VU. TOM PLAYS .A WINNER IN THE STOCK MARKET. "You know I am Steve Johnson?" replied the man the whiskers, slowly. "Yes. I know you escaped from Sing Sing about three weeks ago, and consequently tha t those whiskers you wear are false I also know that you were not guilty of the crime for which yoru have suffered four years' confinement up the river: I have a genera.I idea why Mr. Carrel took such a cowardly means to get yo'li out of his way." "Yoru know all that?" said Steve Johnson, clearly as tonished. "I do. I know also that you are more or less guilty of causing the death of Mr. Carvel's first wife in Silver Creek, Colora,do, by abruptly informing her o f her husband's al leged dea.th by accident in this city." "You know that, too?" "I also understand tha t Mr. Carvel has a daughter living by his former wife. Do you know anything about her pres ent whereabouts?" "Say, son, how did you learn all these facts?" "From your own lips." "From-my-lips!" ejaculated Steve Johnson, evidenUy a ma.zed. "Yes. I was present in Mr. Carvd's room tha.t afternoon when you rehearsed the sbory of old times. l heard every word." "Th e--dickens "Now, Steve Johnson, I've got the papers that prove your i1:mocence. I think they a.re safer with me than with you. Your intention is to use them as a means of revange-to extort bloodmoney from Mr. Carvel. I think you can make better use of them. If you know where his daughter is bring her forward and I will let you have the documents to compel him to recognize her and make suitable provision for her support. Unless you agree to this the papers will remain with me except in the event of your arrest as an escaped convict, in whJch case I should deem it my duty to clear you by producing them in your behalf. That's an I've got to say." The man with the whiskers didn't like Tom's ultimatum. He tried to argue the matter, but the boy was firm. "But I'm flat broke," pro tested Johnson. "I'.11 see that you get some money from Mr. Carvel." "How?" asked the man in surprise. "Don't WOTI'J about tha.t. I'll get it for you. w here is Mr. Carvel's daughter?" "She was with her uncle in Silver Creek five years ago." "I'll get you funds enough to take you orut there. Find the girl ikd bring her on here Tell her tihe whole truth. She is entitled to. kno w it, and it will only be an act of ju stice to her dead mother, as well as an act of reparation o n your part. Will you do it?" will," agreed Johnson. I "All right. Call here to-morrow night and you shall have all the money necessary to carry this plan out." Tha.t ended the interview, and after receiving a dolla.r bill from Tom, the man wit!}. the whiskers took his departure. Next morning Tom took his $500 downto;wn and put it up on 100 shares o f C. & A at 47. During the day he had an interview with Mr Carvel and astonished the broker with ilie statement that the man he rescued from the burning building in the Bronx, and whose name was reported in the papers as William Brown, was none other than Steve Johnson. It is quite possible that Mr. Carvel was not pkticul arly pleased that his messenger's activity and pluck had saved ilie life of the man who was so dangerous to his peace of mind. Had Johnsorn perished in the fire the knowledge would ha.VB given the broker the most so.rid kind of satisfaction He found some slight comfort, however, in Tom's assur a.nce thilt he had made an arrangement with Johnson not to press his advantage, for a.while at any rate, if the broker woo.Id advance him$500. Mr. Carvel naturally was curious to learn how his mes senger had brought a.bout the agreement with Johnson 1'11om wouldn't go into particulars. All he would say was that Johnson's gratitude to him for saving his life, added to another little matter, gavelhim a hold on the exclerk that for the present he was working in Mr. Ca. rvel's interest. He got the $500, and handed it over to Johnson tha.t evening when he called at his hdme, where the final ar rangements relative to St.eve's trip to Colorado were con cluded. Two days later C. & A. began to show some activity and advanced to 50. On the following day it was quoted at 50 3-8 around eleven o'clock. Tom was standing in the messenger s entrance of the Exchange at the time, having brought a message from the ca.shier to a broker who acj:ecl for Mr. Carvel when he had ordeTS to iill for the purchase or sale of railroad stocks. All at onoe there was a flurry aroo.nd the C & A. stand ard. A well-known broker had come on the floor and begun bidding for the st ock at an advance on the market. Then it devielo ped that there was a scarcity 0 the stock, for though he raised the price a point at the time, very little of it came out. Before Tom left C. & A. had jumped to 56. By noon it was selling around 65, amid great excitement, and when the Exchange closed for the day it was up to 70. On his way home Tom left orders at the little bank to sell his 100 shares in the morning at the market price, fo r he believed the stock showed every indication of being top heavy, and consequently was liable to develop a siump any moment. In fact, the market might open with a drop ,in the price, and therefore the young messenger was anxious to get out from under as soon as possible. The market, however, opened strong in the morning, and Tom's shares went at 70 3 -8. But inside of an hour somebody began unloading big ', PAGE 13 \ 12 A FORJTUNE AT STAKE. blocks of the stock on the bro.k.ers, and then the tra.ders be came shy of buying, while thoi;e who were l ong on it hustled around to get rid of their holdings, fore;;eeing that the end of the boom was in sight. The result was tha. t as buyers grew scarce and sellers prices began to sag. This brought more sellers to the fore, anq soon a small panic was on, prices being cut left and right in the efforts to realize. By noon C. & A. was se lling at 61. Tom didn't care what it was selling at now, as he was out of it with a profit tha t he had figured at$2 300 above . commissions and other expenses. His statement and check that reached him next morning showed that he had indeed made amount, and that his capital was now $2,800. } He took the money home to hide away as usual. he to his room after supper, and he was open mg his trunk, it struck him of a sudden that the trunk was not the safest place in the world for so much money. He began to wish that he had left the money in the office safe downtown and not brought it home. To arouse his fea rs still more he noticed that the lock of the trunk showed signs of having been tampered with. He wondered if his mother, suspecting he had made more money in the stock market, had been trying to investiO'ate in a quiet way. 0 He hardly believed that she would adopt such ;means to reach the truth. It would be more like her to ask him right out if he had any money in his possession, and if she found he had, she would demand that he give it up. If she had not been near his trunk who else was there to figure on? Only the new lodger in the next room. His mother had told him that she had rented the room t6. a Frenchman, but though the new lodger had been sev eral days an inma.te of the house iTbm had not caught a glimpse of him yet. Tom hardly thought he would have the nerve to invade his room while he was awa3' and try to get into his trunk. The man had sho,vn good references when he a pplied for and secured the room, but whether his mother had investi gated his credentials or not Tom had not heard. At any rate, the boy was certain somebody had been mon keying with the lock' of his trunk, and he decided that he would be taking gi-eat chances to put his$2,800 in it. He looked around his room to see if there was any other place he could hide it in. There did not seem to be any place he could afford to trust it in longer than overnight, and the trunk would prob ably answer better than any other place for that length of time. Suddenly his eye lighted on a hiding-place that he had not till that moment thought of. The kitchen extension of one story stood right under his window. It had a slanting roof which came up on a lerel with the window sill. This left a good-sized space between the ceiling of the kit chen, which was flat, and the slanting roof. His father had used the space to store odds and ends in, and to reach it had made a small door under the window oi}ening in on Tom's room This door had been so well fitted, the hinges being on the inside, that even a close observation by one not acqua intcd with its existence would fail to reveal the fact that a door was actually there. There was no knob of any kind to open it with, but there was a spring catch under the extension of the sill. By pressing that the secret door would fly open. "That will be just the place to hide my money and those papers belonging to Steve Johnson," thought Torn, glee fully. "No one other than my mother and myself knows a.bout that door. She would never think of rummaging in there for anything, and no stranger would ever get on to the place. I'll make use of it for a safe." There was !lo danger of interruption, for he had heard the lod ger go out half an hour before, and his mother was in the sitting-room talking to her brother, Mr. Arnold, who had called with a friend to see her. Tom went ov1er and touched the spring catch. The door flew open and he look ed inside for a convenient shelf to place his valuables on. He sa.w one within easy reach, and after brushing the dust off of it he went to his trunk, unlocked it and took out the confession of Duggleby and the forged check which he had pinned to it. Then he emptied a small oblong japanned-tin box of various souvenirs he had in it, and carried it over to the secret opening Kneeling down he took his $2,800 in big bills out of an 1nner pocket of his jacket, and proceeded to CO'llnt the money before putting it in the box. He was so absorbed in thi;; pleasant occupation that he did not hear his room door open slowly and softly, nor did he see the foreign-look .ing countenance that peered in and observed what he was doing. The intru. der had a pair of deeply-set twinkling black eyes that great ly resembled the eyes of the man with the whiskers-Steve Johnson. He also had a well-waxed black mustache and a small goatee 'l''he rest of his face was smoothly shaven, with a high forehead, the whole of a swarthy tint. He entered the room with a cat-like tread, similar to the way Johnson had entered Mr. Carvel's office on the day Tom first made his acquaintance He glided over to the spot where the young messenger knelt counting his money. He would have completely surprised Tom but for one circumstance-in passing the ta.ble he bi-ushed against a book that lay close to its edge and displaced it. The noise of the book striking the rug caused Tom to turn his head. He was paralyzed a t seeing a stranger, whom he instantly divined to be his mother's new lodger, advancing stealthily upon him with arms extended to grab him. CHAP'l'ER VIII. TOM A.IDS BEAUTY JN DISTRESS. With a cry of surprise and consternation the boy an effort to get on his feet. \ ro ar pl h1 S" a y 0 PAGE 14 A FORTUNE AT STAKE. 13 The rascal sprang at Tom and seized him by the throat. It was not impoosible but that Frenchrn{m might come "Help!" cried the boy, realizing his disadvantage. back some time during thetnight, for he had a key to the His cry was heard. front door, and as he 11ad seen a wad of money in his The door was flung dpen and Mr. Arnold dashed into the (Tom's) hand, there might be something dning again. room and rushed to Tom's assistance. After some thought the bny the papers and the In the struggle that ensued between the young messenger money in the tin box and hid it between. the two mattresses and the Frenchman, the tin box was overturned a nd com-of his bed. pletely hid the$2,800 in bills which Tom had dropped when Then he sat down to read the book whose fall from the he started to get up and fa<:e the new lodger. table had defeated the purpose of the new lodger. The boy's assailant turned his head when he heard the Somehow or another he couldn't get ip.terested in the door open, and seeing Mr . Arnold, his friend, with Tom's book. mother in the background, he saw that the game was up. That Frenchman's face kept coming between his eyes and Throwing the lad from him, he flung up the window, the printed page. sprang out on the roof of the extension, slid to the giound There was something familiar about that face, particu and disappea red bareheaded into the darkness of the backlarly the eyes, that struck him as very odd, for he was sure yard, which communicated with a vacant lot, by the way he had never met the man before. of which he made his esca. pe. "He certainly puts me in mind of somebody' I've met, "Who was that man and why did he attack you, Tom?" but bless me if I can think who that somebody is," thought 01skM. his sm-prised uncle. 'l'om. "It must be that he looks like SOiffie broker I've run "I believe he's mother's new lodger. I never saw him against down in Wall Street. Yes, that must be-Gfe! before, at any ra.te. He knows best himself why he atI've got it. Those eyes of his a.re just exactly like the eyes tacked me. He came on me unawares from behind, and if of Steve Johnson," he ejaculated, suddenly. "But Steve you hadn't come to my assistance I'm afraid he'd have got didn't look like a Frenchman even a little bit. He looked the better of me, for he was pretty strong." more like a human ourang-outang than anything else with "What were you doing, Tom?" asked his mo ther, looking those whiskers. He ought to be out at Silver Creek by t.his at the open oocret door and then at the overturned tin box time. At any rate, I'll look to hear from him in a few and papers near it, but not seeing the money. days. I hope he'll have no trouble finding IIIr. Carvel's "I was about to stow this box and its contents on a shelf daughter. It's abo;ut time the girl came into her rights. in that place above the kitchen," replied her son, truihfully. If Steve does bring her on, with the documents to prove her "Did you recognize that man as ynur new roomer, identity, Mr. Carvel will have another fit. But he's got to Clara??' asked Mr. Arnold, who was rather puzzled over do the right thing by her, unle.ss he wants me to go back the affair. on him. She must be abnut seventeen years old now: Time "I did not get a fair look at him, but so far as I could she found out who her father is." judge from his figure I am inclined to think that he was Tom read till half-'past ten, then. he not only locked his my new lndger. I cannot understand why he came into door but barricaded it with the table. Tom's room and assaulted him. Can't you explain the Feeling tolerably safe now, he undressed and went to bed. matter at all, my son?" Nothing happened to disturb him during the night, and "No, mother. He. came in withol\t ma.king any noise and he woke up at his usual hour. then sprang at me." When he went dnwntown he carried the tin box with him "These foreigners are very strange people. I almost beand asked the cashier to put it in the safe. lieve that this one can hardly be right in his head," said Mr. Carvel employed no regular stenographer, but he Mrs. Sedgwick. required the services of one for all that. "I think the police ought to be informed of what has So he had an arrangement with Miss Sharp, a public happened," said Mr. Arnold. "The man is either a shady stenographer, several floors above in the same building, to character, or else he is mentally i1Tesponsible. In either send a girl down every day to take dictation. case he ought to be looked after by the authorities." After she took it she returned to her office, transcribed During the talk Tom was more concerned about the the letters and other matter on her typewriter and handed $2,800 hidden by the tin box than he was about the foreignher work to her boss, who charged it up and sent it down to looking rascal who ha.d attacked him. Mr. Carvel by her. office boy. He was afraid that his mother might come foo-ward, pick The same girl didn't come down every 9ay, but that fact up the box and discover the money, in which event it would didn't bother the broker any. be up to him to expla in how such a large sum happened to All he wanted was to have his work done correctly-he. be in his po&5ession. didn't care who did it. To his gieat relief she did not take any special interest So many of the girls ha.d attended on the broker tha.t in the box, or the documents beside it, and presently she Tom thought he lmew all the typewriters connected with left the room with her brother and his friend. Miss Sha rp's establishment. Tom slammed the window down and secured it. On the morning he brought the tin box downtown an Then he picked up the tin box, the documents and the entirely different girl from any he had seen before reported money. for work in the office. After that he at what he had supposed would be 'lorn regarded her with considerable a.dmiration, which a good hiding-place, the hole behind the secret door, and was something nut of the common for him, as he was not decided that he wouldn't use it, at least not for the present. easily "mashed" on girls. PAGE 15 14 A FORT'UNE AT STAKJ!J. He thought she had the sweetest fare he had ever seen. She was a blonde, with golden hair and sapphire-blue eyes. As Mr. Carvel was late in getting down that morning Tom invited her into the private room on his own respon sibility, and then :foi fear she might feel lonesome pmceeded to make himself agreeable to her. He found out that her name was Olive King, and that she was from the West. She _p.ad only been in New Y 0 1rk for a short time, and was livmg in Harlem at the Young Women's Christian As socia tion Building. She had no friends in the city, and was entirely de pendent on herself for her livelihood. By the time Toon had learned all this Mr. Carvel came :in and he had to get out. She took the broker's dictation :for several days in suc and Tom was getting pretty well acquainted with her, when she stopped coming down, much to the young messenger's disappointment. He asked the girl who took her place where she was, and was told she was on some other kin d of work up in the office. Tom felt relieved, fur he had boon afraid that she had left Miss Sharp, and tha t he might lose track of her, which he didn't wa.nt to do. Olive King was the first girl Tom had ever been inter ested in, and s he oceupiecl a good part of his thoughts On Friday a fternoon Tom ha d to go to Brooklyn on busi ness and report at the office before he went home. It was a quarter of five when he got back to the office and handed a letter to. the cashier he had brought back with him. "Take this wonk: up to Miss Sharp's office, tell her that it's wanted as soon as possible in the morning, and then you can go home," said the cashier. "All right, sir," replied Tom, glad of a chance to go up stairs so that he could catch a glimpse of Olive King again. The elevator took him to the tenth floor, where he got out and started down the corridm. Miss Sharp's office was in the rear corridor off the main one. As Tom approached the turn he hea.rd a girlish voice exclaim: "Plea.se let me pass. You haven't any right to detain me!" "My dear Miss King," replied a man's voice. "Why so coy? Y O'll a.re really the most charming young lady I have ever met. P ermit me to escort you to the car you take." Tom stopped short and listened for developments. It struck him that Olive King was being annoyed by whose voice at least intimated that he was no common person. The young messenger was prepared to hasten to per as sistance if she required it, but prudence suggested that he find out first whether it was necessary for him to butt in. "Will you let me pass, sir?" asked the girl again. "I can't lose yoo that way, 'pon my word, I can't. You really must let me accompany you part'way home." "No, sir," she answered, decidedly. "Let me pass. You annoy me!" "Well, let me have a kiss and you shall go." Tom heard a slight scuffie and then a low scream from the girl. He sprang around the corner and saw Olive King strug gling in the grasp of a well-dresseJ. man. That \Vas enough for Tom. \ He grabbed the man by the arm and tore him a .way from the girl. "How dare you interfere? you young jackanapes!" roared Miss King's persecutor, whom Tom recognized as a young broker new to the Street, aiming a. vicious blo1 w a.t the yQung messenger's head just as the boy caught the frightened and staggering girl on one arm. Tam dodged the blow and swung his right fist. It caught the angry broker on the point of the chin and he went aown on the marble floor like a shot. CHAPTER IX. TOM MAKES A DANDY HAUL IN P. & B. Tom released his slight hold on the girl and sto od rearly to def end himself when the trader got on his feet. The man, who name was Windom, picked himself up al mos t sputtering with rage. "You-you infernal young monkey!" he roared. "I'll haV'e you anested for striking me!" "All right, do so," replied Torn, coolly. "I'll show you up in court. You Miss King in my presence. You tried to kiss her against her will. I suppose you call your self a gentleman," the boy added, scornfully. "Well, yoo did not act like one. You ought to be ashamed o.f yourself!" / "How daJ.e you address me that way? you whipper snapper! Do you know who I am?" "I know you're a broker, and that your name is Windom. Tha.t's a.11 I kno w about you; but if you were the President of the United States I'd treat you in the same way for act ing toward this young lady as you did." Olive King made no effort to get away, though she was free to do so, but watc.hed the issue between her defender and her insulter with dila ted eyes and troubled face. She was deeply grateful to iTom for saving her from the broker's advances, and she felt that she would not be treat ing him as he clesetved by running away and leaving him to face the consequenees of his chivalrous conduct alone.. Windom glared at the young messenger in a furiom; way. There Wai$ something in the boy's eye tha.t deterred him from springing at him as he would like to have done. Tom was a stalwart young fellow and full of sancl. His face showed that he was not one who would stand a.ny nonsen se, and the broker seemed to rea.lize that to engagein a scrap with him might not be to his advantage The blow he had got on the chin had also served to take some of the fight out of him, and he was not anxious to get any more of the same kind. "I'll remember you, and fix you for this," he said, with a scowl. "I'm not to be insulted by a young puppy lilrn you with impunity. I'll find out who you. work for ancl report your conduct, then we'll see how you'll come out."
PAGE 16
PAGE 17
16 A FORTUNE AT STAKE. s he was five years old, but what had become of her he had not been able to learn up to that point. He had secured official records of the date of her birth and of her mother's death, which he would with him when he returned. He said he would continue his search for some clue to her present whereabouts as long as his money held out, and would then write Tom for further instructions. Tom was disappointed with the contents of his letter, as he had counted on Steve finqing the girl right away and bringing her on to New York. The story J obnson had gone over that day in Mr. Car vel's office had taken a strong hold on the boy's interest, because his sympathies had been aroused by the heartless way the broker had treated 11is first wife, and be was de termined that, if it was possible for him to bring things about, Mr. Carvel should be compelled to acknowledge his first child, and provide for her future. A few days after Johnson's letter ca.me. to hand, Tom learned by accident that the l\L & N. road had gotten con trol of the P. & B., which furnished them with a monopoly oi the traffic in the eastern section of the State. The P. & B. had been running to seed a s an independent line, and its securities had been going a-begging for some time in the market. By the consolidation arrangements a dividend would be guaranteed the stockholcle1s of this line for 99 yea.rs, ancl consequently as soon as the news of the deal was announced officially the stock was sure to take a big jump. l'l'om saw his chance to make a first-class haul by get ting in on the ground floor with those on the inside, and he got busy right away. P. & B. was then go-ing around 45. Tom left an order with the little bank to buy for his ac count 600 shares on a margin. It took nearly all of his $2,800, but that fact didn't worry him, for he saw his way fo a fine haul the moment the boom set in. The little bank found some difficulty in securing even so small a number of shares, but their representative got them finally, and only just in time, for on the following day the price jumped to 47, on account of the scarce:ness of the stock. 1t kept on going up as the brokers found it was hard to get, for the suspicion got around the Street fuat an effort was being made by some syndicate to corner the visible supply. Under these circumSJtances 'the announcement of the consolidation got out a little sooner than originally con templa ted As soon as the fact was officially confirmed P. & B. became remarkably active, and within a few hours was being_ sought for at 60. Tom felt safe in holding on for the best figure he could get, as it was different from a fictitious boom. A great deal of trading was done in the stock above 60, and finally Tom sold out at 65 3-8. This gave him a profit of$12,000 clear, which was more than he had expected to make. With nearly $15,000 he felt like a small capitalist. CHAPTER X. HOW TOM: M:ADE .A. CONSIDERABLE ADDITION TO HIS CAPITA!, It was around this time tha t Mr. Carvel rnacle a Y e n snc cessful deal in the Curb market. . In some way he found out that a certain copper sto c k that was selling low the market was about to take on a boom. The mine had come into possession of a syndicate of cap italists which had the1facilities to make things hum. At any rate, the broker put into the deal every cent he could scrape together, and the result was he cleared about$100,000 This was the first real lucky transaction he had pulled off in years, and it set him on his feet in good shape.. He immediately hired a better and larger suite of offices in the same building, and began to spread himself. Tom, finding out that he intended to get a stenographer on the premises, asked him as a favor to hire Olive King. The broker had no objection, as he ra .ther liked the girl who had clone a good deal of work for him through Mi8s Sharp's office, so the arrangement was made and Olive came to work regularly fo:r him. One
PAGE 18
A FORTUNE AT S'.rAKE . -17' Dick saw the point :id was silent. "Say, how much money have you got?" "Fifteen or. twenty thousand, more or less," grinned Tom. "Considerably less, I guess You've got $500, anyway, I understand. You couldn't hurt the syndicate with that amount." "No, I don't think I could." "Well, it would be fair for me to let you in on this thing s o you could make a small haul, and divide with me, wouldn't it?" "It would be fair enough on my parl to make use of the information, but I don't think it would be entirely : fojr on your part to give it to r,ne. You can do as you please; you're the boss of your own a.ctions." "Why do you wnnt to make a fellow feel cheap?" "I'm not exactly trying to make you feel cheap All I'm doing is to tell you how I look at such things." "All people don t look at things alike "I know they don't. Still,, right is right, no matter how you may try to twist it about to suit your desires." "Sa)'., you make me tired sometimes. Don't you know that the brokers down here are doing one another when ever they get the chance?" "I've heard something of the kind, b 'ut I don't believe the practice is universal. There is honor in Wall Street as well as elsewhere." "Supposing some broker had overl1eard what I did, wouldn't he make use of the information?" "I guess he would." "Then where is a.11 this honor you're tal king about?" "That isn't a question of honor. If a trader accidentally gets pos sess ion of the plans of a rival he has a perfect right to make the best. use of the knowledge that he can. If the man got hold of his information under a promise that he would not use it, and then broke his promise, that would be dishonorable." "Well, I didn't get ho l d of my information in any such way." "If you hp .dn't been an employee of your office you wouldn't have been in a to find out what you did All employees are expec ted to be loyal to tl!e establishment from which they draw their salary. You have no right to give any of your office secrets away." "Then you don't want me to tell you what I heard?" "It's up to you, Dick. I think, on the whole, ycm'd bet ler not." Dick didn't tell Tom, and went off rather disgusted. Tom, however, found out himself in quite a different way, though he was indebted to his friend in a genera l way for the clue. A few days later when he was at the Exchange he saw Broker Rollins, Dick's boss, buying in H & L shares as fast as they were offered. It recalled to his mind what Dick said about a pool that was being .organized to boom a certain stock, and that his employer had gone into it. Tom wondered if H. & L. was the stock i n question. When he went back to the Exchange l ater o n he saw Rol li ns still buying in the same stock. Meeting Dick shortly afterward he said : "I'll bet I've found out what stock that is that the pool you spoke about is going to boom." "What stock is it?" asked Dick. "H. & L." "How did you find out?" Dick said, in surprise. "By using my eyes "Well, that's the stock, a ll right. It's a sure winner "Glad to hear it. I'll buy a few thousand shares j ust to try my l uck." "A few thousand shares! You give me a pain in the gizzard! One would think you was a capitalist.'1 I am. "Do yo u call yourself a capitalist because you're worth$500 ?" "How do you know ho w much I'm wo r th ?" "You told me some weeks ago that you won $300 on D. & L and that ma de you worth$500." "How do you know but I've made a millipn since?" "Oh, go bag your head! You ha ven't made a cent since or you would have told me." "That so? Don't fly a.way with the idea that I'm telli ng all I know." "And don't you fly away with the idea that you can joll y me into believing a lot of tommyrot." I haven't asked you to believe anything You're d o ing all the howling yourself." "You said you were going to buy a few thousand s hares of H. & L. to try your luck, didn't you?" "What if I did?" "How can you when H & L. is going at 69?" ''.Tha.t's my business, Dicky." "Say, you're all right! Good-bye; I'm in a hurry," and Butterick walked a way. That afternoon 'Tum went around to the little bafilk and gave an order for 2,000 shares of H & L Next day it was up to 69 7-8. On the following afternoon it had craw l ed up to 71. Three days afterward it was quotecr' at 73. That day Tom got a letter from the man with the wh is. kers saying that he believed he had gotten hold of a clue a t last which might lead to results He was going to Denver and wanted: the boy to him another $500 Tom told Mr. Carvel and sent Johnson$300 by draft. On the following day there was great excitement on bhe Exchange. H. & L. started to boom l ike wil dfire In one hour it advanced ten points, and closed that d ay at 85 It opened next morning at 86, and the traders were wild over it. When the price reached a fraction above 90 Tom had a chance to go to the bank and order his shares sol d I nside of ten min u tes he was out of the m arket with a profit of '$42,000. He was now worth$56,000 in good money. Next day he met Dick on his way to the Exchange "I've made a haul out of H. & L.," he said. How much did you make?" asked his friend, curio u s l y. "Enough to make me feel kind of liberal. You didn' t give me the tip, but you said enough to put me on the track
PAGE 19
Its A FORTUXE A'l' STAKE. of the deal. Here's $500. Put it in your vest pocket and say nothing Tom pushed five$100 into Dick's hand and then skipped away before Butterick could recoYer from his astonishment. CHAPTER XI. IN WHICH TOM PASSES THE $100 000 MARK. fom," said Mrs. Sedgwick at the supper table on the foll owing evening, "what does this mean? I found it on the tab l e i n your room this morning Tom looked and beheld the statement he had received the previous day alongwith his cl1eck from the little bank on Nassau Street. It contained-Item one, proiit on 2,000 shaJ.'es of H. & L. stock purchased at G9 and sold at 90 3-8,$42,750; item two, m1d interest, $550; item three, margin de p osit,$13,800-total balance, $56,000. Tom 1ookr1l ruefully a.cross the table at Olfre Kin()' to w h om he had already conficiecl his good fortune, and tJ1E'n somewhat doubtfully at hi s m o ther. "Just a little stock transaction, mother," he replied. "A little stock transaction," s he repeated, glancing at it aguin. 'The Bank of Nassau Street in account with Thomas Sedgwick,$56,000.' How coulcl you be interested i n a stock transaction imolving such a large sum of money?" "Easily enough, if I was forttma te enough to have the margin to put up on the deal." "lt says here, 'margin d epos it, $13 ; 800.' Is this some t h ing that you executed for Mr. Carvel?" "No, mother, it's something I put through for myself." "I should be glad if you would give me a clearer ex pl ana.ti on." "Once UQn a time, mother, I came into possessioo nf$55 I put it up as margin on 10 sha res of A. & 0. at 52. I sold out at 66 and made $145. Tha t sum, together with my margin deposit, which was returned to me, gave me a capital of$200. I told you about the transactio.n and you made me give up the $200. I wanted to keep it ro make more with, but you couldn t see it. You remember that, don't you?" "Oerta.inJy, I do. The inoney is in the Bronx Savings I nstitution with my own funds, a .nd it i$ safe there . One of these days you'll get it back with interest, and everything e lse I own, including this house." "l know it, mother, but I ho;pe it may be a great many years before I get it back that way. I prefer my mother to all the money and property in the world "You're a good boy, Tom," smiled his mother; "but that isn't explaining the meaning of this paper." '"I'm coming to it. When I found you wouldn't let me have that $200 I made up my mind to save another$2.00, and I did." "An d you never told me?" "Not a whisper," laughed Tom. "I invested it in 3D shares of D. & L and made $300. That gave me$500." Tom Sedgwick, are -you telling the truth?" D id know me to tell you an untruth?" "Xo, Tom, never." 1T he $500 I put into 100 of C. & A., < llhl clcare L 1$2,300." His mother almost gasped. "Do you remember the evening that yo1ir F'1x:nc1rnian lodger attacked me in my roorn "Of course I do." "You rememter seeing the tin box orrrtnmecl on the floor?" "Yes." "The $2,800, my capital at the time. \\':lS undrT it." "And you never--" "No, I neYer let on." "Why should you conceal the money from "Because I didn't want it to follow the into lh<' Bronx Savings Bank" l\frs. Sedgwick hardly knew whether to be provoked willi her son or not. '"l'l1e$2,800 enabled me to co1Tal 600 shares of P. & B. at 45, wt1ich I a.fterward i:;okl at G5 3-8, making a proril in round numbers of $12,000. I was tlicn worth$15,000. Row you know how I was able to put. up t!t,it $13,800 on H. & L. The statement shows you lhat J macle$42,000. I am now worth exactly $56,0oo: fm1 gave$.iOO to Dick Butterick because in a way he put me on to the deal. Now youl' e got the whole story." "Do you mean to say that you're worth nt this moment $56,000 ?" asked his mother, incredulously. "Every nickel of it. If you want the you cal1 have it, but the$50,000 is ihe capital by hich I 11lTpe to make a good many more thousands before I'm a :veaJ' olde1. If you hadn't taken tJrn.t $200 from me I might have been worth more." :Mrs. Sedgwick was so paralyzed by Tom's sta.ternent that he forgot to say whether she wanted the$6,000 or not. It was some time before she could realize that her son was so well off. "Money must be made very easily in Wall Street when boys like you can pick up so much." "You forrgc:t how smart I am," laughed Tom. "Olive, dear," said Mrs. Sedgwick, "you are pretty well acquainted with WaJl Street. What do you think abQlut this matter?" "I think Tom is a very lucky boy," the girl answered. As the boy's natural guardian, Mrs. Sedgwick thought it was her dutyto take charge of that $56,000, but under the circumstances she wasn't sure but he could make better use of it himself So, after thinking the matter over she concluded to let things rest for the present as they were, half persuaded that before many wooks he would tell her that he was worth$100,000 rrwo weeks went by after that and Tom ran errands and carried messages like any other Wall Street lad in his line Then one evening when he got home he found a letter from Steve Johnson saying that the clue he was followfog had not panned out as well as he had expected, but that still had hopes of finding out something. He suggested that a couple hundred dollars more wouldn't come amiss, and advised Tom tp stri ke Mr. Carvel for it. Tom forwarded hi m $100 and to l d him to economize. S c J o lrr ti on E: ke1:S won ser e E re a s flu e to t 11 tha a y his l of: ] vat an caf e n loi at io t u s b PAGE 20 t t t e 0 I. ,t n 0 r. n n et at 'th h a 1e. ;er no )l'e vel A FORTUNE AT STAKE. Several times Ur. Carvel asked his messenger about Steve Johnson, !rut Tom always evaded giving any exact informa tion as to that man's 1rhereabouts. Knowing, as the broker clid, that the man with the whis kers ha.d him where the ha.ir 1rns short, he could not help wondering why his ex clerk did not appear and turn the screws on him He was prepared to purchase Steve's si l ence at any reasonable price, but so far, through some mysterious in fluence, presurnedly on his messenger's part, Johnson failed to lake advantage of his grip. Ur. Carvel endeavored to find out from Tom how it was that Steve Johnson kept so quiet, but the boy wasn't sa.ying anything at present, and so the broker could on l y puzzle his own brain for a solution of the enigma .. Four weeks more passed away an d then ''Dom got hold of another good tip. He and Dick were attending a show at a well-known vaudeville house. During intermission they went out to stretch their legs, and after stretching them to some extent tliey entered a cafe for a drink-of lemonade Here Tom heard two brokers conversing about a syndicate they 1rer.e interested in which had just boon formed to boom S. & T. stock. Although Tom did not hear very much, he learned enough to comince him tha. t he would make no mistake in l oading up with the stock in questi@, which was going at 72 He passed the tip on io Dick, as that youth was itching to double or treble the$500 he had received from his friend. Next morning Tom \\"ent to a well known brokerage es tablishment and arranged for the purchase of 5,000 shares of the stock. order with a broker to get it and put up the margin How about yourself?" "I left my order with the bank for 65 shares. I see the price is up half a point now." "You ought to be worth more than a thousand when this deal is over, if you sell out at the right time." "That's what rm looking for "Yes, we' re all looking for the coin thooe days, old man. Well, so-long, I must get back to the office.',. There was not much doing in S. & T. for two-days, the price slowly advancing to 74, then it began to attract some attention owing to its scarcity in the face of buying orders from the outside speculators The demand being greater than the supply, the price be, gan to jump, and "'hen the Exchange closed the third day after the boys had secured a hold on their shares the stock "'as quoted at 76. Next morning quite a crowd of traders gathered a;round the S & T standard looking f or the stock for their cus tomers. It opened at 76 5-8, and at noon reached 7!). The brokers, scenting a boom ahead. were Ycry eager lo get. hold of the stock, and the result was the price kept o n the rise. Other stocks participated in the lmllislt feeling, and the bears got under cover. By two o'clock the Exchange 11 n s in a whirlwind of ex citement. Dick Butterick kept his <') Con thr Lape 1rhencver he got a chance, and was so excit e d that he could hardly a.ttend to his work. It was a new experience {2r him. Every little while h e found himself another $65 ahead of the game, and he felt jus L a s if he wa' finding money by the fistful. "\\'ho is this for?" askefl the head of the house as Tom 'Tom was taking things coolly, notwithstanding that every was counting out the$36,000 maJgin. advance of II. point repres enlecl a profit of $5:000 to him "l\Iake out the order and I'll sign it," replied the boy. At half-past two s. & T. was g oing at 82, and that mean t "Whom do yo11 represent?" if he sold out nnw he woulcl be worth$100,000. "l represent myself. Any objection?" ;From the general appearance of things he was coofiden t "No, not as lnng as you've got the money; but it's rather that it would be sa.fe to hold on for a higher figure u nusual The stock closed at 8 that day. "Unusual things arc constantly happening in Wall Tom and Dick met b y appointment at half-past three Street," replied Torn. and shook hands over the outlook. "I suppose you're acting for somebody who doesn't wish "I think I'll order my shares to be sold at 85. That wili to };e known in tl:e t:a .nsadion," said give me a profit of something over $800," sa i d .Dick. I have no obJcction to you supposmg what you please; "I would if you think yon wont get much chance to get but that doesn't say that your suppos i tion is correct." around to the bank to-morrow," said Tom. The broker Ia ughed "I don't think l'll get any cha.nee. I was kept Lhe He _didn't for a moment bel ieve t hat Tom was the prin-jump all day and it will be the thing to-morrow. c 1pal m the deal. We're loaded up with orders to buy stocks." However, as the boy was putting up Lhe mQney he hacl to "Then rret out while you've the chance," a.dvised 'J.1om. recognize him in that capacity. "It's diff;ent with me We're fairly busy, but nobody Tom signed the order, got his memorandum and left the calls me down if I take a few minutes to mvself." office. So Dick put his selling order in tha.t for the Dick Butterick about the same time managed to get next morning. around to the little bank on Nassau Street and put up the Tom held 011 until eben next day, when S. & T1 h:icl necessaJ.'y margin to secure 65 shares of S. & T. for himself. gone up to 89 1-2, then he on1erec1 his broker to close out That afternoon the two boys met. his holdings Did you get in on S & T., as you said you were going That night he told his mother and Olive at the suppe r to, Tom?" asked Butterick. table that he had been in a big deal on the market and had ''Sur e thing. I bought q u ite a b l ock. .At l east, I left my cleared$86,000.
PAGE 21
, 20 A FORTUNE AT STAKE. "That makes me worth just $142,000," he said, com placently. His mother had ceased to be astonished at anything he might do downtown in the speculative line since she learned that he was worth$56,000, and she accepted his statement as another evidence of his remarkable luck. Olive, JmoWi.ng better how things went in WaJI Street, was amazed a t his good fortune, and judged that he must be a wonderfully sma.rt boy. And while Tom was being patted on the back in his own home, Diqk was in the seventh heaven of delight in Iris, for he had given the whole family a fit by his decla.ratfon that he had made $800 that day in the stock market and was worth, aJI told, a matter of$1,300. OHAPITER XII. TOM GETS HOLD OF A DANDY TIP. not a soul knew me, nor would care for me when I came. And yet, in spite of that, I just had to come. It seemed as if I couldn't help myself." "Well, you have found friends who do care for you, haven't you?" "Yes. I have been very fortunate indeed in that respect. Your mother is very, very good to me, and I have learned to love her very much." "And how about me? Any fault to find with the way I've acted toward you?" "No, no . \'"ou've been very good, too," she said, fl.ashing a grateful look in his face. "And don't you lorveeme just a little bit, too?" Olive blushed and looked a.t the ground. "Well, I suppOBe I've no right to expect you to think so much o f me, but I wish you did, for I think the world of you. If you were my sister I couldn't lik e yo u better." Olive remained silent, and for a few mini1tes Tom sa.id no more. "Say," he blurted out, at last, "don't you believe that I think a lot of you?" That evening Tom took Olive out for a >rnlk. "Yes," she answered, a pa:!lse. It was a fine night, calm and warm, with a round moon "Have you any objection to it?" hanging like a white globe in the sky. "Why should I?" "Glad you shook the Y. W. O. A. and came to live with "The more I see o f you the more I feel that you are the us, Olive?" asked Tom. nicest and sweetest girl in all the world. I don't like to "Oh, yes. It seems just like home to me," she replied. think tha t some day you may meet another fellow tha.t "You have never mentioned anything about your people you'll like better than me. I am sure it fOuld break me since you've been with us. Your father and mother a.re all up." dead, I suppose." Olive said nothing, but kept her head bent down. "Yes." "Olive, don't you !mow that I care for you as much as I "Hadn't you any brothers or sisters?" do for-mother?" Olive shook her hea.d. She made no reply. "Well, you and I a .re in the same hoaL i : 1 th a t r e spect "Don't you ca.re whether I c1o or not?" he asked, anxWe are a pair of lone chicks. You came from St. Louis, iously. I think you told us?" "Yes," she returned in a low tone. "Yes." "If you do ca.re, won't you say tha t you love me just a "How long did you Ii ve there?'' little?"' "Ever since I was a little girl." The street was silent and deserted at that spot, and Tom "And before that?" stopped under a big oveThanging elm. "We lived in Denver." "I want to know, Olive. You are everything to me. If "You were born in Denver, then?" I lost you I shouldn't ca.re whether I lived or not," said the "I'm not sure of tha.t." .boy, earnestly. "I want to find out just how I stand with "Didn't your mother ever tell you where you were born?" you. The uncertainty of the thing is won-ying me. Tell "No. I never thought anythin/6 about the matter. I me, won't you? Do you care for me? Do you love me a suppose I was born in Denver, because I do not remember little?" anything but is associated with that city." He lifted her face gently in his two hands, but she kept "I guess you were born there, then. How did you like her eyes averted. it there?" "You won't speak. I suppose that means that you "I can ha.rdly tell you, as I was very young when we don't--" moved to St. Louis." "No, no, Tom. I do care for you." "How came you to come to New York all by yourself?" "How much?" "I always had a great longing tc come to New York and "With all my heart,'' she cried, dropping her head on live,'' she replied. "I can't tell you just wb.y, but somehis shoulder thing seemed always turning my thoughts in this direction. "Do you love me with all your heart?" I have often wbnderecl what it was. It was just as if some"Yes. I )ove you dearly. Better than any one else in thing was drawing me here-something that I could not the world." resist." '"Then .kiss me, dear." "That was funny." She raised her lips to his, and the moon was the only "Yes. Well, a.fter mother died and I was left entirely witness of their young love, and tha t luminary wasn't givalone, the feeling became stronger than ever. I felt tinrid ing anything away. about making the trip to such a la rge city as this is, where The rest of their walk was a dream of happiness, and '= 'I tl : \\ a a ' }
PAGE 22
l " 0 f a I e 0 . t e I a 11 [ f te h 11 a in n ly v_ A FORiTUNE AT STAKE. 21 Tom thought that winning the biggest kind of a stake in the stock market wasn't a circumstance to it. A week later Tom rec e ived the following laconic epistle from the ma.n with the whiskers: "St. Louis, J unEt 10, 189 "I<'riend Sedgwick: I've strnck the trail a.t last. It's a warm one. S end me $100. Yours, STEVE. "Address me care of the Planter's Hotel." "I wonder if he' s telling me the truth?" mused the boy, as he read the note a second time. "If he couldn't lea.rn anything at Silver Creek where 1\fr. Carvel's wife died, and where alMhe records of the case are, how can the trail be so warm in St. Louis? Well, I must send him the hundred, or he'd be back here bothering me for his papers I hope he does find out where the girl is. It would be a whole lot of satisfaction for me to know. I wonder if she's pretty? Well, one thing is certain-she isn't in it with Olive, I'll bet any money." So Tom sent$100 to Steve Johnson, ca.re of the Pla.ntei-'s Hotel, St. Louis, Mr. Carvel giving it to him. He looked to hear from Steve within two weeks, but four passed and no word came. One day Mr. Carvel sent Tom with a note to the secre tary of the Mining Exchange. The gentleman was not in when he got there, but Tom was told he was expected a.ny minute. As the note was important Tom took a seat by an open window that overlooked a small area. Diagonally across from him was another open window, out of which floated a conversation between two men which attracted the boy's attention and interested him very much "You are sure this information is to be on?" said a deep-toned voice. "Positive. My brother had it straight from one of the directors of the road,'' said another voice. "I know that the B. & 0 has been after that line for a long time, but as it was a close corporation they did not seem able to connect." "The deal is concluded now, and the pa pers will be signed in a day or two." "How much R. & N. stock is there out? We must get a hustle on and buy up a H we ca.n get hold of before the news that it has been absorbed by the B. & 0 gets out. There is a fortune in it for us." "I'm afraid there is very little held in this city prob abl y not over 25,000 shares. There is an old la dy named Sprague in Germantown, Philadelphia, however, who has a block of it that she's been wanting to sell for a long tiine. She has always asked too much for it, as things stood heretofore, and nobody would buy it at her figure." "What does she ask?" "Sixty." "R. & N. hasn't sold highBr than 55 in years." "Tlrnt's right. Ten days from now, however, it will be sought for at 75, so we can afford to pay the old lady 60 for her holdings." "How ma.ny shares has she?" "Thirty thousand." "At the market price her shares are wortli over a million and a half. She seems to be pretty well fixed." "She is. She's worth a million or two beside that stock : "How did she get so much of the stock of that mad?" "Her husband was one of the original stockho l ders a n d directors. He left it to her." 1 "I wou ldn't mind being lier heir-atlaw,'' laughe d the other. "She's got a small army of grandchildren a.nd others to divide her property among. They've been looking for her to die these ten years, but she holds on like a major, and may last ten years yet." "That's the way with some old people. They never know enough to drop out and let their wealth circulate Well, about that stock. If we pay 60 for it, it will coot us $1,800,000 It will be a whole lot of money to raise on short notice. I suppose we'll have to take the who l e b l ock or nothing?" "Yes. We've got the l'.Cst of the week ta get the money. I'll send one of my clerks on to Mrs. Sprague with$50,000 to buy a week's option on the stock. Then we'll be sure of it." "All right. When will you send him?" "To-morrow morning.'' "Very good. I'll get brny at once to raise my half of the amount. I can get half a million easy enough right off the reel, but I'll have to borrow the rest." "It will pay you. We should clear nearly a quarter o f a million a piece There was a shuffling of chairs in the room as if the men had gotten up, and presently Tom heard a door slam. 'l'om medita.ted on what he hacl just heard. "I have $142,000 lying idle I should like to turn it into a quarter of a million. Th.is seems to be a chance The question is, will 'I be a.ble to get hold of any of those 25,0 00 shares in this city? I'm afraid they may have already been snapped up by the p e ople on the outside I'd like to get the inside track on that old lady' s stock. Sh.; wants eight points a bove the market. If the gentlemen next door are willing to pay that for it, it i$ a good sign that the price of the stock will soon take on a boom. If I had a couple of million to spare I'd go to Philadelphia, look her up and make her a n offer o.f 60. By the way, that gentleman spoke about sending his clerk with $50,000 to get a seven-clay option. What's the matter with me taking$100,000 and trying to secure a fifte en-da y option? The boom will be on in ten days, a(!cording to that gentleman next door, who seems to know it all. It will be considerable of a risk, but there seems to be something like half a million profit in it. Those brokers next door wou l d have a fit if I got ahead of them." 1 Just then the secretary of the Exchange came in, and iTom handed him the note he ha.cl brought. In a few minutes he was going downstairs with the an swer in his pocket, and his mind busy with thoughts of what was going to happen in R. & N. stock. CHAPTER XIII. A WALL STREET llfESSENGER'S DEAL. T110 market was rather dead about this time. All the different exchanges were scarcely doing enough .
PAGE 23
. 22 \ A FORJTUNE A'l' STAKE business to keep the brokers in pocket-money-at least that's the way the traders put it. Mr. Carvel was doing hardly anything, and consequently Tom was having a pretty easy time of it. When he delivered the nole from the secretary of the l\Iining Exchange he went to his chair and sat down For the next half-hour he did some pretty tall thinking. Finally he came to a sudden resolution He walked into the private office and asked permission to get off for the rest of the day. l\II'.. Carvel felt that he was under too much of an obliga tion to the boy to refuse him almost any request, so he said he could go It was near noon, and the first thing Tom did was to go and get his lunch Having eaten as much as he wanted he hastened to his box in a safe deposit vau l t and took out $100,000 in big bills. Putting them in an inner pocket, he stmted for the Cort landt Street ferry. He bought a round-trip ticket to Philadelphia. A train was on the point of starting over the Pennsyl vania line. As soon as he reached Jersey City he bomded it and about two hours later he got off at Germantown Junction. He hunted around the drug-stores till he found a city d irectory. This he consulted for the address of Mrs. Sprague. Re found where she lived, hired a cab and was directly to her residence. 10n asking for the old lady he was shown up to a sitting room on the second floor, where l!e found her reading . He lost no time in introducing himself and the object of his visit. He asked her what she wanted for her R. & N. stock. "Sixty dollars a share," she replied. "You ha .ve thirty thousand shares?" "Yes. Six certificates of 5,000 eacl1. I will s ell the whole or none," she &aid. "Will you give me an opti n on. tho stock, good for fif teen days?" .asked Tom. "I wiU, if you pay a deposit of$50,000,rto be forfeited in case you fail to pay for the shares at the end of that time." "I agree to that, ma'am." "Very well. I will give you a note my bank.ers but it is too late for you to do any business to day. In the morning you can take the note to Drexel & Co., pay the $50,000 and get the option. rrhe bank has a power-of attorney from me to transact business jn, my name. You will have the privi l ege to take up'the stock any time within the fifteen days, but if you fail to do it your money will revert to me, and the option will be of no further value." "All right, Mrs Sprag11e That's business," replied Tom, with a smile. old lady tlien wrote the note, handed il io him and he took his leave. The cah took him to a do1rntown hotel, where he pro posed to spend the night. The first thing he did after registering was to send a despatch to his mother informing her tha.t he wouldn't be home that night; then he went out to inspect tlie town and kill time till the dinner hour. After dinner he to a nearby theater, and after that to bed Next morning at ten he was at the Drexel Bank. It tdok him less than. half an hom to transact his busi ness, and then he sta.rtecl for the Pennsylvania depot to return to New York. He felt pretty good, for he he l d the option on 30,000 shares of R. & N. stock, goocLfor fifteen days Tom reported at his office a.bout one o'clock, and ex plained his absence during the morning by saying he had been at Phil adelphia since the previous afternoon. The young messenger chuckled when he thought about the two brokers who were busy raising the money to buy the very stock that he now had a two weeks' call on. When the clerk came back and reported that somebody had secured a fifteen day opt i on on the certificates they would certainly have a good sized fit He didn't know who these traders were, and his l ack of knowledge in this respect did not greatly worry him. What chiefly engaged his attention was how he was to dispose of the stock when the price went up to a figure that would allow him a good profit He could not rajsc the money to take up the stock and therefore would have to sell the option The question that now presented itself was to whom 1ronkl he be able to sell so l arge an amount of the stock as 30,000 shares, which even at 60 invo l ved the i;un1 of$1,800,000. If the price went to 70 it would amounL to $300,000 more. He began to foar that he might have bit.ten off more than he could chew He had fifteen clays in which to figure the matter out., but practically nothing could be done until the boom sta.rted in, and that might not be for ten or even twelve days hence As the case stood he had a fortune a.t stake, and it seemed somewhat of a problem how he woulu come out in the end. That day the attempt of some brokers to buy R. & N in the open market drew attention to its scarcity The resu l t was those who had any of the stock wanted a higher price than 52, and before the Exchange closed for the clay it went to 56. Next day the demand ca .usecl a further rise to 58. This was very sa tisfactory to Tom, who had not looketl to sec any great activity in the price for a week, at least. On the third day it was quoted at 59, and on the next at 60. 1Tfo:lrc it remained for five days Rumors of the consummation of a l ong pending deal between the B & 0 and the R. & N. were now appearing in the newspapers, but there was no offici al confirma.tion of the fact. Still, these reports, taken in connection with the great scarcity of the stock, had the effect of causing R. & N to rise to 63. About noon on the tenth day the news came out from an official source, and then there was excitement to burn in the Exchange vVithin fifteen minutes a .fter the Street had undoubted information about the consolidation 70 was being offered with no talrnrs for R. & N. The price, however, kept going up, and at three o'clock some of the stock was sold for 75. .... T m bt or pl p it. th hi hi p : Of ('0 Ul 8 in th w h w th SU go h co ye N Ji pD PAGE 24 t 1 J f t 0 n n d d : k A FOHfl'UNE AT STAKE. 23 "It is time that J got busy with my option," thought I "That was the name. He and his wife carried her to Torn. 1 If I could dispose of the certificates in sections I Denver." might probably have no great trouble in gdting rid of it, "Where?'' asked the surprised boy. but Mrs. Sprague said it ,\rould only be sold .in "Denver, the 8hief city in ihe State. I hacl a good deal one batch. The s tock is now worth$2,250,000, giving me a of tro11ble trying to locate the King family. When I did profit in sight of nearly half a million. But if I fail to disget track of them I found they had moved to St. Louis." pose of my option my wmic will be Dennis, with a cap"S11ffering jew's-hnrp s !" almost gasped Tom. ital D." "What"s the matter?" Wh e n he w ent home t.hat ni.ght he had almost come to "Nothing. Go on." the conch1sion tha.t he would have to get Mr. Carvel to help "St. Louis is a mighty big town. It ain't easy to ;(incl n him out with 1he matter. person who se name i sn't in the direetory when you.have.n't At s upp e r he \1:as RO preoccupied tha.t his mother asked the ghost of an idea where they're located. I found a.J1_1 him if anything was worr} ing l1im. number of Kings, but not the particular King I was huntin' 'W ell, mother, J made a deal that afternoon I went to for. But ['m a s ticker when I set a.bout doin' anythin'. Philad elphia whi c h lias nette<1 m e a paper profit of $450,I kept up the sea rch arnl got the police to help me. Finally 000. \\' hats bothering me is how to get the profiL that is I l?cat e d t110 right Kings, and thon I that they w e re co111ing t o nJe. matte r s stand there is a fortune at stake, c1ead." un PAGE 25 24 A FOR'TUNE AT STAKE. "Carvel!" exclaimed the girl, looking at Tom. "Exactly Your father--" Steve paused and looked at Tom for instructions. "Is my father alirn?" asked Olive, excitedly. "He is," said Tom. "Where is he? Do you !mow, T 'om ?" "I do. He is living in this city. "If my father is alive why did he not take care of me, after my mother's death? Why was I adopted by Mr. King?" asked the girl anxiously, with a throbbing heart. "Because your father never knew that he had a daughter till a few month5 ago." "He never knew?" said Olive, in a puzzled tone. "No. He believed tha t yom mother died without ha ving given birth to you, consequently for the past seventeen years he has been iu ignorance .of your existence." "Why?" "T:J e was in this city when your mo ther died in Silver CrP.ek." "Could he not have found "There are reasons why he did not." "What are t11ey ?" "I can't explain just now." "You sa. y my father is living in this city?" "Yes." Johnson then told her how h er mother was a ste nog rapher in a Chicago office >1-here he and her father were em ploy e d ; how Carvel became infatuated with her and mar her; how, after three years, her father came to New York while her mother w ent to SilYer Creek, Colorado, where her brother was, for h e r health ; and how un founded report of her hu sband's sudden death reaching her proved to be her death warrant. Olive listened t earfu ll y to his recit al. The name Ca.rvel naturall y made an impression on her, as she was employed by a brok e r of that name. Sl!lddenly a strong suspicion of the truth began to tak e shape in her mind. "Tom," she said, in an excited and earnest tone, "is Mr. Frederick Carvel, the man with whom we are both employed, any relation to me?" "He is." "Is he--is he--my-father ?" "Yes, Olive he is your r eal father." CHAPTER XV. A FORTUNE AT STA KE. "Then you will take me to him won' t you?" "Sure, I will, but not until I Ji-ave s traighten e d matters Tom was down at the u s u a l time next mornin g, but Olive out. Mr. Johns on and I hav e got to first proYc to hi s satdid not come with him as was her custom. isfaction that you arc his dau g hter." When Mr. Ca.rvel came in and was ready to dictate some "And you will do that a t once?" she cried, eager l y l e tters he wanted to ]mow. where his stenog rapher was. "We will do it to-morrow. 'fhc s e papers \rill furnish all Tom told him that she wouldn't be down that day, so the necessa.ry facts to establis h your i PAGE 26 no g e m-11ar Nl'W a. do un her her, take Mr. emOliYe some y, so s t en-& N e out sloch: A FORTUNE AT STAKE. 25 Torn spoke so confidently tlrnt the capitalist began to look I "The forged check and confession of James Duggl eby at the propo sitio n in a new light. implicating you in the plot to ruin Johnson are in my pos" Your option calls for GO) you say?" session," replied the boy, calmly . "Yes, sir." "How did you get hold of them?" asked the broker, in "That is$1,800, 000. How much cleposit clid you surprised trepidation. put up?" '"T'hey came into my possession at the time I saved John" Fifty thousand dollars son's l ife at the fire "The pTi ce 1rill probably go to 80 to day. That repre"That was some months ago, and you neYcr told me." sents a profit 011 paper to you 0 $GOO,OOO. You, howeve r "No, sir. I had a reason for it." stand in the 1 igM of a who has bitten off more than. "Is it your purpose to make u se of them against me, he can chc1r. Yoll haYen't the money to put the deal after all?'' asked l\'Ir. Carvel, bitterly. through, cousC>1p1en U y you stand a good show of los ing your "That depend s deposit arnl the big profit in nnless yo11 can get a "Ah! ''I'hc!n you have a price, af'ter all. You promised mon eyed man lo h e lp you out. I'll teiryou what I'll me--'' do for you) if the option i s aH ri ght. 1111 give you$3$0,000 "I to l d you tha. t day in the cab that I rega.rded your in for it. Tha.t. the amount of your deposit and half the tere s ts as of the first importance as long as my con prnfi ts in e i g Ii t." scj ence---'' "I think that's t oo har PAGE 27 26 A FORJTUNE AT STAKE. I Steve Johnson did so.$1, 75D,OOO, payable to the order of Drex e l & Co., I'11ila-The broker hea .rdhim through and then threw up the delphia had it certified, and handed it to Tom. sponge "I am in the power of both of you," he said, bitterly. 'What is tl price I have to pay for silence?" ''There is only one price and that is-acknowledge your daughter. Take her to your heart and home, a.nd treat her as she is to be trea.ted." "I dare not. My wife--" "Face it out like a man Mr. Carrel. Tell her the trnth." "Confess that I committed bigamy, though uncons c ious ly! l\Iy Heavens! I eannot clo it!" ''You dicl not commit s ir Steve Johnson did 110L tell you the exact truth. Yonr first wife died one day before yo-u married the present. Mr8 Carvel." "ls lhat the truth?" '' ll is, and those pa.pers prove i !. / "Then I yield. I will acknowle THE END. _, Read "HIS LAST NICKEL; OR IT DID FOR JACK RAND," which will b e the next number ( 12!1) of "Fame and Fortune Weekly." I SPECIAL NOTICE: All back numbers of this weekly are always in print. If you cannot obtain them from any newsdealer, send the price in money or postage stamps by mail to FRANK TOUSEY, PUBLISHER, 24 UNION SQUARE, NEW YORK, and you wi ll receive the copies you orc\er b y return ma11. I = si m ro fa 31 dE a1 WI u 0 e1 o l 0 c 0 t fl tl s. v t ] e s a h s e a a I f i
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l ) Ly l.Y J e s FAME AND FO.,RTUNE WEEKLY. 27 Fame and Fortune Weekly :Nmv YonK. 1\fAncn 13, lfl08. Terms to Subscribers. Single Coples ............................................. One Copy Three nonths ................................. One Copy Six nonths ........ ....................... ... One Cop7 One Year .................................... Postage Free. How 'l'o SEND MONEY. .05 Cents .65 u $1.:15 2.50 At our risk send P. 0. Money Order, Check, or Registered Letter; re mittances in any other way are at your risk. \.Ve accept Postage Stamps the same as cash. When sending silver wrap the coin in a separate piecu or paper to a void cutting the envelope. J Vrite lfOUr nam.e and address plainllf. Address letters to Frank Tousey, Publisher, 24 Union Sq., New York. GOOD STORIES. It is learned from reports made to the State Game Commis si-0ner by Illinois farmers who this spring received consignments of pheasants that these eggs showed a 55 percentage of hatch. The great trouble found in distributing the eggs was rough handling by the express companies. The majority of farmers reporting hatches state that the birds are doing well" and are now more than half grown. If some meai:is can be devised whereby the express companies will give greater care and attention to the eggs, this method of restocking the State will be a great success. Next season it is proposed to have the deputies from the various counties of Illinois call at the office of the Game Department in Sprillgfield and take the eggs home with them and distribute them from their own offices. In the last fiscal year we sold to Japan merchandise of our own production to the value of$38,465,000. Our sales in China, including Hongkong, ainount to more than $50,000,000. The Japanese trade reports show that for the calendar year of 1905 the American producers sold in that empire goods to the value of$52,000,000, a statistical statement justified by the fact that during the war we sold more in Japan than after the conclusion of peace. During the same calendar year the sales of Japanese commodities in the United States had a value of $47,000,000, our trade being, in this respect, larger than that which Japan has with any other country, with the ex ception of China. The chief products sent to the United States were tea, camphor, silk fabrics, matting, earthenware and raw silk, the last-named constituting in value more than half of the entire exports. Professor Huxley was once surprised by b eing asked to pre sid e at a meeting of the Anti-Tobacco League. He accepted the invitation, and was heartily greeted by the large audi ence In his speech he told an anecdote of a visit he paid to another scientist to discuss a recent discovery, and they agreed on all subjects except one. "My friend," continued Huxl ey, "was a great smoker, while I hated tobacco in any form. (Great applause.) On one occasion, when nearly suf foca ted by my friend's cigar smoke, I expostulated with him, but he pushed the cigars toward me, saying: 'Take one your self, old man; it's the best remedy.' Reluctantly I took on e and smoked it. And since that time, ladies and gentlemen, nothin g on earth would induce me--(frantic applause)-to forego my after-dinner smoke." The le arned gentleman was ...never again asked to preside a t a similar gathering. Con sul Albert Halstead reports that an a utomatic chainmaking machine has been perfected by o.ne of the directors of an English concern that has factories in Bradford and Bir mingham. He thus describes it: "The idea i s said to have originated in Canada, and for smaller sizes, as reaping and binding machines, was something of a success. It appears that for heavier chains and larger sizes the machine had to be reconstructed and remodeled. This is what has been done here: It draws in a steel bar at one end and the bar issues at the other end in the form of a steel link chain comp l ete ly assembled. In the process of manufacturing the chain by this machine none of the metal is lost, the weight of the chain upon completion being exactly that of the metal before manufacture. The machine is so contrived that the metal bar is pierced and the parts thus formed compose a fiat link. Each perfected link comprises a joint consisting of a. raised projection or lip at one end, having a convex outer surface of about a quarter of a circle, while at the othe r end the centre portion is carried over to form about four-fifths of the circle, hitch ing over the lip end of the next link, an open space permitting detachment sidewise. I have a sample of a chain, the length of each link of which is 3 inches and the width 21;2 inches on the outside and 1 5-16 inches on the inside, that is said to have a breaking strain of 3,400 pounds, corresponding to a malleable link with a breaking strain of 1,600 pounds, aml also a sample 'link 1% inches by 1 5-16 inches on the inside that is said to have a breaking strain of 1,100 pounds, corresponding to a malleable link with a breaking strain of 540 pounds." RIB TICKLERS. "'l'here's one great, trouble about this unparalleled prosper ity.'' "What's that?" "Keeps everybody broke living up to it.'' "You'd better take out some life insurance." "Go on. I'm so healtby I won't die for sixty years yet." "But if yo u get a policy you'll probably work yourself to death paying pre miums." "We want a man for our inquiry office," said the manager, "but he must be able to answer all sorts of questions and not get irritated." "That's all right, sir," repli ed the applicant. "I'm the father of eight children.'' "Heard about Archie?" "No." "Poor beggar! He's in an awful hole. He had arranged to leave for the holidays to-day, and now he can't go. His stupid laundress sent all his pajamas home with the crease down the wrong way.'' "Go od gra cious!" Subbubs-Who's the fellow Backlotz brought out with him last evening? Naybor-That's a fellow he's trying to sell his house to. Subbubs,..-Silly chump! How on earth can he expect to sell the house to the fellow if he lets him see it be forehand? No women have done more for hJimanity and for the in dividual than the o l d-maid reformer and the old-maid aunt. There is none to whom we owe a deeper debt of gratitude, and none whom we could not better spare, says a writer in the Cosmopolitan. For be assured of this: God sends olrl maids into the world to do the work that the rest of us le ave undone. Commenting to a friend the other day on the number of, embezz lements that have been perpetrated by bank employees the last year, Richard Delafield president of the National Park Bank, remarked with a wearied look: "In hiring a bank clerk these days it is a vital mistake to judge a man by his appearance. He may look as innocent as a babe in the cradle, have bang-up references, and may not drink, smoke, or swear. But all these count for naught. The only way you can tell his true character to a dead certainty is when he appropriates a big wad of the bank's money and disappears." PAGE 29 28 FAME AND FORTUNE WEEKLY. I A NIGHT AMONG RATTLESNAKES By Col. Ralph Fenton. ''I've heard a good many yarns about snakes," said the old hunter after he had smoked a pipe, "but I can relate some experiences to make your hair stand up. As a I didn't mind meeting with a rattler now and then, and I ve got up in the morning to shake 'em off my blankets, but there was one time when I was really broken up. "It was on the Upper Pecos River, New Mexico, before the war. I was in the mountains to the north of where Fort Sumner now stands. There was a sort of trading-post there then, and about a company of soldiers was stationed there. "When you come to talk about rattlesnakes you want to go to New Mexico to find the biggest, sassiest, and hardest biter of the Jot. He is always ready for a row, and it's immaterial to him whether he rattles b efore he strikes or waits ten minutes afterward. Some rattlers will crawl away from you sooner than have a row, but these New Mexico fellers won't budge until they are whipped . "I was sort of prosp ecting and hunting together, and 1t was midsummer. I had toggled up a sort of shanty to keep the weather out, and was getting alol:g as well as could be expected, when i began to notice an inqr ease in the number of rattlers. "I'd come across one every hour c,; two, instead of one in tw-0 days, and I had several narrow e3..:apes from being bitten. It struck me that they were also unusually sassy, but I went on my work and didn't get too much upsot. I had made my shanty against a sort of cave in the s ide of a rocky hill, and the fire by which I cooked my fodder and warmed my self was at the door-a l eetle \nside of it, perhaps. "On the ev8fning of which I am speaking in particular, the weather changed cold, and I built an unusually hot fir P to keep the chillS' off. My. bed was crossways of the shanty, and nearer the fire than the back end. When I lay down it was with my face to the fire, and I had a heavy Indian blanket covering me from toes to ears. "I went to sleep directly, and I reckon I should have put in the whole night without a break if something hadn't wriggled ov'er me and woke me up. "I didn't fling off the blankets and rouse up because I natl banishe d sleep. Your. old woodsman learns better than that the first year -Of his experience. I lay there, wondering what had aroused and feeling some anxiety for fear a bear had scented me out, when there was another wriggle, and then I got a pointer. "A hiss or two warned me of the r :e of my visito rs, and as soon as my eyes got a bit use d to the semi-darkness I got a shock that took my breath away. The fire had burned down to a bed of coals, but b etween me and it I could make out a dozen wriggling objects, and I knew they were snakes. They bad' crept out of the rocks behind me, attracted by the light and warmth, and every one must have run over my body. "The space was getting crowded, and the presence of tlie last-comers was apparently objected lo. About the time I &"ot it through my head what was going on, a brand fell a own and made a little blaze, and by this increased light I counted elll1'en old rattlers betw ee n me and the fire. "A few were coiled up and apparently taking solid com fort, but others were running about in a frisky way, and now and then coiling around each other. "As I told you, I was covered clean up, except my head, and I'd have covered that up mighty quick if I had dared to move as murh as a finger. There was only one way to get out of the shanty, and, so I,ong as the snakes held that, I must remain quiet. "I shut my eyes and tried to keep my mind on something else, but in less than five minutes I was sweating like a trotting horse, and it required all my nerve to keep from springing up. I could stand the situation better with my eyes open, and pretty soon I was considerably encouraged by seeing most of the snakes curl up close to the fire and go to sleep. "There were two big fellows, however, who seemed determined to have it out, and when they got the floor to them selves they went at it to. kill. In their struggle they twice brushed my face, and twice one of them chased the other over my body. "One of them was finally crowded into the fire, and he threw up the sponge and ran out doors. The victor curled himself up, and for the next two hours not a snake moved. I might, perhaps, have rolled myself to the back end of the shanty, but that would not have llettered the situation. "When the snakes moved it would be toward their quar ters in the rocks, and if I stood in their way it would be all aay with me. I could see the starlit sky over t11e smoul dering fire, and you can guess how anxiously I watched for the coming of day. "It was fully two hours before daylight came. The fire had by this time died almost out, and t)J.e snakes had begun to grow uneasy. Orie after another uncoiled himself and crept lazily about, but not one made the least move to retreat over my body or go out by the front way. "I was now suffering a thousand torments from having Jain so long in one position, but I dared not move even a finger. The sweat trickled into my eyes and I hardly dared to wink It had been daylikht 'three-quarters of an hour when I felt that I had got to make a move, even if it was into the jaws of death. My only show was to roll over toward the back of the shanty and make a grab for my gun. "If there were any snakes curled up back of me I was a goner. If those in front were not frightened by the discharge of the gun I would surely get bitten. I had just drawn a full breath, to make ready for the move, when every snake suddenly slipped out by the front way and whisked out of sight. You can guess I wasn't long getting hold of my gun, and as soon as I could ge t the numbness out of my legs I advanced to rekindle the fire. "Then I saw the snakes congregated around and darting their fangs into a big toad thirty or forty feet away. It was his hopping by the doorway which drew them out. I got the fire blazing, and then went at the serpents with rocks and clubs, and had the satisfaction of killing four or five of them. "When the others had escaped me, I returned to the shanty to hang out my blankets and cook breakfast. I pulled the steaming blankets to the door to give them a shake, and out dropped a rattler, with a body almost as large as my arm, which made a pass at me and disappearjld under a ledge before I was ready to act." ASPIN"VV' ALL A traveler at Aspinwall writes as follows: When the Pacific Mail steamer drew up alongside the pie_ I was leaning over the rail looking at the 'longshoremen gath ered there to unload the ship. The ship's crew made the ship fast, and then, when all was ready for sending the baggage ashore, I made this sketch of what I could see on the pier directly before me. A little further along the pier were three of them with umbrellas over their heads to keep the sun off. One of them smoked a pipe and the rest sm' oked cigarettes. As fast as each one finished his sruoke he sauntered down the pier to a stack of trucks and eyed it leisurely. If the on e he was accustomed to was on the outside of the stack he took if away deliberately; if not, he lighted another cigarette and waited until the others had cleared away the trucks that were ou tside of his. To the stranger this was a novel proceeding; to the officers of the ship it was a subject not noticeabl e because it couldn't be helped. A piece of iron trestle happened to lie on the main deck of the steamer, where it was in the way of the baggage, and the ship's' mate ordered it removed. All hands dropped the trucks, while of the darkies caught hold of the trestle. Then one perched himself on a spile close beside the gangplank and began to sing. PAGE 30 FAME AND FORTUNE WEEKLY. I The refrain was a mixture of a sailor's shantiga and a naI raw. The ship's coo k m a d e a pie of plantains one day, and I song, but at the end of eac h two li nes there was a c horus. When they came to the chorus, they all sang toge ther, and gave the iron a yank for the first word of eac h line, moving it about a foot for eac h yanK Ten goo d New York longshore men would have carri ed the tres tl e ashore in thre" minutes. These men required h a l f an hour. With the trestle out of the way .they resumed their trucks an!;! started for the gangplank. Som e how one of them walked clear up the plank to the steamer's si d e before the rest got started. He was just going to allow a sai lor to put a trunk on the truck, when lhe singer, who was also a foreman, yelled "Whoa!" It was dinner time. The darky with the truck had business a s hore, and he hastened to r eac h the pier. For this sort of l abor, amounting, perh aps, to two hours of actual toil of this sort in a day, the longshoremen of Aspin w all get$1.75 per day. Since white men die as fast as im po rted, only co l ored men can be u sed, a nd that is how these 'longshoremen are abl e to do as they plea se. Although landing at Aspinwall has some drawback s, I found the landing at some of the Pacific ports somewhat l ess agree able. A boat d avit, a swinging chair, and a boat to do duty in place of the pier. It was with such aid that I l a nded at San Corinto. I sat down in the c h air as the vesse l came on a l e v e l floor and the sailors haul ed the tackle taut. Then as the ship roll ed toward the shore they swayed a lo f t, and out I went; pendulum fashion It was an even bet whether I would drop in the water among the sharks or get dashed against the ship as she rolled back, but the quartermaster in charge of the rope was accustomed to his work, and by l etting go of every thing let me down on the run s o that the chair landed fai r on the thwart o f the waiting boat. I had two friends with me, and each reached the boat safely as I had done found it equa l to the best pumpkin pie. Af t e r we h a d see n the s i ghts of the m arke t we got back to t h e hote l just in time to meet a Chinese man of a ll work about the hot el. He could have invited us to s t e p inside and sit dow,r to dinne r. but that would h ave b ee n contrary to his not10n s of what propriety dem a nd e d in s u c h a case. He had b ee n trained o n lloard a pa sse nger s hip, where a gong was u se d to call the p assengers to t h eir m ea l s He had improvised a gong out o f t h e tin c over of a bread ca n and was beating it vigorously but gravel y as we arrived. The dinner served from a mat on the ground, and consiste d chiefly o f swe e t po tatoes, pl anta in s, and boil e d c hi c ken, wi t h fruits of variou s sorts, inc lu d in g d e li c ious oranges for d esser t. Las t of all tbe Chinaman se r ved so me black coffee, that was the one thing the n n ee d ed to make the meal exceedingly satisfactory and comforting. The pric e was twenty-five cents in Am e rican silver. The Chin aman was wonderfully d elighted with a ti p of a tencent piece. However, prices are higher in native cur r e ncy. I bou gh t a pair of leather trousers at a native store. The pri ce was $8, native money, but two American silv:er dol lars paid t h e bill. Probably a s good and serviceable trousers as these co uld not b e had in New York. I h ave seen the m sold in the West at$10 a p air for hunters and cowboys. One peculiarity o f this country is that a mul e is e mplo ye d to ca1:ry the water to the beach, where it is sent off to a ship that is in need of it, and, in addition, the mule must carry its driver, while men carry the coff ee in huge sac ks, such as one may see on the piers at the Brooklyn stores, on thei r backs. The sac k of coffee weighs abou t as much as t h e mule load of water, il.nd half the weight of the driver thrown in. Of the mule could carry two sacks of coffee easily, but he does not have to d o so It is not the style; that seems t o be the only reason for k eeping the burden off the mul e When the men By and by we landed. There were two Cu s tom House office r s work at carrying coffee to market they make drudges of them waiting for us. One of my friends had a poriabl e photographic s e l ves, but on o t h e r o c cas ion s they do not work very hard or ou tfit wi t h him. The boss customs office r spoke to him in very l ong. The water carrier we met got his mule in the way Spanish, which he did not understand. We a ll bow e d politely. of our carriage, or our drive r got iri the way of the mule, and It wouldn't do. The custom s office r pointed his bayonet at my I the mule was upset by the colli sio n Although it was no fault friend's stomach, and held out his le f t hand for the apparatus. of ours, the mule driver p icked himse lf up, and waving his We understood that, and the thing was d e liv e red. A fter a club threat e ningly, advance d on u s, j abbering at a rate and long explanation, by which we persuaded the office r that it was with looks that seemed particularly ugly. not dangerous, we got it b ac k. It was a qu estio n with us whether to u se a pistol or run Then we went to the hot.el and ordered dinner. I observed to save ourse l ves from a beating, whe n our driver came to the that the house had no chimney. It was a swe ll affair. The resc ue by telling u s that the collisio n had ruined the water upright was built of lumber, on l y t h e kitchen being made 0. r ca rrier, and that no thing short of twenty-five cents American cane. The roof was a thatch of grass. We sat outside for a silver could retrieve t he broken fortune. That coin produc e d time while the meal was cooking, but learning that we would the water carrier went away with many express ions which we have to wait awhile, we strolled off to the m arket to pass the could not unde r stand, except by the deprecatory waving of his time. No newspaper picture can do fu ll justice t o the rounded hands and the bowin g of his h ead forms and comely features of the younge r market women in At the beach the coffee and whatever e l se is taken off to the general in this country. In the markets here, as in the candy shi p in big bo ats rowed by a dozen or more men. Some of stor es and behind cashiers' desks at home, the prettier girls these boats a r e dug-outs, made of a s i ng l e tree trunk. Others are employed, but stroll down the street at any time, and the are boats obtained from p assing s hip s There are no wharves presence of the stranger will attract all the inmates of the or piers along the south coast, and non e a re like ly to be con hous es to the front. structed, for, although there are a number of goou h a rbors, the The wom en a r e of a c opper color, but their complexio n is clear when they are youn!l'. As they grow old it b ec omes yel low, and no t pleasant to look at, the lives whic h they live not tending to preserve beauty. They h a v e the most b eautiful dark, liquid eyes found anywhere, and long straight black hair. Their dress invariably consists of a snow-w hite linen wai st, cut low in the neck and without s l eeves, with a skirt of some dark, J i ght-weight stuff. Occasionally this dress is set off with a bright-colored scarf of some sort that contrasts well with their complexion. T h ey are very p articular about the cleann ess of their dresses. Low s h oes and d ark silk stockings are worn, particularly at fetes, b u t the women are commonly barefo oted. The market is stocked chiefly with fruits, and of these the banana and plantain are the most abundant. The natives use the plantai n, which is r e ally the frui t u s u a lly so ld in N e w York as the banana, as we use sweet potatoes. They fry it, bake it, roast it, and make puddi n gs of it, but s e ldom eat it p '>pi e lack both money and e nterprise and the Government is not stable enough to invite foreign capi t al. In St. P etersburg an Associ ation for the Promotion of Home mad e Articles is in course of organization. It is projected to establish trade sc hool s and workshop s in all the principal in dustrial districts of Russia, in order to in struct the workers. Technical improveme nts are to be introduced and artists and technical experts will be employed to furnis h designs and to superintend the l abors. Artists and artisans will also be sent to for eign countries for the purpose of studying the markets and artistic proclivities e xi sting there, so as t o gather useful information in adapting the productions of the Russian home industries to foreign taste. Ag enc i es are to be establi shed in foreign countries for the s al e of these products. The associa tion furthermore inten ds to organize the trade in hom e-ma de articles in a uniform manner and to s u pp l y raw materials to the workers.
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2018-11-14 04:34:37
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http://advances.sciencemag.org/content/3/9/e1700077.full
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Research ArticleSOCIAL PSYCHOLOGY
# Dynamics in charity donation decisions: Insights from a large longitudinal data set
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Vol. 3, no. 9, e1700077
## Abstract
Despite the vast body of research on charitable giving and its drivers, no research has investigated the longitudinal dynamics of individual donation decisions. We analyzed unique data with nearly 300,000 real donation decisions made by more than 20,000 individuals for a period of 10 months. Each decision entailed a choice of what to do with money received for completing a survey (on average, €0.67 per survey): keep it or donate to charity. We found that most of the participants (89%) always chose to keep the money. Within the group of people who sometimes kept and sometimes donated the money (that is, Switchers), we find that people do not change their decision very often (cf. moral consistency). However, the likelihood of donating increases when people kept the money the previous time, and the amount at stake differs substantially (both positively and negatively). Finally, once Switchers donated, they are more likely to keep the money next time if they can earn more (for example, €2 now versus €0.50 last time), signaling moral compensation. These longitudinal data provide a first step to better understand charity donation decisions, not only in terms of a more nuanced description of decision-makers but also in terms of the dynamics of charity donations.
## INTRODUCTION
Charities benefit societies by taking on its most serious challenges. To do so, they are dependent on people’s willingness to donate. In 2015, a total of $373.35 billion was donated by Americans [2.1% of gross domestic product (GDP)] (1). Although this number is lower in Europe ($22.4 billion; 0.2% of GDP) (2), it highlights the importance of understanding charitable donation decisions and the drivers of these decisions. Although many people donate more than one time in their life, and previous donation decisions most likely influence subsequent decisions, so far, research has mainly studied single observations of donations. In the past, a large variety of researchers—political scientists, sociologists, economists, and social psychologists—by using a variety of methodologies have created a vast body of knowledge on which factors influence a single (or aggregated) decision of whether and how much to donate (37). Up to now, hardly any research is carried out on the longitudinal aspects of charity donation decisions. To put it differently, we do not know the influence of previous decisions on subsequent decisions. This study will address this void.
To be able to answer this research question, we obtained a large longitudinal data set in which more than 20,000 individuals made nearly 300,000 donation decisions in a 10-month period. Specifically, the data set is from a Dutch panel research organization. Participants of this panel complete surveys and receive money for each completed survey. Specifically, they receive €0.10 per question. After each survey, they are asked whether they want to have this money paid to their own account (listed first) or whether they want to donate it to 1 of 20 charities, including, for example, United Nations Children’s Fund, STOP AIDS NOW!, and the World Wildlife Fund. With an average of 13.80 decisions per panel member, we have multiple observations per panel member to study people’s donation decisions.
The decisions people made were real and not measures of hypothetical donation or self-report. Large-scale charity research often uses these self-report measures, for instance, the Household Giving Surveys by the Gallup Organization (8) or the Giving in the Netherlands Panel Study (9, 10). An important limitation of these surveys is the social desirability bias (11): People’s answers can be biased toward what they think is the correct way of answering (12). People generally overreport the donations in self-report surveys, exceeding actual donations by 30.5% (13). Our data set provides us with real decisions, therefore increasing the external validity of the results.
Moreover, a crucial aspect of studying how previous decisions influence subsequent decisions is to have data not only on the instances when people decided “Yes, I donate” but also on the instances when they decided “I keep the money myself.” As trivial as this may sound, most charities do not have any individual-level data on small donations, such as door-to-door campaigns, because address information is often missing (13). As a consequence, when analyzing the administrations of charities, only the people’s recorded yearly overall donations to a charity (or to charities in general) are used as the main dependent variable, aggregating all separate instances when they were asked to donate. Note that in other experimental (field) studies on charity donations, these individual data on donation decisions (yes and no decisions) are available as well. However, within this type of research donation, decisions are often only measured once (1416), or it concerns experimental research on other types of prosocial decisions, such as repeated dictator games (17, 18). Moreover, research on direct mailing effects within a charity context (1921) studied the effects of the frequency of direct mailings on donation decisions over time. Despite the rich insights of that research, the emails contained different ways to persuade people to donate (that is, the content of the emails varied). Because our data set contains the information about each time a person was asked the very same question to donate over a longer period of time, we were able to study these dynamics of donation decisions in a more controlled setting.
The decision to donate to charity or to keep the money to yourself is essentially a choice between furthering your own self-interest and acting prosocially. The field of behavioral ethics has extensively studied prosocial behavior, and we will build on these insights to speculate about predictions regarding behavior of those who did not consistently decided to keep or to donate (that is, the so-called Switchers). Within this domain of research, there are three processes known that take into account past and future (un)ethical behavior to predict subsequent behavior: moral consistency, moral habits, and moral licensing (2224).
According to research on moral consistency, past behavior can serve as a signal to the self of how moral one is (2228). Thus, when people decided to help out at a fundraising in the past, they will infer from that behavior that they value voluntarism. This subsequently leads to, for example, the decision to help out during an event of your child’s school. In particular, past behavior can be seen as a signal of someone’s identity: What I do defines who I am. Moral consistency would therefore imply that people are not very likely to switch a lot between behaviors and thus would predict relative static patterns of decisions: People will always donate (that is, the so-called Donators) or always keep the money (that is, so-called Keepers).
Like moral consistency, moral habits would also imply that people are not very likely to switch a lot between behaviors. Habits formation is used when we make the same decision multiple times, and habits often reflect our personal values toward that behavior (22, 29, 30). Personality traits, such as social value orientation (SVO) (31) and greed (32), which have been shown to influence prosocial behavior, might thus be important drivers of habitual donation decisions.
Both the moral habits literature and the moral consistency literature suggest the relative stability of people’s ethical behavior, including charitable behavior. However, other research has shown that people also balance their (un)ethical behavior: Once they behave ethically, they subsequently behave more unethically, and vice versa. This process is known as moral licensing and basically implies that people balance between their ethical and unethical acts (22, 3335). Sometimes they will keep the money, and sometimes they will donate. If moral licensing takes place, we would thus expect to see people switch between donating and keeping (that is, the so-called Switchers).
Moral licensing also implies that what people decided to do in the past determines which behavior is needed to balance it out again. Note that panel members in our data set can remember two aspects of their previous decision. First, they can remember their behavior in broad aspects: Did I donate—yes or no? Second, they can also remember the specifics: How much money was at stake last time? This distinction is particularly important because people always try to keep up a positive moral self-image (MSI) (36) and remember past behavior in such a way to maintain this positive MSI (37). For example, suppose you chose to donate €0.50 last time, and now you have to make a decision to donate or keep €2. You could base your current decision on the fact that you decided to donate last time to license yourself to keep the money this time, and by doing so, you would disregard the fact that you only donated €0.50 to charity last time and now will be keeping €2 for yourself. By taking into account exactly how much was at stake the previous and current time, we can test whether people base their current decision on the previous choice and amount at stake. That is, within the group of Switchers, we tested the dynamics of donation decision based on previous choice and on how much is at stake now compared to the last time.
We acknowledge that this test is based on the assumption that people can actually recall their past behavior and the amount at stake. To check this assumption, we measured people’s recall ability (n = 916) (see the Supplementary Materials). We found that 99.3% of the participants correctly remembered whether (yes or no) they donated or kept the money, and 32.9% of the participants correctly remembered the exact amount at stake. In total, 78.2% reported an amount at stake within the range that we define as “similar amount” in the analyses (see Materials and Methods). All in all, we have sufficient reason to believe that people are able to remember their past decisions.
## RESULTS
We will first present the results of the type of decision-makers on an aggregate level and then zoom in on the dynamics within Switchers. To study how stable (that is, Keepers or Donators) or dynamic (that is, Switchers) people’s donation decisions were, we first analyzed the frequency of these different types of decision-makers. First, we find that the vast majority of individuals (89.3%) decided to always keep the money (see Table 1). Only 6.4% always donated, and 4.4% of the people were Switchers. Both moral consistency and habitual decision-making predicted these stable decisions. As argued before, personality traits, such as SVO (31) and greed (32), have been shown to be predictors of habitual behaviors. To gain more insights into the process of decision-making, we tested whether SVO and greed could predict the type of decision-maker.
Table 1 Descriptives of full sample and the three decision types.
View this table:
SVO is generally known as an indicator of the relative importance of the self and the other in interpersonal settings (3841). Specifically, SVO differentiates three types of orientations: cooperators (who try to maximize the joined outcome), individualists (who try to maximize their own outcome), and competitors (who try to maximize the difference between themselves and the other). Commonly, individualists and competitors are referred to as proselfs and cooperators as prosocials (40). Prosocials are reported to have donated more to charities than proselfs (31).
To see whether SVO could predict the type of decision-maker in our data set, we randomly selected 1048 participants from the original pool of panel members and had them complete the SVO measure (40). The classifications of SVO types in this sample match previous descriptions of the general population (see table S3), indicating that the participants in our study are not a biased representation of the population. However, SVO could not predict the type of decision-maker. That is, Keepers, Donators, and Switchers could not be described in terms of different SVO types.
Second, we studied the role of dispositional greed, which is the tendency to always want more and to never be satisfied (32, 42). Dispositional greed has been found to predict greedy behavioral intentions and behavior in a Dictator game (32). Therefore, we expected that Keepers would be more greedy than Donators. We asked another randomly selected group of 1027 participants to complete the seven-item greed scale (for example, “One can never have enough money” and “I can’t imagine having too much things”; Cronbach’s α = 0.88). However, Donators (M = 2.95), Switchers (M = 2.91), and Keepers (M = 2.89) did not significantly differ on greed (see Materials and Methods for the statistical analyses). All in all, personality traits, such as SVO and greed, could not predict whether people are Keepers, Switchers, or Donators. Thus, they can also not account for the high percentage of stable preferences.
Because personality traits could not predict decision type, we studied the role of more general demographic variables: gender, age, political preference, and income. Previous research showed that Donators are often younger, female, less conservative, and have a lower income than nondonators (46, 4345), and we tested whether these findings would be replicated here. The second column in Table 1 shows overall descriptives of the full sample, whereas the three rightmost columns show the descriptives of the three specific donation types. Multinomial logit models (see tables S1 and S2) with donation type as the dependent variable and Switchers as the reference group show that liberals (as compared to conservatives) and people who earn more than two times a modal income (as compared to less than standard) are less likely to be Keepers than Switchers. In addition, females are more likely to be Donators than Switchers. Multinomial logit models with Keepers as the reference category show that older people, people who earn a modal income (as compared to less than standard), are less likely to be Donators than Keepers. In addition, females, liberals (as compared to conservatives), and those who earn more than two times a modal income (as compared to less than standard) are more likely to be Donators than Keepers. Combined, these results suggest that Switchers seem to be a different group of people compared to Keepers and Donators, although they do share common demographics.
### Dynamics of donation decisions
To study the dynamics of longitudinal donation decisions within the group of Switchers, we looked at how the choice at t − 1 (donate versus not donate) and the money involved at t − 1 and t (using the number of questions as a direct measure of the amount of money at stake for potential donation or income) influenced people’s decisions, controlling for age, gender, and political orientation. Parameters and interpretation of panel data probit model analysis are presented in Table 2. We found that (i) those who donated at the first observation are more likely to donate at any time (t = 0) and that (ii) those who donated at the previous occasion are more likely to donate at the current occasion. These results are in line with moral consistency.
Table 2 Predictors of donation decisions within Switchers.
View this table:
We split the discussion of the results between cases in which a panel member did not donate at the previous occasion (at t − 1) and cases in which a panel member did donate at the previous occasion (at t − 1) to present the interactions. For those who did not donate at t − 1, we found the following effects: When the number of questions was substantially lower now than the last time (for example, €0.50 now versus €2 last time), people were more likely to donate compared to when the number of questions was more or less equal (for example, €0.50 now and €0.70 last time). In addition, when the number of questions was substantially larger now than the last time (for example, €2 now versus €0.50 last time), people were more likely to donate compared to when the number of questions was more or less equal (for example, €2 now and €1.80 last time). In short, changes in the number of questions (either positive or negative changes) make previous nondonators more likely to donate.
These effects were different when participants decided to donate at t − 1. The positive effect of having substantially fewer questions than the last time is not significant. The positive effect of having substantially more questions becomes negative. That is, when the number of questions was substantially larger now than the last time (for example, €2 now versus €0.50 last time), people who donated last time were less likely to donate compared to when the number of questions was more or less equal (for example, €2 now and €1.80 last time). To put it differently, changes in the number of questions at best make previous Donators not more likely to donate now but even less likely to donate now if the number of questions is larger. This suggests moral licensing.
## DISCUSSION
The current work investigated the dynamics in charitable decision-making using longitudinal data of real donation decisions. Results showed that many people make very stable decisions, which could be a sign of habit or moral consistency. However, we did not find that personality traits—often related to habitual behavior—are able to predict decision types. Moreover, when people kept the money previously, and the amount at stake differs substantially (both positively and negatively) from the last time, the likelihood of donating increases. However, once people have donated previously, they decide to keep the money more often the next time when they can earn more (for example, €2 now versus €0.50 last time), signaling moral licensing. Our findings corroborate survey research on self-reported momentary experiences of morality in general (and thus, not charitable giving specifically), which also showed evidence of both stable decisions and licensing (46).
The moral licensing effect in our data is especially interesting with close examination of the formal definition of psychological licensing: “people’s perception that they are permitted to take an action or express a thought without fear of discrediting themselves” [(47), p.116]. This fear of discrediting oneself basically implies that people want to uphold a positive MSI. MSI is strongly influenced by past recollections of situations in which a person engaged in (un)ethical behaviors (36). Our results seem to suggest that people are able to uphold a positive MSI when making the choice to keep the €2 now when they donated €0.50 the previous time.
Related to these licensing results, a recent meta-analysis (24) suggested that the effect size of moral licensing is relatively small and suggested that statistical power be increased when studying moral licensing. Given the large n in our data set, we had sufficient power to study moral licensing in the field. Moreover, the authors emphasized that researchers often studied the effect with two consecutive behaviors. We are able to study more than two decisions per panel member to provide a full picture of the pattern in donation decisions. In addition, although we found more evidence for stable patterns, we also found evidence for moral licensing.
Another interesting observation is our finding that most of the decisions are to always keep the money. This is not in line with research on self-reported donations (26) or other prosocial behaviors (1418), suggesting that people are altruistic. In addition, 70 to 90% of U.S. households donate to charity in a given year (www.philanthropyroundtable.org/), which would imply that they would be classified as Switcher or even as Donator. Our observed low rate of Switchers (and Donators) does not seem to align with these numbers. The first explanation might be that there is a selection bias in our sample, with more selfish people signing up to be panel members. However, the distribution of SVO types in our sample matched previous studies among Dutch samples (40). Moreover, we replicated previous findings on the effects of general demographics on donations, giving our data strong external validity (46). All in all, we do not believe selection bias to be driving our results. Still, an alternative possibility is that signing up leads to a business mind-set among these participants—because they earn money for filling in the survey—rather than an ethical or prosocial mind-set [cf. studies of Tenbrunsel and Messick (48) and Tenbrunsel and Northcraft (49)]. Although all participants might become less prosocial because of this, we still observe a distribution of proselfs and prosocials that is in line with the findings in the general Dutch population (40). However, we cannot rule out this entry decision effect with our data, but future research could study the potential differences in mind-sets between people who signed up and those who did not.
Another explanation might be that the amounts of money at stake are too small to have a meaningful psychological impact. However, money has not only instrumental value but also psychological value (50, 51). Moreover, research on moral licensing and consistency using charity donations also used low amounts, varying from donations up to $5 or$10 [for example, see the studies of Young et al. (16), Sachdeva et al. (22), and Mazar and Zhong (52)]. Therefore, we also believe that the amounts are not too small. The final explanation might be that most previous studies on charitable giving used one-time-only decisions, hypothetical decisions, and/or self-report measures, whereas we report observations of longitudinal and actual donation decisions. This difference might explain the high rate of Keepers, but we acknowledge that we do not have empirical data to support this.
Studying longitudinal dynamics of donation decisions could provide additional unique insights in future research. For example, we could study the longitudinal aspects of the well-known default effect [cf. study of Goswami and Urminksy (53)]. To date, the default effect—people’s preference for the option that needs no response—has been mainly shown on one-time-only decisions, that is, whether or not to be an organ donor (54). By changing the setup within the panel research organization of how people make their changes, people will make multiple choices over time with the same default. Specifically, when we would make the decision in a two-step procedure—first, people decide to keep or to donate, and second, when deciding to donate, panel members can choose which charity to donate to—one could study the longitudinal effects of the default effect by making the “keep to myself” or the “donate to charity” the default.
When we generalize our findings to implications for charities raising money, our results suggest that charities should make different appeals to nondonators and Donators. By changing the requested donation amount, nondonators might reconsider their decision and decide to donate. People who already donated after a previous appeal should not receive an appeal with a higher requested amount. This advice actually goes against the foot-in-the-door technique (55), which suggests that compliance with a small request increases the likelihood of complying to a larger request later on. Our data suggest that this principle does not hold for repeating donation appeals.
In summary, the present study was one of the first to investigate longitudinal patterns in people’s real (rather than self-reported) donation decisions. The results reveal that most people choose not to donate to charity. However, once they have donated previously, they decide to keep the money more often the next time when there is more money to be earned.
## MATERIALS AND METHODS
### Data set
The original data set contained 308,704 observations. Note that we followed the international review board guidelines in the entire project. Each observation represents a survey started by a panel member. Here, we are interested in a panel member’s donation decisions. Panel members make the donation decision after completing a survey. Therefore, we only used the data on completed surveys for our study (n = 296,651; 96.10%). We excluded the donations to Serious Request (n = 256), which is a yearly fundraising event of a Dutch public national radio station, because we are interested in understanding regular donation behavior to charities. Serious Request is a unique event that takes place in December, and therefore, it is completely different from regular charities and may thus distort the donation behavior we are interested in. Finally, given that we studied donation behavior, we needed at least one question per survey to make sure that people made a decision involving money. We used the number of questions as a direct measure of the amount of payment: The number of questions of a survey determines the payment a participant will receive. Three things are important in this regard: (i) Participants will only be paid when completing the entire survey; (ii) the length of a survey is a random factor for participants because they cannot choose themselves the surveys they are invited to participate in; and (iii) participants cannot determine themselves how much they will earn by varying the effort they put in. Together, this indicates that the number of questions is related only to the payment and not, for instance, to the effort the participants decided to put in.
The resulting data set consisted of 282,232 donation decisions made by 20,457 unique panel members in the period of March 2014 to January 2015. The second column in Table 1 shows the descriptives of the full sample. The panel members have a mean age of 42.75 (SD, 15.60), and 64% is female. There are slightly more conservatives (38%) than liberals (32%), and 44% of the sample has an income above the national modal income.
We divided the panel members into three types on the basis of their donation behavior over time. Keepers are defined as panel members who always keep the money to themselves. Donators always donate the money to charity, and Switchers at least donated once but did not donate always.
### Statistical analyses: Describing Keepers, Donators, and Switchers
To investigate the differences between the three donation types, we used several univariate tests. More specifically, we applied Pearson’s χ2 tests for the categorical variables and one-way analysis of variance (ANOVA) tests followed by Tukey post hoc tests for the metric variables. We applied a multinomial logit model to simultaneously assess the relationships between the donation type and multiple independent variables.
First, age is significantly different across the three types (F2,20454 = 4.17, P = 0.016). On the basis of the Tukey post hoc tests, we concluded that Keepers are significantly older than Donators (contrast, 1.26; confidence interval, 0.22 to 2.31]). Second, the gender distribution differs across the donation types [χ2(2) = 41.77, P = 0.000]. Third, the distribution of political orientation differs across the types [χ2(4) = 48.27, P = 0.000]; the proportion of liberals seems the largest among the Switchers. Finally, the distribution of income differs significantly across the types [χ2(12) = 88.55, P = 0.000]. The results suggest that the proportion of the 2× modal income group is slightly larger for the Switchers than for the other types.
We also tested the predictive value of the demographics on the classification of the type of decision-maker using multinomial logit models. Results of these analyses are presented in tables S1 and S2 and reported in the Results section.
### SVO and greed as predictors of donation decisions
We randomly selected 1048 participants from the original pool of panel members and had them complete the SVO measure (40). This measure consisted of nine items, and each item consisted of three sets of outcomes describing how many valuable points the participant and how many another unknown person will get. Each item contained a competitive (for example, 480 for self and 80 for another), an individualist (for example, 540 for self and 280 for another), and a prosocial choice (for example, 480 for self and 480 for another). When participants chose six of nine items, consistent with one of the orientations, they were classified as that specific orientation. In the end, a total of 642 participants were classified as prosocial, 41 as competitive, and 261 as individualist (see table S3). Similar to other research on SVO [for example, the study of Van Lange (40)], we combined individualist and competitors into one group of proselfs.
SVO was not related to the type of decision-maker [χ2(2) = 0.61, P = 0.736]. To determine whether these nonsignificant results support a null hypothesis over a theory or whether the data are just insensitive, we calculated the Bayes factor (56). The Bayes factor of a model assuming dependence (between donation type and SVO type) compared to a model assuming independence is 0.042, which is lower than 1/3 (that is, sufficient evidence to conclude no dependence between donation type and SVO type). Moreover, in an extended version of the multinomial logit model with donation decision-maker type as the dependent variable (base category, Switchers), the SVO parameters did not significantly predict the decision-maker type (Donators, P = 0.957; Keepers, P = 0.657). That is, Keepers, Donators, and Switchers could not be described in terms of different SVO types.
We asked another randomly selected group of 1027 participants to complete the seven-item greed scale (for example, “One can never have enough money” and “I can’t imagine having too much things”; Cronbach’s α = 0.88). However, Donators (M = 2.95; SD, 1.14; n = 40), Switchers (M = 2.91; SD, 1.23; n = 46), and Keepers (M = 2.89; SD, 1.11; n = 941) did not significantly differ on greed [F2,1024 = 0.06, P = 0.942 (Kruskall-Wallis, P = 0.978)]. Similar to the study on SVO, we calculated the Bayes factor for a model based on dependence (between donation type and greed) compared to a model assuming independence. The Bayes factor was 0.051, which is smaller than 1/3; therefore, there is sufficient evidence for the alternative model (that is, no effect of the donation type on greed). Moreover, in an extended version of the multinomial logit model with decision-maker type as the dependent variable (base category, Switchers), the parameters of greed were also not significant (Donators, P = 0.737; Keepers, P = 0.785). That is, Keepers, Donators, and Switchers could not be described in terms of different levels of greed.
### Statistical analyses: Patterns in Switchers’ donation decisions
The model we proposed is a panel data probit model, because we observed multiple binary decisions per panel member (0, keeping to self; 1, donating to charity). We accounted for potential state dependence by including the donation decision in the previous period and for unobserved heterogeneity by including a random intercept. Although the data set is large (T > 3) (57), we included the first observed donation decision to account for the initial conditions problem (58) and used the Stata command gllamm to obtain the appropriate robust SE for this model (59). On the basis of earlier work in this area (46, 4345), we included the demographic variables, age, gender, and political orientation. To study the interaction between the donation decision at the previous occasion and the difference between the number of questions in the previous and the current survey, we created interaction variables. We defined (the natural logarithm of) the number of questions to be different if the difference was smaller than the 25th percentile (−1.098; that is, substantially fewer questions) or larger than the 75th percentile (1.098; substantially more questions) of the distribution. Results of the analyses are in Table 2.
### Recall of previous decision and amount
We checked whether people could accurately recall whether, and how much, they donated the last time they entered the survey. To do so, we collected additional data in July 2017. From the original sample, we asked a randomly selected group of 916 participants to answer the following questions: (i) “Please recall the last time you participated in a survey from PanelWizard (so not this time). Please indicate whether you decided to keep the money to yourself or to donate the money” (I kept the money versus I donated the money); (ii) “Please indicate how much money was at stake that last time? If you are not sure, please make an estimation” (answer could be typed in). In both questions, we excluded the “don’t know” option. Of all the 282,232 observations from our original data set, the highest amount paid for a survey was €3.40. We excluded 141 observations from further analyses because they indicated a higher amount than this natural cutoff value. We also excluded the observations of nine participants who did not complete both questions. The remaining number of participants was 766.
Of those 766 participants, 761 (99.34%) participants correctly remembered their decision to donate (yes or no). With respect to the amount at stake, 252 (32.90%) participants correctly remembered the exact amount. Moreover, 599 (78.20%) participants reported an amount at stake within the range that we defined as “similar amount” in the analyses (see Statistical analyses: Patterns in Switchers’ donation decisions).
## SUPPLEMENTARY MATERIALS
table S1. Results of multinomial logit model (base category, Keepers) to predict decision type.
table S2. Results of multinomial logit model (base category, Switchers) to predict decision type.
table S3. Distribution of SVO types in our sample and previous studies.
This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.
## REFERENCES AND NOTES
Acknowledgments: We thank PanelWizard Direct for letting us use their data. We thank J.-W. Bolderdijk, I. Schneider, and two anonymous reviewers for their insightful comments on an earlier draft of this manuscript. Funding: This research was financially supported by the Customer Insights Center of the University of Groningen (RUGCIC) awarded to both authors and by a Veni grant (#451-13-031) awarded to M.C.L. by the Netherlands Organisation for Scientific Research (NWO). Author contributions: M.C.L. wrote the main manuscript text. H.R. did the analyses and wrote the Results section. Both authors were involved in the setup of the extra studies for SVO, greed, and recall behavior. Both authors reviewed the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All statistical information needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Data sets are available upon financial compensation via PanelWizard at info{at}panelwizard.com (refer to RUG#general for the entire data set, RUG#SVO for the data set testing SVO, RUG#greed for the data set testing greed, and RUG#recall for the data set testing people’s recalling ability).
View Abstract
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2018-03-23 14:26:00
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http://www.usaco.org/index.php?page=viewproblem2&cpid=643
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## Problem 2. Diamond Collector
Contest has ended.
Bessie the cow, always a fan of shiny objects, has taken up a hobby of mining diamonds in her spare time! She has collected $N$ diamonds ($N \leq 50,000$) of varying sizes, and she wants to arrange some of them in a pair of display cases in the barn.
Since Bessie wants the diamonds in each of the two cases to be relatively similar in size, she decides that she will not include two diamonds in the same case if their sizes differ by more than $K$ (two diamonds can be displayed together in the same case if their sizes differ by exactly $K$). Given $K$, please help Bessie determine the maximum number of diamonds she can display in both cases together.
#### INPUT FORMAT (file diamond.in):
The first line of the input file contains $N$ and $K$ ($0 \leq K \leq 1,000,000,000$). The next $N$ lines each contain an integer giving the size of one of the diamonds. All sizes will be positive and will not exceed $1,000,000,000$.
#### OUTPUT FORMAT (file diamond.out):
Output a single positive integer, telling the maximum number of diamonds that Bessie can showcase in total in both the cases.
#### SAMPLE INPUT:
7 3
10
5
1
12
9
5
14
#### SAMPLE OUTPUT:
5
Problem credits: Nick Wu and Brian Dean
Contest has ended. No further submissions allowed.
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2018-01-21 22:32:04
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https://physics.stackexchange.com/questions/430328/reversing-magnet-polarity-to-increase-decrease-eddy-currents
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# Reversing magnet polarity to increase/decrease Eddy currents?
I have a cast iron wheel with magnets around the inner radius as a braking mechanism. If I were to add additional magnets around the outer radius, would the amount of Eddy currents increase or crease if the polarity of the outer magnets was opposite?
EDIT:
Here's a diagram
where black circle, red and green rectangles depict the wheel, existing magnets and new magnets, respectively. The existing magnets have the S side facing the wheel. So my question is, if the green magnets have the N side facing the wheel, will Eddy currents increase or decrease? What if the S sides face the wheel? In fact, do the polarities of any of the magnet matter?
• Can you include a diagram? There are a few different ways to interpret this. – rob Sep 23 '18 at 6:32
• @rob Sure. I've drawn something up which I hope is understandable. – John M. Sep 23 '18 at 6:43
• If you increase the magnetic field in which the conducting wheel moves then this will increase the induced emf, the eddy currents and hence the braking effect. – Farcher Sep 23 '18 at 8:05
• Related question by same user : Increasing Eddy current induced within surface by attaching a magnet on surface – sammy gerbil Sep 23 '18 at 9:41
If the magnets in the two sets were facing each other (i.e., if green outer magnets were shifted to the $$6$$ o'clock position), it would be pretty obvious that, in order to increase eddy currents, the outer magnets would have to be installed with their north poles facing the wheel, so that the magnetic fields of the two sets boosted each other rather than canceled each other.
When the outer magnets are located as shown on the diagram (at about $$3$$ o'clock), the interaction of the magnetic fields of the two sets is not as significant.
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2019-06-26 03:59:22
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https://www.physicsforums.com/threads/gibbs-paradox-in-the-bohmian-interpretation.723699/
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# Gibbs paradox in the Bohmian interpretation
1. Nov 19, 2013
### atyy
The Gibbs paradox in statistical mechanics is usually resolved by saying that particles do not have distinct trajectories, and so are truly identical.
For example, http://ocw.mit.edu/courses/physics/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2007/lecture-notes/ [Broken] says "The above treatment of identical particles is somewhat artificial. This is because the concept of identical particles does not easily fit within the framework of classical mechanics. To implement the Hamiltonian equations of motion on a computer, one has to keep track of the coordinates of the N particles. The computer will have no difficulty in distinguishing exchanged particles. The indistinguishability of their phase spaces is in a sense an additional postulate of classical statistical mechanics. This problem is elegantly resolved within the framework of quantum statistical mechanics. Description of identical particles in quantum mechanics requires proper symmetrization of the wave function."
In the Bohmian interpretation identical particles have distinct trajectories, and so are not truly identical. How is the Gibbs paradox resolved in the Bohmian interpretation?
Last edited by a moderator: May 6, 2017
2. Nov 19, 2013
### Demystifier
Easily! Even though the particles are not identical, their wave functions are. The entropy to which the Gibbs paradox refers is the entropy of the density matrix, which corresponds to an uncertainty of the WAVE FUNCTION, not an uncertainty of the particle position.
More specifically, assume that the system is in the thermal equilibrium. This means that the density matrix is thermal. But particles are not in the thermal equilibrium; particles are in the quantum equilibrium.
3. Nov 19, 2013
### atyy
Is it permissible to think of quantum equilibrium as a sort of thermal equilibrium? If it is, can we say that there are multiple time scales of equilibration, with the wave function coming to equilibrium more slowly than the particles?
4. Nov 19, 2013
### Jano L.
It should be also said that the term "Gibbs paradox in statistical mechanics" is a misnomer. Gibbs did not refer to the result of entropy calculation as to a paradox. The factor $1/N!$ is no paradox in classical statistical mechanics. Jaynes explained this very well in his paper
Jaynes, E. T., 1992, `The Gibbs Paradox, ' in Maximum-Entropy and Bayesian Methods, G. Erickson, P. Neudorfer, and C. R. Smith (eds.), Kluwer, Dordrecht
available on the website with Jaynes' works
From the paper:
As I understand him, whether we calculate entropy with assumption that permutations count, or that they do not, depends on how much information we admit to the calculation. If we do not have any means of distinguishing the particles (molecules of $\text{N}_2$) experimentally, we do not have reason to count their permutations. If in future some bright physicist finds out that all nitrogen molecules are little bit different, we will count their permutations into the entropy. This can happen in principle, the present state of knowledge does not preclude it. The entropy will be different than what we use today, but that is alright, because there is no such thing as ultimate value of entropy. It depends on the available information and particular situation we choose to describe.
5. Nov 20, 2013
### Demystifier
Good point!
6. Nov 20, 2013
### Demystifier
Something like that. Both quantum and thermal equilibrium are examples of the general concept of equilibrium.
7. Nov 20, 2013
### atyy
So in attempts to derive statistical mechanics from quantum mechanics in which the entire system is pure, but the reduced density matrix is mixed and thermal, the quantum equilibrium hypothesis effectively enters when using the Born rule to get the reduced density matrix?
8. Nov 21, 2013
### Demystifier
Yes.
9. Dec 20, 2013
### HPt
In Eur. J. Phys. 35 (2014) 015023 http://dx.doi.org/10.1088/0143-0807/35/1/015023 (also available as arXiv preprint) you will find the resolution of the Gibbs paradox for distinguishable particles (classical or not).
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2017-08-19 15:37:02
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https://deepai.org/publication/computational-hardness-of-certifying-bounds-on-constrained-pca-problems
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# Computational Hardness of Certifying Bounds on Constrained PCA Problems
Given a random n × n symmetric matrix W drawn from the Gaussian orthogonal ensemble (GOE), we consider the problem of certifying an upper bound on the maximum value of the quadratic form x^ W x over all vectors x in a constraint set S⊂R^n. For a certain class of normalized constraint sets S, we give strong evidence that there is no polynomial-time algorithm certifying a better upper bound than the largest eigenvalue of W. A notable special case included in our results is the hypercube S = {± 1 / √(n)}^n, which corresponds to the problem of certifying bounds on the Hamiltonian of the Sherrington-Kirkpatrick spin glass model from statistical physics. Our proof proceeds in two steps. First, we give a reduction from the detection problem in the negatively-spiked Wishart model to the above certification problem. We then give evidence that this Wishart detection problem is computationally hard below the classical spectral threshold, using a method of Hopkins and Steurer based on approximating the likelihood ratio with a low-degree polynomial. Our proof can be seen as constructing a distribution over symmetric matrices that appears computationally indistinguishable from the GOE, yet is supported on matrices whose maximum quadratic form over x ∈S is much larger than that of a GOE matrix.
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## Authors
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07/19/2017 ∙ by Anton V. Eremeev, et al. ∙ 0
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## 1 Introduction
An important phenomenon in the study of the computational characteristics of random problems is the appearance of statistical-to-computational gaps
, wherein a problem may be solved by an inefficient algorithm—typically a brute-force search—but empirical evidence, heuristic formal calculations, and negative results for classes of powerful algorithms all suggest that the same problem cannot be solved by any algorithm running in polynomial time. Many examples of this phenomenon arise from Bayesian estimation tasks, in which the goal is to recover a
signal from noisy observations. Bayesian problems exhibiting statistical-to-computational gaps in certain regimes include graph problems such as community detection [DKMZ11]
, estimation for models of structured matrices and tensors
[LKZ15, HSS15], statistical problems arising from imaging and microscopy tasks [PWBM18a, BBLS18], and many others. A different family of examples comes from random optimization problems that are signal-free, where there is no “planted” structure to recover; rather, the task is simply to optimize a random objective function as effectively as possible. Notable instances of problems of this kind that exhibit statistical-to-computational gaps include finding a large clique in a random graph [Jer92]
, finding a large submatrix of a random matrix
[GL18], or finding an approximate solution to a random constraint satisfaction problem [AC08].
In this paper, we study a problem from the latter class, the problem of maximizing a quadratic form over a constraint set , where is a random matrix drawn from the Gaussian orthogonal ensemble,111Gaussian orthogonal ensemble (GOE): is symmetric with for and independently. . Unlike previous works that have studied whether an efficient algorithm can optimize and find that achieves a large objective value, we study whether an efficient algorithm can certify an upper bound on the objective over all . In the notable case of the Sherrington-Kirkpatrick (SK) Hamiltonian [SK75, Pan13], where , while there is an efficient algorithm believed to optimize arbitrarily close to the true maximum [Mon18], we show that, conditional on the correctness of the low-degree likelihood ratio method recently developed by [HS17, Hop18], there is no efficient algorithm to certify an upper bound that improves on a simple spectral certificate. Thus, the certification task for this problem exhibits a statistical-to-computational gap, while the optimization task does not.
#### Signal-free random optimization problems.
The general task we will be concerned with is the optimization of a random function,
maximizefω(x)subject tox∈Swhereω∼P (1)
where
is a probability distribution on some measurable space
. Sometimes, such a task arises in statistical estimation, in particular as a likelihood maximization task, where the random function is the likelihood of an observed dataset for a given parameter value . But the same formal task, stripped of this statistical origin, is still very common: in statistical physics, random functions arise in models of magnetism in disordered media; in optimization, random functions encode uncertainty in the parameters of a problem; and in theoretical computer science, random instances of algorithmic tasks describe the average-case rather than worst-case computational characteristics of a problem. Below, we review a well-studied example showing the connection between a prominent statistical estimation problem and a related signal-free random optimization problem.
###### Example 1.1.
Consider the Rademacher-spiked Wigner model, a family of probability distributions indexed by and . Letting , is the law of the random matrix . If is fixed in advance, then the log-likelihood of for some observed data is
logPλ,x[Y]=−n4∥Y−λxx⊤∥2F=cY+λn2x⊤Yx,
where depends on but not on .
Thus, drawing defines a random optimization problem,
maximizex⊤Yxsubject tox∈{±1/√n}nwhereY∼Pλ,x⋆. (2)
Success in the associated estimation problem corresponds to recovering as the solution to this problem; the “overlap” is often used as a quantitative measure of success in this task.
A natural “signal-free” version of this problem arises by setting . In this case, note that does not actually depend on , leaving us with the optimization
maximizex⊤Wxsubject tox∈{±1/√n}nwhereW∼GOE(n). (3)
Up to scaling and a change of sign, this task is the same as that of identifying the ground state configuration or energy in the Sherrington-Kirkpatrick (SK) spin glass model [SK75, Pan13]. For this reason we refer to (3) as the SK problem. Note that there is no “planted” solution with respect to which we may measure an algorithm’s performance; rather, the quality of the an algorithm obtains is measured only by the value of .
#### Computational tasks: optimization vs. certification.
Let us contrast two computational tasks of interest for a given optimization problem. The first, most obvious task is that of optimization, producing an algorithm computing such that is as large as possible (say, in expectation, or with high probability as the size of the problem diverges).
Another task is that of certification, producing instead an algorithm computing a number , such that for all and all we have . The main additional challenge of certification over optimization is that must produce a valid upper bound on for every possible value of the data , no matter how unlikely is to occur under . Subject to this requirement, we seek to minimize (again, in a suitable probabilistic sense when ). Convex relaxations are a common approach to certification, where is relaxed to a convex superset admitting a sufficiently simple description that it is possible to optimize exactly over using convex optimization.
If is the true maximizer of , then for any pair of optimization and certification algorithms as above, we have
fω(algopt(ω))≤fω(x⋆)≤algcert(ω). (4)
Thus, in the case of a maximization problem, optimization algorithms approximate the true value from below, while certification algorithms approximate it from above. We are then interested in how tight either inequality is in the limit for a given sequence of random problems (indexed by some notion of problem size ). Of course, we can achieve “perfect” optimization and certification by exhaustive search over all , but we are interested only in computationally efficient (polynomial-time in ) algorithms.
To make these definitions concrete, let us review a simple instance of each type of algorithm for the problem of Example 1.1.
###### Example 1.1 (Continued).
In the SK problem (3), two related spectral algorithms give simple examples of algorithms for both optimization and certification.
For certification, writing for the largest eigenvalue of , we may take advantage of the bound
x⊤Wx≤λmax⋅∥x∥2=λmax≈2 (5)
for all , whereby is a certifiable upper bound on (3). From classical random matrix theory (see, e.g., [AGZ10]), it is known that as .
For optimization, if
is the eigenvector corresponding to
, then we may produce the feasible point where denotes the -valued sign function, applied entrywise. The vector is distributed as an isotropically random unit vector in , so the quality of this solution may be computed as
x⊤Wx=λmax⋅⟨x,vmax⟩2+O(1√n)=λmax⋅∥vmax∥21n+O(1√n)≈4π≈1.2732 (6)
with high probability as . (The error term in the first equality may be computed as , where the sum is over all eigenvectors except . This analysis appeared in [ALR87], one of the first rigorous mathematical works on the energy landscape of the SK model.)
On the other hand, from the origins of this problem in statistical physics, its true optimal value as is known to approach
x⋆⊤Wx⋆≈2P∗≈1.5264, (7)
where the constant is expressed via the celebrated Parisi formula for the free energy of the SK model [Par79, Pan13, Tal06]. The approximate value we give above was estimated with numerical experiments in previous works (see, e.g., [Par80, CR02]).
The recent result of [Mon18] implies, assuming a widely-believed conjecture from statistical physics, that for any there exists a polynomial-time optimization algorithm achieving with high probability a value of on the SK problem. This work builds on that of [ABM18, Sub18], and these works taken together formalize the heuristic idea from statistical physics that optimization is tractable for certain optimization problems exhibiting full replica symmetry breaking. On the other hand, there are few results addressing the SK certification problem. The only previous work we are aware of in this direction is [MS15], where a simple semidefinite programming relaxation is shown to achieve the same value as the spectral certificate (5).
#### Our contributions.
The main result of this paper, which we now state informally, shows that for the SK certification problem, the simple spectral certificate (5) is optimal. See Corollary 3.9 for the formal statement.
###### Theorem 1.2 (Informal).
Conditional on the correctness of the low-degree likelihood ratio method of Hopkins and Steurer (see Section 2.4), for any , there is no polynomial-time algorithm that certifies the upper bound on the SK problem (3) with probability as .
As mentioned earlier, Theorem 1.2 reveals a striking gap between optimization and certification: it is possible to efficiently give a tight lower bound on the maximum objective value by exhibiting a specific solution , but impossible to efficiently give a tight upper bound. The same result in fact holds more generally for a wide variety of constraints other than (see Corollary 3.9). Due to the high-dimensional nature of the problem, we expect that the value of a certification algorithm should concentrate tightly; thus we also expect Theorem 1.2 to still hold if is replaced by any positive constant.
Our result has important consequences for convex programming. A natural approach for optimizing the SK problem (3) would be to use a convex programming relaxation such as a semidefinite program based on the sum-of-squares hierarchy [Sho87, Par00, Las01]. Such a method would rewrite the objective of the SK problem as for for some , and relax this constraint on to a weaker constraint for which the associated optimization problem can be solved efficiently. One can either hope that the relaxation is tight and outputs a valid solution for (with high probability), or employ a rounding procedure to extract a valid solution from . Note that the optimal value of any convex relaxation of (3) provides an upper bound on the optimal value of (3) and therefore gives a certification algorithm. Thus Theorem 1.2 implies that no polynomial-time computable convex relaxation of (3) can have value and in particular cannot be tight. This suggests that any convex programming approach for optimization should fail to find a solution of value close to (even if a rounding procedure is used). This highlights a fundamental weakness of convex programs: even the most powerful convex programs (such as sum-of-squares relaxations) should fail to optimize (3), even though other methods succeed (namely, the message-passing algorithm of [Mon18]).222In contrast, simple rounded convex relaxations are believed to approximate many similar problems optimally in the worst-case (rather than average-case) setting [KKMO07]. An explanation for this suboptimality is that convex programs are actually solving a fundamentally harder problem: certification.
#### Related work.
The SK problem is not the first known instance of a problem where perfect optimization is tractable but perfect certification appears to be hard. One example comes from random constraint satisfaction problems (CSPs).
###### Example 1.3 (Random 3-SAT).
In the canonical random - problem, the decision variable is a Boolean , and the optimization task is to maximize the number of satisfied clauses , each of which is a Boolean expression of the form where each is chosen uniformly among the and their Boolean negations . Let us write for the number of satisfied clauses a given assignment achieves, a random function of .
Provided as , the optimal value is with probability [CGL04]. This is achieved by the trivial optimization algorithm that chooses a uniformly random assignment . On the other hand, sum-of-squares lower bounds suggest that it is hard to certify even unless [KMOW17].
Prior work has used sum-of-squares lower bounds to argue for hardness of certification in problems such as random CSPs [KMOW17], planted clique [BHK16a], tensor injective norm [HSS15], community detection in hypergraphs [KBG17], and others. These results prove that the sum-of-squares hierarchy (of constant degree) fails to certify effectively, which suggests that all polynomial-time algorithms will fail to certify as well. In our case, it appears difficult to prove sum-of-squares lower bounds for the SK problem, so we instead take a novel approach based on a different heuristic for computational hardness, which we explain in the next section.
#### Overview of techniques.
The proof of our main result (Theorem 1.2) has two parts. First, we give a reduction from a certain hypothesis testing problem, the negatively-spiked Wishart model [Joh01, BBP05, BS06, PWBM18b], to the SK certification problem. We then use a method introduced by [HS17, Hop18] based on the low-degree likelihood ratio to give strong evidence that detection in the negatively-spiked Wishart model is computationally hard (in the relevant parameter regime).
In the spiked Wishart model, we either observe i.i.d. samples , or i.i.d. samples where the “spike” is a uniformly random hypercube vector, and . The goal is to distinguish between these two cases with probability as . In the negatively-spiked () case with , this task amounts to deciding whether there is a hypercube vector that is nearly orthogonal to all of the samples . When , a simple spectral method succeeds when [BBP05, BS06], and we expect the problem to be computationally hard when .
Let us now intuitively explain the relation between the negatively-spiked Wishart model and the SK certification problem. Suppose we want to certify that
SK(W)\colonequalsmaxx∈{±1/√n}nx⊤Wx≤2−ε
where , for some small constant . Since the eigenvalues of
approximately follow the semicircle distribution on
[Wig93], we need to certify that the top
-dimensional eigenspace of
does not (approximately) contain a hypercube vector, for some small depending on . In particular, we need to distinguish between a uniformly random -dimensional subspace (the distribution of the actual top -dimensional eigenspace of ) and a -dimensional subspace that contains a hypercube vector. Equivalently, by taking orthogonal complements, we need to distinguish between a uniformly random -dimensional subspace and a -dimensional subspace that is orthogonal to a hypercube vector. This is essentially the problem of detection in the negatively-spiked Wishart model with and , and these parameters lie in the “hard” regime .
More formally, our reduction constructs a distribution over symmetric matrices such that when . This also has the property that (conditional on the hardness of the detection problem described above) it is computationally hard to distinguish between and . Note that the existence of such a implies hardness of certification for the SK problem, because if an algorithm could certify that when , then it could distinguish from .
This idea of “planting” a hidden solution (in our case, a hypercube vector ) in such a way that it is difficult to detect is referred to as quiet planting [ZK08, ZK11]. Roughly speaking, our quiet planting scheme draws and then rotates the top eigenspace of to align with a random hypercube vector , while leaving the eigenvalues of unchanged. We remark that the more straightforward planting scheme, with , is not quiet because it changes the largest eigenvalue of [FP07]. The question of how to design optimal quiet planting schemes in general remains an interesting open problem.
The final ingredient in our proof is to argue that detection in the spiked Wishart model is computationally hard below the spectral threshold. We do this through a calculation involving the projection of the likelihood ratio between the “null” and “planted” distributions of this model onto the subspace of low-degree polynomials. This method may be viewed as an implementation of the intuitive idea that the correct strategy for quiet planting is to match the low-degree moments of the distributions
and . We discuss the details of this “low-degree method” further in Section 2.4.
Our results on hardness in the spiked Wishart model may be of independent interest: our calculations indicate that, for a large class of spike priors, no polynomial-time algorithm can successfully distinguish the spiked and unspiked models below the classical spectral threshold [BBP05, BS06], both in the negatively-spiked and positively-spiked regimes.
## 2 Background
### 2.1 Probability Theory
All our asymptotic notation (e.g., ) pertains to the limit . We consider parameters of the problem (e.g., ) to be held fixed as . Thus, the constants hidden by and do not depend on but may depend on the other parameters.
###### Definition 2.1.
If is a sequence of probability spaces, and is a sequence of events with , then we say holds with high probability if .
###### Definition 2.2.
We say that a real-valued random variable
with is subgaussian if there exists a constant (the variance proxy) such that for all of exists and is bounded by .
It need not be the case that is equal to the variance of , but it can be shown that if is subgaussian with variance proxy . The name subgaussian refers to the fact that
is the moment-generating function of the Gaussian distribution
. A random variable with law is then trivially subgaussian. A more interesting example is that any bounded centered random variable is subgaussian: by Hoeffding’s lemma, if almost surely, then is subgaussian with variance proxy .
We next give some background facts from random matrix theory. Their proofs and further information may be found in a general reference such as [AGZ10].
###### Definition 2.3.
The Gaussian orthogonal ensemble is a probability distribution over symmetric matrices , under which and when , where the entries are independent for distinct pairs with .
The choice of variances ensures the following crucial invariance property of .
###### Proposition 2.4.
For any fixed orthogonal matrix
, if , then the law of is also .
Our scaling of the entries of is chosen to ensure a spectrum of constant width, as shown by the following classical result.
###### Proposition 2.5.
Let . Then, almost surely,
limn→∞λmax(Wn)=2andlimn→∞λmin(Wn)=−2.
In particular, for any , with high probability.
Furthermore, by Wigner’s semicircle law [Wig93], the empirical distribution of eigenvalues of converges weakly to a semicircle distribution supported on .
### 2.2 Constrained PCA
###### Definition 2.6.
A constraint set is a sequence where . The
constrained principal component analysis (PCA) problem with constraint set
, denoted , is
maximizex⊤Wxsubject tox∈SnwhereW∼GOE(n).
We will work only with constraint sets supported on vectors of approximately unit norm.
###### Example 2.7.
Several problems previously considered in the literature may be described in the constrained PCA framework:
• the Sherrington-Kirkpatrick (SK) spin glass model: [SK75, Pan13],
• the sparse PCA null model: [DM14a, KXZ16],
• the spherical -spin spin glass model: [CS92, CHS93],
• the positive PCA null model: [MR16].
Our results in this paper will apply to the first two examples: the SK model, and sparse PCA on a Wigner matrix when .
###### Definition 2.8.
Let be a (randomized) algorithm that takes a square matrix as input and outputs a number . We say that certifies a value on if
1. for any symmetric matrix , , and
2. if then with high probability.
For purposes of generality, we have allowed to be a randomized algorithm (i.e., it is allowed to use randomness in its computations, but the output must be a true upper bound almost surely). We do not expect certification algorithms to need randomness in an essential way, but sometimes it may be convenient, e.g., to obtain a random initialization for an iterative optimization procedure.
### 2.3 Spiked Wishart Models
###### Definition 2.9.
A normalized spike prior is a sequence where is a probability distribution over , such that if then in probability as .
###### Definition 2.10 (Spiked Wishart model).
Let be a normalized spike prior, let , and let . Let . We define two probability distributions over :
1. Under , draw independently for .
2. Under , draw . If , then draw independently for . Otherwise, draw independently for .
We call the planted model and the null model. Taken together, we refer to these two distributions as the spiked Wishart model . For fixed and we denote the sequence by .
Several remarks on this definition are in order. First, we make the explicit choice for concreteness, but our results apply to any choice of for which as .
Second, often the Wishart model is described in terms of the distribution of the sample covariance matrix . We instead work directly with the samples so as not to restrict ourselves to algorithms that only use the sample covariance matrix. (This modification only makes our results on computational hardness of detection more general.)
Finally, the definition of has two cases in order to ensure that the covariance matrix used as a parameter in the Gaussian distribution is positive semidefinite. We will work in the setting where the first case () occurs with high probability. Priors for which this case occurs almost surely will be especially important, so we define the following terminology for this situation.
###### Definition 2.11.
Let and let be a normalized spike prior. We say that is -good if when then almost surely.
We will often consider spike priors having i.i.d. entries.
###### Definition 2.12.
Let be a probability distribution over such that and . Let denote the normalized spike prior that draws each entry of independently from . (We do not allow to depend on .)
We will sometimes need to slightly modify the spike prior to ensure that it is -good and has bounded norm.
###### Definition 2.13.
For a normalized spike prior , let the -truncation of denote the following normalized spike prior. To sample from , first sample and let
x={x′if β∥x′∥2>−1 and ∥x′∥2≤20otherwise. (8)
If then since is normalized ( in probability), the first case of (8) occurs with high probability. The upper bound is for technical convenience, and there is nothing special about the constant . Note also that the -truncation of an i.i.d. prior is no longer i.i.d.
We consider the algorithmic task of distinguishing between and in the following sense.
###### Definition 2.14.
For sequences of distributions and over measurable spaces , we say that an algorithm achieves strong detection between and if
Qn[fn(y)=0]=1−o(1)andPn[fn(y)=1]=1−o(1).
The celebrated BBP transition [BBP05] implies a spectral algorithm for strong detection in the spiked Wishart model whenever .
###### Theorem 2.15 ([Bbp05, Bs06]).
Let be any normalized spike prior. If then there exists a polynomial-time algorithm for strong detection in .
The algorithm computes the largest eigenvalue (if ) or smallest eigenvalue (if ) of the sample covariance matrix . This eigenvalue converges almost surely to a limiting value which is different under and .
In this paper we will argue (see Corollary 3.3) that if is an i.i.d. subgaussian prior (in the sense of Definition 2.12 with subgaussian), then no polynomial-time algorithm achieves strong detection below the BBP threshold (i.e., when ). It is known that for some priors, there is an exponential-time algorithm for strong detection below the BBP threshold [PWBM18b]. For very sparse priors, e.g., if is supported on entries, we enter the sparse PCA regime where polynomial-time strong detection is possible below the BBP threshold (see, e.g., [JL04, DM14b]). Note that a normalized spike prior with this level of sparsity cannot take the form , since we require to be independent of .
### 2.4 The Low-Degree Likelihood Ratio
Inspired by the sum-of-squares hierarchy (e.g., [Sho87, Par00, Las01]) and in particular the pseudo-calibration approach [BHK16b], Hopkins and Steurer [HS17, Hop18]
proposed a strikingly simple method for predicting whether Bayesian inference problems are computationally easy or hard. This method is known to recover widely-conjectured computational thresholds for many high-dimensional inference problems such as planted clique, densest-
-subgraph, random constraint satisfaction, community detection in the stochastic block model, and sparse PCA (see [Hop18]). We now give an overview of this method.
Consider the problem of distinguishing two simple hypotheses and which are probability distributions on some domain (where typically the dimension grows with ). One example is the spiked Wishart model for some fixed choice of the parameters . The idea is to take low-degree polynomials (for some notion of “low”) as a proxy for polynomial-time algorithms and examine whether there is a sequence of low-degree polynomials that can distinguish from .
It will be convenient to take as the “null” distribution, which is often i.i.d. Gaussian (as in the Wishart case) or i.i.d. Rademacher (having entries i.i.d. taking values with equal probability). The distribution induces an inner product on square-integrable functions given by , as well as a corresponding norm . For , let denote the space of polynomial functions of degree at most . For a function , let denote the orthogonal projection (with respect to ) of onto . The following result relates the distinguishing power of low-degree polynomials to the so-called low-degree likelihood ratio.
###### Theorem 2.16 ([Hs17]).
Let and be probability distributions on for each . Suppose is absolutely continuous with respect to , so that the likelihood ratio is defined. Then
maxf∈R[y]≤D∖{0}Ey∼Pnf(y)√Ey∼Qnf(y)2=∥L≤Dn∥L2(Qn). (9)
We include the short proof here for completeness.
###### Proof.
The left-hand side can be rewritten as
maxf∈R[y]≤D∖{0}⟨f,Ln⟩L2(Qn)∥f∥L2(Qn),
so by basic linear algebra (in particular, the variational description of orthogonal projection), the maximum is attained by taking . ∎
Note that the left-hand side of (9) is a heuristic measure of whether there is a degree- polynomial that can distinguish from . Thus we expect if there is a degree- polynomial that achieves strong detection, and if there is no such polynomial.
We take -degree polynomials as a proxy for polynomial-time computable functions. One justification for this is that, in practice, many polynomial-time algorithms compute the leading eigenvalue of a symmetric matrix whose entries are constant-degree polynomials in the data; in fact, there is formal evidence that such low-degree spectral methods are as powerful as the sum-of-squares hierarchy [HKP17]. Typically, rounds of power iteration are required to compute the leading eigenvalue, i.e., we can distinguish from using the polynomial for some . The above motivates the following informal conjecture.
###### Conjecture 2.17 (Informal [Hs17, Hop18]).
For “nice” distributions and , if for some , then there is no randomized polynomial-time algorithm for strong detection between and .
This conjecture is useful because the norm of the low-degree likelihood ratio, , can be computed (or at least bounded) for various distributions such as the stochastic block model [HS17] and the spiked tensor model [Hop18].
###### Remark 2.18.
The “converse” of Conjecture 2.17 is not quite expected to be true. If for some then we should expect an -time algorithm but not necessarily a polynomial-time algorithm. This is because not every -degree polynomial can be evaluated in polynomial time.
Conjecture 2.17 is informal in that we have not specified what is meant by “nice” distributions. See [Hop18] for a precise variant of Conjecture 2.17; however, this variant uses the more refined notion of coordinate degree and so does not directly apply to the calculations we perform in this paper. Roughly speaking, “nice” distributions and are assumed to satisfy the following:
1. should be a product distribution, e.g., i.i.d. Gaussian or i.i.d. Rademacher;
2. should be sufficiently symmetric with respect to permutations of its coordinates; and
3. we should be able to further add a small amount of noise to , ruling out distributions with brittle algebraic structure (such as random satisfiable instances of XOR-SAT, which can be identified using Gaussian elimination [CD99]).
We refer the reader to [Hop18] for further details and evidence in favor of Conjecture 2.17.
## 3 Main Results
### 3.1 Spiked Wishart Models
We expect that Conjecture 2.17 applies to the spiked Wishart model. The following states this assumption formally.
###### Conjecture 3.1.
Fix , and a normalized spike prior . Let and be the sequences of planted and null models, respectively, of the spiked Wishart model . Define the likelihood ratio . If there exists some such that , then there is no randomized polynomial-time algorithm for strong detection in .
We now give bounds on .
###### Theorem 3.2.
Fix constants and .
1. Suppose . Let where is subgaussian with and . Then, for any , we have .
2. Suppose . Let where is symmetric about zero with and . Suppose also that is -good. Then, for any , we have .
Section 5 is devoted to the proof of Theorem 3.2. Part 1 of Theorem 3.2, when combined with Conjecture 3.1, implies that for i.i.d. subgaussian priors, strong detection is computationally hard below the BBP threshold.
###### Corollary 3.3.
Suppose Conjecture 3.1 holds. Fix constants and . Let be subgaussian with and . Let be either or . If , then there is no randomized polynomial-time algorithm for strong detection in .
###### Proof.
The case follows immediately from Part 1 of Theorem 3.2. If strong detection is impossible for , then strong detection is also impossible for , as these two spike priors differ with probability (under the natural coupling). ∎
A number of technical remarks on the content of Theorem 3.2 and Corollary 3.3 are in order.
###### Remark 3.4.
Even if Conjecture 3.1 does not hold, we still obtain a concrete result on the effectiveness of low-degree polynomials for detection in the spiked Wishart model: the conclusion of Part 1 of Theorem 3.2 implies that the value of the optimization (9) must be for any .
###### Remark 3.5.
Part 2 of Theorem 3.2
is merely a sanity check to ensure that the low-degree likelihood ratio indeed exhibits a phase transition at
and does not predict computational hardness when (as we know polynomial-time strong detection is possible in this regime; see Theorem 2.15). The assumption that is symmetric about zero is for convenience only and should not be essential.
###### Remark 3.6.
In Part 1 of Theorem 3.2 and in Corollary 3.3, the requirement that be a (-truncated) i.i.d. prior can be relaxed. All that we require of is that it is the -truncation of a normalized spike prior that admits a local Chernoff bound, as described in Definition 5.11. One type of prior that does not have this property is one where is very sparse, e.g., supported on entries; this is the sparse PCA regime (see e.g., [JL04, DM14b]) for which polynomial-time strong detection is possible below the BBP threshold.
###### Remark 3.7.
Note that Part 1 of Theorem 3.2 holds for any , which is much larger than the required by Conjecture 3.1. Since we expect degree- polynomials to correspond to -time algorithms [Hop18], this suggests that the conclusion of Corollary 3.3 holds not only for polynomial-time algorithms but for -time algorithms, for any . In other words, nearly-exponential time is required to achieve strong detection.
### 3.2 Constrained PCA
We now give a reduction from strong detection in the spiked Wishart model to certification in the constrained PCA problem.
###### Theorem 3.8.
Let be a constraint set and let be a normalized spike prior such that if then with high probability. Suppose that for some there is a randomized polynomial-time algorithm that certifies the value on . Then there exist and (depending on ) such that there is a randomized polynomial-time algorithm for strong detection in .
We give the proof in Section 4. Note that the parameters above satisfy (the “hard” regime).
###### Corollary 3.9.
Suppose Conjecture 3.1 holds. Let be subgaussian with and . Let be a constraint set such that, if , then with high probability. Then, for any , there is no randomized polynomial-time algorithm to certify the value on .
###### Proof.
The result is immediate from Theorem 3.2 and Theorem 3.8. ∎
In particular, we obtain the hardness of improving on the spectral certificate in the SK model.
###### Corollary 3.10.
If Conjecture 3.1 holds, then, for any , there is no randomized polynomial-time algorithm to certify the value on the SK problem .
###### Proof.
Apply Corollary 3.9 with having the Rademacher distribution (equal to with equal probability) and . ∎
## 4 Proof of Reduction from Spiked Wishart to Constrained PCA
###### Proof of Theorem 3.8.
Let be a constraint set and let be a normalized spike prior such that, if , then with high probability. Suppose that for some there is a randomized polynomial-time algorithm that certifies the value on . We will show that this implies that there is a polynomial-time algorithm for strong detection in with certain parameters and (depending on ). Note that these parameters lie in the “hard” regime .
Our algorithm for detection in the Wishart model is as follows. Fix , to be chosen later. Since we have (for sufficiently large ). Given samples , let and let be its orthogonal complement. We sample having the distribution conditioned on the event that the span of the top eigenvectors of is . Concretely, we can obtain a sample in the following way. Let be a uniformly random orthonormal basis for and let be a uniformly random orthonormal basis for . Sample and let be the eigenvalues of . Then, let . Finally, run the certification algorithm for on . The detection algorithm then thresholds :
˜f(y1,…,yN)={0 (% report samples came from null distribution Qn)if f(W)≤2−ε/2,1 (report samples came from planted distribution Pn)if f(W)>2−ε/2. (10)
We now prove that indeed achieves strong detection in . First, if the samples are drawn from the null model , then is a uniformly random -dimensional subspace of , so by Proposition 2.4 the law of constructed above is . Thus with high probability by assumption, and therefore with high probability, i.e., our algorithm correctly reports that the samples were drawn from the null model.
Next, suppose the samples are drawn from the planted model with planted spike . We will choose and so that with high probability. Since with high probability, this would imply , so we will have with high probability, i.e., our algorithm will correctly report that the samples were drawn from the planted model.
It remains to show that . Let be the eigenvalues of and let be the corresponding (unit-norm) eigenvectors. By Proposition 2.5, with high probability, for all , . Furthermore, by the semicircle law [Wig93], with high probability, where is a function satisfying as (recalling that ). Letting denote the norm of the orthogonal projection of onto , we have, with high probability,
x⊤Wx =x⊤(n∑i=1λiviv⊤i)x =n∑i=1λi⟨x,vi⟩2 ≥λ1∥x∥2V+λN+1∥x∥2V⊥ ≥(−2−o(1))∥x∥2V+(2−g(γ))(∥x∥2−∥x∥2V) =(2−g(γ))∥x∥2+(−4+g(γ)−o(1))∥x∥2V ≥2−g(γ)−4∥x∥2V−o(1). (11)
Thus we need to upper bound . Let denote the orthogonal projection matrix onto . Since is the span of , we have where
Y=1NN∑i=1yiy⊤i
and is the smallest nonzero eigenvalue of . (Here denotes Loewner order.) Since is a spiked Wishart matrix, it follows from Theorem 1.2 of [BS06] that its smallest nonzero eigenvalue converges almost surely to as . Thus we have . Therefore,
∥x∥2V=∥PVx∥2=x⊤PVx≤1μx⊤Yx=1μNN∑i=1⟨x,yi⟩2.
We have and so
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2021-10-20 12:31:29
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http://forums.nesdev.com/viewtopic.php?f=2&t=13113&start=15
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## What do we want in a tutorial?
Discuss technical or other issues relating to programming the Nintendo Entertainment System, Famicom, or compatible systems.
Moderator: Moderators
tepples
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### Re: What do we want in a tutorial?
nicklausw wrote:If you're going to teach beginners with ca65, that might as well be a tutorial on its own...(although I suppose config files are the only thing you'd HAVE to comprehend).
That's what I meant by "A later lesson would explain what goes on in nrom128.cfg (linker script)". It'd probably be around when it gets to mappers.
1. What version do you use?
Currently 2.7, but on a forward-oriented tutorial, perhaps switching to 3.4 might be better. In Ubuntu and probably other Debian-based distros, sudo apt-get install python-imaging gives Pillow in the former, and sudo apt-get install python3-imaging gives Pillow in the latter.
2. How to install Pillow on Windows?
Recent versions of Python include pip, for which the procedure is \path\to\pip.exe install Pillow from an elevated Command Prompt.
Pokun wrote:Still if you made it in C++ you could just include a binary for Windows users
But then I'd need regular access to an up-to-date Windows PC on which to test all build procedures in the tutorial. And the user would still need to install a compiler for the Sound chapter in which I teach the reader how to make a lookup table generator.
JRoatch
Formerly 43110
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### Re: What do we want in a tutorial?
If I would teach someone with a NES programing tutorial, when I get to the graphics section I would teach it under a CHR-RAM setup first and save CHR-ROM for a more advance side section. CHR-RAM is much more similar to how GPUs of modern, and not so modern, systems where the only thing that's read only is the initial program package. Uploading tile data by $2006 and$2007 also demonstrates more clearly the real separation between CPU and PPU buses.
As for tool dependency issues, the only thing I can think of is to illustrate the native NES data structures, and how the bytes behave with single pixel changes, so that it will be possible for human beings to enter data manually by .db statements or make a tool for themselves, and or point out other options like YY-CHR.
tepples
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### Re: What do we want in a tutorial?
I've put the outline on a wiki page.
What emulator should we use on each platform? On Windows, FCEUX is probably fine until you get to the raster effects part, at which point you need to buy an EverDrive N8 or PowerPak. On Debian family, I've been using FCEUX (SDL), which Debian packages, for Ctrl+R in my editor and FCEUX (Windows) in Wine for debugging. Fedora doesn't package any console emulators because Red Hat fears Nintendo's legal department. OS X native emulators tend to rely on a payware "Emulator Enhancer" plug-in for half their features.
And which text editor? I use gedit 2 on Xubuntu 14.04 (a Debian derivative), but gedit 3's "new face" without a menu bar scares me. I'd prefer not to depend on Vim or Emacs because each of those editors differs from mainstream desktop UI conventions so much that it would need a separate full-fledged tutorial by itself. In any case, it needs a way to easily run a program from within the editor (the Ctrl+R binding).
Finally, I've never been entirely sure about the copyright license of NESdev Wiki. Otherwise, we'll need to build this tutorial on a wiki with a well-defined license, such as my own wiki which is CC-BY.
Pokun
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### Re: What do we want in a tutorial?
For text editors I liked KDEvelop (although it's more of an IDE). For Windows I'd use Notepad++ (I have highlighting file for 6502). It has a standard plugin that can execute external programs when pressing F6.
43110 wrote:If I would teach someone with a NES programing tutorial, when I get to the graphics section I would teach it under a CHR-RAM setup first and save CHR-ROM for a more advance side section. CHR-RAM is much more similar to how GPUs of modern, and not so modern, systems where the only thing that's read only is the initial program package. Uploading tile data by $2006 and$2007 also demonstrates more clearly the real separation between CPU and PPU buses.
What's so advanced with CHR-ROM? It's super straightforward. CHR-RAM on the other hand requires a mapper which should come in a later chapter. I don't think teaching things out of order is a very good idea.
tepples wrote:
nicklausw wrote:
Pokun wrote:Still if you made it in C++ you could just include a binary for Windows users
But then I'd need regular access to an up-to-date Windows PC on which to test all build procedures in the tutorial. And the user would still need to install a compiler for the Sound chapter in which I teach the reader how to make a lookup table generator.
Why is that? I don't see the difference between the CHR conversion tool and other tools like the assembler. Wouldn't you need to do that anyway in that case?
But if you are using other Python scripts you might as well go with Python from the beginning.
JRoatch
Formerly 43110
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### Re: What do we want in a tutorial?
Pokun wrote:What's so advanced with CHR-ROM? It's super straightforward. CHR-RAM on the other hand requires a mapper which should come in a later chapter. I don't think teaching things out of order is a very good idea.
NES development was once new to me, and I can tell you the single most surprising unintuitive thing to me was the CHR-ROM, both that the tile gfx was fixed in rom, and that the data has to be included after the end CPU vectors. That second point is especially important when working with a flat file as it has caused confusion in the past.
Learning CHR-RAM before CHR-ROM may seem out of order historically because CHR-ROM games came first, but I argue that CHR-RAM first is natural, not only because of the possible confusion, but because it can follow the lesson about uploading nametable bytes via the same PPU ports. CHR-ROM can then come later as a precursor to CHR page switching for faster animation.
tepples wrote:And which text editor?
If ubuntu includes gedit by default, recommend it. If not, consider recommending it anyway. gedit has not lost functionality through it's face lift. As long as it's not wordpad or libreoffice, and is a plain text editor, it should be fine.
tepples
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### Re: What do we want in a tutorial?
43110 wrote:As for tool dependency issues, the only thing I can think of is to [...] enter data manually by .db statements
Note to self: 43110 likes to trace the holes.
Before the MArtist rant in ''The New Tetris'', there was the Y.S. rant in the Famicom cassette version of ''Pachi Com''.
In [i]Pachi Com[/i], Y.S. wrote:Does company N develop with company I's PROS80? I'm AMAZED they can make stuff on that weird (3″ floppy disk) machine! Do they 'trace the holes' when drawing art, too? If you're sick of tracing holes, I'll sell Bear's art machine (ROM) and debugger for \$40 grand... [phone omitted] That's cheap if you want pretty art!!!
("Tracing holes" means programming graphic data directly without the use of any artist tools.)
But anyway, I've slotted in a chapter that explains CHR RAM, tile data formats, and the tile converter tool. I'm just trying not to front-load the exposition too much.
43110 wrote:both that the tile gfx was fixed in rom, and that the data has to be included after the end CPU vectors.
ld65 allows specifying segment contents in any order in the .s files, so long as memory areas are in the correct order in the linker script. An NROM-128 linker script would automatically place CHR ROM contents after PRG ROM, just as it places the header before PRG ROM.
43110 wrote:I argue that CHR-RAM first is natural, not only because of the possible confusion, but because it can follow the lesson about uploading nametable bytes via the same PPU ports.
In my opinion, CHR ROM improves pacing. Copying a full alphabet from PRG ROM into CHR RAM requires use of the (d),Y addressing mode because the alphabet is more than 16 letters long, and 16 tiles is the limit of a,X or a,Y. This in turn would move the introduction of (d),Y addressing mode forward to the start of chapter 2, when I had hoped to introduce it midway through. Or should I include filling CHR RAM in libstufftobeexplainedlater the way I am doing for the iNES header, reading the controller, and clearing OAM?
43110 wrote:gedit has not lost functionality through it's face lift.
If we recommend both pre- and post-facelift gedit, we'll have to walk the user through configuring Ctrl+R in both pre- and post-facelift gedit depending on what apt-get decides to give him.
mikaelmoizt
Posts: 120
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Location: Gothenburg, Sweden
### Re: What do we want in a tutorial?
Now for my post that took like 6 hours to write, because I had a hard time conveying that I am really VERY positive to this, and I just want to help out in some way by giving some ideas. Also, swedish is my 'modersmål' so it is pretty hard sometimes to express exactly what I intend to.
I think this is the start of a great initiative! I for one would have loved this back in mid 2013 staring at a grey/gray screen
What comes to mind is the professional aspect of this setup. I don't have anything against the setup nor the 'tools' themselves. In fact, this approach could be the very defacto standard of comming NES dev. The answer to: how do I make my own NES game? to keep it simple. Well, you do this.
A lot of folks here use ca65. I can't complain since I never had the time nor patience to actually try it out for myself.
It would really be easier to help people if every piece of code and tool "worked the same" for everyone. It is a neat idea.
However, for a lot of people starting from pretty much nothing - not all of them, the intimidation factor of having to install, script and configure "this" and "that" in order to get "that and this" to work is what might keep them from even starting.
Yes, sooner or later you will have to do this anyway in some form.
Even though most of us don't see a problem with a bit of configuration, I can see why newbies would prefer to "drag and drop" instead of having all this setup for some 8 pixel sprite on a background that 'doesn't even stomp Goombas'. I was one of them.
"I need to do all that?? Nah screw that, here is something much simpler.."
And that might be the reason why many eventually come to this forum with NN based tutorial code for NESASM3 asking for help.
Don't get me wrong, we (as a community) need the best, most experienced and talanted people to make a once and for all tutorial as good as the wiki, in a 'real life situation' whereto people can look for reference.
But now, that will also require the reader to adapt to a more complex set of tools in order to get started.
I really like my ASM6. I know it may not be as advanced as ca65+stuff, but I haven't yet found anything I can't do with it. As long as I can't find a reason to change, why do it? The png to chr converter (?) sure would be sweet though..
Anyway.. So maybe there could be... 2 or 3 different options for the newcommer to start with in order to adjust to their taste? Anyone want/able to translate the tutorial code from one assembler to another to keep every bit of choice there could be?
Just some thoughts.
Like I wrote, it is hard for me to type in english exactly how I mean, but I hope my opinion is of any use.
I´ve got %01100011 problems but the BITs aint one.
JRoatch
Formerly 43110
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### Re: What do we want in a tutorial?
tepples wrote:
43110 wrote:As for tool dependency issues, the only thing I can think of is to [...] enter data manually by .db statements
Note to self: 43110 likes to trace the holes.
100% true. It's why I love understanding file format definitions, and that this was never finished.
tepples wrote:In my opinion, CHR ROM improves pacing...
I agree it would be a bit much to explain in the Hello World chapter, since the point there is showing the shortest path to displaying a word on screen. Since for that chapter you'll most likely be providing the CHR page and skimming over all the assembly details, it would not matter if it's CHR-RAM or CHR-ROM. CHR-RAM with a unexplained upload routine has the benefit of keeping the cart setup the same all the way to the part where 16-bit indexing is explained, but either choice is fine.
About gedit, I guess I never got used to using a hot key for compiling, so I failed to see it missing. I don't know what further to say about choice of text editor.
Also before I start editing your outline or anything, Nerdy Nights has been often praised for it's sound and music engine tutorials. Would taking it's outline be a good start for the sound and music sections?
dougeff
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### Re: What do we want in a tutorial?
Re:Sound and music
I would like to see a tutorial explain how to go from a DAW to produce a MIDI, to Famitracker, to exporting data, to incorporating into an actual NES game. I've never seen such a step-by-step beginning to end music tutorial. And ca65 seems like the best choice. I would nominate Rainwarrior for writing that one.
nesdoug.com -- blog/tutorial on programming for the NES
tepples
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### Re: What do we want in a tutorial?
dougeff wrote:I would like to see a tutorial explain how to go from a DAW to produce a MIDI, to Famitracker, to exporting data, to incorporating into an actual NES game.
Once it's in FamiTracker, the manual for Shiru's FamiTone takes it the rest of the way. But I myself would need a tutorial to get from zero to MIDI. Which free DAW should I use for this tutorial?
One problem with authoring NES music directly in MIDI is that NES music engines tend to prefer repeated phrases/patterns to save space. Listen to the music from WORLD 1-1 in Super Mario Bros. or the bass line in the song that few Silver Surfer players had heard all the way through before NSFs. I'm not sure if MIDI supports any analogous construct.
dougeff
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### Re: What do we want in a tutorial?
Perhaps you could export the Treble and Bass line separately, as 2 separate MIDI file. Import them separately, and loop the Bass. And, I'm not sure that there are any good free/open DAWs out there. I have 2 that were fairly expensive, and 1 that came with a Computer Music magazine. I thought, maybe, you could have a more advanced tutorial than Nerdy Nights.
nesdoug.com -- blog/tutorial on programming for the NES
rainwarrior
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### Re: What do we want in a tutorial?
tepples wrote:One problem with authoring NES music directly in MIDI is that NES music engines tend to prefer repeated phrases/patterns to save space. ... I'm not sure if MIDI supports any analogous construct.
MIDI files can be annotated with events, but it can also be practical to detect loops during export. 4klang does this already with MIDI. (I suppose some forms of LZ compression are generic forms of loop detection?)
If it's your own exporter, you can create whatever method for identifying loops/repeats that works for you. In my own engine the exporter automatically detects patterns/instruments/macros that are the same and merges them. The pattern order is rebuilt based on unique data, rather than just using what Famitracker gives. I prefer to do it this way than try to optimize within Famitracker, because it makes it easier to split shared ones later.
Startropics has a really cute music data format. Each track has up to 256 bytes per channel, and there are loop/repeat command codes. It's nice and compact, though it limits song length/complexity quite a bit.
Also, why would you want to use anything besides Famitracker to make your NES music? (Or even PPMCK / Muse / Deflemask.) These things already give a great 1:1 NES composition experience, why do you want to use a generic format like MIDI?
A lot of people seem to have good luck with shiru's Famitone too. It's one of the only "drop in" solutions that this homebrew community has.
dougeff
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### Re: What do we want in a tutorial?
why do you want to use a generic format like MIDI?
I don't use MIDI this way, currently. But, the DAW interfaces are so much better than the Famitracker interface. I can record direct from a MIDI keyboard into a DAW and edit the notes directly and easily.
nesdoug.com -- blog/tutorial on programming for the NES
rainwarrior
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### Re: What do we want in a tutorial?
Famitracker actually has MIDI input support, if you want to use a MIDI keyboard to enter notes into it.
dougeff
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### Re: What do we want in a tutorial?
Oh. I can't know everything.
Well, that sort of proves my original point. A new tutorial should show how to do music with Famitracker.
nesdoug.com -- blog/tutorial on programming for the NES
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2020-08-04 17:41:13
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http://www.dailykos.com/story/2007/11/21/413260/-Kucinich-Real-Libertarianism?detail=hide
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The more I read, the more I think Kucinich is the right person for libertarian socialists to support. Wait, libertarian socialist? Click the prior links, or if you're familiar with their writings... think Noam Chomsky or Bertrand Russell (my personal favorite) (he was brilliant!) (\end flattery.sh).
So, back to Kucinich. Like all libertarians, he believes people should make their own moral choices. Ron Paul, on the other hand, does not... here is one example, and there are others.
Abortion:
Kucinich is self-described as pro-life. He believes that abortion should remain legal, thereby letting everyone come to their own moral decision on the issue -- because it is a moral issue. He thinks abortion should be minimized through good sex education.
On the other hand, Ron Paul believed first that abortion should be illegal. Since then, due to being heavily scrutinized, he has changed course and says it's a "state's issue". The point is, liberty does not vary by state. Since we have all equated liberty with morality in the US, then morality does not vary by state either.
Ok, fine. Another example?
Gay Marriage.
Ron Paul believes gay marriage should not be recognized, as it is a redefinition of marriage, and people should not "look to the government for moral guidance", whatever that means. Obviously, he is married himself, so by his own reasoning, he himself looked to the government for moral guidance. Also, technically he voted against the FMA, but this was simply because he believes Federal laws should not trump State laws. Another case of liberty/morality varying by state.
Kucinich believes the government should recognize gay marriage, and the general population can decide who to marry for themselves. Essentially this is saying, in the eyes of the government one person should be treated as any other person.
A last note on gay marriage, I think in the ideal sense the government would recognize no marriages -- if it is in fact a religious institution. I don't believe any heterosexually married people would voluntarily give up their government endorsed marriage rights -- including Kucinch and Paul. The second best approach, considering practical things, is opening up government benefits to everyone. What does the government care about the sex of the person visiting their spouse in the hospital? Inheriting money? etc. Also, I'm pretty sure Paul and Kucinich are both open to allowing churches to marry who they want, sans government impedance.
Maybe you're thinking, "Thank you, jamesia, for those two exhaustive examples... Now what does that mean to me/us?" Hey, I'm glad you asked! What this means is that Ron Paul advocates either the State or Federal government to legislate morality, whereas Kucinich believes morality should be decided by you and me. Which is libertarian, and which is your average conservative?
Finally, Ron Paul wants to eliminate most of the government. We all know this. The FDA, IRS, EPA, DoE, etc... I can't agree with any of those eliminations, except maybe the IRS. I hate paying taxes. HOWEVER, upon closer inspection of my own ideas, the reason I don't like paying taxes is because I feel like I have no control over how they're spent. If we Americans did have control -- there'd be no Iraq war. 60-70% of the population wants out of the war, so why is our money still going toward it? So, I can agree with almost none of Ron Paul's government eliminations.
Kucinich, on the other hand, is calling for complete reform. He wants universal health care and probably universal education. Why? He thinks everyone should make their own moral choices, but how can you if you're not educated and worrying about yours or your loved ones healthcare bills? Why would you care about voting if you're continually concerned that the bulk of your income goes toward paying for a debilitating illness? Can you really be expected to treat a different race equally if you've never been exposed, through education, to their views? Basically Kucinich's plan, in a nutshell, is allowing people to make their own moral judgments, but give them the tools with which to make good choices. When you think about it, this is kind of a "well, duh" idea.
That said -
On December 15th, there will be a funding bomb a la Ron Paul for Kucinich. At least pass the link on... we deserve a Constitutionalist that's not insane!
The goal is $100 x 100,000 people =$10 million
Just so this doesn't turn into a Ron Paul bash, I think we can all agree with certain of his ideals. Government reform and a return of Constitutional rights are great goals! But then, there are those other completely incomprehensible ideas of his. I am writing this diary specifically to show the underlining similarity between Ron Paul and Dennis Kucinich, and pointing out that Paul approaches libertarianism from the right, whereas Kucinich does from the left.
ps. sorry for the verbal diarrhea. i get wordy when excited.
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2015-05-26 06:17:17
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http://economics.stackexchange.com/questions/3372/is-there-any-standard-measure-of-economic-significance
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# Is there any standard measure of economic significance?
One measure is to look at standard deviations. If a one standard deviation increase in X leads to a more than a 0.5 (or 1, or ⅓, or whatever) standard deviation increase in Y, then we say that X has a economically significant effect on Y.
Is this standard? And if not, what other measures are there to formalize the notion of "economic significance"?
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Imagine the basic linear regression setup:
$Y_i = \alpha + X_i \beta + \epsilon, \epsilon \sim N(0,\sigma^2)$
Holding everything else fixed, increasing $\sigma$ will increase the standard deviation of $Y$ and therefore, for a fixed relationship between $X$ and $Y$, eventually move the relationship between them to economic insignificance by the standard you present. But the relationship might still be quite economically important. It might be better to instead ask about the standard deviation effects on $\sigma_\hat{Y}$, the standard deviation of the fitted values of $Y$, to ask if the effect is large relative to the total variation that can be explained by the model.
In accounting, they use a concept of immateriality which seems quite similar to economic insignificance. That might be a helpful definition for some problems.
This quote from Signifying Nothing: Reply to Hoover and Siegler by Deirdre N. McCloskey and Stephen T. Ziliak may also be helpful:
The sheer probability statement about one or two standard errors is useless, unless you have judged by what scale a number is large or small for the scientific or policy or personal purpose you have in mind. This applies to the so-called "precision" or "accuracy" of the estimate, too, beloved of Hoover and Siegler — the number we calculate as though that very convenient sampling theory did in fact apply.
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2016-04-29 04:02:43
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https://forum.snap.berkeley.edu/t/how-to-define-new-data-types-today-and-future/9137
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# How to define new data types (today and future)?
To define a tree as node or leaf (Caps = type, lower = constructor or record field):
Tree = leaf | node
leaf = Number
node = left: Tree, right: Tree
Today I believe I need to write:
• leaf(n) and node(l, r) constructors to encode a type tag + fields as a list
• isLeaf, isNode predicates to check type tag
• leafNumber, nodeLeft, nodeRight accessors
• etc.
Would this be the recommended approach today?
Would any of the macro-like initiatives make this easier in the future? Snap does wonderfully on the function-design side, I'm hoping to also teach data design with type-based design principles, akin to HtdP, with less overhead than today.
Thanks for the awesome work!!!
Yes, that's what you need. Depending on what algorithms you plan to use with trees the "etc." part would be mutators for the nodes.
You could avoid the need for type tags, if you want, by using the block. Then a leaf would just be a number (supposing you don't intend to mutate leaf nodes), and a branch node (in my dialect, a leaf is a node, and the distinction is leaf node vs. branch node) would just be a list. In effect you'd be using Snap!'s internal type tags as your type tags.
And yes, one of the things you could accomplish with macros once we have them is a Define Type block that would take a list of fields and generate the corresponding constructor, selectors, and mutators.
Thanks, Brian, good to know!
• Could a single Define Type expand into a single (compound?) Snap form that included all constructors, accessors, predicates, etc? Any hint what that might look like?
• Is v7 likely to have enough functionality for Define Type?
Definitely not v7! Macros are still a ways away.
Define Type would carry out a bunch of definitions of custom blocks, so if you say Define Type cereal [Snap, Crackle, Pop] you get new blocks
make cereal, snap: %snap crackle: %crackle pop: %pop
Snap from cereal %cereal
Crackle from cereal %cereal
Pop from cereal %pop
cereal? %thing
and maybe (via a Boolean input to Define Type?)
replace Snap of cereal %cereal with %thing
replace Crackle of cereal %cereal with %thing
replace Pop of cereal %cereal with %thing
Lots of questions to answer, e.g., does this new type get a new palette category color? But, the thing is, Define Type would be defined entirely in user code, so if you don't like my version you can write your own! (Some flavor of user-defined categories will be in v7, for the benefit of extension writers.)
I'm interested enough in this that I might enter the source code rabbit hole ... any suggestion where I might start if I wanted to build a Define Type button? Also, which version / branch should I dig into?
Thanks for any pointers!
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2022-07-01 08:50:28
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http://www.neverendingbooks.org/category/absolute
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Category: absolute
‘Gabriel’s topos’ (see here) is the conjectural, but still elusive topos from which the validity of the Riemann hypothesis would follow.
It is the latest attempt in Alain Connes’ 20 year long quest to tackle the RH (before, he tried the tools of noncommutative geometry and later those offered by the field with one element).
For the last 5 years he hopes that topos theory might provide the missing ingredient. Together with Katia Consani he introduced and studied the geometry of the Arithmetic site, and later the geometry of the scaling site.
If you look at the points of these toposes you get horribly complicated ‘non-commutative’ spaces, such as the finite adele classes $\mathbb{Q}^*_+ \backslash \mathbb{A}^f_{\mathbb{Q}} / \widehat{\mathbb{Z}}^{\ast}$ (in case of the arithmetic site) and the full adele classes $\mathbb{Q}^*_+ \backslash \mathbb{A}_{\mathbb{Q}} / \widehat{\mathbb{Z}}^{\ast}$ (for the scaling site).
In Vienna, Connes gave a nice introduction to the arithmetic site in two lectures. The first part of the talk below also gives an historic overview of his work on the RH
The second lecture can be watched here.
However, not everyone is as optimistic about the topos-approach as he seems to be. Here’s an insightful answer on MathOverflow by Will Sawin to the question “What is precisely still missing in Connes’ approach to RH?”.
Other interesting MathOverflow threads related to the RH-approach via the field with one element are Approaches to Riemann hypothesis using methods outside number theory and Riemann hypothesis via absolute geometry.
About a month ago, from May 10th till 14th Alain Connes gave a series of lectures at Ohio State University with title “The Riemann-Roch strategy, quantizing the Scaling Site”.
The accompanying paper has now been arXived: The Riemann-Roch strategy, Complex lift of the Scaling Site (joint with K. Consani).
Especially interesting is section 2 “The geometry behind the zeros of $\zeta$” in which they explain how looking at the zeros locus inevitably leads to the space of adele classes and why one has to study this space with the tools from noncommutative geometry.
Perhaps further developments will be disclosed in a few weeks time when Connes is one of the speakers at Toposes in Como.
The Fibonacci sequence reappears a bit later in Dan Brown’s book ‘The Da Vinci Code’ where it is used to login to the bank account of Jacques Sauniere at the fictitious Parisian branch of the Depository Bank of Zurich.
Last time we saw that the Hankel matrix of the Fibonacci series $F=(1,1,2,3,5,\dots)$ is invertible over $\mathbb{Z}$
$H(F) = \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix} \in SL_2(\mathbb{Z})$
and we can use the rule for the co-multiplication $\Delta$ on $\Re(\mathbb{Q})$, the algebra of rational linear recursive sequences, to determine $\Delta(F)$.
For a general integral linear recursive sequence the corresponding Hankel matrix is invertible over $\mathbb{Q}$, but rarely over $\mathbb{Z}$. So we need another approach to compute the co-multiplication on $\Re(\mathbb{Z})$.
Any integral sequence $a = (a_0,a_1,a_2,\dots)$ can be seen as defining a $\mathbb{Z}$-linear map $\lambda_a$ from the integral polynomial ring $\mathbb{Z}[x]$ to $\mathbb{Z}$ itself via the rule $\lambda_a(x^n) = a_n$.
If $a \in \Re(\mathbb{Z})$, then there is a monic polynomial with integral coefficients of a certain degree $n$
$f(x) = x^n + b_1 x^{n-1} + b_2 x^{n-2} + \dots + b_{n-1} x + b_n$
such that for every integer $m$ we have that
$a_{m+n} + b_1 a_{m+n-1} + b_2 a_{m+n-2} + \dots + b_{n-1} a_{m+1} + a_m = 0$
Alternatively, we can look at $a$ as defining a $\mathbb{Z}$-linear map $\lambda_a$ from the quotient ring $\mathbb{Z}[x]/(f(x))$ to $\mathbb{Z}$.
The multiplicative structure on $\mathbb{Z}[x]/(f(x))$ dualizes to a co-multiplication $\Delta_f$ on the set of all such linear maps $(\mathbb{Z}[x]/(f(x)))^{\ast}$ and we can compute $\Delta_f(a)$.
We see that the set of all integral linear recursive sequences can be identified with the direct limit
$\Re(\mathbb{Z}) = \underset{\underset{f|g}{\rightarrow}}{lim}~(\frac{\mathbb{Z}[x]}{(f(x))})^{\ast}$
(where the directed system is ordered via division of monic integral polynomials) and so is equipped with a co-multiplication $\Delta = \underset{\rightarrow}{lim}~\Delta_f$.
Btw. the ring structure on $\Re(\mathbb{Z}) \subset (\mathbb{Z}[x])^{\ast}$ comes from restricting to $\Re(\mathbb{Z})$ the dual structures of the co-ring structure on $\mathbb{Z}[x]$ given by
$\Delta(x) = x \otimes x \quad \text{and} \quad \epsilon(x) = 1$
From this description it is clear that you need to know a hell of a lot number theory to describe this co-multiplication explicitly.
As most of us prefer to work with rings rather than co-rings it is a good idea to begin to study this co-multiplication $\Delta$ by looking at the dual ring structure of
$\Re(\mathbb{Z})^{\ast} = \underset{\underset{ f | g}{\leftarrow}}{lim}~\frac{\mathbb{Z}[x]}{(f(x))}$
This is the completion of $\mathbb{Z}[x]$ at the multiplicative set of all monic integral polynomials.
This is a horrible ring and very little is known about it. Some general remarks were proved by Kazuo Habiro in his paper Cyclotomic completions of polynomial rings.
In fact, Habiro got interested is a certain subring of $\Re(\mathbb{Z})^{\ast}$ which we now know as the Habiro ring and which seems to be a red herring is all stuff about the field with one element, $\mathbb{F}_1$ (more on this another time). Habiro’s ring is
$\widehat{\mathbb{Z}[q]} = \underset{\underset{n|m}{\leftarrow}}{lim}~\frac{\mathbb{Z}[q]}{(q^n-1)}$
and its elements are all formal power series of the form
$a_0 + a_1 (q-1) + a_2 (q^2-1)(q-1) + \dots + a_n (q^n-1)(q^{n-1}-1) \dots (q-1) + \dots$
with all coefficients $a_n \in \mathbb{Z}$.
Here’s a funny property of such series. If you evaluate them at $q \in \mathbb{C}$ these series are likely to diverge almost everywhere, but they do converge in all roots of unity!
Some people say that these functions are ‘leaking out of the roots of unity’.
If the ring $\Re(\mathbb{Z})^{\ast}$ is controlled by the absolute Galois group $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$, then Habiro’s ring is controlled by the abelianzation $Gal(\overline{\mathbb{Q}}/\mathbb{Q})^{ab} \simeq \hat{\mathbb{Z}}^{\ast}$.
In The Da Vinci Code, Dan Brown feels he need to bring in a French cryptologist, Sophie Neveu, to explain the mystery behind this series of numbers:
13 – 3 – 2 – 21 – 1 – 1 – 8 – 5
The Fibonacci sequence, 1-1-2-3-5-8-13-21-34-55-89-144-… is such that any number in it is the sum of the two previous numbers.
It is the most famous of all integral linear recursive sequences, that is, a sequence of integers
$a = (a_0,a_1,a_2,a_3,\dots)$
such that there is a monic polynomial with integral coefficients of a certain degree $n$
$f(x) = x^n + b_1 x^{n-1} + b_2 x^{n-2} + \dots + b_{n-1} x + b_n$
such that for every integer $m$ we have that
$a_{m+n} + b_1 a_{m+n-1} + b_2 a_{m+n-2} + \dots + b_{n-1} a_{m+1} + a_m = 0$
For the Fibonacci series $F=(F_0,F_1,F_2,\dots)$, this polynomial can be taken to be $x^2-x-1$ because
$F_{m+2} = F_{m+1}+F_m$
The set of all integral linear recursive sequences, let’s call it $\Re(\mathbb{Z})$, is a beautiful object of great complexity.
For starters, it is a ring. That is, we can add and multiply such sequences. If
$a=(a_0,a_1,a_2,\dots),~\quad \text{and}~\quad a’=(a’_0,a’_1,a’_2,\dots)~\quad \in \Re(\mathbb{Z})$
then the sequences
$a+a’ = (a_0+a’_0,a_1+a’_1,a_2+a’_2,\dots) \quad \text{and} \quad a \times a’ = (a_0.a’_0,a_1.a’_1,a_2.a’_2,\dots)$
are again linear recursive. The zero and unit in this ring are the constant sequences $0=(0,0,\dots)$ and $1=(1,1,\dots)$.
So far, nothing terribly difficult or exciting.
It follows that $\Re(\mathbb{Z})$ has a co-unit, that is, a ring morphism
$\epsilon~:~\Re(\mathbb{Z}) \rightarrow \mathbb{Z}$
sending a sequence $a = (a_0,a_1,\dots)$ to its first entry $a_0$.
It’s a bit more difficult to see that $\Re(\mathbb{Z})$ also has a co-multiplication
$\Delta~:~\Re(\mathbb{Z}) \rightarrow \Re(\mathbb{Z}) \otimes_{\mathbb{Z}} \Re(\mathbb{Z})$
with properties dual to those of usual multiplication.
To describe this co-multiplication in general will have to await another post. For now, we will describe it on the easier ring $\Re(\mathbb{Q})$ of all rational linear recursive sequences.
For such a sequence $q = (q_0,q_1,q_2,\dots) \in \Re(\mathbb{Q})$ we consider its Hankel matrix. From the sequence $q$ we can form symmetric $k \times k$ matrices such that the opposite $i+1$-th diagonal consists of entries all equal to $q_i$
$H_k(q) = \begin{bmatrix} q_0 & q_1 & q_2 & \dots & q_{k-1} \\ q_1 & q_2 & & & q_k \\ q_2 & & & & q_{k+1} \\ \vdots & & & & \vdots \\ q_{k-1} & q_k & q_{k+1} & \dots & q_{2k-2} \end{bmatrix}$
The Hankel matrix of $q$, $H(q)$ is $H_k(q)$ where $k$ is maximal such that $det~H_k(q) \not= 0$, that is, $H_k(q) \in GL_k(\mathbb{Q})$.
Let $S(q)=(s_{ij})$ be the inverse of $H(q)$, then the co-multiplication map
$\Delta~:~\Re(\mathbb{Q}) \rightarrow \Re(\mathbb{Q}) \otimes \Re(\mathbb{Q})$
sends the sequence $q = (q_0,q_1,\dots)$ to
$\Delta(q) = \sum_{i,j=0}^{k-1} s_{ij} (D^i q) \otimes (D^j q)$
where $D$ is the shift operator on sequence
$D(a_0,a_1,a_2,\dots) = (a_1,a_2,\dots)$
If $a \in \Re(\mathbb{Z})$ is such that $H(a) \in GL_k(\mathbb{Z})$ then the same formula gives $\Delta(a)$ in $\Re(\mathbb{Z})$.
For the Fibonacci sequences $F$ the Hankel matrix is
$H(F) = \begin{bmatrix} 1 & 1 \\ 1& 2 \end{bmatrix} \in GL_2(\mathbb{Z}) \quad \text{with inverse} \quad S(F) = \begin{bmatrix} 2 & -1 \\ -1 & 1 \end{bmatrix}$
and therefore
$\Delta(F) = 2 F \otimes ~F – DF \otimes F – F \otimes DF + DF \otimes DF$
There’s a lot of number theoretic and Galois-information encoded into the co-multiplication on $\Re(\mathbb{Q})$.
To see this we will describe the co-multiplication on $\Re(\overline{\mathbb{Q}})$ where $\overline{\mathbb{Q}}$ is the field of all algebraic numbers. One can show that
$\Re(\overline{\mathbb{Q}}) \simeq (\overline{\mathbb{Q}}[ \overline{\mathbb{Q}}_{\times}^{\ast}] \otimes \overline{\mathbb{Q}}[d]) \oplus \sum_{i=0}^{\infty} \overline{\mathbb{Q}} S_i$
Here, $\overline{\mathbb{Q}}[ \overline{\mathbb{Q}}_{\times}^{\ast}]$ is the group-algebra of the multiplicative group of non-zero elements $x \in \overline{\mathbb{Q}}^{\ast}_{\times}$ and each $x$, which corresponds to the geometric sequence $x=(1,x,x^2,x^3,\dots)$, is a group-like element
$\Delta(x) = x \otimes x \quad \text{and} \quad \epsilon(x) = 1$
$\overline{\mathbb{Q}}[d]$ is the universal Lie algebra of the $1$-dimensional Lie algebra on the primitive element $d = (0,1,2,3,\dots)$, that is
$\Delta(d) = d \otimes 1 + 1 \otimes d \quad \text{and} \quad \epsilon(d) = 0$
Finally, the co-algebra maps on the elements $S_i$ are given by
$\Delta(S_i) = \sum_{j=0}^i S_j \otimes S_{i-j} \quad \text{and} \quad \epsilon(S_i) = \delta_{0i}$
That is, the co-multiplication on $\Re(\overline{\mathbb{Q}})$ is completely known. To deduce from it the co-multiplication on $\Re(\mathbb{Q})$ we have to consider the invariants under the action of the absolute Galois group $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$ as
$\Re(\overline{\mathbb{Q}})^{Gal(\overline{\mathbb{Q}}/\mathbb{Q})} \simeq \Re(\mathbb{Q})$
Unlike the Fibonacci sequence, not every integral linear recursive sequence has an Hankel matrix with determinant $\pm 1$, so to determine the co-multiplication on $\Re(\mathbb{Z})$ is even a lot harder, as we will see another time.
Reference: Richard G. Larson, Earl J. Taft, ‘The algebraic structure of linearly recursive sequences under Hadamard product’
Once in every six months there’s a flurry of online excitement about Mochizuki’s alleged proof of the abc-conjecture.
It seems to be that time of the year again.
The twitter-account of the ever optimistic @math_jin is probably the best source for (positive) news about IUT/ABC. He now announces the latest version of Yamashita’s ‘summary’ of Mochizuki’s proof:
Another informed source is Ed Frenkel. He sometimes uses his twitter-account @edfrenkel to broadcast Ivan Fesenko‘s enthusiasm.
Googling further, I stumbled upon an older (newspaper) article on the subject: das grosse ABC by Marlene Weiss, for which she got silver at the 2017 science journalism awards.
In case you prefer an English translation: The big ABC.
Here’s her opening paragraph:
“In a children’s story written by the Swiss author Peter Bichsel, a lonely man decides to invent his own language. He calls the table “carpet”, the chair “alarm clock”, the bed “picture”. At first he is enthusiastic about his idea and always thinks of new words, his sentences sound original and funny. But after a while, he begins to forget the old words.”
The article is less optimistic than other recent popular accounts of Mochizuki’s story, including:
Monumental proof to torment mathematicians for years to come in Nature by Davide Castelvecchi.
Hope Rekindled for Perplexing Proof in Quanta-magazine by Kevin Hartnett.
Baffling ABC maths proof now has impenetrable 300-page ‘summary’ in the New Scientist by Timothy Revell.
Marlene Weiss fears a sad ending:
“Table is called “carpet”, chair is called “alarm clock”, bed is called “picture”. In the story by Peter Bichsel, the lonely man ends up having so much trouble communicating with other people that he speaks only to himself. It is a very sad story.”
Perhaps things will turn out for the better, and we’ll hear about it sometime.
In six months, I’d say…
In several of his talks on #IUTeich, Mochizuki argues that usual scheme theory over $\mathbb{Z}$ is not suited to tackle problems such as the ABC-conjecture.
The idea appears to be that ABC involves both the additive and multiplicative nature of integers, making rings into ‘2-dimensional objects’ (and clearly we use both ‘dimensions’ in the theory of schemes).
So, perhaps we should try to ‘dismantle’ scheme theory, and replace it with something like geometry over the field with one element $\mathbb{F}_1$.
The usual $\mathbb{F}_1$ mantra being: ‘forget all about the additive structure and only retain the multiplicative monoid’.
So perhaps there is yet another geometry out there, forgetting about the multiplicative structure, and retaining just the addition…
In the forgetting can’t be that hard, can it?-post we have seen that the forgetful functor
$F_{+,\times}~:~\mathbf{rings} \rightarrow \mathbf{sets}$
(that is, forgetting both multiplicative and additive information of the ring) is representable by the polynomial ring $\mathbb{Z}[x]$.
So, what about our ‘dismantling functors’ in which we selectively forget just one of these structures:
$F_+~:~\mathbf{rings} \rightarrow \mathbf{monoids} \quad \text{and} \quad F_{\times}~:~\mathbf{rings} \rightarrow \mathbf{abelian~groups}$
Are these functors representable too?
Clearly, ring maps from $\mathbb{Z}[x]$ to our ring $R$ give us again the elements of $R$. But now, we want to encode the way two of these elements add (or multiply).
This can be done by adding extra structure to the ring $\mathbb{Z}[x]$, namely a comultiplication $\Delta$ and a counit $\epsilon$
$\Delta~:~\mathbb{Z}[x] \rightarrow \mathbb{Z}[x] \otimes \mathbb{Z}[x] \quad \text{and} \quad \epsilon~:~\mathbb{Z}[x] \rightarrow \mathbb{Z}$
The idea of the comultiplication being that if we have two elements $r,s \in R$ with corresponding ring maps $f_r~:~\mathbb{Z}[x] \rightarrow R \quad x \mapsto r$ and $f_s~:~\mathbb{Z}[x] \rightarrow R \quad x \mapsto s$, composing their tensorproduct with the comultiplication
$f_v~:~\mathbb{Z}[x] \rightarrow^{\Delta} \mathbb{Z}[x] \otimes \mathbb{Z}[x] \rightarrow^{f_r \otimes f_s} R$
determines another element $v \in R$ which we can take either the product $v=r.s$ or sum $v=r+s$, depending on the comultiplication map $\Delta$.
The role of the counit is merely sending $x$ to the identity element of the operation.
Thus, if we want to represent the functor forgetting the addition, and retaining the multiplication we have to put on $\mathbb{Z}[x]$ the structure of a biring
$\Delta(x) = x \otimes x \quad \text{and} \quad \epsilon(x) = 1$
(making $x$ into a ‘group-like’ element for Hopf-ists).
The functor $F_{\times}$ forgetting the multiplication but retaining the addition is represented by the Hopf-ring $\mathbb{Z}[x]$, this time with
$\Delta(x) = x \otimes 1 + 1 \otimes x \quad \text{and} \quad \epsilon(x) = 0$
(that is, this time $x$ becomes a ‘primitive’ element).
Perhaps this adds another feather of weight to the proposal in which one defines algebras over the field with one element $\mathbb{F}_1$ to be birings over $\mathbb{Z}$, with the co-ring structure playing the role of descent data from $\mathbb{Z}$ to $\mathbb{F}_1$.
As, for example, in my note The coordinate biring of $\mathbf{Spec}(\mathbb{Z})/\mathbb{F}_1$.
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2020-01-24 05:57:48
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http://www.koreascience.or.kr/article/JAKO200924934792682.page
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# MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITIES WITH FQ-COMPLEMENTARITY PROBLEMS
Lee, Byung-Soo
• Accepted : 2009.03.18
• Published : 2009.06.25
• 30 6
#### Abstract
This paper introduces new mixed vector FQ-implicit variational inequality problems and corresponding mixed vector FQ-implicit complementarity problems for set-valued mappings, and studies the equivalence between them under certain assumptions in Banach spaces. It also derives some new existence theorems of solutions for them with examples under suitable assumptions without monotonicity. This paper generalizes and extends many results in [8, 10, 19-22].
#### Keywords
Mixed vector FQ-implicit complementarity problem;Mixed vector FQ-implicit variational inequality problem;KKM-mapping;Fan-KKM Theorem;Positively homogeneous mapping;Convex cone;Upper semicontinuity;Lower semicontinuity
#### References
1. A. Carbone, A note on complementarity problem. Internat. J. Math. & Math. Sci. Vol. 21(3) (1998), 621-623. https://doi.org/10.1155/S0161171298000878
2. S. S. Chang and N. J. Huang, Generalized multivalued implicit complementarity problems in Hilbert spaces, Math. Japonica 36(6) (1991), 1093-1100.
3. G. Y. Chen and X. Q. Yang. The vector complementarity problems and its equivalences with the weak minimal element in ordered spaces, J. Math, Anal. Appl. 153(1990). 136-158. https://doi.org/10.1016/0022-247X(90)90270-P
4. R. W. Cottle, J. S. Pang and R. E. Stone, The Linear Complementarity Problem, Academic Press. New York. 1992.
5. R. W. Cottle and J. C. Yao, Pseudo-monotone complementarity Problems in Hilbert space, J. Opti, Th. & Appl. Vol. 75(2) (1992), 281-295. https://doi.org/10.1007/BF00941468
6. F. Facchinei and J. S. Pang, Finite-dimensional Variational Inequalities and Complementarity Problems, Springer-Verlag, New York, 2003.
7. K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310. https://doi.org/10.1007/BF01353421
8. Y. P. Fang and N. J. Huang, The vector F-complementarity problem with demipseudomonotone mapping in Banach spaces, Appl. Math. Lett. 16 (2003), 1019-1024. https://doi.org/10.1016/S0893-9659(03)90089-9
9. F. Ferro, A minimax theorem for vector-valued functions, J. Optim, Theory Appl. 60 (1989), 19-31. https://doi.org/10.1007/BF00938796
10. N. J. Huang and J. Li, F-implicit complementarity problems in Banach spaces, Z. Anal. Anwendungen 23 (2004), 293-302.
11. G. Isac. Complementarity Problems, Lecture Notes in Math. No. 1528, Springer-Verlag. New York. 1992.
12. G. Isac. Topological Methods in Complementarity Theory, Kluwer Academic Publishers. Dordrecht, Boston, London. 2000.
13. G. Isac. Condition $(S)_{+}^{1}$, Altman's condition and the scalar asymptotic derivative: applications to complementarity theory, Nonlinear Analysis Forum Vol. 5 (2000), 1-13.
14. G. Isac. A special variational inequality and the implicit complementarity problems, J. Fac. Sci. Univ. Tokyo 37 (1990), 109-127.
15. G. Isac, A generalization of Karamardian's condition in complementarity theory, Nonlinear Analysis Forum Vol. 4 (1999), 49-63.
16. G. Isac, On the implicit complementarity problem in Hilbert spaces. Bull. Australian Math. Soc. 32 (1985), 251-260. https://doi.org/10.1017/S000497270000993X
17. G. Isac and Jinlu Li. Complementarity problem, Karamardian's condition and a generalization of Harker-Pang condigion. Nonlinear Analysis Forum Vol. 6(2) (2001), 383-390.
18. S. Karamardian, Generalized complementarity problem, J. Optim. Theory Appl. 8 (1971), 161-168. https://doi.org/10.1007/BF00932464
19. B. S. Lee, M. F. Khan and Salnhuddln, Vector F-implicit complementarity problems with corresponding variational inequality problems, Appl. Math. Lett. 20 (2007), 433-438. https://doi.org/10.1016/j.aml.2006.05.010
20. J. Li and N. J. Huang, Vector F-implicit complementarity problems in Banach spaces, Appl. Math, Lett. 19 (2006), 464-471. https://doi.org/10.1016/j.aml.2005.07.003
21. K. Q. Wu and N. J. Huang, General mixed vector F-implicit complementarity problems in Banach spaces, Journal of Applied Analysis Vol. 14(1) (2008), 73-88. https://doi.org/10.1515/JAA.2008.73
22. H. Y. Yin, C. X. Xu and Z. X. Zhang. The F-complementarity problems and its equivalence with the least element problem. Acta Math. Sinica 44 (2001). 679-686.
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2019-04-21 04:31:48
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https://www.wikiplanet.click/enciclopedia/en/Black_hole_thermodynamics
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# Black hole thermodynamics
In physics, black hole thermodynamics[1] is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black-hole event horizons. As the study of the statistical mechanics of black-body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.[2]
An artist's depiction of two black holes merging, a process in which the laws of thermodynamics are upheld
## Overview
The second law of thermodynamics requires that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed.
Starting from theorems proved by Stephen Hawking, Jacob Bekenstein conjectured that the black hole entropy was proportional to the area of its event horizon divided by the Planck area. In 1973 Bekenstein suggested ${\displaystyle (1/2\cdot \ln {2})/4\pi }$ as the constant of proportionality, asserting that if the constant was not exactly this, it must be very close to it. The next year, in 1974, Hawking showed that black holes emit thermal Hawking radiation[3][4] corresponding to a certain temperature (Hawking temperature).[5][6] Using the thermodynamic relationship between energy, temperature and entropy, Hawking was able to confirm Bekenstein's conjecture and fix the constant of proportionality at ${\displaystyle 1/4}$:[7][8]
${\displaystyle S_{\text{BH}}={\frac {k_{B}A}{4\ell _{\text{P}}^{2}}},}$
where ${\displaystyle A}$ is the area of the event horizon, ${\displaystyle k_{B}}$ is Boltzmann's constant, and ${\displaystyle \ell _{\text{P}}={\sqrt {G\hbar /c^{3}}}}$ is the Planck length. This is often referred to as the Bekenstein–Hawking formula. The subscript BH either stands for "black hole" or "Bekenstein–Hawking". The black-hole entropy is proportional to the area of its event horizon ${\displaystyle A}$. The fact that the black-hole entropy is also the maximal entropy that can be obtained by the Bekenstein bound (wherein the Bekenstein bound becomes an equality) was the main observation that led to the holographic principle.[2] This area relationship was generalized to arbitrary regions via the Ryu-Takayanagi formula, which relates the entanglement entropy of a boundary conformal field theory to a specific surface in its dual gravitational theory.[9]
Although Hawking's calculations gave further thermodynamic evidence for black-hole entropy, until 1995 no one was able to make a controlled calculation of black-hole entropy based on statistical mechanics, which associates entropy with a large number of microstates. In fact, so called "no-hair" theorems[10] appeared to suggest that black holes could have only a single microstate. The situation changed in 1995 when Andrew Strominger and Cumrun Vafa calculated[11] the right Bekenstein–Hawking entropy of a supersymmetric black hole in string theory, using methods based on D-branes and string duality. Their calculation was followed by many similar computations of entropy of large classes of other extremal and near-extremal black holes, and the result always agreed with the Bekenstein–Hawking formula. However, for the Schwarzschild black hole, viewed as the most far-from-extremal black hole, the relationship between micro- and macrostates has not been characterized. Efforts to develop an adequate answer within the framework of string theory continue.
In loop quantum gravity (LQG)[nb 1] it is possible to associate a geometrical interpretation to the microstates: these are the quantum geometries of the horizon. LQG offers a geometric explanation of the finiteness of the entropy and of the proportionality of the area of the horizon.[12][13] It is possible to derive, from the covariant formulation of full quantum theory (spinfoam) the correct relation between energy and area (1st law), the Unruh temperature and the distribution that yields Hawking entropy.[14] The calculation makes use of the notion of dynamical horizon and is done for non-extremal black holes. There seems to be also discussed the calculation of Bekenstein–Hawking entropy from the point of view of LQG.
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2019-09-15 05:28:10
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http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-fmv155i1p1bwm
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## Fundamenta Mathematicae
1998 | 155 | 1 | 1-31
Tytuł artykułu
### Topological realization of a family of pseudoreflection groups
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EN
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EN
We are interested in a topological realization of a family of pseudoreflection groups $G ⊂ GL(n,{\sym F}_p )$; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants ${\sym F}_p [x_1,..., x_n]^G$. Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over ${\sym F}_p$ can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product $ℤ/q ≀Σ_n$ where q divides p - 1 and where p is odd. Let G be such a subgroup acting on the polynomial algebra $A:= {\sym F}_p [x_1,..., x_n]$. We show that there exists a space X such that $H*(X;{\sym F}_p )≅ A^G$ which is again a polynomial algebra. Examples of polynomial algebras of this form are given by the mod-p cohomology of the classifying spaces of special orthogonal groups or of symplectic groups.
The construction uses products of classifying spaces of unitary groups as building blocks which are glued together via information encoded in a full subcategory of the orbit category of the group G. Using this construction we also show that the homotopy type of the p-adic completion of these spaces is completely determined by the mod-p cohomology considered as an algebra over the Steenrod algebra. Moreover, we calculate the set of homotopy classes of self maps of the completed spaces.
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EN
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Czasopismo
Rocznik
Tom
Numer
Strony
1-31
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-01-24
poprawiono
1997-03-03
Twórcy
autor
Bibliografia
• [1] J. F. Adams and Z. Mahmud, Maps between classifying spaces, Invent. Math. 35 (1976), 1-41.
• [2] J. F. Adams and C. W. Wilkerson, Finite H-spaces and algebras over the Steenrod algebra, Ann. of Math. 111 (1980), 95-143.
• [3] J. Aguadé, Constructing modular classifying spaces, Israel J. Math. 66 (1989), 23-40.
• [4] J. Aguadé, C. Broto and D. Notbohm, Homotopy classification of some spaces with interesting cohomology and a conjecture of Cooke, Part I, Topology 33 (1994), 455-492.
• [5] A. Bousfield and D. Kan, Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer, 1972.
• [6] T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups, Springer, 1985.
• [7] H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press, 1956.
• [8] A. Clark and J. Ewing, The realization of polynomial algebras as cohomology rings, Pacific J. Math. 50 (1974), 425-434.
• [9] W. Dwyer and D. Kan, Centric maps and realization of diagrams in the homotopy category, Proc. Amer. Math. Soc. 114 (1992), 575-584.
• [10] W. Dwyer, H. Miller and C. Wilkerson, Homotopical uniqueness of classifying spaces, Topology 31 (1992), 29-45.
• [11] W. G. Dwyer and C. W. Wilkerson, A cohomology decomposition theorem, Topology 31 (1992), 433-443.
• [12] W. G. Dwyer and C. W. Wilkerson, A new finite loop space at the prime two, J. Amer. Math. Soc. 6 (1993), 37-63.
• [13] W. G. Dwyer and C. W. Wilkerson, Homotopy fixed point methods for Lie groups and finite loop spaces, Ann. of Math. 139 (1994), 395-442.
• [14] W. G. Dwyer and C. W. Wilkerson, The center of a p-compact group, in: The Čech Centennial (Boston, Mass., 1993), Contemp. Math. 181, Amer. Math. Soc., 1995, 119-157.
• [15] W. Dwyer and A. Zabrodsky, Maps between classifying spaces, in: Algebraic Topology (Barcelona, 1986), Lecture Notes in Math. 1298, Springer, 1987, 106-119.
• [16] P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory, Springer, 1967.
• [17] K. Ishiguro, Unstable Adams operations on classifying spaces, Math. Proc. Cambridge Philos. Soc. 102 (1987), 71-75.
• [18] S. Jackowski and J. McClure, Homotopy decomposition of classifying spaces via elementary abelian subgroups, Topology 31 (1992), 113-132.
• [19] S. Jackowski, J. McClure and B. Oliver, Homotopy classification of self-maps of BG via G-actions, Ann. of Math. 135 (1992), 183-270.
• [20] S. Jackowski, J. McClure and B. Oliver, Self homotopy equivalences of classifying spaces of compact connected Lie groups, Fund. Math. 147 (1995), 99-126.
• [21] S. Jackowski, J. McClure and B. Oliver, Homotopy of classifying spaces of compact Lie groups, in: Algebraic Topology and its Applications, Springer, 1994, 81-123.
• [22] S. Lang, Algebra, Addison-Wesley, 1965.
• [23] J. Lannes, Sur les espaces fonctionnels dont la source est le classifiant d'un p-groupe abélien élémentaire, Publ. Math. I.H.E.S. 75 (1992), 135-244.
• [24] H. Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. 120 (1984), 39-87.
• [25] J. M. Møller, Rational isomorphisms of p-compact groups, Topology 35 (1996), 201-225.
• [26] J. M. Møller and D. Notbohm, Centers and finite coverings of finite loop spaces, J. Reine Angew. Math. 456 (1994), 99-113.
• [27] J. M. Møller and D. Notbohm, Connected finite loop spaces with maximal tori, Math. Gott. Heft 14 (1994).
• [28] D. Notbohm, Maps between classifying spaces, Math. Z. 207 (1991), 153-168.
• [29] D. Notbohm, Homotopy uniqueness of classifying spaces of compact connected Lie groups at primes dividing the order of the Weyl group, Topology 33 (1994), 271-330.
• [30] B. Oliver, Higher limits via Steinberg representations, Comm. Algebra 22 (1994), 1381-1393.
• [31] D. Quillen, On the cohomology and K-theory of the general linear groups over a finite field, Ann. of Math. 96 (1972), 552-586.
• [32] G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canad. J. Math. 6 (1954), 274-304.
• [33] N. E. Steenrod, Polynomial algebras over the algebra of cohomology operations, in: H-spaces (Neuchâtel, 1970), Lecture Notes in Math. 196, Springer, 1971, 85-99.
• [34] Z. Wojtkowiak, On maps from holim F to Z, in: Algebraic Topology (Barcelona, 1986), Lecture Notes in Math. 1298, Springer, 1987, 227-236.
• [35] C. Xu, The existence and uniqueness of simply connected p-compact groups with Weyl groups W such that |W| is not divisible by the square of p, thesis, Purdue University, 1994.
• [36] A. Zabrodsky, On the realization of invariant subgroups of $π_*(X)$, Trans. Amer. Math. Soc. 285 (1984), 467-496.
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2020-07-03 14:10:53
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http://openstudy.com/updates/55a43c81e4b05bcb08a20807
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• anonymous
The equation V = -2000t + 20,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $14,000, find the age of the car. Algebra At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat. • anonymous The equation V = -2000t + 20,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth$14,000, find the age of the car.
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2017-03-24 10:45:42
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https://stats.stackexchange.com/questions/383973/hypotheses-check-with-mixed-anova-ancova-regression-or-multilevel-linear-model
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# Hypotheses check with mixed ANOVA, ANCOVA, regression or multilevel linear model?
I conducted a repeated-measures experiment and obtained for each subject the following data:
IV - continous (personality trait)
DV - continous, under condition 0 (default condition)
DV - same variable as above, but under condition 1
DV - same variable as above, but under condition 2
From theory, I have multiple hypotheses:
• The higher IV in a subject is, the higher is the change of DV between condition 1 and 0 (DV.1 - DV.0).
• The higher IV in a subject is, the higher is the change of DV between condition 2 and 0 (DV.2 - DV.0).
• DV under condition 2 is higher than under condition one for subjects with a high IV.
What is the recommended way to check those hypotheses?
1. First I thought about using a median split on IV to separate it in a low/high group so that IV is categorial, and hence a mixed ANOVA would work (dependent variable = DV, whitin = condition, between = IV). But doing a median split loses a lot of information and might lead to wrong conclusions, so I am not happy with this. Also, I get unequal group sizes which are problematic for mixed ANOVAs. Other than that ANOVA would be good, I could just use planned contrast to check my hypotheses.
2. Then I thought about using an ANCOVA, because an ANCOVA is an ANOVA with an added continous covariate (in this case IV), meaning IV does not have to be split artificially and can stay metric. The problem here is that if I understood it correctly the ANCOVA would partial out the effect of IV - which would not be acceptable, because I am mainly interested in the effect of IV on the DV under different conditions.
3. I then thought I just use a simple linear regression: lm(DV.1 ~ IV + DV.0), or lm(DV.1 - DV.0 ~ IV). With that I can check if I get a significant regression coefficient. But how do I know whether the difference between DV.1 and DV.0 is significant? Because if they are not, I have to reject my first hypothesis.
4. I also thought about using a multilevel linear models to model my problem and circumvent the problems that a mixed ANOVA can only have categorial independent variables. But I am not sure if that is even possible? I thought about using lme in R with subject as a random argument to account for the repeated measures design. Would that work?
As you probably can tell, I am new to the world of statistics, especially to hypothesis testing. I would appreciate it if you could help me choose the right kind of analysis method for my hypotheses!
Your explanation of your design is incorrect. You have just 1 DV (not 3) and 2 IVs (not 1). Your IVs are trait and condition. You also appear to have measured the same individual under multiple conditions, which suggests that you need a linear mixed-effects model with a random intercept (and possibly slope) for individual.
The simplest model that would be appropriate for this problem is (in lmer syntax ):
lmer(DV ~ trait + condition + (1|individual))
Of course, you may want to consider whether there could be interactions between trait and condition, and differences in how individuals respond to changes in condition
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2022-01-21 00:53:28
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https://particlesandfriends.wordpress.com/2016/08/26/particles-and-forces-a-brief-intro/
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# Particles and forces
Beyond the force that holds us back in bed in the morning, there are other four fundamental forces, in Nature.
At the present state of our knowledge, Nature is presented as the result of the composition of the four fundamental interactions (electromagnetic, weak, strong and gravitationalwith a set of elementary particles which can be classified according to how they interact with each other and with respect to these forces.
The Standard Model (SM) of Particle Physics is a theory aimed to describe the elementary constituents of matter and their interactions.
The theory has been soundly confirmed by a variety of direct and indirect measurements performed by several experiments, like those realized at $\textsf{Large Electron--Positron}$ collider ($\textsf{LEP}$), at the $\textsf{Standford Linear Collider}$ ($\textsf{SLC}$), at the $\textsf{Tevatron}$ and recently at $\textsf{Large Hadron Collider}$ ($\textsf{LHC}$).
The recent discovery to find the last missing piece of the SM, the Higgs boson, was announced at $\textsf{CERN}$ on $4^{th}$ of July 2012 and it completes the model prediction to give mass to the elementary particles.
Anyway, many theoretical limitations of the SM let physicists think that a more fundamental theory should exist. In fact, search for new phenomena beyond the SM constitutes the main goal of the experiments at $\textsf{LHC}$.
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2018-03-23 12:54:39
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https://www.semanticscholar.org/paper/Controllability-and-Stabilizability-of-the-System-Chowdhury-Ramaswamy/99febde78a9bd31536b779c0abab7159c19304d4
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# Controllability and Stabilizability of the Linearized Compressible Navier-Stokes System in One Dimension
@article{Chowdhury2012ControllabilityAS,
title={Controllability and Stabilizability of the Linearized Compressible Navier-Stokes System in One Dimension},
author={Shirshendu Chowdhury and Mythily Ramaswamy and J. P. Raymond},
journal={SIAM J. Control. Optim.},
year={2012},
volume={50},
pages={2959-2987}
}
• Published 2 October 2012
• Mathematics
• SIAM J. Control. Optim.
In this paper we consider the one-dimensional compressible Navier--Stokes system linearized about a constant steady state $(Q_0, 0)$ with $Q_0 > 0$. We study the controllability and stabilizability of this linearized system. We establish that the linearized system is null controllable for regular initial data by an interior control acting everywhere in the velocity equation. We prove that this result is sharp by showing that the null controllability cannot be achieved by a localized interior…
30 Citations
Some Controllability Results for Linearized Compressible Navier-Stokes System
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• 2022
. In this article, we study the boundary null-controllability properties of the one-dimensional linearized (around ( Q 0 ,V 0 ) with constants Q 0 > 0 ,V 0 > 0) compressible Navier–Stokes equations
Null controllability of the linearized compressible Navier–Stokes equations using moment method
• Mathematics
• 2015
In this paper, we consider one-dimensional compressible Navier–Stokes equations linearized around a constant steady state (Q0, V0), Q0 > 0, V0 > 0 with periodic boundary condition. We explore the
Local exact controllability for Navier-Stokes-Korteweg model in dimension $d\in\{2,3\}$
In this paper, we investigate the local null controllability for a compressible Navier-Stokes-Korteweg with quantum pressure in dimension d ∈ {2, 3}, when the control acts on the whole boundary of a
LARGEST SPACE FOR THE STABILIZABILITY OF THE LINEARIZED COMPRESSIBLE NAVIER-STOKES SYSTEM IN ONE DIMENSION
• Mathematics
• 2015
In this paper we determine the largest space in which the linearized compressible Navier-Stokes system in one dimension, with periodic boundary conditions, is stabilizable with any prescribed
Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations
• Mathematics
• 2018
In this article, we show a local exact boundary controllability result for the 1d isentropic compressible Navier Stokes equations around a smooth target trajectory. Our controllability result
Local exact controllability for the 1-d compressible Navier-Stokes equations
Let us emphasize that the boundary conditions do not appear in the equation (1.1), as frequently happens when controlling hyperbolic equations like the equation of the density. They will be used as
Local exact controllability for the 2 and 3-d compressible Navier-Stokes equations
• Mathematics
• 2015
The goal of this article is to present a local exact controllability result for the 2 and 3-dimensional compressible Navier-Stokes equations on a constant target trajectory when the controls act on
## References
SHOWING 1-10 OF 24 REFERENCES
On the Controllability of the Linearized Benjamin--Bona--Mahony Equation
• S. Micu
• Mathematics
SIAM J. Control. Optim.
• 2001
This work studies the boundary controllability properties of the linearized Benjamin--Bona--Mahony equation and proves a finite controllable result and estimates the norms of the controls needed in this case.
Boundary feedback stabilization of the two dimensional Navier-Stokes equations with finite dimensional controllers
• Mathematics
• 2010
We study the boundary stabilization of the two-dimensional Navier-Stokes equations about an unstable stationary solution by controls of finite dimension in feedback form. The main novelty is
Local Exact Controllability for the One-Dimensional Compressible Navier–Stokes Equation
• Mathematics
• 2012
In this paper we deal with the isentropic (compressible) Navier-Stokes equation in one space dimension and we adress the problem of the boundary controllability for this system. We prove that we can
Tangential boundary stabilization of Navier-Stokes equations
• Mathematics
• 2006
Introduction Main results Proof of Theorems 2.1 and 2.2 on the linearized system (2.4): $d=3$ Boundary feedback uniform stabilization of the linearized system (3.1.4) via an optimal control problem
Stabilization for the 3D Navier-Stokes system by feedback boundary control
We study the problem of stabilization a solution to 3D Navier-Stokes system given in a bounded domain $\Omega$. This stabilization is carried out with help of feedback control defined on a part
Local exact controllability of the Navier – Stokes system ✩
In this paper we deal with the local exact controllability of the Navier–Stokes system distributed controls s upported in small sets. In a first step, we present a new Carleman ineq for the
Optimal control of unsteady compressible viscous flows
• Engineering, Mathematics
• 2002
The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can
Some Controllability Results for Linear Viscoelastic Fluids
• Mathematics
SIAM J. Control. Optim.
• 2012
The large time approximate-finite dimensional controllability of the system, with distributed or boundary controls supported by arbitrary small sets, is established and the large time exact controllable of fluids of the same kind with controls support by suitable large sets is proved.
Boundary stabilizability of the linearized viscous Saint-Venant system
• Mathematics
• 2011
We consider a shallow water flow in a channel modeled by the Saint-Venant equations with a viscous term. We are interested in the stabilization of the flow at a steady state. We establish that the
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2022-07-04 11:24:01
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https://www.eduzip.com/ask/question/in-the-figure-160angle-xln100circ-angle-ymn165circ-160angle-znm95-520453
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Mathematics
# In the figure $\angle XLN=100^{\circ}$, $\angle YMN=165^{\circ}$, $\angle ZNM=95^{\circ}$ find the measures of $\angle MLN$.
80
##### SOLUTION
In the above figure $\angle MLN=180-\angle XLN$ ( Linear pair of angles)
$\angle MLN=180-100=80$
You're just one step away
Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87
#### Realted Questions
Q1 Single Correct Medium
Which of the following is obtuse angle?
• A. Two right angles
• B. One and half right angles
• C. One right angle
• D. Half a right angle
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q2 Single Correct Medium
If two supplementary angles are in the ratio $1:2$, then the bigger angle is
• A. $125^o$
• B. $110^o$
• C. $90^o$
• D. $120^o$
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q3 Single Correct Medium
In the figure given above, $PQ$ is parallel to $RS$. What is the angle between the lines $PQ$ and $LM$?
• A. $175^{\circ}$
• B. $177^{\circ}$
• C. $179^{\circ}$
• D. $180^{\circ}$
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q4 Single Correct Medium
If a line divides any two sides of a triangle in same ratio, then line must be ______ to third side.
• A. perpendicular
• B. not predictable
• C. imaginary
• D. parallel
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q5 Single Correct Medium
Find the measure of the complementary angle of $90^\circ$.
• A. $45^\circ$
• B. $90^\circ$
• C. $60^\circ$
• D. $0^\circ$
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
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2022-01-27 11:43:14
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https://bookdown.org/mike/data_analysis/linear-regression.html
|
Chapter 5 Linear Regression
Estimator Desirable Properties
1. Unbiased
2. Consistency
• $$plim\hat{\beta_n}=\beta$$
• based on the law of large numbers, we can derive consistency
• More observations means more precise, closer to the true value.
1. Efficiency
• Minimum variance in comparison to another estimator.
• OLS is BlUE (best linear unbiased estimator) means that OLS is the most efficient among the class of linear unbiased estimator Gauss-Markov Theorem
• If we have correct distributional assumptions, then the Maximum Likelihood is asymptotically efficient among consistent estimators.
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2021-06-16 21:06:52
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https://www.ncatlab.org/nlab/show/multiplicative+spectral+sequence
|
# nLab multiplicative spectral sequence
Contents
### Context
#### Homological algebra
homological algebra
Introduction
diagram chasing
### Theorems
#### Higher algebra
higher algebra
universal algebra
# Contents
## Idea
A spectral sequence is called multiplicative or a spectral ring if there is a bi-graded algebra structure on each page such that the differentials act as graded derivations of total degree 1.
For example the Serre-Atiyah-Hirzebruch spectral sequence with coefficients in a ring spectrum.
## Constructions
### From spectral products on Cartan-Eilenberg systems
The following gives sufficient conditions for a Cartan-Eilenberg spectral sequence to be multiplicative. This is due to (Douady 58). The following is taken from (Goette 15a).
###### Definition
Let $(H,\eta,\partial)$, $(H',\eta',\partial')$ und $(H'',\eta'',\partial'')$ be Cartan-Eilenberg systems. A spectral product $\mu\colon(H',\partial')\times(H'',\partial'')\to(H,\partial)$ is a sequence of homomorphisms
$\mu_r\colon H'(m,m+r)\otimes H''(n,n+r)\to H(m+n,m+n+r)$
such that for all $m$, $n$, $r\ge 1$, the following two diagrams commute:
$\array{ H'(m, m+r) \otimes H''(n, n+r) &\stackrel{\mu_r}{\longrightarrow}& H(m+n, m+n+r) \\ \downarrow^{\mathrlap{\eta' \oplus \eta''}} && \downarrow^{\mathrlap{\eta}} \\ H'(m, m+1) \otimes H''(n, n+1) &\stackrel{\mu_1}{\longrightarrow}& H(m+n, m+n+1) }$
and
$\array{ H'(m, m+r) \otimes H''(n, n+r) &\stackrel{\mu_r}{\longrightarrow}& H(m+n,m+n+r) \\ \downarrow^{\mathrlap{\partial' \otimes \eta'' \oplus \eta' \otimes \partial''}} && \downarrow^{\mathrlap{\partial}} \\ H'(m+r, m+r+1) \otimes H''(n,n+1) \\ \oplus &\stackrel{\mu_1 + \mu_1}{\longrightarrow}& H_{p+q-1}(m+n+r, m+n+r+1) \\ H'(m,m+1) \otimes H''(n+r, n+r+1) } \,.$
###### Remark
The first diagram in def. is weaker than in (Douady 58). The second may be read as a Leibniz rule.
Write $E$ for the Cartan-Eilenberg spectral sequence induced from the Cartan-Eilenberg system $H$.
###### Proposition
A spectral product $\mu\colon(H',\partial')\times(H'',\partial'')\to(H,\partial)$ as in def. induces products
$\mu^r\colon E^{\prime r}_m\otimes E^{\prime\prime r}_n\to E^r_{m+n}\;,$
such that
1. $\mu^1=\mu_1$
2. $d^r_{m+n}\circ\mu^r=\mu^r\circ(d^{\prime r}_m\otimes\mathrm{id})\pm\mu^r\circ(\mathrm{id}\circ d^{\prime\prime r}_n)$,
3. $\mu^{r+1}$ is induced by $\mu^r$.
(Goette 15a, following Douady 58, theorem II).
###### Proof
Assume by induction that $\mu^r$ is induced by $\mu_1$. In particular,
$Z^{\prime r}_m\otimes Z^{\prime\prime r}_n\stackrel{\mu_1}\to Z^r_{m+n}\;,$
$B^{\prime r}_m\otimes Z^{\prime\prime r}_n\stackrel{\mu_1}\to B^r_{m+n}\;,$
$Z^{\prime r}_m\otimes B^{\prime\prime r}_n\stackrel{\mu_1}\to B^r_{m+n}\;.$
This is clear for $r=1$ if we put $\mu^1=\mu_1$ because $E^1_p=Z^1_p=H(p,p+1)$ and $B^1_p=0$.
Let $[a]\in Z^{\prime r}_m$, $[b]\in Z^{\prime\prime r}_n$ be represented by $a=\eta'(a_0)\in H'(m,m+1)$, $b=\eta''(b_0)\in H''(n,n+1)$ with $a_0\in H'(m,m+r)$, $b_0\in H''(n,n+r)$. Using the first diagram and the construction of $d^r_{m+n}$, we conclude that
$(d^r_{m+n}\circ\mu^r)([a]\otimes[b])=d^r_{m+n}[\mu_1(a\otimes b)]=d^r_{m+n}[\eta(\mu_r(a_0\otimes b_0))]=(\partial\circ\mu_r)(a_0\otimes b_0) \;.$
From the second diagram, we get
$(\partial\circ\mu_r)(a_0\otimes b_0)=\mu_1(\partial'a_0\otimes\eta''b_0)\pm\mu_1(\eta'a_0\otimes\partial''b_0)=\mu^r(d^{\prime r}_m[a]\otimes[b])\pm\mu^r([a]\otimes d^{\prime\prime r}_n[b]) \;.$
This proves the Leibniz rule (2).
From the Leibniz rule and the facts that $\ker(d^r_p)=Z^{r+1}_p/B^r_p$ and $\mathrm{im}(d^r_p)=B^{r+1}_p/B^r_p$, we conclude that $\mu^r$ induces a product on $E^{r+1}_p\cong\ker(d^r_p)/\mathrm{im}(d^r_p)$, which proves (3). Because $\mu^r$ is induced by $\mu_1$, so is $\mu^{r+1}$, and we can continue the induction.
## Examples
### AHSS for multiplicative cohomology
We discuss that the multiplicative structure on the cohomology Serre-Atiyah-Hirzebruch spectral sequence for multiplicative generalized cohomology. This is taken from (Goette 15b).
###### Definition
For $\pi\colon X\to B$ a Serre fibration over a CW-complex $B$. And for $(\tilde h^\bullet,\delta,\wedge)$ a multiplicative reduced generalized (Eilenberg-Steenrod) cohomology theory, define a Cartan-Eilenberg system $(H,\eta,\partial)$ by
$H(p,q)=\tilde h^\bullet(X^{q-1}/X^{p-1})$
(where $X^k=\pi^{-1}(B^k)$) for $p\le q$ with the obvious maps $\eta\colon H(p',q')\to H(p,q)$ for $p\le p'$, $q\le q'$.
The Cartan-Eilenberg spectral sequence of this Cartan-Eilenberg system is the Serre-Atiyah-Hirzebruch spectral sequence.
###### Definition
The spectral product $\mu\colon(H,\eta,\partial)\times(H,\eta,\partial)\to(H,\eta,\partial)$, def. , on the Cartan-Eilenberg system of def. is that given by the following morphism
\begin{aligned} F_{m,n,r} & \colon (X\wedge X)^{m+n+r-1}/(X\wedge X)^{m+n-1} \cong \bigcup_{a+b=m+n+r-1}(X^a\wedge X^b) / \bigcup_{c+d=m+n-1}(X^c\wedge X^d) \\ & \twoheadrightarrow \bigcup_{a+b=m+n+r-1} (X^a\wedge X^b)/(\bigcup_{a=0}^m(X^{a-1}\wedge X^{m+n+r-a}) \cup\bigcup_{b=0}^n(X^{m+n+r-b}\wedge X^{b-1}) \\ & \cong \bigcup_{a=m+1}^{m+r}(X^{a-1}\wedge X^{m+n+r-a}) / \bigl(X^{m+r-1}\wedge X^{n-1}\cup X^{m-1}\wedge X^{n+r-1}\bigr) \\ & \hookrightarrow X^{m+r-1}\wedge X^{n+r-1}/(X^{m+r-1}\wedge X^{n-1}\cup X^{m-1}\wedge X^{n+r-1}) \\ & \cong (X^{m+r-1}/X^{m-1})\wedge(X^{n+r-1}/X^{n-1}) \;. \end{aligned}
Together with the diagonal map $\Delta$, for $r\ge 1$, we define
\begin{aligned} \mu_r & \colon H(m,m+r)\otimes H(n,n+r) \\ & \cong\tilde h(X^{m+r-1}/X^{m-1})\otimes\tilde h(X^{n+r-1}/X^{n-1}) \\ &\stackrel\wedge\longrightarrow\tilde h\bigl((X^{m+r-1}/X^{m-1})\wedge(X^{n+r-1}/X^{n-1})\bigr) \\ &\stackrel{F_{m,n,r}^*}\longrightarrow\tilde h\bigl((X\wedge X)^{m+n+r-1}/(X\wedge X)^{m+n-1}\bigr) \\ &\stackrel{\Delta_X^*}\longrightarrow\tilde h(X^{m+n+r-1}/X^{m+n-1})=H(m+n,m+n+r)\;. \end{aligned}
###### Proposition
With def. 3, then for all $m$, $n$, $r\ge 1$, the following [[commuting diagram|diagram commutes]]
$\array{ H(m,m+1) \otimes H(n,n+1) &\stackrel{\mu_1}{\longrightarrow}& H(m+n, m+n+1) \\ \uparrow^{\mathrlap{\eta \oplus \eta}} && \uparrow^{\mathrlap{\eta}} \\ H(m,m+r) \otimes H(n,n+r) &\stackrel{\mu_r}{\longrightarrow}& H(m+n,m+n+r) \\ \downarrow^{\mathrlap{\partial \otimes \eta \oplus \eta \otimes \partial}} && \downarrow^{\mathrlap{\partial}} \\ H(m+r, m+r+1) \otimes H(n,n+1) \\ \oplus &\stackrel{\mu_1 \pm \mu_1}{\longrightarrow}& H(m+n+r, m+n+r+1) \\ H(m,m+1) \otimes H(n+r, n+r+1) } \,.$
Hence by prop. 1 the spectral product of def. 3 defines a mutliplicative structure on the Serre-WhiteheadAtiyah-Hirzebruch spectral sequence for multiplicative generalizted cohomology.
###### Proof
The upper square commutes because the maps $F_{m,n,r}$ are [[natural transformations]]. For the lower square, we consider the boundary morphism $\delta$ of the triple
\begin{aligned} (& X^{m+r}\wedge X^{n+r-1}\cup X^{m+r-1}\wedge X^{n+r}, \\ & X^{m+r}\wedge X^{n-1}\cup X^{m+r-1}\wedge X^{n+r-1}\cup X^{m-1}\wedge X^{n+r}, \\ & X^{m+r}\wedge X^{n-1}\cup X^{m-1}\wedge X^{n+r}) \end{aligned} \;.
The following diagram commutes:
$\array{ \tilde h^{-p}(X^{m+r-1}/ X^{m-1}) \otimes \tilde h^{-q}(X^{n+r-1}/X^{n-1}) &\stackrel{\wedge}{\longrightarrow}& \tilde h^{-p-q}((X^{m+r-1}/X^{m-1}) \wedge (X^{n+r-1}/X^{n-1}) \\ \downarrow^{\mathrlap{\delta \wedge id \oplus id \wedge \delta}} && \downarrow^{\mathrlap{\delta}} \\ \tilde h(1-p)(X^{m+r}/X^{m+r-1}) \otimes \tilde h^{-q}(X^{n+r-1}/X^{n-1}) && \tilde h^{1-p-q}((X^{m+r}/X^{m+r-1}) \wedge (X^{n+r-1}/X^{n-1})) \\ \oplus &\stackrel{\wedge \oplus \wedge}{\longrightarrow}& \\ \tilde h^{-p}(X^{m+r-1}/X^{m-1}) \otimes \tilde h^{1-q}(X^{n+r}/X^{n+r-1}) && \tilde h^{1-p-q}( (X^{m+r-1}/ X^{m-1}) \wedge (X^{n+r}/ X^{n+r-1}) ) } \,.$
By extend this diagram to the right using the maps $F_{m,n,r}$ once concludes that the lower square above also commutes.
• [[multiplicative cohomology theory]]
## References
• [[Adrien Douady]], La suite spectrale d’Adams : structure multiplicative Séminaire Henri Cartan, 11 no. 2 (1958-1959), Exp. No. 19, 13 p (Numdam)
• Brayton Gray, Products in the Atiyah-Hirzebruch spectral sequence and the calculation of $M SO_\ast$, Trans. Amer. Math. Soc. 260 (1980), 475-483 (web)
• [[Stanley Kochmann]], prop. 4.2.9 of [[Bordism, Stable Homotopy and Adams Spectral Sequences]], AMS 1996
• [[John McCleary]], section 2.3 in A User’s Guide to Spectral Sequences, Cambridge University Press (2000)
• [[Daniel Dugger]], Multiplicative structures on homotopy spectral sequences I (arXiv:math/0305173)
• [[Daniel Dugger]], Multiplicative structures on homotopy spectral sequences II (arXiv:math/0305187)
• [[Sebastian Goette]], MO comment a, MO comment b Feb 15, 2015
[[!redirects multiplicative spectral sequences]]
Last revised on May 6, 2016 at 12:23:53. See the history of this page for a list of all contributions to it.
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2021-09-28 14:20:43
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http://clay6.com/qa/18302/let-omega-neq-1-be-a-cube-root-of-unity-and-s-be-the-set-of-all-non-singula
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# Let $\omega\neq 1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form $\begin{vmatrix}1&a&b\\\omega&1&c\\\omega^2&\omega&1\end{vmatrix}$ where each of a,b and c is either $\omega$ or $\omega^2$.Then the number of distinct matrices in the set S is
$(a)\;2\qquad(b)\;6\qquad(c)\;4\qquad(d)\;8$
For the given matrix to be non-singular $\begin{vmatrix}1 &a&b\\\omega&1&c\\\omega^2&\omega&1\end{vmatrix}\neq 0$
$\Rightarrow 1-(a+c)\omega+ac\omega^2\neq 0$
$\Rightarrow (1-a\omega)(1-c\omega)\neq 0$
$\Rightarrow a\neq \omega^2$ and $c\neq \omega^2$
Where $\omega$ is complex cube root of unity.
As $a,b$ and $c$ are complex cube root of unity.
$\therefore a$ and $c$ can take 2 values (i.e) $\omega$ and $\omega^2$
$\therefore$ Total number of distinct matrices=$1\times 1\times 2$
$\Rightarrow 2$
Hence (a) is the correct answer.
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2017-08-24 10:41:03
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http://mathhelpforum.com/calculus/120152-rate-problem-separation-variables.html
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# Math Help - rate problem with separation of variables
1. ## rate problem with separation of variables
The rate at which a substance dissolves in a solution is proportional to the amount of the substance that is present. Thirty grams of sodium chloride are put in a litre of water , and is found that 1 hr later only 10g are left. How much will be left after 30min?
i have no idea how to do this!
2. Originally Posted by shawli
The rate at which a substance dissolves in a solution is proportional to the amount of the substance that is present. Thirty grams of sodium chloride are put in a litre of water , and is found that 1 hr later only 10g are left. How much will be left after 30min?
i have no idea how to do this!
The rate of change of the substance is porportional to the amount of the substance. The instantanous rate of change in the derivitive. $N'=\alphaN$Use this to work out what the feunction for N is. Then input your numbers.
3. Originally Posted by shawli
The rate at which a substance dissolves in a solution is proportional to the amount of the substance that is present. Thirty grams of sodium chloride are put in a litre of water , and is found that 1 hr later only 10g are left. How much will be left after 30min?
i have no idea how to do this!
The rate of change of the substance is proportional to the amount of the substance. The instantaneous rate of change in the derivative. $N' =\alpha N$Use this to work out what the function for N is. Then input your numbers.
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2015-12-02 04:16:03
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https://mathematica.stackexchange.com/questions/189448/find-and-number-sublists
|
# Find and number sublists
I implemented the following routine.
array1 = {12, -12, 14, 12, 1, -3, 1, 1, 2, 7, 8, 102, 2, 3, 3, 1, 332,
11, 23, 2, -2, 13, 12, 1, 1, 1, 1, 1, 1, -121, 131};
I want to find sublists which consist of consecutive numbers which absolute values are smaller than a certain treshold (Lim=5). I also want to have a parameter for the length of the sublists (Len=3).
Module[{Ar, Pos, Lim, Len},
Ar = #;
Lim = 5;
Len = 3;
Position[Ar, x_ /; Abs[x] < Lim] // Flatten[#] & // Set[Pos, #] &;
Select[Split[Pos, #2 - #1 == 1 &], Length[#] > Len &]
] &[array1] // Set[PosInt, #] &;
Now I have the positions of the sublists.
PosInt // Print;
{{5,6,7,8,9},{13,14,15,16},{24,25,26,27,28,29}}
The next thing I would like to have is an array which includes the number and the position of the sublists. I have the following solution.
array2 = ConstantArray[0, Length@array1];
Module[{IntNum, Num, Pos},
Pos = #;
MapIndexed[(
IntNum = First@#2;
Num = #1;
Map[(array2[[#]] = IntNum
) &, Num];
) &, Pos]
] &[PosInt];
The desired result is saved as array2.
array2 // Print;
{0,0,0,0,1,1,1,1,1,0,0,0,2,2,2,2,0,0,0,0,0,0,0,3,3,3,3,3,3,0,0}
My implementation yields the right result. Nevertheless I'm sure it is possible to find a more elegant solution. Do you have any suggestions?
• Are you aware that in Mathematica expression standing by itself on a line at top-level is essentially the same as expression // Print;? – m_goldberg Jan 14 '19 at 8:12
• @m_goldberg Thx for your comment. You are right, that's superfluous. – RMMA Jan 14 '19 at 8:18
• But the first position smaller than 5 is for -12 which is 2 right then why it starts with 5 in the position list {5,6,7,8,9} – Hubble07 Jan 14 '19 at 9:32
• @Hubble07 Thank you! The absolute Number Abs[] has to be smaller. I did edit the question. – RMMA Jan 14 '19 at 9:40
• One more doubt. What about position 20 and 21. I mean what if the after taking absolute value we get two same numbers. – Hubble07 Jan 14 '19 at 9:45
Here is the CompiledFunction that I use; It goes linearly through the list and collects starting and ending index of each run in a InternalBag.
cf = Compile[{{a, _Integer, 1}, {Lim, _Integer}, {Len, _Integer}},
Block[{c, bag, x, α},
α = 0;
c = 0;
bag = InternalBag[Most[{0}]];
Do[
x = CompileGetElement[a, i];
If[Abs[x] < Lim,
If[c == 0, α = i;];
c++;
,
If[c > Len,
InternalStuffBag[bag, α];
InternalStuffBag[bag, i - 1];
];
c = 0;
],
{i, 1, Length[a]}];
Partition[InternalBagPart[bag, All], 2]
],
CompilationTarget -> "C",
RuntimeOptions -> "Speed"
];
Here is your method in a (IMHO) more legible form:
f = {a, Lim, Len} \[Function] Select[
Split[Flatten[Position[a, x_ /; Abs[x] < Lim]], #2 - #1 == 1 &],
Length[#] > Len &
];
Let's create a large array of pseudorandom integers and run the two functions on it:
a = RandomInteger[{-10, 10}, {1000000}];
PosInt = f[a, Lim, Len]; // AbsoluteTiming // First
PosInt2 = cf[a, Lim, Len]; // RepeatedTiming // First
The output of cf is slightly different from that of f; it returns only the first and last position index of each desired sublist. So we can compare the results in either of the two follwoing ways:
PosInt[[All, {1, -1}]] == PosInt2
PosInt == Range @@@ PosInt2
True
True
• Thank you for your answer. Until now I didn't use CompiledFunction at all. Maybe I should start using, your impelementation of AppendTo is very useful as well. – RMMA Jan 14 '19 at 13:05
• You're welcome. – Henrik Schumacher Jan 14 '19 at 13:35
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2021-01-18 04:21:47
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http://heimatstube-werda.de/online-casino/expected-value-probability-formula.php
|
# Expected value probability formula
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### Expected value probability formula Video
How to find an Expected Value
### Expected value probability formula - US-Sender, die
The minimum rate of return on a project or investment required by a manager or investor. B6 into the cell where A2: By Stephanie August 27, Binomial Distribution 10 Comments. Because you are rolling one die, there are only six possible outcomes on any one roll. Hat zum Beispiel eine Serie von zehn Würfelversuchen die Ergebnisse 4, 2, 1, 3, 6, 3, 3, 1, 4, 5 geliefert, kann der zugehörige Mittelwert. Set this number aside for a moment.
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2018-07-22 08:38:20
|
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|
https://brilliant.org/problems/tricky-dot-product-2/
|
# Tricky dot product 2
Geometry Level 1
True or False?
If $\vec{a}$ and $\vec{b}$ are vectors such that $\vec{a} \cdot \vec{b} = 1$, then $\vec{a}$ and $\vec{b}$ must be parallel.
×
|
2020-06-02 11:44:30
|
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http://mrwhatis.net/what-is-the-exact-area-of-a-circle-with-a-diameter-of-23-inches-.html
|
Search What is?:
# WHAT IS THE EXACT AREA OF A CIRCLE WITH A DIAMETER OF 23 INCHES ?
What is the exact area of a circle with a diameter of 15 inches? 176.714586764 square inches. What is the area of a circle with a diameter of 23?
http://wiki.answers.com/Q/What_is_the_exact_area_of_a_circle_with_a_diameter_of_23_inches
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What is the exact circumference of a circle with a diameter of 23 inches? (Points : 5) 72.3...
https://answers.yahoo.com/question/index?qid=20110317180416AACa7Ax
Question 311526: What is the exact circumference of a circle with a diameter of 23 inches? (a) 72.3p inches (b) 11.5p inches (c) 23p inches
http://www.algebra.com/algebra/homework/Angles/Angles.faq.question.311526.html
SOLUTION: What is the exact area of a circle with a diameter of 19 inches? (a) {{{9.5pi}}} square inches (b) {{{19pi}}} square inches (c) {{{38pi}}} square inch
http://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.311541.html
What is the exact circumference of a circle with a diameter of 23 inches? ? asked 2 years ago; please show me steps,, ... 23 x ~3.14 ~72.22 inches But, to be exact you would have to say "23(pi) ... Circle circumference question? Someone whos good with circles, ...
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What is the exact area of a circle with a diameter of 23 inches? Area of a circle = (pi) R2 R = radius = 1/2 diameter = 11.5 inches Area = (pi) ... What is the exact area of a circle with a diameter of 14 inches? 153.9384 sq inches What is the area of a circle if it has a diameter of 1.5?
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The circumference of a circle with diameter. Ask a Question Q&A Articles theKnow Science; Alternative Archaeology Astronomy Biological Sciences ... the exact circumference is. 11pi inches. ... Your answer is quite close, I got 116,23. Are you sure you shouldn't calculate the area, not the ...
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What is the exact circumference of a circle with a diameter of 23 inches? (Points : 5)? ... If the diameter of a circle is 5 inches what is the circumference? What is the exact circumference of a circle with a diameter of 27 inches? Discover Questions. What is this thing? Trig doubt?
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What is the area of a circle that has a diameter of 11 inches round to nearest hundredth
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Circumference of a circle = Diameter * Pi Therefore; the EXACT circumference of your circle is: 23 * Pi inches. . . . . an approximation can be made if you assume Pi = 3.14
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... what is the circumference of the circle? 34.54 and the area 95.03 on the circle. Ask; Answer; Leaderboard; Top; Recent; Popular; Categories; ... You're reading If the diameter of a circle is 11 inches; what is the circumference of the circle? Follow us on Facebook! Related Ads ...
http://www.answerbag.com/q_view/1751418
Obtain the area of the given circle. Write the exact area and the approximate area to the nearest square unit. ... 23 . Compute the circumference of a circle with diameter 7 cm. Problem: ... A pizza has a diameter of 18 inches.
http://hotmath.com/help/gt/genericprealg/section_9_3.html
Circumference of a circle explained with examples, ... (circumference) because the diameter of a circle =2• radius. So you can use whichever formula is more convenient. ... Problem 6) A circle's circumference is $$22\pi \text{ inches}$$.
http://www.mathwarehouse.com/geometry/circle/circumference-of-circle.php
What is the exact circumference of a circle with a diameter of 21 inches? 2. ... 65.97345 inches Compliments from. Comments (3) ... What is the area and the circumference of a circle with a diameter of 8 yards? Do not round the answ. From jenn8968 in other. 3
http://www.askpedia.com/q/2F96D/What_is_the_exact_circumference_of_a_circle_with_a_diameter_of_21_inches
Instructions of how to calculate area of a circle knowing the radius. Mathematical formula ... Important thing to notice though is that exact calculation is not possible as it is impossible to find out the ... The diameter is a line that connects two points of a circle and passes ...
http://www.areaofacircle.info/
Exercise 2: The circumference of a circle equals 10 meters. How long is the diameter of that circle? Solution: Solving this exercise requires to turn the equation around as the circumference is the known factor while the diameter is the unknown we need to find.
http://www.areaofacircle.info/circumference-of-a-circle.html
diameter The circumference of a circle is measured in linear units, not square units. W a t c h O u t! diameter d d d d. ... The circumference of a circle is 22 inches. ... 23. Challenge How fast ...
http://www.gaston.k12.nc.us/schools/cramerton/faculty/kllasky/Course%20Outline%20and%20Syllabus/Textbook/Ch%2011/Text%2011.6%20Circumference%20of%20Circle.pdf
To estimate the area of the circle, ... the error in finding the area of a circle with a diameter of 4 inches. 9. Calendars The surface of the Aztec calendar stone is a circle 12 feet in diameter. ... 23. C 9.42 in. 24. C 37.68 cm 25. C 21.98 yd 26.
http://www.gaston.k12.nc.us/schools/cramerton/faculty/kllasky/Course%20Outline%20and%20Syllabus/Textbook/Ch%2011/Text%2011.7%20Area%20of%20Circle.pdf
Enter the radius, diameter, circumference or area of a Circle to find the other three. The calculations are done "live": How to Calculate the Area.
http://www.mathsisfun.com/geometry/circle-area.html
What is the exact circumference of a circle with a diameter of 23 inches? (Points : 5) 72.3π inches 11.5π inches 23π inches 46π inches
http://ca.answers.yahoo.com/question/index?qid=20110317180416AACa7Ax
what is the exact circumference of a circle with a diameter of 37 inches Click here to find answers. Its Free & Simple, 100s of community experts will answer your questions.
http://www.akaqa.com/question/q1919104543-What_Is_The_Exact_Circumference_Of_A_Circle_With_A_Diameter_Of_37_Inches?page=1
... or just solving a math problem for school, knowing how to find the circumference of a circle will come in handy in a ... Write down the formula for finding the circumference of a circle using the diameter. ... The radius of the pie is 5 inches. To find the circumference that ...
http://www.wikihow.com/Calculate-the-Circumference-of-a-Circle
Solve area, diameter, and circumference, circle equations. | Home | Search | FAQ | Message Forum | What's New | Contact Us | Welcome to OnlineConversion.com Circle Solver Calculator Enter the circle area ...
http://www.onlineconversion.com/circlesolve.htm
Be sure to lookup exact wiper blade part numbers by vehicle make, ... Area of a circle = (1/2 x diameter) 2 x pi Area of a 24 inch diameter circle: (12 inches) ...
http://www.answers.com/mt/24-inch
The diameter of a circle is 14 inches. Find the area of the circle to the ... Critical ThinkingHow is finding the diameter of a circle when given its area different from finding the radius when given its area? ... circle. Round to the nearest whole number. 23. A 254 m2 24. A 615 cm2 25. A 1109 ...
http://www.lemars.k12.ia.us/webfiles/mboyd/Pre-Algebra%20Textbook%20(e-edition)/Source/J9C10DBD.pdf
convert 8 inch diameter into square inches convert 6 inch diameter into square inches. dvangossen . Top. Re: ... Here are the formulas for determining the area of a circle when you have either the radius or the diameter: PI * Radius^2 or PI/4 * Diameter^2 I'll do the first circle.
http://www.convert-me.com/en/bb/viewtopic.php?t=6641
A circle has a diameter of inches (in.). ... Find the area of a circle whose diameter is 4.8 centimeters (cm). Remember that the formula refers to the radius. ... 23. 24. 25. 26. Solve the following applications. 27. Jogging.
http://mhhe.com/math/devmath/streeter/bms/graphics/streeter5bms/ch04/others/strB_4.4.pdf
Center of a Circle - the point inside the circle that is the same exact distance from every point on the circle's ... If the circumference of a circle is 6.28 inches, the diameter is 6.28 inches / 3 ... Here's an example of how to find the diameter of a circle if the circle's area is given:
http://www.brighthubeducation.com/homework-math-help/101920-how-to-find-the-diameter-of-a-circle/
I'm not sure of the exact range but some US battleships could fire a shell 23 miles. ... Area of a 12-inch circle: 113.1 square inches. Area of a 16-inch circle: ... Area of a circle = pi R 2 R = radius = 1/2 diameter. For diameter = 16 inches, Area = pi (8) 2 = 64 pi = 201.1 square inches ...
http://www.answers.com/mt/16-inch
Area of a circle, formula for area explained with examples, pictures, interactive examples and quiz. ... A circle has a diameter of 12 inches. Calculate its area. (Need a hint) . Answer = = Problem 6 If a circle's radius is doubled, then how much did its area ...
http://www.mathwarehouse.com/geometry/circle/area-of-circle.php
Find the exact circumference of a circle with the ... Circumference = 2 x pi x radius = pi x diameter where pi = 3.1416 Diameter = circumference / pi = 36/3.1416 = 11.46 ... Find the exact circumference of a circle with the given radius. 3¼ inches Weegy: C = 2 * p * r C = 2 * p * 3 ...
http://www.weegy.com/?ConversationId=HAF8P5ZR
The above example will clearly illustrates how to calculate the Area, Diameter and Circumference of a Circle, Area of Sector manually. Related Calculator: >> Circle Calculator. This tutorial will help you dynamically to find the Math area problems.
http://www.easycalculation.com/area/learn-circle.php
Answer: The circumference of the circle is 10 π ≈ 31.42 inches. This video will explore the relationship between the radius, diameter and circumference of a circle.
http://www.onlinemathlearning.com/circles.html
Add this diagram to your notes diameter radius c i r c u m f e r e n c e What do you notice? 3 inches 6 inches What do you notice? 12 inches 24 inches What do you ... Ratio of a circle circumference = π diameter Mathematical Pi I ... It is impossible to calculate the exact value of ...
http://www.orland135.org/userfiles/file/mreeves/Math/Circumference%20of%20a%20Circle%20school.ppt
This quiz was created to demonstrate understanding of finding the radius, diameter, and circumference of a circle.
http://www.proprofs.com/quiz-school/story.php?title=finding-circumference-diameter--circle
Edit Article How to Calculate the Area of a Circle. Calculate Area Examples Sample Calculator Area of the Circle Finding the Area of a Sector Special circles Measuring the Diameter of Round Physical Objects
http://www.wikihow.com/Calculate-the-Area-of-a-Circle
Date: 02/20/2002 at 12:33:05 From: Doctor Ian Subject: Re: Finding the Area of a circle with a radius less than 1 Hi Kelly, I ... (22/7)(1/2 in)(1/2 in) = 11/14 in^2 which is about 0.785 in^2. The exact conversion between inches and cm is 1 in = 2.54 cm, so when we use cm as the units ...
http://mathforum.org/library/drmath/view/55433.html
... and diameter of 8 inch pizza i.e. its diameter is eight inches. The diameter of a circle is twice as long as the radius and this ... O- is the exact middle of a circle. Diameter: ... • the number is the ratio of the circumference of a circle to the diameter.
http://winpossible.com/lessons/Geometry_Circumference_of_a_Circle.html
If you didn't find what you were looking for you can always try Google Search
Add this page to your blog, web, or forum. This will help people know what is WHAT IS THE EXACT AREA OF A CIRCLE WITH A DIAMETER OF 23 INCHES
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2014-04-23 22:12:14
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https://brilliant.org/problems/limits-dilemma/
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# Limit's Dilemma
Calculus Level 3
$\large \lim_{x\to0} (1+ax+bx^2)^\frac 2x = e^3$
If the equation above holds true for constants $a$ and $b$, which of the following options must be true?
Notation: $\mathbb R$ denotes the set of all real values.
×
Problem Loading...
Note Loading...
Set Loading...
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2020-11-24 12:40:40
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https://habr.com/en/company/reactos/blog/439580/?mobile=no
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# Making Git for Windows work in ReactOS
Good day to you!
My name is Stanislav and I like to write code. This is my first english article on Habr which I made due to several reasons:
This article is an english version of my very first article on russian.
Let me introduce the main figures in this story who actually fixed the bug preventing Git from running in ReactOS — the French developer Hermès Bélusca-Maïto (or just Hermes with hbelusca nickname) and of course me (with x86corez nickname).
The story begins with the following messages from the ReactOS Development IRC channel:
Jun 03 18:52:56 <hbelusca> Anybody want to work on some small problem? If so, can someone figure out why this problem https://jira.reactos.org/browse/CORE-12931 happens on ReactOS? :D
Jun 03 18:53:13 <hbelusca> That would help having a good ROS self-hosting system with git support.
Jun 03 18:53:34 <hbelusca> (the git assertion part only).
## Debriefing
Since ReactOS target platform is Windows Server 2003, Git version 2.10.0 was chosen for the investigation — it's the last one supporting Windows XP and 2003.
Testing was done in the ReactOS Command Prompt, external symptoms of the problem were rather ambiguous. For instance, when you run git without additional parameters, it displays the help message in the console without any problems. But once you try git clone or even just git --version in most cases the console just remains empty. Occasionally it displayed a broken message with an assertion:
git.exe clone -v "https://github.com/minoca/os.git" "C:\Documents and Settings\Administrator\Bureau\minocaos"
A s s e r t i o n f a i l e d !
P r o g r a m : C : \ P r o g r a m F i l e s \ G i t \ m i n g w 3 2 \ b i n \ g i t . e x e
F i l e : e x e c _ c m d . c , L i n e 2 3
E x p r e s s i o n : a r g v 0 _ p a t h
This application has requested the Runtime to terminate in an unusual way.
Please contact the application's support team for more information.
Fortunately git is an open source project, and it helped a lot in our investigation. It was not too hard to locate the actual code block where unhandled exception happened: https://github.com/git-for-windows/git/blob/4cde6287b84b8f4c5ccb4062617851a2f3d7fc78/exec_cmd.c#L23
char *system_path(const char *path)
{
/* snip */
#ifdef RUNTIME_PREFIX
assert(argv0_path); // it asserts here
assert(is_absolute_path(argv0_path));
/* snip */
#endif
strbuf_addf(&d, "%s/%s", prefix, path);
return strbuf_detach(&d, NULL);
}
And argv0_path variable value is assigned by this code:
const char *git_extract_argv0_path(const char *argv0)
{
const char *slash;
if (!argv0 || !*argv0)
return NULL;
slash = find_last_dir_sep(argv0);
if (slash) {
argv0_path = xstrndup(argv0, slash - argv0);
return slash + 1;
}
return argv0;
}
Once I obtained all this information I've sent some messages to the IRC channel:
Jun 03 19:04:36 <x86corez> hbelusca: https://github.com/git-for-windows/git/blob/4cde6287b84b8f4c5ccb4062617851a2f3d7fc78/exec_cmd.c#L23
Jun 03 19:04:41 <x86corez> assertion is here
Jun 03 19:04:57 <hbelusca> yes I know, I've seen the code yesterday. The question is why it's FALSE on ROS but TRUE on Windows.
Jun 03 19:06:02 <x86corez> argv0_path = xstrndup(argv0, slash - argv0);
Jun 03 19:06:22 <x86corez> xstrndup returns NULL %-)
Jun 03 19:06:44 <hbelusca> ok, so what's the values of argv0 and slash on windows vs. on ROS? :P
Jun 03 19:08:48 <x86corez> good question!
The variable name suggests that the actual value is derived from argv[0] — usually it contains the executable name in zero index. But subsequently everything was not so obvious...
Jun 03 20:15:21 <x86corez> hbelusca: surprise... git uses its own xstrndup implementation
Jun 03 20:15:35 <x86corez> so I can't simply hook it xD
Jun 03 20:15:56 <hbelusca> well, with such a name "xstrndup" it's not surprising it's its own implementation
Jun 03 20:16:04 <x86corez> probably I would need an user-mode debugger... like OllyDbg
Jun 03 20:16:09 <hbelusca> that's everything but standardized function.
Jun 03 20:16:24 <hbelusca> x86corez: ollydbg should work on ROS.
Jun 03 20:16:30 <mjansen> what are you breaking today?
Jun 03 20:16:44 <x86corez> mjansen: https://jira.reactos.org/browse/CORE-12931
Jun 03 20:16:51 <hbelusca> (of course if you also are able to compile that git with symbols and all the stuff, it would be very nice)
## Action
After that I decided to compile git straight from the source, so I'll be able to print variables of the interest "on the fly" directly to the console. I've followed this step-by-step tutorial and in order to compile compatible git version I've selected this branch: https://github.com/git-for-windows/git/tree/v2.10.0-rc2
Setting up mingw32 toolchain went smoothly and I just started building. However almost always there are undocumented pitfalls in such step-by-step tutorials, and I immediately encountered one of them:
Through trial and error, as well as using hints from the hall (IRC channel), all compile time errors were fixed. If somebody wants to follow my steps, here is the diff to make compiler happy: https://pastebin.com/ZiA9MaKt
In order to avoid calling multiple functions during initialization and to reproduce the bug easily, I decided to put several debug prints right in the beginning of the main() function, which is located in common-main.c in the case of git:
int main(int argc, const char **argv)
{
/*
* Always open file descriptors 0/1/2 to avoid clobbering files
* in die(). It also avoids messing up when the pipes are dup'ed
* onto stdin/stdout/stderr in the child processes we spawn.
*/
//DebugBreak();
printf("sanitize_stdfds(); 1\n");
sanitize_stdfds();
printf("git_setup_gettext(); 1\n");
git_setup_gettext();
/*
* Always open file descriptors 0/1/2 to avoid clobbering files
* in die(). It also avoids messing up when the pipes are dup'ed
* onto stdin/stdout/stderr in the child processes we spawn.
*/
printf("sanitize_stdfds(); 2\n");
sanitize_stdfds();
printf("git_setup_gettext(); 2\n");
git_setup_gettext();
printf("before argv[0] = %s\n", argv[0]);
argv[0] = git_extract_argv0_path(argv[0]);
printf("after argv[0] = %s\n", argv[0]);
restore_sigpipe_to_default();
printf("restore_sigpipe_to_default(); done\n");
return cmd_main(argc, argv);
}
I've got the following output:
C:\>git --version
sanitize_stdfds(); 1
git_setup_gettext(); 1
sanitize_stdfds(); 2
git_setup_gettext(); 2
before argv[0] = git
after argv[0] = git
restore_sigpipe_to_default(); done
A s s e r t i o n f a i l e d !
(cutted a part of error message which is the same as the one above)
One can assume everything is fine here, argv[0] value is correct. I've got an idea to run git inside the debugger, OllyDbg for example, but something went wrong...
Jun 04 01:54:46 <sanchaez> now please try gdb/ollydbg in ROS
Jun 04 01:58:11 <sanchaez> you have gdb in RosBE
Jun 04 01:58:20 <sanchaez> just in case :p
Jun 04 01:59:45 <x86corez> ollydbg says "nope" with MEMORY_MANAGEMENT bsod
Jun 04 02:00:07 <x86corez> !bc 0x0000001A
Jun 04 02:00:08 <hTechBot> KeBugCheck( MEMORY_MANAGEMENT );
Jun 04 02:00:13 <hbelusca> :/
Jun 04 02:00:49 <sanchaez> welp
Jun 04 02:00:56 <sanchaez> you only have one option now :D
And right here sanchaez suggested an excellent idea that shed light on many things!
Assertion no longer occurred, and git successfully printed its version.
Jun 04 02:23:40 <x86corez> it prints!
Jun 04 02:23:44 <x86corez> but only in gdb
Jun 04 02:23:53 <hbelusca> oh
Jun 04 02:24:00 <hbelusca> C:\git/git.exe
Jun 04 02:24:13 <hbelusca> I wonder whether it's the same in windows, or not.
The case moved from the dead center, and I tried different ways to run git in the command prompt, and found the right way!
The problem was clearly that git expected the full path on the command line. So I compared its debug output on Windows. The results surprised me a bit.
For some reason argv[0] value contained the full path to the git.exe binary.
Jun 05 23:01:44 <hbelusca> x86corez: can you try to run git also by not using cmd.exe?
Jun 05 23:02:05 <hbelusca> (to exclude the possibility it's cmd that doesn't call Createprocess with a complete path)
Jun 05 23:02:09 <hbelusca> while I think it should...
Jun 05 23:02:30 <x86corez> not using cmd... moment
Jun 05 23:02:55 <hbelusca> x86corez: alternatively, on windows, try starting git using our own cmd.exe :)
Hermes suggested to check whether ReactOS cmd.exe is a guilty component here...
But this screenshot confirmed that the actual problem is somewhere else.
Jun 05 23:04:38 <x86corez> ROS cmd is not guilty
Jun 05 23:07:57 <hbelusca> If there was a possibility to consult the received path, before looking at the contents of argvs... ?
Jun 05 23:08:30 <x86corez> dump contents of actual command line?
Jun 05 23:08:39 <hbelusca> yeah
Jun 05 23:09:39 <hbelusca> The thing you retrieve using GetCommandLineW
Jun 05 23:10:03 <hbelusca> (which is, after simplifications, basically : NtCurrentPeb()->ProcessParameters->CommandLine )
Jun 05 23:10:59 <hbelusca> Also I was thinking it could be a side-effect of having (or not having) git path into the env-vars....
Jun 05 23:12:17 <x86corez> hbelusca, command line is "git --version"
Jun 05 23:12:34 <hbelusca> Always?
Jun 05 23:12:39 <x86corez> Yes, even on Windows
Jun 05 23:15:13 <hbelusca> ok but then it would be nice if these different results are at least the same on Windows and on ROS, so that we can 100% exclude problems outside of msvcrt.
The last option was to test ReactOS msvcrt.dll in Windows. I tried to place the file in the same directory where git.exe is located, but it didn't help. Mark suggested to add an .local file:
Jun 05 22:59:01 <mjansen> x86corez: add .local file next to msvcrt.dll ;)
Jun 05 22:59:47 <mjansen> exename.exe.local
Jun 05 23:00:17 <x86corez> just an empty file?
Jun 05 23:00:21 <mjansen> yea
Jun 05 23:00:49 <hbelusca> mjansen: do we support these .local files?
Jun 05 23:00:52 <mjansen> we dont
Jun 05 23:00:54 <mjansen> windows does
Jun 05 23:15:48 <x86corez> moment... I'll try with .local
Jun 05 23:18:43 <x86corez> mjansen: I've created git.exe.local but it still doesn't load msvcrt.dll in this directory
But for some reason this method did not work either. Perhaps the fact that I did all the experiments on the server edition of Windows (2008 R2).
The last idea was suggested by Hermes:
Jun 05 23:19:28 <hbelusca> last solution: patch "msvcrt" name within git and perhaps other mingwe dlls ^^
Jun 05 23:20:12 <x86corez> good idea about patching!
So I replaced all occurrences of msvcrt in git.exe with msvcrd using WinHex, and renamed ReactOS msvcrt.dll accordingly, and here we are:
Jun 05 23:23:29 <x86corez> Yes! guilty is msvcrt :)
Jun 05 23:25:37 <hbelusca> ah, so as soon as git uses our msvcrt we get the problem on windows.
Jun 05 23:25:38 <x86corez> hbelusca, mjansen, https://image.prntscr.com/image/FoOWnrQ4SOGMD-66DLW16Q.png
Jun 05 23:25:58 <hbelusca> aha and it asserts <3
Jun 05 23:26:03 <hbelusca> (it shows the assertion now)
bug becameNow we hit the same assertion, but in Windows! And that means the source of our problems is in the one of ReactOS msvcrt functions.
It's also worth to note that the assertion message is displayed correctly in Windows.
Jun 05 23:26:13 <x86corez> but it prints text and correctly.
Jun 05 23:26:20 <hbelusca> oh
Jun 05 23:26:33 <x86corez> and on ROS it doesn't print in most cases xD
Jun 05 23:26:38 <hbelusca> so also it excludes another hypothesis, namely that it could have been a bug in our msvcrt/crt
Jun 05 23:26:56 <hbelusca> So possibly a strange bug in our console
So, to solve the actual problem, we had to find the API function in msvcrt which gives the full path of the current application. I googled a bit and assumed the problem is with _pgmptr function.
Jun 06 00:07:43 <x86corez> https://msdn.microsoft.com/en-us/library/tza1y5f7.aspx
Jun 06 00:07:57 <x86corez> When a program is run from the command interpreter (Cmd.exe), _pgmptr is automatically initialized to the full path of the executable file.
Jun 06 00:08:01 <x86corez> this ^^)
Jun 06 00:08:50 <hbelusca> That's what GetModuleFileName does.
Jun 06 00:09:04 <x86corez> yeah
Jun 06 00:10:30 <hbelusca> Of course in ROS msvcrt we don't do this, but instead we initialize pgmptr to what argv[0] could be.
Jun 06 00:11:08 <hbelusca> That's one thing.
Jun 06 00:11:34 <hbelusca> The other thing is that nowhere it appears (in MS CRT from VS, or in wine) that argv is initialized using pgmptr.
Jun 06 00:13:33 <x86corez> hbelusca, I've checked argv[0] in some ROS command line tools, running them in Windows
Jun 06 00:13:56 <x86corez> they all interpret argv[0] as command line, not full path
Jun 06 00:14:04 <x86corez> so... I think it's git specific behaviour
Jun 06 00:14:16 <x86corez> or specific mingw compiler settings
Jun 06 00:28:12 <hbelusca> x86corez: I'm making a patch for our msvcrt, would be nice if you could test it :)
Jun 06 00:28:21 <x86corez> I'll test it
Hermes sent a link to the patch, I manually applied it and rebuilt the system, and after these moves the original problem magically disappeared!
Jun 06 00:34:26 <x86corez> hbelusca, IT WORKS!
Jun 06 00:35:10 <hbelusca> L O L
Jun 06 00:35:18 <hbelusca> So it seems that something uses pgmptr to rebuild an argv.
Jun 06 00:35:52 <x86corez> I've even able to clone :)
Jun 06 00:36:19 <hbelusca> \o/
Jun 06 00:36:21 <gigaherz> 2.10.0-rc2? not the release?
Jun 06 00:36:24 <hbelusca> ok I'm gonna commit that stuff.
Jun 06 00:36:43 <hbelusca> x86corez: gonna have ROS self-hosting <33
Jun 06 00:36:48 <x86corez> yeah!
Jun 06 00:37:01 <x86corez> gigaherz: I've built that from sources
Jun 06 00:37:37 <gigaherz> oh, for testing this bug? o_O
Jun 06 00:37:50 <sanchaez> yes, you missed the fun :p
Jun 06 00:39:46 <x86corez> git 2.10.0-windows.1 (release) works too!
Jun 06 00:39:54 <encoded> commit!!!
## Afterword
That said, another bug that indirectly prevents ReactOS from building itself has been fixed thanks to collective efforts. The funny coincidence is the fact that not long before another bug was fixed in the same msvcrt dynamic library (namely, in the qsort function) which did not allow to compile the USB drivers in ReactOS.
I participate in the development of many projects written in different programming languages, both closed and open source. I'm contributing to the ReactOS project since 2014, but I began to actively help and actually write code only in 2017. It's especially interesting to work in this area because it's an entire operating system! You feel a huge scale of the result in which the efforts were invested, as well as a pleasant feeling that there's one less bug! :)
Someone may wonder why I'm contributing to ReactOS and not Linux for example. So historically in most cases I write programs for Windows and my favorite programming language is Delphi. Perhaps that's why the architecture of Windows NT together with the Win32 API is very interesting to me, and the ReactOS project of the free Windows alternative makes the old dream come true — it allows you to find out how everything works under the hood in practice.
I hope you enjoyed my first english article here. I'm looking forward to your comments!
Фонд ReactOS
278.57
Операционная система
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## Comments 1
+1
Thank you for the good story with a happy end!
Only users with full accounts can post comments. Log in, please.
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2019-03-22 06:16:36
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https://www.projecteuclid.org/euclid.tmna/1463081848
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## Topological Methods in Nonlinear Analysis
### Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type
#### Abstract
New criteria are established for the existence of multiple positive solutions of a Hammerstein integral equation of the form $$u(t)= \int_{0}^1 k(t,s)g(s)f(s,u(s))\,ds \equiv Au(t)$$ where $k$ can have discontinuities in its second variable and $g \in L^{1}$.
These criteria are determined by the relationship between the behaviour of $f(t,u)/u$ as $u$ tends to $0^+$ or $\infty$ and the principal (positive) eigenvalue of the linear Hammerstein integral operator $$Lu(t)=\int_{0}^1 k(t,s)g(s)u(s)\,ds.$$ We obtain new results on the existence of multiple positive solutions of a second order differential equation of the form $$u''(t)+g(t)f(t,u(t))=0 \quad\text{a.e. on } [0,1],$$ subject to general separated boundary conditions and also to nonlocal $m$-point boundary conditions. Our results are optimal in some cases. This work contains several new ideas, and gives a unified approach applicable to many BVPs.
#### Article information
Source
Topol. Methods Nonlinear Anal., Volume 27, Number 1 (2006), 91-115.
Dates
First available in Project Euclid: 12 May 2016
https://projecteuclid.org/euclid.tmna/1463081848
Mathematical Reviews number (MathSciNet)
MR2236412
Zentralblatt MATH identifier
1146.34020
#### Citation
Webb, J. R. L.; Lan, K. Q. Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topol. Methods Nonlinear Anal. 27 (2006), no. 1, 91--115. https://projecteuclid.org/euclid.tmna/1463081848
#### References
• H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces , SIAM Rev., 18(1976), 620–709 \ref\key 2
• Ch. Bai and J. Fang, Existence of multiple positive solutions for nonlinear $m$-point boundary value problems , J. Math. Anal. Appl., 281(2003), 76–85 \ref\key 3 ––––, Existence of multiple positive solutions for nonlinear $m$-point boundary value problems , Appl. Math. Comp., 140(2003), 297–305 \ref\key 4
• L. Erbe, Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems , Math. Comput. Modelling, 32(2000), 529–539 \ref\key 5
• L. H. Erbe, S. Hu and H. Wang, Multiple positive solutions of some boundary value problems , J. Math. Anal. Appl., 184(1994), 640–648 \ref\key 6
• D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press (1988) \ref\key 7
• C. P. Gupta, S. K. Ntouyas and P. CH. Tsamatos, On an $m$-point boundary-value problem for second-order ordinary differential equations , Nonlinear Anal., 23(1994), 1427–1436 \ref\key 8 ––––, Solvability of an $m$-point boundary-value problem for second-order ordinary differential equations , J. Math. Anal. Appl., 189(1995), 575–584 \ref\key 9
• G. Infante and J. R. L. Webb, Nonzero solutions of Hammerstein integral equations with discontinuous kernels , J. Math. Anal. Appl., 272(2002), 30–42 \ref\key 10
• G. L. Karakostas and P. Ch. Tsamatos, Multiple positive solutions for a nonlocal boundary-value problem with response function quiet at zero , Electron. J. Differential Equations (2001, 13 ), 10 pp \ref\key 11 ––––, Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems , Electron. J. Differential Equations (2002, 30 ), 17 pp \ref\key 12
• M. A. Krasnosel'skiĭ and P. P. Zabreĭko, Geometrical Methods of Nonlinear Analysis, Springer–Verlag, Berlin (1984) \ref\key 13
• K. Q. Lan, Multiple positive solutions of Hammerstein integral equations with singularities , Dynam. Systems Differential Equations, 8 (2000), 175–192 \ref\key 14 ––––, Multiple positive solutions of semilinear differential equations with singularities , J. London Math. Soc. (2), 63(2001), 690–704 \ref\key 15
• K. Q. Lan and J. R. L. Webb, Positive solutions of semilinear differential equations with singularities , J. Differential Equations, 148(1998), 407–421 \ref\key 16
• Y. Li, Abstract existence theorems of positive solutions for nonlinear boundary value problems , Nonlinear Anal., 57(2004), 211–227 \ref\key 17
• F. Li and G. Han, Generalization for Amann's and Leggett–Williams's three-solution theorems and applications , J. Math. Anal. Appl., 298(2004), 638–654 \ref\key 18
• Z. Liu and F. Li, Multiple positive solutions of nonlinear two-point boundary value problems , J. Math. Anal. Appl., 203(1996), 610–625 \ref\key 19
• R. Ma and N. Castaneda, Existence of solutions of nonlinear $m$-point boundary-value problems , J. Math. Anal. Appl., 256(2001), 556–567 \ref\key 21
• R. H. Martin, Nonlinear operators and differential equations in Banach spaces, Wiley, New York (1976) \ref\key 22
• R. D. Nussbaum, Eigenvectors of nonlinear positive operators and the linear Krein–Rutman theorem , Fixed Point Theory (E. Fadell and G. Fournier, eds.), Springer (1981, Lecture Notes in Math., 886 ), 309–330 \ref\key 23
• J. R. L. Webb, Positive solutions of some three point boundary value problems via fixed point index theory , Nonlinear Anal., 47(2001), 4319–4332 \ref\key 24 ––––, Remarks on positive solutions of three point boundary value problems , Dynamical Systems and Differential Equations (Wilmington, NC, 2002) Discrete Contin. Dynam. Systems (2003). Added Volume, 905–915 \ref\key 25
• G. Zhang and J. Sun, Positive solutions of $m$-point boundary value problems , J. Math. Anal. Appl., 291 (2004), 406–418
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2019-10-22 00:03:12
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http://www.qnx.com/developers/docs/6.6.0_anm11_wf10/com.qnx.doc.qt/topic/qt_library_packaging_in_qtapp.html
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# Packaging Qt apps with the library
After the library has been added to the project of a Qt app, the packaging process for the app remains mostly the same, except for two extra steps.
To package QtApp so it can use QtLibrary, you must:
1. Edit the project file (QtApp.pro) to add this line:
QMAKE_LFLAGS += "-Wl,-rpath,app/native/lib"
This instruction embeds the path of the library file (libQtLibrary.so) into the QtApp binary. When the launcher service runs QtApp in its sandbox environment, the service uses a root path of app/native. All files within the Blackberry ARchive (BAR) package are relative to this location. For instance, from the perspective of QtApp, its icon file is found at app/native/icon.png.
To package libQtLibrary.so into the lib subdirectory in the BAR file, we set rpath to the root path appended with this subdirectory (i.e., app/native/lib).
2. Update the arguments for the packaging command as follows:
QtApp.bar %{sourceDir}\bar-descriptor.xml QtApp
-C %{sourceDir} %{sourceDir}\icon.png
-e ProjectBuildDir\libQtLibrary.so.1.0 lib/libQtLibrary.so.1
The newly added –e option is followed by two paths. The first is the library file's build location on the host system (in this case, replace ProjectBuildDir with the path containing the output library file) and the second is the relative location of the library file within the BAR package. Note that the file is purposely renamed from libQtLibrary.so.1.0 to libQtLibrary.so.1.
Note: The directory separators in this example are backslashes (\), which are used for Windows, but you must use the appropriate separator for your OS (i.e., "/" if you're running Linux). The exception is the second path for -e; this must use the Linux separator because it specifies a relative location on the QNX target, which follows the POSIX directory convention.
If you're using Qt Creator to package the app, you must access the Build & Run tab and edit the build step for the packaging command to add these arguments, as explained in . In the above example, ProjectBuildDir is the build directory specified in the General section of the Build Settings page.
You can also package the app from the command line, by passing these arguments to blackberry-nativepackager in a QNX Neutrino terminal, as described in .
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2018-02-24 21:58:50
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https://nrich.maths.org/822
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### Timing
These two challenges will test your time-keeping!
### Millennium Man
Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?
### Calendar Sorting
The pages of my calendar have got mixed up. Can you sort them out?
# Palindromic Date
##### Stage: 2 Challenge Level:
The number $2002$ is palindromic because it is the same read from left to right as it is read from right to left.
There was one date in February of the year $2002$ where the eight digits are palindromic if the date is written in the British way (dd/mm/yyyy).
This is not palindromic written the American way (mm/dd/yyyy).
Is there any palindromic date written the American way that year?
Find the next occasions when palindromic dates occur written in each way and the number of days between them.
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2017-10-18 04:08:49
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http://math.stackexchange.com/questions/451927/n-and-n5-have-the-same-units-digit
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# $n$ and $n^5$ have the same units digit?
Studying GCD, I got a question that begs to show that $n$ and $n^5$ has the same units digit ... What would be an idea to be able to initiate such a statement? testing $0$ and $0^5=0$ $1$ and $1^5=1$ $2$ and $2^5=32$
In my studies, I have not got "mod", please use other means, if possible of course.
I demonstrated in a previous period that $$2|n^5-n$$because $$n^5-n=(n+1)n(5n^4+5n+5)$$, and$$5|n^5-n$$By Fermat's Little Theorem
Only I do not understand what should happen to the units of the two numbers are equal ... What must occur?
-
Well, $n\equiv n^5\pmod2$ and $n\equiv n^5\pmod5$. – awllower Jul 25 '13 at 14:48
Although not studied'' mod''. Using GCD has no like? – marcelolpjunior Jul 25 '13 at 14:52
Well, mod is gcd, since $a\equiv b\pmod n$ if and only if $\gcd(n,a-b)=n$. – awllower Jul 25 '13 at 14:56
Without using any modular arithmetic:
$$n^5-n=n(n-1)(n+1)(n^2+1)=n(n-1)(n+1)(n^2-4+5)=n(n-1)(n+1)(n^2-4)+5n(n-1)(n+1)=$$ $$=(n-2)(n-1)n(n+1)(n+2)+5(n-1)n(n+1)$$
$(n-2)(n-1)n(n+1)(n+2)$ is the product of 5 consecutive integers thus divisible by 2 and 5.
$5n(n-1)(n+1)$ is multiple of $5$ and even.
-
We know if unit digits of two numbers are same, their difference is divisible by 10 and vice versa.
Method $1a:$
Using Fermat's Little Theorem $n^5-n\equiv0\pmod 5$
and $n^5-n=n(n^4-1)=n(n^2-1)(n^2+1)=n(n-1)(n+1)(n^2+1)$ which is divisible by $n(n-1)$ which is always even
$\implies 2|(n^5-n)$ and we have $5|(n^5-n)$
$\implies n^5-n$ is divisible by lcm $(2,5)=10$
Method $1b:$
As $10=2\cdot5,$
using Fermat's Little Theorem, we have $$n^5-n\equiv0\pmod 5\text{ and } n^2-n\equiv0\pmod 2$$
Now, lcm $(n^5-n,n^2-n)=n(n^4-1,n-1)=n(n^4-1)$ as $(n-1)|(n^4-1)$
$\implies$lcm $(n^5-n,n^2-n)=n^5-n$ which is divisible by $5,2$ hence by lcm$(2,5)=10$
Method $2:$
Alternatively, $$n^5-n=n(n^4-1)=n(n^2-1)(n^2+1)=n(n^2-1)(n^2-4+5)$$ $$=n(n^2-1)(n^2-4)+5n(n^2-1)$$ $$=\underbrace{(n-2)(n-1)n(n+1)(n+2)}_{\text{ product of }5\text{ consecutive integers }}+5\cdot \underbrace{(n-1)n(n+1)}_{\text{ product of }3\text{ consecutive integers }}$$
Now, we know the product $r$ consecutive integers is divisible by $r!$ where $r$ is a positive integer
So, $(n-2)(n-1)n(n+1)(n+2)$ is divisible by $5!=120$ and $(n-1)n(n+1)$ is divisible by $3!=6$
$$\implies n^5-n\equiv0\pmod{30}\equiv0\pmod{10}$$
-
Damn, too fast! – Arkamis Jul 25 '13 at 14:48
Or $n$ and $n^5$ are both even or both odd ... – Mark Bennet Jul 25 '13 at 14:48
@lab bhattacharjee: Is there another way? Without using mod. – marcelolpjunior Jul 25 '13 at 14:54
@MarkBennet Then either $n$ is of the form $2k$ or $2k +1$ order. Right? – marcelolpjunior Jul 25 '13 at 14:55
@marcelolpjunior, I am adding an alternative solution – lab bhattacharjee Jul 25 '13 at 14:57
The result can be verified using minimal machinery. first note that the units digit of $n^5$ is completely determined by the units digit of $n$.
The units digit of $n^5$ is one of $0,1,2,\dots,9$. We can verify the result for each of the $10$ cases by a direct calculation.
There are $10$ calculations to do, none of them painful. We do one of them. Let $n$ end in $8$. Then $n^2$ ends in $4$, so $n^4$ ends in $6$. Thus $n^5$ ends in $8$.
-
You can write $n=10a+b$, with $b$ the units digit. Then $n^5=(10a)^5+5(10a)^4b+10(10a)^3b^2+10(10a)^2b^3+5(10a)b^4+b^5$. As all the terms but the last have a factor of $10$, the units digit of $n^5$ is the same as the units digit of $b^5$. This justifies testing each units digit to see if the units digit of its fifth power is the same as the digit. Ten tests and you are done-they all succeed.
-
Actually 6 tests are enough, since you can write $n=10a \pm b$ where $b$ is a digit $\leq 5$. – N. S. Jul 25 '13 at 15:08
@N.S.: Good point. – Ross Millikan Jul 25 '13 at 15:11
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2014-10-24 11:29:58
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https://meteo.unican.es/trac/wiki/WRF4GConfigurationFiles?version=8
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Version 8 (modified by carlos, 10 years ago) (diff)
--
Configuration files
In order to configure WRF4G framework, you have to edit the files below:
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2022-07-05 13:58:40
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https://atarnotes.com/forum/index.php?topic=4197.15
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FREE Head Start Lectures this January - book now! HSC: register here | QCE: register here | VCE: register here
January 21, 2020, 04:44:18 pm
### AuthorTopic: Bachelor of Business (Monash Caulfield) (Read 14702 times) Tweet Share
0 Members and 1 Guest are viewing this topic.
#### clinton_09
• Victorian
• Posts: 959
• Respect: +1
##### Re: Bachelor of Business (Monash Caulfield)
« Reply #15 on: July 09, 2008, 05:19:52 pm »
0
Once you gain experience your degree IMO becomes less of a priority to employers
Your not wrong there. Experience plays a big role
#### costargh
• Guest
##### Re: Bachelor of Business (Monash Caulfield)
« Reply #16 on: July 09, 2008, 07:49:43 pm »
0
Aside from that, if you like some of the subjects @ Clayton that aren't @ Caulfield, u can jst take the shuttle bus that runs between Caulfield and Clayton every 25 mins 2g2 classes @ Clayton.
How does that work? So could I do some of the BCom subjects in first semester? =S
#### mand3e
• Victorian
• Trailblazer
• Posts: 36
• Year 12 makes me emo.
• Respect: 0
##### Re: Bachelor of Business (Monash Caulfield)
« Reply #17 on: July 21, 2008, 11:19:59 pm »
0
The BEco is at Clayton (which I would prefer to do actually) but once again my shitness @ methods has made me ineligible for selection =(
25 in methods or spesh and 25 in English... unless this years VTAC guide changes that (OMG WOOD BE THE HAPPIEST PERSON EVER!!!)
Thanks btw
dude, im totally in the same boat as you. i dropped methods as well... and REALLY REALLY wanted to get into clayton, but alas can't get into a business course in clayton unless your doing at least methods not cool, not cool at all.
2007: International Studies (38)
2008: Accounting, Economics, English, Further Maths, Psychology.
If we're doing similar subjects, feel free to befriend me.
"You scratch my back and I'll scratch yours!" LOL
#### droodles
• Guest
##### Re: Bachelor of Business (Monash Caulfield)
« Reply #18 on: July 21, 2008, 11:23:47 pm »
0
rofl BL methods is like cake and vanilla milkshakes
#### excal
• VN Security
• Victorian
• ATAR Notes Legend
• Posts: 3493
• Über-Geek
• Respect: +21
##### Re: Bachelor of Business (Monash Caulfield)
« Reply #19 on: July 21, 2008, 11:30:27 pm »
0
The BEco is at Clayton (which I would prefer to do actually) but once again my shitness @ methods has made me ineligible for selection =(
25 in methods or spesh and 25 in English... unless this years VTAC guide changes that (OMG WOOD BE THE HAPPIEST PERSON EVER!!!)
Thanks btw
dude, im totally in the same boat as you. i dropped methods as well... and REALLY REALLY wanted to get into clayton, but alas can't get into a business course in clayton unless your doing at least methods not cool, not cool at all.
You could always do a diploma at Monash College? You'll be paying more though.
costargh - they are equivalent units. MGC1010 = MGF1010 for example. They are simply named differently (I believe MGC1010 is Managing People and Organisations as is Business Law = Commerical Law).
There will be subtle differences, but the general gist of the subjects will be similar.
excal (VCE 05/06) BBIS(IBL) GradCertSc(Statistics) MBBS(Hons) GCertClinUS -- current Master of Medicine candidate
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#### AppleXY
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##### Re: Bachelor of Business (Monash Caulfield)
« Reply #20 on: July 21, 2008, 11:42:49 pm »
0
The BEco is at Clayton (which I would prefer to do actually) but once again my shitness @ methods has made me ineligible for selection =(
25 in methods or spesh and 25 in English... unless this years VTAC guide changes that (OMG WOOD BE THE HAPPIEST PERSON EVER!!!)
Thanks btw
dude, im totally in the same boat as you. i dropped methods as well... and REALLY REALLY wanted to get into clayton, but alas can't get into a business course in clayton unless your doing at least methods not cool, not cool at all.
If you dropped methods, I don't think doing commerce is good sign. Commerce is math in every sense (yes, even in management!), and it can get complicated at times. I'm not saying that you shouldn't do commerce, but without having a sound mathematical background (especially to read, interpret and create graphs and other forms of statistics) is a definite necessity, most importantly in finance (Financial Services).
My A\$0.02.
$\mathbb{A}\mathbb{P}\mathbb{P}\mathbb{L}\mathbb{E}\mathbb{X}\mathbb{Y}$ $\mathbf{A}\mathbf{K}\mathbf{A}$ $\mathbb{P}\mathbb{R}\mathbb{A}\mathbb{V}$
2009 - BBus (Econometrics/Economics&Fin) @ Monash
Need a question answered? Merspi it!
[quote="Benjamin F
#### costargh
• Guest
##### Re: Bachelor of Business (Monash Caulfield)
« Reply #21 on: July 21, 2008, 11:52:46 pm »
0
I completely disagree with you Applexy. Not boasting here, but the fact that I get all A's/A+'s in my commerce/ey subjects (legal, business management, accounting and economics) says more about my ability to perform well in Commerce than methods does. Maths methods isn't the only indicator of mathematical ability and one should not be judged on how well they can perform in a commerce degree purely on the fact that the aren't good with integrals.
Btw- thanks excalibur. do you know though say, If I would be able to do 1 or 2 subjects @ clayton towards my degree? (with the intention being to transfer to BCom after I pass (hopefully) the maths methods equivilant subject @ Uni after 1st year?
does anyone know what subject that is called?
mande- I didnt drop methods, I did it last year and got 24 cause im retarded
#### Collin Li
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##### Re: Bachelor of Business (Monash Caulfield)
« Reply #22 on: July 22, 2008, 12:39:42 am »
0
I completely disagree with you Applexy. Not boasting here, but the fact that I get all A's/A+'s in my commerce/ey subjects (legal, business management, accounting and economics) says more about my ability to perform well in Commerce than methods does. Maths methods isn't the only indicator of mathematical ability and one should not be judged on how well they can perform in a commerce degree purely on the fact that the aren't good with integrals.
Btw- thanks excalibur. do you know though say, If I would be able to do 1 or 2 subjects @ clayton towards my degree? (with the intention being to transfer to BCom after I pass (hopefully) the maths methods equivilant subject @ Uni after 1st year?
does anyone know what subject that is called?
mande- I didnt drop methods, I did it last year and got 24 cause im retarded
Being bad with integrals would cost you less than 20% on the exams, and you could have done well in Methods still. That said, however, calculus is probably one of the more important parts of Methods with regards to its relevance to a commerce degree.
It's a pre-requisite for a reason. And I can say that quite confidently because those pre-requisites aren't arbitrarily assigned by some government agency -- they are assigned by the universities themselves, the ones that actually have an interest to filter out the crap from the good.
I wouldn't really use VCE subjects as an indicator. Universities don't. They don't use it as a pre-requisite, and I don't think they use it in middle-band considerations.
« Last Edit: July 22, 2008, 12:41:48 am by coblin »
#### costargh
• Guest
##### Re: Bachelor of Business (Monash Caulfield)
« Reply #23 on: July 22, 2008, 01:02:25 am »
0
The integrals thing was just a reference to methods, I really don't know what's in the methods course to be honest. I know a person who got <50 as her ENTER and is studying BCom. Didn't get straight in through VTAC obviously
ANU doesn't have methods as pre-req for Com. That doens't make the degree harder or the subjects harder. If Monash was keen on filtering out the crap from their uni then they would put methods as a pre-req for all their commerce/ey degrees; Business and Commerce @ Berwick and Business @ Caulfield because they are basically the same/equivalent subjects.
Methods is a pre-req (VCE subject) so I don't knwo why they would be using it as an indicator and not using the similar VCE subjects as an indicator. Eg. Science degrees usually need English + 1 or 2 VCE science subjects right?
Meh- I know methods isnt a good indicator for com but it is of no importance to me anymore cause im gonna get where i wanna be by doing the uni subject that is equivalent and transfering. Just some stupid rule that I have to live with
« Last Edit: July 22, 2008, 01:04:51 am by costargh »
#### pepsi
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##### Re: Bachelor of Business (Monash Caulfield)
« Reply #24 on: July 22, 2008, 01:29:34 am »
0
I have the same problem as Costargh last year and have posted on the 'other vce forum' regarding the exact same concern. I did further maths (the easier option) not knowing that methods was a prerequisite for Clayton until it was too late. Now im doing really well on my BCommerce degree at Deakin Burwood.
Would I still need to do a method equivalent uni subject to be able to transfer to Clayton next year? I really wanna finish my degree at Clayton since i can get there by car very easily. Deakin's study environment is apparently quite good though.
« Last Edit: July 22, 2008, 02:12:01 am by pepsi »
#### Collin Li
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##### Re: Bachelor of Business (Monash Caulfield)
« Reply #25 on: July 22, 2008, 02:01:33 am »
0
I meant the VCE commerce subjects, as an indicator for entry into commerce.
#### AppleXY
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##### Re: Bachelor of Business (Monash Caulfield)
« Reply #26 on: July 22, 2008, 08:12:40 am »
0
I was just saying, If you can't do methods, then uni math subjects would be difficult.
Eg. Quantitative Methods 1,2.
NPVs (Net Present Value) for Accounting
Brownian Motion for Finance
Advanced Productivity and production measures in management.
Calculus (finding the rate of increase of an asset etc)
I know, you could say, I could use a scientific calc blah... but it's really useful to know them.
$\mathbb{A}\mathbb{P}\mathbb{P}\mathbb{L}\mathbb{E}\mathbb{X}\mathbb{Y}$ $\mathbf{A}\mathbf{K}\mathbf{A}$ $\mathbb{P}\mathbb{R}\mathbb{A}\mathbb{V}$
2009 - BBus (Econometrics/Economics&Fin) @ Monash
Need a question answered? Merspi it!
[quote="Benjamin F
#### Collin Li
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##### Re: Bachelor of Business (Monash Caulfield)
« Reply #27 on: July 22, 2008, 09:12:11 am »
0
Note that the first two units (or their equivalents) that AppleXY listed are compulsory in the BCom at Melbourne.
Quantitative Methods 1 and 2.
#### Fyrefly
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##### Re: Bachelor of Business (Monash Caulfield)
« Reply #28 on: July 22, 2008, 10:04:06 am »
0
TBH... I don't think u need that much mathematical knowledge.
McTaggart, D., Findlay, C. & Parkin, M., Economics 5th edition, Pearson Education Australia, 2007 = my micro and macro eco txtbook.
It has an appendix to chapter one that explains how to understand a linear equation >.>
Year 8 stuff.
As long as you can stumble through the compulsory core units that require maths, I don't think the emphasis is on maths *that* much in majors like Business Law, Management, Marketing, Asian Development and Transition, Human Resource Management, or... there's a new major that's done cross-faculty with IT... don't know much about that one tho.
It's easy to say "Oh, Commerce needs maths".
But BCom covers such a broad area of topics, and I don't think it's fair to say that they ALL involve maths.
I think u'll do fine in a BCom degree, so long as u're particularly careful about wot units, majors and minors u do.
And it's not like u and maths r totally incompatible - u did only miss out by a single point after all.
|| BComm + DipLang (Jap) @ Monash ||
#### excal
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##### Re: Bachelor of Business (Monash Caulfield)
« Reply #29 on: July 22, 2008, 08:19:44 pm »
0
Still early days Jess...just wait until you get into your econometrics (ETC1100 I think?) stuff
excal (VCE 05/06) BBIS(IBL) GradCertSc(Statistics) MBBS(Hons) GCertClinUS -- current Master of Medicine candidate
Former Global Moderator
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2020-01-21 05:44:19
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 6, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24793307483196259, "perplexity": 10586.720691926734}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250601615.66/warc/CC-MAIN-20200121044233-20200121073233-00473.warc.gz"}
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https://www.enotes.com/homework-help/int-z-3-e-z-dz-evaluate-integral-615199
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# `int z^3 e ^ z dz` Evaluate the integral
`intz^3e^zdz`
If f(x) and g(x) are differentiable functions, then
`intf(x)g'(x)=f(x)g(x)-intf'(x)g(x)dx`
If we write f(x)=u and g'(x)=v, then
`intuvdx=uintvdx-int(u'intvdx)dx`
Using the above integration by parts,
Let `u=z^3 , u'=3z^2`
and let `v=e^z, v'=e^z`
`intz^3e^z=z^3inte^zdz-int(3z^2inte^zdz)dz`
`=z^3e^z-int(3z^2e^z)dz`
`=z^3e^z-3intz^2e^zdz`
again applying integration by parts,
`=z^3e^z-3(z^2inte^zdz-int(d/dz(z^2)inte^zdz)dz`
`=z^3e^z-3(z^2e^z-int(2ze^z)dz`
`=z^3e^z-3z^2e^z+6intze^zdz`
again applying integration by parts,
`=z^3e^z-3z^2e^z+6(zinte^zdz-int(d/dz(z)inte^zdz)dz)`
`=z^3e^z-3z^2e^z+6(ze^z-int(1*e^z)dz)`
`=z^3e^z-3z^2e^z+6(ze^z-e^z)`
`=z^3e^z-3z^2e^z+6ze^z-6e^z+C`
Approved by eNotes Editorial Team
Posted on
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2020-11-26 08:56:46
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https://science.lpnu.ua/taxonomy/term/2478
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expansion
Diversification of Foreign Economic Activities of Domestic Carpet Market Enterprises
At the present stage of dynamic development of the world economy, active processes of interpenetration of technologies and capital, expansion of economic relations, economic entities are increasingly faced with various socio-economic challenges. In view of this, the role of foreign economic activity is increasing not only for economic entities, but also for the country as a whole, since all systemic transformations of the economy affect the characteristic features of the development of the specified sphere of activity.
The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions
An algorithm for constructing recurrence relations of geometric Gaussian functions, in which the displacement of parameters is equal to $0$, $1$ or $-1$, is described. On the basis of such recurrence relations, the expansion for the ratio of Gaussian functions into continued fractions is developed. The obtained continued fractions are the development of the corresponding hypergeometric Gaussian functions in the case when the parameters of the function are integers.
Фізико-механічні властивості модифікованих полегшених тампонажних сумішей
Influence of different functional purpose additives complex on mechanical properties of light-weight plugging mortar was investigated. Prescriptions of expanding light-weight plugging mortars with usage of low reactive lime were made.
Physico-Mechanical Properties of Cements with Application of Barium-Containing Sulfateferrite Clinkers
In the work the results of research the physico-mechanical properties of cements with the use of barium-containing sulfateferrite clinkers and gypsum stone are given. As a result of research of barium-containing sulfateferrite clinkers hydraulic properties it is found out that while concretion they show too fast hardening and low solidity therefore they cannot be used as an independent binder. For the purpose of regulation the hardening terms the influence of the gypsum stone additive was studied.
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2022-08-09 04:21:22
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http://clay6.com/qa/23525/ordinary-dice-are-rolled-the-probability-that-at-least-half-of-them-will-sh
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Browse Questions
# Ordinary dice are rolled. The probability that at least half of them will show at least 3 is
$\begin {array} {1 1} (A)\;41 \times \large\frac{2^4}{3^6} & \quad (B)\;\large\frac{2^4}{3^6} \\ (C)\;20 \times \large\frac{2^4}{3^6} & \quad (D)\;None\: of \: these \end {array}$
The probability of getting atleast 3 in a throw = $\large\frac{4}{6}=\large\frac{2}{3}$
$\therefore$ The required probability
$= 6C_3 \bigg( \large\frac{2}{3} \bigg)^3 \bigg( \large\frac{1}{3} \bigg)^3 + 6C_4 \bigg( \large\frac{2}{3} \bigg)^4 \bigg( \large\frac{1}{3} \bigg)^2 + 6C_5 \bigg( \large\frac{2}{3} \bigg)^5 \large\frac{1}{3} + 6C_6 \bigg( \large\frac{2}{3} \bigg)^6$
$= \large\frac{41(2^4)}{3^6}$
Hence Ans (A)
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2017-03-29 07:19:18
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http://docs.quantumatk.com/manual/technicalnotes/atk_pseudo_basis/atk_pseudo_basis.html
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# Pseudopotentials and basis sets available in QuantumATK¶
PDF version
The accuracy of the calculations with the LCAO model in QuantumATK depends on the pseudopotential and basis sets used for the calculations. In recent years we have put a large effort into providing a robust set which can provide good accuracy at reasonably computational resources. Thus, there is an evolution in quality of the pseudopotentials we provide, with the best sets being the SG15 pseudopotentials available from the ATK-2016 release and PseudoDojo pseudopotentials available from the O-2018.06 release. The theoretical background of the basis sets and pseudopotentials are described in the QuantumATK Manual, and the purpose of this note is to guide the user towards the best setting.
## Pseudopotentials¶
The pseudopotentials available for the QuantumATK software are listed in the below table. We see that it shows an evolution with quality of the pseudopotentials for each release. However, not all exchange correlation functionals are available for each type of pseudopotential. For GGA and SOGGA we recommend to use the PseudoDojo pseudopotential. For LDA we recommend the FHI pseudopotential. For SOLDA we recommend the OMX, it can also give higher accuracy for LDA, however, the required mesh cutoff needs to be tested carefully.
Table 13 Pseudo- and PAW potential types available for the DFT calculators.
Name Notes
FHI Trouiller–Martins type.
HGH Hartwigsen–Goedecker–Hutter type.
OMX Fully relativistic. OMX webpage.
SG15 ONCV type, scalar-relativistic (SG15) and fully relativistic (SG15-SO). SG15 webpage.
PseudoDojo ONCV type, scalar-relativistic (PseudoDojo) and fully relativistic (PseudoDojo-SO). PseudoDojo webpage.
GPAW PAW potentials. GPAW webpage.
JTH PAW potentials. JTH webpage.
Suggested A mixture of GPAW and JTH, chosen to give optimal results for each element.
Through the use of the keyword NormConservingPseudoPotential, it is also possible to specify a pseudopotential from a user-specified file. Not all pseudopotentials are available for all QuantumATK DFT calculators and exchange-correlation functional types. Please see the following table for details on each of the pseudopotential types:
Table 14 Details about the pseudo- and PAW potential types available for the QuantumATK DFT calculators.
Name Introduced Basis types XC-types Cutoff [Ha] Accuracy Efficiency
FHI ATK-2008 LCAO, PW LDA, GGA, MGGA, HGGA 30-100 Low High
HGH ATK-2011 LCAO, PW LDA, GGA, MGGA, HGGA 75-500 Medium Low
OMX ATK-2015 LCAO LDA, GGA, MGGA 75-500 High Low
OMX-SO ATK-2015 LCAO SOLDA, SOGGA, SOMGGA 75-500 High Low
SG15 ATK-2016 LCAO, PW GGA, HGGA 30-220 High Medium
SG15-SO ATK-2016 LCAO, PW GGA, SOGGA, HSOGGA 30-220 High Medium
PseudoDojo O-2018.06 LCAO, PW GGA, HGGA 30-125 High Medium
PseudoDojo-SO P-2019.03 LCAO, PW GGA, SOGGA, HSOGGA 30-125 High Medium
PAW-GPAW Q-2019.12 PW LDA, GGA N/A High Medium
PAW-JTH Q-2019.12 PW LDA, GGA N/A High Medium
PAW-Suggested Q-2019.12 PW GGA N/A High Medium
Warning
The higher values for OMX pseudopotentials, about 300 Hartree or more, are especially relevant for pseudopotentials with semi-core states. They often need these very high mesh cutoffs to give accurate forces.
## LCAO basis sets¶
QuantumATK mainly uses a numerical LCAO basis sets. The accuracy depends on the number of orbitals and the range of the orbitals. Increasing the number of orbitals and their range decrease the efficiency and increase the memory requirement. For the latest SG15 and PseudoDojo pseudopotentials we provide basis sets which systematically improve the accuracy. For the other pseudopotentials the improvement in accuracy is less systematic.
### SG15/PseudoDojo¶
Three different basis sets are available for each element when using the SG15/PseudoDojo pseudopotentials; Medium, High, and Ultra. All three derive from the numerical atom-centered basis sets of the FHI-aims package, but have been significantly modified and optimized with respect to computational speed with the DFT: LCAO calculator.
The Medium basis set is default for the SG15/PseudoDojo pseudopotentials, and should be sufficient for most applications. However, if extreme accuracy is needed, the High and Ultra basis sets add more basis functions at the expense of increased computational load.
### OMX¶
The OMX basis sets were developed in Refs. [Oza03] and [OK04], and are optimized towards maximum computational speed and accuracy with the OMX pseudopotentials. The DFT: LCAO calculator offers three different OMX basis set sizes for most elements; Low, Medium, and High, which include increasingly more pseudo-atomic orbitals in the basis set. More details are available on the website for the OpenMX database (2013).
### FHI¶
Four different types of basis functions can be used for the FHI pseudopotentials:
The basis sets available for FHI pseudopotentials are listed below. They are ordered with increasing number of basis orbitals – those with more orbitals are often more accurate, at the expense of increased computational load. The DZP basis set is default.
### Visualizing the basis functions¶
To see the type of the basis sets it is most easy to plot the basis functions, like this:
• Open the scripter
• Add an LCAOcalculator block from the Calculators section
• Go to the Basis set tab at click the plot widget in the line where you define the basis set.
You will then get the following plot.
## Accuracy tests for elemental solids¶
To give an overall idea of the accuracy of each pseudopotential and basis sets we have performed so-called $$\Delta$$-tests [LBBjorkman+16] (see the web-site Comparing Solid State DFT Codes, Basis Sets and Potentials). These tests checks accuracy for the pseudopotential and basis set compared with state of the art all-electron calculations. The tests check the accuracy of the pseudopotential and basis sets in reproducing the equation of state of all the elemental solids in the periodic system using the GGA-PBE exchange-correlation functional.
Table 15 Accuracy and performance of PBE pseudopotentials and basis types available for the DFT calculators. Performance is an approximate measure of time spent, relative to FHI-DZP. Lower numbers are faster.
Pseudo Basis $$\Delta$$ (meV) Performance
FHI SZP 39.4 0.5
FHI DZP 18.2 1
FHI DZDP 19.1 2
HGH Tier4 12.8 6
OMX Medium 8.0 3
OMX High 2.2 10
SG15 Medium 3.45 2
SG15 High 1.88 6
SG15 Ultra 2.03 25
SG15 PW 1.32 N/A
PseudoDojo Medium 4.53 2
PseudoDojo High 1.52 6
PseudoDojo Ultra 1.40 25
PseudoDojo PW 1.04 N/A
PAW-GPAW PW 1.44 N/A
PAW-JTH PW 0.86 N/A
PAW-Suggested PW 0.64 N/A
A $$\Delta$$ value below 2 meV indicates a state of the art DFT calculation. PAW-Suggested is a combination of the two PAW sets where we have selected the best PAW potential for each element. The performance number given in the Table is an average indication of how much time a calculation of a 64 atom supercell takes, using the different models relative to the FHI-DZP model. Lower numbers are faster. There are large variations among the elements and the performance number should only be used as a rough guide.
## Accuracy tests for mixed solids¶
The $$\Delta$$-tests are done for ideal systems, in order to illustrate that these results are transferable to general systems we have performed a number of additional accuracy tests. The first test is for a number Rock Salt (RS) and Perovskite(P) structures provided in Ref. [GBRV14]. The reference points are FHI-aims all electron calculations. We see the deviations for the $$a$$ (lattice constant), $$B$$ (Bulk modulus) and $$E_f$$ (formation energy) compared to the Ref. [GBRV14] in the below Table.
Table 16 Accuracy of selected methods in QuantumATK on RockSalt (RS) geometries [GBRV14]. The formation energy is not available for the Ultra-soft and PAW plane-wave calculations. The reference is a fully converged all-electron calculation using FHI-aims.
Pseudo Basis $$a$$ (%) $$B$$ (%) $$E_f$$ (%) Source
Ultra-Soft PW 0.13 5.0 N/A [GBRV14]
PAW PW 0.15 4.5 N/A [GBRV14]
PseudoDojo Ultra 0.15 1.90 1.83 QuantumATK
PseudoDojo High 0.18 2.12 2.79 QuantumATK
PseudoDojo Medium 0.5 5.32 15.59 QuantumATK
PseudoDojo PW (40 Ha) 0.09 1.86 0.85 QuantumATK
SG15 High 0.3 8.6 4.6 QuantumATK
SG15 Medium 0.6 13.0 12.5 QuantumATK
FHI DZP 3.0 23.2 15.5 QuantumATK
Table 17 Accuracy of selected methods in QuantumATK on Perovskites (P) geometries from Ref. [GBRV14]
Pseudo Basis $$a$$ (%) $$B$$ (%) $$E_f$$ (%) Source
Ultra-Soft PW 0.08 5.5 N/A [GBRV14]
PAW PW 0.13 6.1 N/A [GBRV14]
PseudoDojo Ultra 0.13 1.87 0.91 QuantumATK
PseudoDojo High 0.21 3.04 1.18 QuantumATK
PseudoDojo Medium 0.35 3.68 2.73 QuantumATK
PseudoDojo PW (40 Ha) 0.06 0.66 0.23 QuantumATK
SG15 High 0.3 5.7 1.4 QuantumATK
SG15 Medium 0.4 6.4 2.6 QuantumATK
FHI DZP 3.5 18.3 12.8 QuantumATK
## Notes for each pseudopotential type¶
### PseudoDojo Pseudopotentials and basis sets¶
The PseudoDojo are state of the art norm-conserving pseudopotentials including multiple projectors, semi-core states and non-linear core correction [vSGB+18]. They are only provided for the GGA-PBE functional, and comes in both a scalar relativistic and a fully relativistic version. The latter is used for calculations including spin-orbit. The pseudopotentials are smooth and all elements converge with a mesh cutoff below 125 Ha.
A large effort has been put into providing high accuracy basis sets. Three sets are provided: Ultra, High and Medium. The basis sets have been optimized to describe bulk systems, dimers and trimer systems.
Below are given the $$\Delta$$-tests for the different elements.
### SG15 Pseudopotentials and basis sets¶
The SG15 are state of the art norm-conserving pseudopotentials including multiple projectors, semi-core states and non-linear core correction [Ham13][SG15]. They are only provided for the GGA-PBE functional, and comes in a scalar relativistic and a fully relativistic version. The latter is used for calculations including spin-orbit. The pseudopotentials are smooth and all elements converge with a mesh cutoff below 220 Ha.
A large effort has been put into providing high accuracy basis sets. Three sets are provided: Ultra, High and Medium. The basis sets have been optimized to describe bulk systems, dimers and trimer systems.
Below are given the $$\Delta$$-tests for the different elements.
### PAW data sets¶
For the Projector Augmented Wave (PAW) method, we need data describing the system inside the augmentation sphere (partial waves, projectors, core densities, ...). This is gathered in a PAW data set file. We support data set files in the .xml format, as specified on the ESL website. We ship two different data sets, the GPAW and JTH [JTH14] data sets, for which we found default wave function cutoffs that are as low as possible without losing accuracy. We made a combined PAW-Suggested data set for GGA, that gives the best results.
Below are given the $$\Delta$$-tests for the different elements.
### FHI pseudopotentials and basis sets¶
The FHI pseudopotentials are the oldest pseudopotentials in QuantumATK. These pseudopotentials are generated with the Fritz-Haber Institute (FHI) pseudopotential code. They are numerical norm-conserving pseudopotentials with a single projector for each angular momentum and without semicore states. For a number of elements the exclusion of semi-core states gives a low accuracy.
The basis sets provided with the FHI pseudopotentials use generic parameters, which are not optimized for each element and generally not of high accuracy. However, the basis sets and pseudopotentials are rather efficient and for some elements can give satisfactory accuracy. We only recommend the SZP and DZP basis sets. Below are given $$\Delta$$ values for these settings and the table can be used to estimate the accuracy of the model for various elements.
### OMX Pseudopotentials and basis sets¶
The OMX pseudopotentials are from the OpenMX packages. They are fully relativistic, multiple projectors and with semi-core states. Thus, these are generally high accuracy pseudopotentials which can be used for both LDA, GGA and spin-orbit calculations. The drawback of the pseudopotentials is that they for some elements require very high mesh cutoffs.
The basis sets provided are from the original openMX package. This means that they are not calculated on the fly, and therefore only accurate for the exchange-correlation potential for which they were calculated. Thus, if other exchange-correlation functionals than LDA-PZ or GGA-PBE are used, the accuracy will be lower. For our other pseudopotentials the basis sets are generated on the fly with the selected exchange-correlation potential, thus, even if the pseudopotential is not generated for the exchange-correlation functional the basis set will conform to the exchange-correlation functional.
For the OMX pseudopotentials, we have defined two basis set types, Medium and High. It is also possible for the user to define custom basis sets through the atomic_species keyword, see OpenMXBasisSet.
The basis sets was pre-calculated using GGA-PBE or LDA-PZ and included together with the pseudopotential. Thus, if other exchange-correlation functionals than LDA-PZ or GGA-PBE are used, the accuracy will be low.
For the other pseudo potentials the basis sets are calculated on the fly, using the selected exchange-correlation potential. i.e. only core electrons are treated with the GGA-PBE functional, while valence electrons are treated with the selected exchange-correlation functional.
Below we provide the $$\Delta$$ values for the Medium and High basis sets. For the High basis set we also provide the $$\Delta$$ value when a 100 Ha mesh cutoff is used. This, gives an indication for which elements the default mesh cutoff needs to be increased.
### HGH Pseudopotentials and basis sets¶
The Hartwigsen–Goedecker–Hutter (HGH) type pseudopotentials are also norm-conserving pseudopotentials, however, include multiple projectors and semi-core states. The pseudopotentials use analytical functions which are slightly lower accuracy than numerical pseudopotentials. These pseudopotentials require high values for the mesh cutoff for some elements.
For each pseudopotential we provide a hierarchy of basis sets. The basis sets were optimized to describe the total energy of dimers with different bondlengths. This was an early version of our basis set optimization tool and not all elements are well described.
Generally the pseudopotentials and basis sets have better accuracy than the FHI pseudopotentials but can be computationally heavy and require high mesh cutoffs. The sets are only provided for backwards compatibility and are no longer recommended.
## References¶
[GBRV14] (1, 2, 3, 4, 5, 6, 7, 8) Kevin F. Garrity, Joseph W. Bennett, Karin M. Rabe, and David Vanderbilt. Pseudopotentials for high-throughput DFT calculations. Computational Materials Science, 81:446 – 452, 2014. doi:10.1016/j.commatsci.2013.08.053.
[Ham13] D. R. Hamann. Optimized norm-conserving vanderbilt pseudopotentials. Phys. Rev. B, 88:085117, Aug 2013. doi:10.1103/PhysRevB.88.085117.
[JTH14] François Jollet, Marc Torrent, and Natalie Holzwarth. Generation of projector augmented-wave atomic data: A 71 element validated table in the xml format. Computer Physics Communications, 185(4):1246 – 1254, 2014. URL: http://www.sciencedirect.com/science/article/pii/S0010465513004359, doi:https://doi.org/10.1016/j.cpc.2013.12.023.
[LBBjorkman+16] Kurt Lejaeghere, Gustav Bihlmayer, Torbjörn Björkman, Peter Blaha, Stefan Blügel, Volker Blum, Damien Caliste, Ivano E. Castelli, Stewart J. Clark, Andrea Dal Corso, Stefano de Gironcoli, Thierry Deutsch, John Kay Dewhurst, Igor Di Marco, Claudia Draxl, Marcin Dułak, Olle Eriksson, José A. Flores-Livas, Kevin F. Garrity, Luigi Genovese, Paolo Giannozzi, Matteo Giantomassi, Stefan Goedecker, Xavier Gonze, Oscar Gr\r anäs, E. K. U. Gross, Andris Gulans, François Gygi, D. R. Hamann, Phil J. Hasnip, N. A. W. Holzwarth, Diana Iuşan, Dominik B. Jochym, François Jollet, Daniel Jones, Georg Kresse, Klaus Koepernik, Emine Küçükbenli, Yaroslav O. Kvashnin, Inka L. M. Locht, Sven Lubeck, Martijn Marsman, Nicola Marzari, Ulrike Nitzsche, Lars Nordström, Taisuke Ozaki, Lorenzo Paulatto, Chris J. Pickard, Ward Poelmans, Matt I. J. Probert, Keith Refson, Manuel Richter, Gian-Marco Rignanese, Santanu Saha, Matthias Scheffler, Martin Schlipf, Karlheinz Schwarz, Sangeeta Sharma, Francesca Tavazza, Patrik Thunström, Alexandre Tkatchenko, Marc Torrent, David Vanderbilt, Michiel J. van Setten, Veronique Van Speybroeck, John M. Wills, Jonathan R. Yates, Guo-Xu Zhang, and Stefaan Cottenier. Reproducibility in density functional theory calculations of solids. Science, 2016. doi:10.1126/science.aad3000.
[Oza03] T. Ozaki. Variationally optimized atomic orbitals for large-scale electronic structures. Phys. Rev. B, 67:155108, 2003. doi:10.1103/PhysRevB.67.155108.
[OK04] T. Ozaki and H. Kino. Numerical atomic basis orbitals from h to kr. Phys. Rev. B, 69:195113, 2004. doi:10.1103/PhysRevB.69.195113.
[SG15] M. Schlipf and F. Gygi. Optimization algorithm for the generation of oncv pseudopotentials. Computer Physics Communications, 196:36 – 44, 2015. doi:10.1016/j.cpc.2015.05.011.
[vSGB+18] M.J. van Setten, M. Giantomassi, E. Bousquet, M.J. Verstraete, D.R. Hamann, X. Gonze, and G.-M. Rignanese. The pseudodojo: Training and grading a 85 element optimized norm-conserving pseudopotential table. Computer Physics Communications, 226:39 – 54, 2018. URL: http://www.sciencedirect.com/science/article/pii/S0010465518300250, doi:https://doi.org/10.1016/j.cpc.2018.01.012.
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The ratio is a measure of short-term liquidity, with a higher payable turnover ratio being more favorable. Next » By Rashid Javed (M.Com, ACMA) Back to: Accounting ratios (calculators) Show your love for us by sharing our contents. The average payment period ratio represents the average number of days taken by the firm to pay its creditors. In the past I have used a similar speadsheet, but cannot remember the formula (I also didn't have the forsight to copy the details). The accounts payable turnover ratio is a short-term liquidity measure used to quantify the rate at which a company pays off its suppliers. The average collection period, therefore, … However, if information for the credit purchases is not be available, you can also use the formula below that will produce comparable results: Creditor Days Ratio = (Trade Creditors/Cost of Sales)*365. Debtors's Collection Period = Debtors (amount of money owed) x 365 = Number of days taken to collect debt _____ Sales Turnover. The most commonly purchased type of credit insurance is: credit life insurance. Calculate your payable payment period. not preferred by the companies for the reason already explained above (creditor Example of Average Collection Period. Ideal creditor payment If the firm’s credit policy allows a credit of say 2 months. of shorter creditor payment period is availing the discount available on the Average payment period calculator. Keep in mind that the payable payment period figure represents an average time allotted as well as the average time your company takes to pay its creditors. A business shows opening trade creditors on their balance sheet of £50,000 and a closing balance of £70,000. The formula is as below, Creditors Turnover ratio = $$\frac{Credit Purchases}{Average Creditors}$$ OR. Accounts payable at the beginning and end of the year were $12,555 and$25,121, respectively. Purpose of the paper: This conceptual paper examines formulas and offers recommendations on how to calculate the average payment period to trade creditors. Accounts payable include both sundry creditors and bills payable. During the year, total credit sales are 1,000,000 USD. How do you calculate average days to pay accounts payable? The collection period may differ from company to company. Formula for Average Collection Period. The payment period is the period of time from the point a debt is incurred to the due date of the repayment. Creditor Days is calculated as: [Trade Creditors] / [Creditor Expenses] * 365. Annual cost of a discount . Days payable outstanding (DPO) is an efficiency ratio that measures the average number of days a company takes to pay its suppliers.. If creditors give you no credit for payments made during the billing period, this is called the: previous balance method. 365 ÷ TAPT = Average Accounts Payable Days. Second, knowing the collection period beforehand helps a company decide means to collect the money that is due to the market. It calculates the velocity with which creditors are paid off during the year. source of funding (funding without cost). It is calculated as accounts payable / (total annual purchases / 360). Does Hermione die in Harry Potter and the cursed child? The accounts payable turnover ratio measures how quickly a business makes payments to creditors and suppliers that extend lines of credit. In other words, a reducing period of time is an indicator of increasing efficiency. By delaying payment to suppliers companies face possible problems: ... if the firm is short of funds, it might wish to make maximum use of the credit period allowed by suppliers regardless of the settlement discounts offered. This formula reveals the total accounts payable turnover. Typically such agreements involve a short interest-free credit period during which the buyer can make its payment. Asked By: Saihou Mendiberrygaray | Last Updated: 19th June, 2020. Determine the tax deduction for the pay period using the F2 amount in 2. This period represents the time it takes from when a credit transaction takes place to when credit payment is made and received. longer payment is better. Creditor payment period vary industry to industry. Creditor Days Ratio = (Trade Creditors/Credit Purchases)*365. Here is the formula you’ll need to use: Creditor days = Average Trade creditors/Purchases x 365. What is the Japanese influence on Filipino literature? Creditors / Payable Turnover Ratio (or) Creditors Velocity = Net Credit Annual Purchases / Average Trade Creditors Trade Creditors = Sundry Creditors + Bills Payable Average Trade Creditors = (Opening Trade Creditors + Closing Trade Creditors) / 2 Creditors Payment Period is a term that indicates the time (in days) during which remain current liabilities outstanding (the enterprise use free trade credit). Then divide the resulting turnover figure into 365 days to arrive at the number of accounts payable days. Develop better payment … The formula for DPO is: = / / where ending A/P is the accounts payable balance at the end of the accounting period being considered and Purchase/day is calculated by dividing the total cost of goods sold per year by 365 days. A debtor collection period is the amount of time that is required for customers of a business to receive invoicing for goods and services rendered, schedule payment for those invoices and ultimately tender that payment to the provider. One of the main advantages So to calculate the average collection period, we use the following formula: (($10,000 ÷$100,000) x 365). This channel has now moved to the official Business Loan Services Channel. Generally, lower the ratio, the better is the liquidity position of the firm and higher the ratio, less liquid is the position of the firm. Example. Against the simplicity of the formula, the calculation and practical usability of this formula have certain questions. The inverse of this ratio, when multiplied by 365, gives the average number of days a payable remains unpaid. It is important to note those creditors are free NEGOTIATE PAYMENT TERMS WITH YOUR SUPPLIERS. Days = Creditors / (Purchases / 30) Days = 19,000 / (18,000 / 30) = 32 days Average Payment Period is one of the important solvency ratios of the company and helps a company track and know its ability to pay the amount payable to its creditors. Secondly, what is the formula for average payment period? Advantages Collection period normally depends on Step 2 - Formula to calculate basic federal tax (T3) T3 = Annual basic federal tax = (R × A) – K – K1 – K2 – K3 – K4 Before you can calculate Creditor Days, you’ll need to have the following numbers available to you. Instead, total purchases will have to be calculated by adding the ending inventory to the cost of goods sold and subtracting the beginning inventory. (Note: Use total purchases made if the number for credit purchases is not known.) Creditor payment period is Creditors Payment Period (or Payables Turnover Ratio, Creditor days) is a term that indicates the time (in days) during which remain current current liabilities outstanding (the enterprise use free trade credit). It can be calculated by multiplying the days in the period by the average accounts receivable in that period and dividing the result by net credit sales during the period. Same as debtors turnover ratio, creditors turnover ratio can be calculated in two forms, creditors turnover ratio and average payment period. important calculation, because longer period means that company is enjoying F1 = If the F1 amount is implemented after the first pay period in the year, F1 must be adjusted using the following formula: (P × F1) / PR. Here is the formula: Accounts Receivable Payment Period = Average Receivables / (Net Credit Sales / 365 days) Net Credit Sales =1,000,000 USD; Average Receivables = (20,000 + 25,000) / 2 =22,500; Accounts Receivable Payment Period = 22,500 / (1,000,000 / 356) = 8 Days. As trade payables relate to credit purchases so credit purchases figure should be used in calculating this ratio. Companies that can pay off supplies frequently throughout the year indicate to creditor that they will be able to make regular interest and principle payments as well. The equation to calculate Creditor Days is as follows: Creditor Days = (trade payables/cost of sales) * 365 days (or a different period of time such as financial year) [CP_CALCULATED_FIELDS id=”5″] What you’ll need to calculate Creditor Days. Creditor payment period calculation has been explained with an example; Creditor payment Period = Average Creditor x 365 Net Credit Purchases = Gross Credit Purchases – Purchase Return. What happens after creditor wins judgment? and Goodwill of the company is also at stake with delayed payments. The discount period is the period between the last day on which the discount terms are still valid and the date when the invoice is normally due. It helps the management judge how efficiently the accounts payables are being handled. Credit Period refers to the average time given by the seller to its customer for making the payments against the credit sales. the market practice and therefore company has little choice for selection of Average Payment Period: Average payment period ratio gives the average credit period enjoyed from the creditors. early payment. The average payment period formula is calculated by dividing the period’s average accounts payable by the derivation of the credit purchases and days in the period.Average Payment Period = Average Accounts Payable / (Total Credit Purchases / Days)To calculate, first determine the average accounts payable by dividing the sum of beginning and ending accounts payable balances by two, as in this equation:Average Accounts Payable = (Beginning + Ending AP Balance) / 2Now, use the answer to solv… What is a good average collection period? Variable Overhead Expenditure Variance Formula, Variable Overhead Efficiency Variance Formula, Fixed Overhead Efficiency Variance Formula. is source of free financing). In that case, the formula for the average collection period should be adjusted as per the necessity. Thump rule is Under this mechanism, all claims of secured financial creditors must be fully paid before payments are made to unsecured financial creditors, who must in turn be fully paid before operational creditors. You might be wondering what is the difference between these two formulas. Ask for Contact Information. Average Payment Period Ratio = Average Accounts Payable / (Total Credit Purchases / Days) Where, Average Accounts Payable = It is calculated by firstly adding the beginning balance of the accounts payable in the company with its ending balance of the accounts payable and then diving by 2. 4] Working Capital Turnover Ratio How to Calculate Creditor Days. With these cashflow settings Calxa uses standard accounting ratios to create payment profiles that are applied to the Creditor Days and Debtor Days accounts. It signifies the credit period enjoyed by the firm in paying creditors. This ratio helps creditors analyze the liquidity of a company by gauging how easily a company can pay off its current suppliers and vendors. It measures the average amount of days the business takes to pay its creditors i.e. has been shown below. How do you analyze/interpret the Creditors (Accounts Payable) Payment Period? Debtors and creditors may be defined as follows; Debtors – In a business scenario, a person or a legal body who owes money to another party is called a debtor. The more days available to pay the better. For example, if monthly purchases are 18,000 and month end creditors are 19,000 the creditor days is calculated as follows. The account receivable outstanding at the end of December 2015 is 20,000 USD and at the end of December 2016 is 25,000 USD. If payment is not received by the due date, interest charges will apply. How do you calculate it? Plugging these numbers into the formula, you get a receivables turnover of 12.1457 and a credit period of 30.05. Disadvantages Creditor Days = (trade payables/cost of sales) * 365 days (or a different period of time such as financial year). Definition The average payment period (APP) is defined as the number of days a company takes to pay off credit purchases. A business shows opening trade creditors on their balance sheet of £50,000 and a closing balance of £70,000. Formula: Solved Example: Click on Analysis of Financial Statement of a Business to read the solved example of trade receivable collection period ratio. [Trade Creditors] / [Creditor Expenses] * 365. It is a type of loan which doesn’t have any interest in it. It indicates the speed with which the payments are made to the trade creditors. The number of days in the corresponding period is usually taken as 365 for a year and 90 for a quarter. average payment period. What is the formula for calculating the Creditors (Accounts Payable) Payment Period? The creditors' payment period is an activity ratio. Result: « Prev. free credit for long period. options are available, and goodwill of the company is on the higher side. The average payment period of Metro trading company is 60 days. 6 ways to reduce your creditor / debtor days. Assess the Accounts Receivable Payment Period of the company. Creditor payment period formula has been shown below. Definition - What is Average Payment Period? It can be calculated using the following formula: Average Payment Period = Trade Creditors / Average Daily Credit Purchase. Example . Creditors turnover ratio is also know as payables turnover ratio. Average Collection Period = (365 Days or 12 Months) / (Debtor / Receivable Turnover Ratio) You can use the receivable turnover calculator to calculate the receivable turnover ratio and the collection period. [Creditor Expenses] Includes all accounts where the Cashflow Setting indicates Creditors apply. Here is the formula you’ll need to use: Creditor days = Average Trade creditors/Purchases x 365. As the receivables’ collection period provides an insight into the credit terms offered to the credit customers. The average time (in months and days) it takes a business to make payments to its creditors is known as the average payment period, or days payable outstanding (DPO).. Creditor Days show the average number of days your business takes to pay suppliers. Formula to Calculate Creditor’s Turnover Ratio. For example, if the credit period is 2.5 months and the current month is April, then March and April will be “whole months” where no payment has been received, with half of February’s monies still outstanding too. credit accident and health insurance. Trade payables – the amount that your business owes to sellers or suppliers. How do you calculate creditor days on a balance sheet? Then divide the resulting turnover figure into 365 days to arrive at the number of accounts payable days. Analysis and Interpretation: Short collection period is usually preferred. Delayed payment shows that company For example, let's say your company had a beginning accounts payable balance of $700,000 at the start of the year. Click to see full answer People also ask, what does creditors payment period mean? Creditor payment period formula Here is the formula: Accounts Receivable Payment Period = Average Receivables / (Net Credit Sales / 365 days) normally preferred by the companies due to free financing, however, delayed Accounts payable … It is on the pattern of debtors turnover ratio. The ratio is a useful indicator when it comes to assessing the liquidity position of a business. I want to be able to input Sales and Purchases data for the P&L and automatically calculate Debtors and Creditors for the B/S (ideally I would also like to be able to adjust the Debtor/Creditor days etc.) During the period the cost of sales was £300,000. Copyright 2020 FindAnyAnswer All rights reserved. The trade payables’ payment period ratio represents the time lag between a credit purchase and making payment to the supplier. It enables the enterprise to compare the real collection period with the granted/theoretical credit period. The Creditor (or payables) days number is a similar ratio to debtor days and it gives an insight into whether a business is taking full advantage of trade credit available to it. Beside above, how can I improve my creditors payment period? Get the caller's name, company name, mailing address, and phone number. However , Shorter payment period has number of Include all … If you are using purchases for a different period then replace the 365 with the number of days in the management accounting period. During that year the company had credit sales of$400,000. Write down the following formula and apply your own figures. The formula can be modified to exclude cash payments to suppliers, since the numerator should include only purchases on credit from suppliers. Creditor days estimates the average time it takes a business to settle its debts with trade suppliers. payment may have number of disadvantages. It finds out how efficiently the assets are employed by a firm and indicates the average speed with which the payments are made to the trade creditors. How long does a creditor have to collect a debt in New York? The accounts payable turnover formula is calculated by dividing the total purchases by the average accounts payable for the year.The total purchases number is usually not readily available on any general purpose financial statement. An alternate formula for calculating the average collection period is: the average accounts receivable balance divided by the average credit sales per day. The creditors' payment period is an activity ratio. advantages i.e. Days = Creditors / (Purchases / 365) Days = 70,000 / (311,000 / 365) = 82 days It takes the business on average 82 days to pay its suppliers. week financial position, creditor confidence also shakes with delayed payment, supplier , continuity or stability of supplies is guaranteed, more credit Creditors Turnover ratio = $$\frac{Credit Purchases}{Creditors + Bills Payable}$$ Average Creditors = $$\frac{Opening Creditors + Closing Creditors}{2}$$ Now using the same ratio, we can also calculate the average payment period in the number of days/weeks/months. of Longer Creditor payment period. Posted in: Accounting ratios (calculators) Average accounts payable: Net credit purchases: Number of working days (select one): Calculate Reset. Payable Payment Period = Trade Creditors / Average Daily Credit Purchase Average Daily Credit Purchase = Credit Purchase / Annual Number of Work Days The shorter version of this formula is: Payable Payment Period = (Trade Creditors x Number of Work Days) / Net Credit Purchase. The average collection period ratio calculates the average amount of time it takes for a company to collect its accounts receivable, or for its clients to pay. Which type of credit insurance repays your debt in the event of a loss of income due to illness or injury? Use the following steps to determine the cost of credit for a payment transaction: Determine the percentage of a 360-day year to which the discount period will be applied. suppliers. Can a Judgement creditor force the sale of my home? of … shorter creditor payment period improves the confidence of the For a business, the amount to be received is usually a result of a loan provided, goods sold on credit, etc. The reason for the IF statement here is to prevent calculations considering periods before the beginning of the forecast period. Average Payment Period = $$\frac{Number of days/weeks/months}{Creditors T/O Ratio}$$ Again creditors turnover ratio has great importance. its creditor or company. The creditor days ratio is calculated as follow. What is the difference between a secured creditor and an unsecured creditor? Average Daily Credit Purchase= Credit Purchase / No. What's the difference between Koolaburra by UGG and UGG? of Shorter Creditor Payment Period. On average, a lower debtor collection period is seen as more positive than a high debtor collection period as it means that a company is collecting payment at a faster rate. But a higher payment period also implies greater credit period enjoyed by the firm and consequently larger the benefit reaped from credit suppliers. Average payment period = 360 days /6 times = 60 days * Computation of net credit purchases: = $570,000 –$150,000 = $420,000 ** Computation of average accounts payable: = [(A/R opening + N/R opening) + (A/R closing + N/R closing)] / 2 = [($65,000 + $20,000) + ($40,000 + $15,000)] / 2 =$70,000. period means is difficult to establish. It measures the average amount of days the business takes to pay its creditors i.e. It is a ratio of net credit purchases to average trade creditors. It is crucial for you to be aware of the average payable period in order for you to be prepared to take necessary action when the time comes to pay creditors. that period. During the period the cost of sales was £300,000. Typically, the collection period begins on the date the invoice is issued and ends on the date that the payment for that invoice is posted. with an example; It means that at average company takes 47 days to pay A company may sell seasonally. Debtor’s ageing is a very good tool to check the implementation of its credit policy. It is calculated by dividing trade payables by the average daily purchases … Let’s imagine our fictional business Learnmanagement bookshop LM2 sales turnover is £100000 for the year and they have received most of the money from customers for the books sold. The company wants to measure how many times it paid its creditors over the fiscal year Fiscal Year (FY) A fiscal year (FY) is a 12-month or 52-week period of time used by governments and businesses for accounting purposes to formulate annual. Where: [Trade Creditors] Equals the combined closing balance at the Last Actuals Period for all accounts nominated in the Default Accounts screen as Trade Creditors. How long can a creditor collect on a Judgement in California? Debtor Collection Period = (Average Debtors / Credit Sales) x 365 ( = No. The average payment period is the average time a company takes to make payments to its creditors. By debtor’s ageing, debtors are classified in groups of say collection period between 0-2 months, 2-4 months and greater than 4 months. In this lesson, we explain what the Creditors Payment Period is and go through the formula and a clear example of how to calculate it. Assume that a company had on average $40,000 of accounts receivable during the most recent year. Liquidation amount would be distributed to companys creditors in accordance with the “waterfall” mechanism set out in Section 53 of Insolvency and Bankruptcy Code, as per the plan. Accounting professionals quantify the ratio by calculating the average number of times the company pays its AP balances during a specified time period. The formula is: Total supplier purchases ÷ ((Beginning accounts payable + Ending accounts payable) / 2) This formula reveals the total accounts payable turnover. Creditor payment period calculation has been explained The following formula is used to calculate creditors / payable turnover ratio. Shorter payment period is Calculation of Creditors Payment Period Creditors Payment Period = Trade creditors / credit purchases Number of days) Total Credit Purchases = It refers to the total amount of credit purchases made by the company … How do you calculate creditors on a balance sheet? The accounts payable turnover ratio, also known as the payables turnover or the creditor’s turnover ratio, is a liquidity ratio that measures the average number of times a company pays its creditors over an accounting period. What cars have the most expensive catalytic converters? suppliers. Example Debtor's Collection Period Calculation. 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Time period of$ 400,000 times the company pays its AP balances during a specified period! Recommendations on how to calculate creditors payment period formula average number of advantages i.e the payment is... Is normally preferred by the seller to its creditors i.e longer payment period normally... Daily purchases … creditor payment period is creditors payment period formula activity ratio also know as payables turnover ratio being more favorable cost. Difference between these two formulas the cursed child a reducing period of.. Creditors and bills payable calculate creditors on their balance sheet of £50,000 and a closing balance of $.! Include both sundry creditors and suppliers that extend lines of credit insurance repays your in... Before you can calculate creditor days on a balance sheet measures how quickly a business to its! Loan which doesn ’ t have any interest in it at the end of 2016. 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And offers recommendations on how to calculate the average number of accounts payable days for payment... Companies due to the market helps creditors analyze the liquidity of a company by gauging easily... Is incurred to the creditor days show the average amount of days a payable unpaid! The cursed child figure into 365 days to pay accounts payable … the creditors ' payment period is the payment. Have any interest in it purchases – Purchase Return an unsecured creditor £50,000 and closing! Days, you get a receivables turnover of 12.1457 and a closing balance of £70,000 cursed child increasing efficiency or... Greater credit period enjoyed by the firm ’ s credit policy allows a credit Purchase and payment... Purchases are 18,000 and month end creditors are free source of free financing however., variable Overhead Expenditure Variance formula, the amount that your business to! Helps a company had a beginning accounts payable days larger the benefit reaped credit. By 365, gives the average amount of days your business owes to sellers or suppliers taken as for. Sundry creditors and suppliers that extend lines of credit insurance repays your in...: previous balance method the early payment from credit suppliers other words, a reducing period the. Paper examines formulas and offers recommendations on how to calculate creditors on their sheet. Which doesn ’ t have any interest in it is called the: balance... To settle its debts with trade suppliers that company is enjoying free credit for payments during. Turnover of 12.1457 and a closing balance of £70,000 ( = No can calculated. Of increasing efficiency credit from suppliers a beginning accounts payable turnover ratio is a ratio of net credit is! Companies for the reason for the pay period using the following formula is as below, turnover! Caller 's name, company name, company name, mailing address and... You analyze/interpret the creditors time period can calculate creditor days estimates the average period! Calculate the average number of days a company can pay off its suppliers you can calculate creditor days is by! Recommendations on how to calculate creditors / payable turnover ratio = \ ( \frac { purchases... Days accounts you get a receivables turnover of 12.1457 and a closing balance £70,000! Purchases on credit from suppliers your own figures you can calculate creditor days, you get a receivables of. Debts with trade suppliers receivables ’ collection period normally depends on the market previous. } { average creditors } \ ) or | Last Updated: 19th June, 2020 month end creditors 19,000. To arrive at the number of disadvantages, with a higher payment period definition the average of! Multiplied by 365, gives the average number of days a company its... Payment may have number of days the business takes to pay its creditors i.e of a loan,... Of net credit purchases is not preferred by the seller to its for... Average time a company takes to pay its suppliers the point a debt is incurred the! Days estimates the average amount of days a company by gauging how easily a company by gauging easily... At the beginning and end of December 2016 is 25,000 USD year ) a useful indicator it. During that year the company had on average$ 40,000 of accounts payable days incurred! Of say 2 months be calculated using the following formula: average payment period is an ratio... Moved to the market average amount of days a company takes to make payments to its customer making. To when credit payment is made and received 's say your company had on average \$ 40,000 accounts... Can be calculated in two forms, creditors turnover ratio, creditors turnover ratio measures how quickly a business opening... Are 1,000,000 USD pay accounts payable time from the creditors ( accounts payable include both sundry creditors and that... Ideal creditor payment period is not received by the average payment period is usually preferred is on the early.! Standard accounting ratios to create payment profiles that are applied to the creditor on... Numbers available to you ideal creditor payment period of the forecast period formula and apply own.
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2021-04-11 07:08:09
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http://www.myundergradlabs.com/2012/08/identifying-unknown-organic-compounds.html
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## Labels
### Identifying Unknown Organic Compounds By Solubility Properties
Summary
In this experiment we learned to identify an unknown organic compound based on its solubility properties.
We were provided with an unknown solid compound and five liquid solvents. The unknown was one of three possible organic compounds which we were able to identify based on its solubility in each of the provided solvents. The following report explores some of the molecular properties of the given solutes and solvents and explains the effects of these properties on solubility.
Note: For the purposes of this experiment, we consider the salute soluble if 0.01 g of it can be dissolved in 1ml of the solvent at room temperature.
How intermolecular forces effect solubility
There are three main steps involved in dissolution of a solid solute in a liquid solvent.
1. Breakdown of the bonds between solute particles. This step requires energy and is therefore endothermic.
2. Breakdown of the bonds between solvent particles which is also an endothermic step.
3. Formation of new bonds between solute and solvent particles. This step is exothermic since it results in energy release.
The more exothermic the entire process is, the more soluble the solute. In order for the dissolution to proceed in the standard laboratory conditions, the process has to be exothermic or require very little energy (as much as can be provided by room temperature). In other words, the total energy required to break the bonds between solute particles and solvent particles has to be less than, equal to or only slightly greater than the energy release during formation of the bonds between the salute and solvent particles. Therefore, salute-solvent intermolecular forces has to be greater than or similar to the salute-salute and solvent-solvent intermolecular forces.
The strength of the intermolecular forces of a compound depends on the size, structure, polarity and hydrogen-bonding capabilities of its particles. Therefore, compounds with similar characteristics to the solvent are more likely to be soluble.
The solvents and their properties
Water molecules are highly polar with a relatively low mass. In addition, they are capable of forming hydrogen bonds. Each water molecule is capable of forming four hydrogen bonds with its surrounding molecules.
A hydrogen bond is a strong form of dipole–dipole interaction but it also has some qualities that is similar to covalent bonds. Hydrogen bonds are stronger than van der Waals and dipole–dipole interactions but weaker than ion-dipole, ionic and covalent bonds. A compound is soluble in water if its particles are capable of forming bonds with water molecules that are similar to or greater than hydrogen bonds in force.
Many organic compounds contain a non-polar backbone but also have a polar functional group. Water solubility of such compounds depends on their size, structure and the functional group's bonding capabilities. We will see some examples of these compounds in this experiment.
Hydrochloric Acid is a very strong aqueous acid and reacts with compounds with basic functional groups to form salts. If an organic compound is insoluble in water but dissolves in hydrochloric acid, we can conclude that the compound has a basic functional group and reacts with hydrochloric acid to form a water soluble salt. The water insolubility of such compound probably means that it contains more than 5 carbons since longer carbon chains decreases water solubility. The reactions are as follows:
Formation of Hydrochloric Acid
Hydrogen chloride (HCl) + Water (H2O) → Hydronium ion (H3O+) + Chloride ion (Cl−)
Reaction of basic water-insoluble organic compound with hydrochloric acid
Amine (R-NH2) + Hydrochloric acid (H3O+, Cl-) → R-ammonium chloride (R-NH3+ Cl-) + Water (H2O)
The reaction produces R-NH3+ Cl- which is a water soluble salt.
Aqueous Sodium Hydroxide (NaOH(aq)) is a strong basic solution and can help dissolve organic water-insoluble compounds that have an acidic functional group. NaOH(aq) reacts with the acidic functional group and forms a water soluble salt. For example, sodium hydroxide can be used to de-protonate weak acidic organic compounds such as phenols to create water soluble salts:
C6H5OH + Na+ + OH- + H2O → C6H6ONA+ + OH- + H3O+
Phenoxide anion (C6H6O-) is highly soluble in water.
Aqueous Sodium Bicarbonate (NaHCO3(aq)) is a weak basic solution that can also help dissolve water-insoluble organic compounds with an acidic functional group by salt formation. However, the acidic functional group needs to be stronger than the previous example since sodium bicarbonate is a much weaker base than sodium hydroxide. The following is an example of such reaction:
Reaction of Sodium Bicarbonate in Water
NaHCO3 + H2O $\rightarrow$ H2CO3 + OH- + Na+
H2CO3 + H2O $\rightleftarrows$ HCO3- + H3O+
HCO3- + H2O $\rightleftarrows$ CO32- + H3O+
Reaction of Aqueous Sodium Bicarbonate with a Carboxylic Acid
R-COOH + Na+ + OH- + H2O → R-COONA+ + OH- + H3O+
The above reaction produces R-COO- NA+ which is a water soluble salt.
Diethyl ether (C2H5)2O is a colourless organic solvent suitable for dissolving compounds with weaker intermolecular forces. Ether molecules are slightly polar due to the electronegative oxygen. They are however unable to form hydrogen bonds with each other and are only connected by dipole-dipole interactions which is much weaker than hydrogen bonds and ion-dipole interactions that existed in the previously discussed solvents. In other words, breaking the bonds between ether molecules takes less energy and so ether is able to dissolve even non-polar compounds. Keep in mind that because of its weak intermolecular forces, ether is not a good solvent for more polar solvents.
The solutes and their properties
The unknown compound that we had to identify was one of the following three compounds:
Glucose C6H12O6
In Water: Glucose has five hydroxyl groups and they are all capable of forming hydrogen bonds with water. This makes glucose highly soluble in water.
In Hydrochloric Acid: The high polarity of glucose makes is soluble in hydrochloric acid. The hydroxyl groups are likely to form ion-dipole bonds with the H+ ion. In addition, as before, many hydrogen bonds with water molecules will help dissolve glucose in hydrochloric acid.
In Aqueous Sodium Hydroxide: Glucose is soluble in the solution of sodium hydroxide in water. Hydrogen bonds with water molecules will help the solubility of glucose in this solvent. Also, glucose is likely to react with the hydroxide ions, losing some of the hydrogens attached to the hydroxyl groups to them. This might result in some ion-dipole interactions which also help the the solubility of glucose.
In Aqueous Sodium Bicarbonate: The high polarity of glucose in addition to the hydroxyl groups will again make glucose soluble in aqueous sodium bicarbonate solution.
In Diethyl ether (C2H5)2O: The high polarity of glucose has the reverse effect this time. As mentioned before, ether has a low polarity and is not good at dissolving highly polar compounds. The ether molecules are unable to break the intermolecular forces of glucose and this makes glucose insoluble in ether.
P-toluidine C7H9N
In Water: P-toluidne is slightly basic due to the amino functional group but it is insoluble in water because of the benzene ring. The polarity of the amine group is simply not enough to make a molecule of p-toluidine's shape and size water soluble.
In Hydrochloric Acid: P-toluidine reacts with HCl.H2O to form a water soluble ammonium salt. It is therefore soluble in hydrochloric acid. This is an example of water solubility by salt formation.
In Aqueous Sodium Hydroxide: Sodium Hydroxide is a strong base and so it is unable to protonate p-toluidine to form a water soluble salt. P-toluidine is therefore insoluble in aqueous sodium hydroxide.
In Aqueous Sodium Bicarbonate: Unlike hydrochloric acid, sodium bicarbonate is not a strong enough acid to protonate the amine group. As a result, P-toluidine remains insoluble in aqueous sodium bicarbonate solution.
In Diethyl ether (C2H5)2O: P-toluidine is soluble in ether due to the low polarity of its molecules and weak intermolecular forces.
Benzoic Acid C6H5COOH
In Water: Benzoic acid is a kind of carboxylic acid (R-COOH). Water-solubility of carboxylic acids decrease as the number of carbons increase. In case of benzoic acid, the molecule contains seven carbons and six of them form a benzene ring. Benzoic acid is capable of forming hydrogen bonds with water molecules and if you increase the temperature some benzoic acid molecules even loose their hydrogen to water molecules and form ions. Solubility of benzoic acid increases as more molecules lose a proton to form ions. This causes benzoic acid to be insoluble in cold water but soluble in hot water.
In Hydrochloric Acid: Hydrochloric acid is a very strong acid. Hydrogen chloride molecules like to lose a proton and become ions. In order for benzoic acid to become soluble in an aqueous solution the benzoic acid molecules need to also lose protons and this is harder to accomplish in the presence of acidic compounds such HCL. This makes benzoic acid insoluble in hydrochloric acid.
In Aqueous Sodium Hydroxide: Sodium Hydroxide is a strong base and helps deprotonate benzoic acid molecules. As a result, more benzoic acids turn to water soluble ions and this makes benzoic acid soluble in the aqueous sodium hydroxide solution
In Aqueous Sodium Bicarbonate: Although the aqueous sodium bicarbonate solution is slightly basic, it is not strong enough to deprotonate enough benzoic acid molecules to dissolve it. As a result, benzoic acid is insoluble in aqueous sodium bicarbonate solution.
In Diethyl ether (C2H5)2O: Benzoic acid is soluble in ether due to the low polarity of its molecules and weak intermolecular forces.
The Experiment
1. Add 0.01 g of the unknown compound to five different test tube.
2. Add 1 ml of each of the available solvents to each test tube.
3. Record the solubility of the unknown compound in each solvent.
4. If the compound is insoluble in water, try heating the test tube. Record your observation.
5. Identify the unknown compound based on its solubility in each solvent.
My sample displayed similar solubility properties to benzoic acid. I was therefore able to conclude that my sample is in fact benzoic acid.
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2014-04-24 20:07:30
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http://wiki.eveonline.com/en/wiki/DPS
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DPS (Damage Per Second)
Damage Per Second (DPS) is a measure of the rate of combat damage dealt over time by a ship, module, or drone. It is expressed in hitpoints destroyed per second. DPS does not indicate the damage types done; that is usually indicated separately. Note also that DPS is measured against a zero resistance target; actual damage done to the target will be reduced by the target's resistances to the damage type(s) dealt.
DPS is an important quantity in tanking. Ships and structures have a buffer of hitpoints which must be damaged for them to be destroyed. Doing damage at a higher rate of DPS will reduce the time required to destroy a ship or structure. Many ships or structures are able to repair or regenerate hitpoints through shield, armour or structure repair. In these situations it is necessary to do damage at a greater rate than it can be repaired if the target is to be destroyed.
Generally, DPS is averaged over a long period as ships tend not to deal consistent damage, but rather do damage in short bursts. The damage done in a single burst (usually the initial burst) is known as alpha damage or alpha-strike damage. The concept of alpha damage is important because a ship which does high alpha damage is capable of doing more damage than a comparable DPS ship over a short period, but both are capable of doing the same amount of damage over a longer time.
Actual DPS
It is the sum of the theoretical damage done by firing all weapons consecutively averaged over one second. The theoretical DPS would be expressed as the sum of the products of the rate of fire plus flight time and theoretical damage output per cycle, all multiplied by one second:
Equation 1, for the case of N modules:
$DamagePerSecond=\sum_{n=1}^N(RateOfFire(n)+PayloadFlightTime(n))*DamagePerCycle(n)$
Theoretical Damage
As a setup-specific value, DPS is dependent on bonuses from ship type, other fitted modules, and fitted rigs. Character skills and implants in-turn affect DPS directly and indirectly via ship, module, and rig bonuses.
Conventional DPS
Due to the varying amount of time required for different weapon modules to cycle and for payload delivery, the actual moment at which the damage is done does not occur over each second, but rather at the time of weapon contact with the target. In the case of laser weapons, this is effectively instantaneous. In the case of propelled weapons such as missiles, flight time affects actual DPS. However, due to the environment-specific nature of the 'flight_time' variable in Equation 1, it is dropped from the equation, leaving the expression typically referred to by the term 'DPS':
Equation 2
$DamagePerSecond=\sum_{n=1}^NRateOfFire(n)*DamagePerCycle(n)$
Therefore, the practical accuracy of the DPS value for a given ship and fitting approaches actual output as the period of time being considered increases and flight time becomes a smaller fraction of total payload delivery time.
For the specific case of identical weapon modules and an instantaneous payload delivery, the DPS calculation can be simplified to:
Equation 3
$DamagePerSecond=N*RateOfFire*DamagePerCycle$
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2013-05-19 19:43:45
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https://www.andrewszot.com/posts/on_lfo/
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# Practical Challenges of Imitation Learning from Observation
## Overview
In this post, I will explore some practical details in popular imitation learning from observation methods. Learning from observation (LfO) is the problem of learning a policy from a set of state-only expert demonstrations. The goal of LfO is to eventually enable agents to learn by observing humans or other robots. However, LfO is difficult because it both requires learning perception of what the expert is doing, and then learning a control policy on top of this learned perception. We cannot directly apply standard imitation learning approaches like Behavioral Cloning or Generative Adversarial Imitation Learning [2].
Popular LfO methods adapt the standard imitation learning algorithms for the case of having no actions. Behavioral Cloning from Observations (BCO), first learns an inverse model from agent experience, and then uses this to infer the missing expert actions and ultimately perform standard Behavioral Cloning (BC) [1]. Generative Adversarial Imitation from Observation (GAIfO), adapts Generative Adversarial Imitation Learning to LfO by learning a discriminator from state, next state pairs rather than state, action pairs [3]. GAIfO-s is another method sometimes used in practice, which changes the GAIfO discriminator to only take a single state as input [4].
In this post, I will share my experience training BCO, GAIfO, and GAIfO-s. Hyperparameters and implementation details are important for these algorithms. I use the HalfCheetah-v3 environment from OpenAI Gym to show how the algorithm details affect performance. In all sections, the expert dataset is 50 episodes of 1k steps with 6678 average reward on the HalfCheetah-v3 environment.
## BCO
In my experience, the biggest pitfall of BCO is when the policy cannot produce meaningful experience for the inverse model to learn from, resulting in bad action inference on the expert dataset. If the policy begins to produce bad data, the inverse model and policy can get stuck in a bad cycle. The inverse model predicts bad actions, which results in a bad policy, which results in bad experience for the policy, and the cycle continues.
All this means that BCO struggles in problems where a decent inverse model cannot be learned from random exploration. While updating from additional policy data can help, it needs a “good foundation” to start from, or the policy will never have good data to learn from. The importance of exploration and good data for the inverse model leads to two important hyperparameter considerations.
Pre-exploration: There should be a phase before policy learning where a random policy collects data to train the inverse model. Collecting data with only the untrained policy will not be random enough to get meaningful diverse data for the inverse model.
Stochastic Policy: The policy should output a distribution over actions. Increasing the stochasticity of the policy increases the diversity of data for the inverse model.
Below are plots comparing these hyperparameters. While the stochastic policy does not matter for HalfCheetah, I experienced that it is necessary for learning in more complex control tasks like pick and place in robotic manipulation. Its little effect in HalfCheetah could be because exploration is easy and the task is repetitive. The table of hyperparameters used for this plot is below.
Hyperparam Value
$\alpha$ (num updates) 50
Inverse model architecture (400,300)
Inverse model learning rate 3e-4
Inverse model learning rate decay No
# epochs per inverse model update 1
BC policy architecture (400,300)
BC learning rate 3e-4
BC learning rate decay No
# epochs per BC update 10
State normalization Yes, from expert state data
BC stochastic policy Yes, learned mean and standard dev for norm dist
# random exploration steps 200k
total # environment steps 10M
## GAIfO
Reward Type: Since GAIfO relies on adversarial training it can be very sensitive to hyperparameters. Most surprising to me was the importance of the reward function implementation. There are several ways you can implement the reward function in adversarial imitation learning methods (where $D(s)$ is the discriminator with a sigmoid output):
• AIRL: $\log D(s) + \log (1 - D(s))$, expert with label $1$ [6].
• GAIL: $\log D(s) + \log (1 - D(s))$, expert with label $1$ [2].
• Raw: $D(s)$, expert with label $1$.
• GAIfO: $\log D(s)$, expert with label $0$ [3].
The fourth choice is what the GAIfO paper uses. Note that this is a different reward than what popular GAIL codebases use [5]. Using the correct GAIfO reward is crucial for learning. Below are the different rewards in HalfCheetah. All the hyperparameters except the reward type are fixed across runs. Interestingly, some reward types struggle to learn.
Hyperparam Value
Policy architecture (400,300)
Policy optimizer PPO
PPO entropy coefficient 0.001
Policy learning rate 0.001
Policy learning rate decay Yes
Discriminator architecture (400,300)
Discriminator learning rate 0.001
# of discriminator updates per policy update 2
total # environment steps 10M
Another important consideration is the discriminator should be updated more frequently than the policy. By updating the discriminator more, it will be a better fit for the current on-policy state distribution, providing a better reward. A comparison of 1 versus 2 discriminator updates per policy update is shown below.
Since a discriminator accurate for the current distribution of policy data is important, a higher discriminator learning rate is important as well. As shown in the figure below, a lower learning rate results in poor performance.
Finally, while maybe obvious, it’s important to have a high discriminator and network capacity. The below figure compares using a policy and discriminator network architecture with hidden layers of size (400, 300) versus (64, 64).
## GAIfO-s
Intuitively, GAIfO-s should perform worse than GAIfO because it only has access to a single state and therefore cannot infer dynamics. However, I have found that GAIfO-s performance can be better than GAIfO when the state includes temporal information such as velocity. In that case, a single state is enough to infer dynamics information. While GAIfO performs better than GAIfO-s in HalfCheetah, I have found the opposite to be true for harder tasks in robot manipulation.
## Takeaways
• Have an exploration phase in BCO where a random policy collects data.
• Use a stochastic policy in BCO.
• Use the correct GAIfO reward type from the original paper for GAIfO.
• The discriminator should learn faster than the policy in GAIfO. This means increasing the discriminator learning rate and updating it multiple times per policy update.
• Use large networks. This will vary by task, but this is often an issue I forget about.
• GAIfO-s can work well for some problems.
## References
All plots were made with W&B.
• [1] Torabi, Faraz, Garrett Warnell, and Peter Stone. “Behavioral cloning from observation.” arXiv preprint arXiv:1805.01954 (2018).
• [2] Ho, Jonathan, and Stefano Ermon. “Generative adversarial imitation learning.” Advances in neural information processing systems. 2016.
• [3] Torabi, Faraz, Garrett Warnell, and Peter Stone. “Generative adversarial imitation from observation.” arXiv preprint arXiv:1807.06158 (2018).
• [4] Yang, Chao, et al. “Imitation learning from observations by minimizing inverse dynamics disagreement.” Advances in Neural Information Processing Systems. 2019.
• [5] Kostrikov, Ilya. “pytorch-a2c-ppo-acktr.” (2018). https://github.com/ikostrikov/pytorch-a2c-ppo-acktr-gail
• [6] Fu, Justin, Katie Luo, and Sergey Levine. “Learning robust rewards with adversarial inverse reinforcement learning.” arXiv preprint arXiv:1710.11248 (2017).
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2020-09-26 08:13:23
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http://viiia.org/dpuc2/index-2.00.yml
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# dPUC 2
## Domain Prediction Using Context
### by Alejandro Ochoa García, Manuel Llinás, Mona Singh
Extend your Pfam predictions without loss of precision using domain context!
VIIIA
- -
The dPUC (Domain Prediction Using Context) software improves domain prediction by considering every domain in the context of other domains, rather than independently as standard approaches do. Our specific framework maximized the probability of the data assuming a naive Bayes approximation, which reduces to a pairwise context problem, and we have shown that our probabilistic method is indeed more powerful than competing methods.
The dPUC 2.xx series is a major update from dPUC 1.0. For the average user, what matters is that now dPUC works with HMMER 3 and Pfam 24 onward, and dPUC is much faster than before. If you were a dPUC 1.0 user, you should know that inputs and outputs are completely different; the new setup is simpler due to the changes that HMMER3 and the new Pfams have brought. Lastly, there are improvements in the context network parametrization, most notably the addition of directed context. See the release notes for more information.
## Source code
Dpuc-2.00.tgz (73 KB)
Download our Perl source code, in a gzip-compressed tar archive file. It is a large project, with 13 packages and 3 scripts totalling 1746 lines of code (according to cloc).
All my code is released under the GNU GPLv3 (GNU General Public License version 3).
This project is now on GitHub, where you can contribute and improve this software.
### Previous versions
Beta code Dpuc-2.00b.tgz (192 KB), which was larger than subsequent releases because it contained sample files that are no longer included.
The original 1.00 release is available and documented on the dPUC 1.0 website.
## Installation, dependencies
dPUC 2 requires Perl 5 and the Inline::C Perl package, which can be installed with cpan (which is included in standard Perl installations) by running the following command as the root user,
cpan Inline::C
and proceeding with their instructions (you may be asked to install additional packages). Do not hesitate to email me if the installation fails and you need further assistance.
This code also requires the lp_solve 5.5 library (but not the executable). In Fedora/RedHat Linux, you can install it using the following command as root,
yum install lpsolve-devel
Other than that, all you have to do is unpack the code and run the scripts from the directory that contains them. In this mode, the scripts and all packages should stay together in the same directory. You can also run my scripts from arbitrary directories.
You will also need HMMER3 (only the hmmpress and hmmscan executables are needed). Our code also assumes gzip is available in your system.
## Compiling C code
Once the two outside dependencies have been installed correctly, you will need to compile the C portion of dPUC. This compilation will happen automatically the first time 1dpuc2.pl is run, so you may simply run
perl -w 1dpuc2.pl
which will take a little while, then show the "usage" message. If you see an error about not finding the lp_solve library, you may have to change the hardcoded path to the library in my package DpucLpSolve.pm (please email me about this or any other errors, I'd like to know about them).
## Running the dPUC scripts
### HMM databases
The current version of dPUC only works with Pfam. You must download Pfam-A.hmm.gz and Pfam-A.hmm.dat.gz from the Pfam FTP site. It will be necessary to use HMMER3's hmmpress on this HMM database before hmmscan can use it. The following commands achieve that.
# uncompress HMM database first
gunzip Pfam-A.hmm.gz
# prepare HMM database for searching with HMMER3 (which provides hmmpress)
# four files will be generated, with names Pfam-A.hmm.h3{f,i,m,p}
hmmpress Pfam-A.hmm
# (optional) recompress the original HMM file (HMMER3 doesn't use it)
gzip Pfam-A.hmm
You may keep these file compressed from now on, dPUC will read them correctly!
### dPUC context count network
For completeness, my distribution includes a script that will generate the dPUC directed context network of domain family pair counts from Pfam-A.full.gz. However, downloading Pfam-A.full.gz takes a long time (in Pfam 27, that file is 4.1 GB!). For most users it makes more sense to download my precomputed network files, which I provide for every Pfam release starting with version 23.
dpucNet.pfam27.txt.gz (659 KB)
dpucNet.pfam26.txt.gz (524 KB)
dpucNet.pfam25.txt.gz (327 KB)
dpucNet.pfam24.txt.gz (286 KB)
dpucNet.pfam23.txt.gz (198 KB)
### Sample sequence file
To run through these examples, any FASTA format protein sequence file can be used. If you want, you can try this minimal sample file, sample.fa.gz, which consists of only 10 random proteins from the Plasmodium falciparum proteome. The two sample outputs are sample.27.txt.gz and sample.27.dpuc.txt.gz.
Sample outputs for these proteins were created using Pfam 27 and the 64-bit version of HMMER 3.1b1. Small differences in output arise even from using a 32-bit architecture, be aware of that. Additionally, HMMER 3.1b1 timestamps the output, so every run will appear to generate a different file if compared with hash functions such as SHA or MD5, so don't use them. It is better to compare each line with a tool such as zdiff, which is like diff but for compressed files.
### Synopsis of scripts
The following commands can be run on the sample file provided above, plus two Pfam files, all placed in the same directory as the code and called from that location. All input files may be compressed with gzip and they may be specified with or without the GZ extension. Output files are compressed with gzip, whether the outputs indicate a GZ extension or not. So the commands as they are below produce and will work entirely with compressed files, without a single GZ extension indicated.
# create the dPUC context count network for your Pfam version
perl -w dpucNet.pl Pfam-A.full dpucNet.txt
# produce domain predictions with HMMER3 (provides hmmscan) with weak filters.
# this is the slowest step
perl -w 0runHmmscan.pl hmmscan Pfam-A.hmm sample.fa sample.txt
# (optional) compress output, our scripts will read it either way
gzip sample.txt
# produce dPUC predictions with default parameters
perl -w 1dpuc2.pl Pfam-A.hmm.dat dpucNet.txt sample.txt sample.dpuc.txt
### dpucNet.pl 1.00 - Extract the context count network from Pfam predictions
perl -w dpucNet.pl <Pfam-A.full> <dpucNet output>
The required inputs are
• Pfam-A.full: Input "full" domain prediction file from Pfam.
• dpucNet output: Directed context network of domain family pair counts.
This Pfam-specific script counts every ordered domain family pair observed in the full predictions of standard Pfam releases. The code is very optimized to parse such a large file quickly and to store the domain predictions with minimal memory usage (unfortunately, Pfam-A.full lists domains grouped first by family, whereas these family pair counts can only be calculated if predictions are grouped first by protein, so all the data must be in memory before it can be rearranged). The run for Pfam 27 used 3.2 GB of RAM, but it completes quickly (~5 minutes).
You will only need to run this command once per Pfam release. Moreover, you can skip this step altogether by downloading the precomputed dPUC context count networks I provide above (which I recommend, since downloading Pfam-A.full takes a very long time). This script is mostly provided for completeness and so the community can inspect it, find bugs, and otherwise improve it.
### 0runHmmscan.pl 1.01 - Get domain predictions from your protein sequences
perl -w 0runHmmscan.pl <hmmscan> <Pfam-A.hmm> <FASTA input> <output table>
The required inputs are
• hmmscan: the path to the HMMER3 hmmscan executable.
• Pfam-A.hmm: the path to your HMM library of choice (in HMMER3 format).
• FASTA input: the FASTA sequence file, may be compressed with gzip.
• output table: the hmmscan output is plain text table delimited by whitespace (always uncompressed).
This script doesn't simply run hmmscan with default parameters, in fact it changes a few options that are important for dPUC to work. In particular, it makes sure outputs report $$p$$-values in place of $$E$$-values, and it relaxes the heuristic $$p$$-value filters to allow more predictions through. This script sets the most stringent $$p$$-value threshold at 1e-4, which matches the domain candidate $$p$$-value threshold that dPUC uses, and which worked best in our benchmarks.
### 1dpuc2.pl 1.00 - Produce dPUC domain predictions from raw hmmscan data.
perl -w 1dpuc2.pl <Pfam-A.hmm.dat> <dpucNet> <input table> <output table>
The required inputs are
• Pfam-A.hmm.dat: Pfam annotation file, contains GA thresholds and nesting network.
• dpucNet: Directed context network of domain family pair counts.
• input table: the output from hmmscan (previous script).
• output table: input with most domains removed by dPUC. Format is identical to input.
It is your responsability to ensure that the same Pfam version is used for Pfam-A.hmm.dat, the dPUC context network, and the input table.
Note that dPUC 2 has many options that are hardcoded in this script, and for simplicity they are not documented. They are experimental features, but most of them haven't been useful in my benchmarks. If you know what you're doing, feel free to modify this script to change these parameters.
This script uses a permissive overlap definition, in which only overlaps that exceed 40 amino acids or 50% of the length of the smaller domain are removed. These parameters are hardcoded in the script, modify them if you know what you're doing!
## Compatibility
Code was tested with HMMER versions 3.0 and 3.1b1, against the Pfam 25 and 27 HMM databases. The code worked with Inline::C 0.53 and 0.62, and with lp_solve 5.5.2.0.
## Notes shared with other projects
My public code, description of my original Perl packages
The union of code across the latest DomStratStats, dPUC, and RandProt distributions.
## Citations
Alejandro Ochoa, Manuel Llinás, and Mona Singh. Using context to improve protein domain identification. BMC Bioinformatics 2011, 12:90. 2011-03-31. Pubmed Article
Alejandro Ochoa, John Storey, Manuel Llinás, and Mona Singh. Beyond the E-value: stratified statistics for protein domain prediction. Submitted. arXiv 2014-09-23.
## Release notes
### 2014-09-18 - dPUC 2.00
This was the first public release of the second series of the code.
Compared to the 1.0 version, lots has changed. In summary, the 2.xx series works with HMMER3/Pfam 24 (and newer), and it is very highly optimized to reduce runtime. Importantly, the output format has changed (now it is simply like the HMMER3 domain tabular output files).
• Installation. It's easier now.
• The previous version had more dependencies, particularly more external Perl packages. The previous version required the executable lp_solve, whereas the current version requires the lp_solve library instead (note some installers include one but not the other). The new version requires the gzip executable to be available.
• The previous version included sample files with the source code, while the new version has source code separate from sample files (which are available on this web manual).
• The previous version required modifying a package, FilePaths.pm, to specify the paths of required Pfam and other files. The new version does not require any such source code modification to work (unless the lp_solve library is in an unusual place, I believe that is the only exception). All required files are now passed as arguments on the command line.
• Pipeline. It's simplified.
• The new version first runs HMMER3 on all proteins, then uses dPUC to filter those results as a separate step. The previous version would take each protein, run HMMER2 on it for both old modes (ls and fs, which no longer exist), then parse that result and run dPUC on it. The biggest disadvantage of the old way is I/O, the constant back and forth with writing very small files (single sequences) to disk for HMMER, parsing the output back in dPUC, and iterating. Also, since HMMER3 is now multithreaded, while dPUC is not, it may make more sense to run HMMER3 separely, perhaps on different machines with more cores, for example.
• The previous version included the Standard Pfam and dPUC predictions in the same output. The new version only shows dPUC. The new output format is exactly the HMMER3 domain tabular format (the input is simply filtered by dPUC, without altering any of the original columns or adding information). The previous version's output used to have more information, but it was hard to interpret, so it is currently ommited in favor of simplicity (this could change in the future).
• dPUC now has many hidden parameters that are not accessible on the command line. The previous version allowed the selection of an $$E$$-value threshold for candidate domains, but the new script has the equivalent threshold hardcoded. Again, this is in favor of simplicity. All parameters can be modified by modifying the 1dpuc2.pl script.
• The previous version required parsing large Pfam files before the first run, or use the files provided with the distribution. This is no longer required now that Pfam-A.hmm.dat exists (it wasn't available when dPUC 1.0 came out; Pfam-A.hmm.dat is so small now dPUC parses it at load time).
• There is no longer a daemon version of dPUC. The previous version used it for my website to generate predictions, but that functionality is also no longer available on the website (dPUC2 is so much faster and easier to use, that I expect people to be happier running it in their own machines).
Parametrization. The current dpucNet.pl differs from the equivalent procedure from dPUC 1.0 (which was three separate scripts) in important ways. These changes also affect how dPUC uses context scores for prediction. The changes allow for greater flexibility but also lead to modest improvements in statistical power.
• Domain family pairs are now ordered, or in other words, the network is directed. At load time, dPUC can treat the network as undirected with a score parameter that computes weighted averages of the counts of each direction (usage of this and other score parameters is currently not documented). The default is to keep the network fully directed.
• The previous procedure would output bitscores instead of raw counts. The new approach computes the bitscores when dPUC is loaded, it is very fast and provides the most flexibility since arbitrary scoring parameters can be tried immediately (instead of generating new network files for each parameter set).
• The counts are now of every domain family pair, rather than pairs counted only once per protein (so a protein with domain architecture A-A-B used to contribute a single A-B count, whereas now it contributes two A-B counts, in both cases also contributing an A-A count).
• The previous procedure applied an architecture count filter, whereas the new procedure outputs pair counts without any filters. The new approach allows for filtering the context network by pair count at dPUC load time, again providing maximum flexibility. We found that removing pair counts of 1 (the current default behavior) performs better than the previous architecture count filtering, presumably it removes more false positive context pairs per true positive context pair removed. The difference can be understood conceptually for a domain family pair that is observed in one architecture that was only observed once, but which contains such a family pair multiple times (the previous approach would remove such a family pair, the new approach will keep it and treat it as having higher confidence depending on the count).
• Other aspects of the score parametrization have changed and/or have been extended. For example, the prior count distribution may be more complex, the shape of the count and score distributions can be altered by exponentating, shifting, and scaling. However, in my benchmarks I haven't found useful ways of wielding these parameters, so by default they are not used. The default prior "pseudocount" is the same for every domain family pair, now fixed at $$2^{-23}$$ (about 1e-7) times the number of family pair counts observed (which is comparable to the prior of the previous version). The new parametrization makes it clear that unobserved domain pairs will have a score of approximately -23 bits.
• To agree with my other project, DomStratStats, dPUC now assumes $$p$$-values, rather than $$E$$-values, are present in the input from HMMER3. The default threshold for candidate domains is $$p \le \mbox{1e-4}$$, which is comparable to the previous recommendation with the exception that now the threshold is independent of the size of the database used.
• Runtime performance. In my benchmarks, dPUC2 is ~16x faster than its predecessor (excluding HMMER runtime, although it is itself reportedly 100x faster from version 2.3.2 to 3.0).
• The way dPUC interacts with lp_solve has been completely revamped. The previous approach generated a text file for every protein and threshold, which was the input for the lp_solve executable, the output of which was parsed by dPUC and processed to become the final domain predictions. Now dPUC and lp_solve interact more directly using the lp_solve C library. The previous approach was expensive not just because of the I/O overhead, but also because each lp_solve run required starting a new process via a process fork, which is also more expensive than the newest solution.
• The dPUC constraints used for lp_solve were also optimized. Although there are now more statements, they are stronger constraints that make it more likely that lp_solve will either find the exact integer solution when the continuous relaxation is solved, or it will converge more quickly to the integer solution at the branch-and-bound steps.
• dPUC now detects many trivial cases that do not need to be sent to lp_solve. The most useful one is the case when, after the dPUC positive elimination, the domains that are left do not overlap and do not have negative context with each other, in which case they constitute the final solution (in the previous approach, they were sent to lp_solve anyway, which would solve the problem much more slowly, especially if too many domains are present). Detecting trivial problems also scales much better than solving them with lp_solve (worst-case time complexities of $$O(m^2)$$ versus $$O(2^m)$$ for $$m$$ domains).
• There are two hidden "pre-filter" options that nobody should used. The idea was to speed up dPUC by removing overlaps in the input domains, either using $$p$$-value ranking or using one of my extensions of CODD (also using $$p$$-value ranking but additionally requiring strictly positive directed context between all predictions, always using the top-ranking domain as the only trusted domain). Both forms make dPUC faster but lead to considerable loss of statistical power, the second version in particular is terrible. I may remove these pre-filters completely in the future.
Compared to the beta version, many packages were reorganized, in general for the better. Also, I include code to generate the dPUC count network (the beta version simply provided the network for Pfam 24, and that network had strange filters that I have removed in this new public version).
### 2014-02-37 - dPUC 2.00 beta
I prepared this version for Juliana Bernardes, but until I posted it with the final version 2.00, I believe nobody else had seen this version, so I do not consider it a public version.
### 2011-02-06 - dPUC 1.0
Last change recorded on the public source code. See the dPUC (1.0) website and our paper for more information.
VIIIA
History
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2018-04-21 01:58:04
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https://www.physicsforums.com/threads/work-integration-problem.381796/
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# Homework Help: Work Integration problem
1. Feb 26, 2010
### Precursor
1. The problem statement, all variables and given/known data
A leaky 12 lb bucket is lifted from the bottom of a 10 ft well to the top at
a constant speed with a rope that weighs 0.6 lb/ft. Initially the bucket contains 60 lb
of water but the water leaks at a constant rate and finishes draining just as the bucket
reaches the top of the well. How much work is done?
2. Relevant equations
$$w = \int_{a}^{b} [F(x)]dx$$
3. The attempt at a solution
$$w = \int_{a}^{b} [F(x)]dx$$
$$w = \int_{0}^{10} [0.6(10 - x) + 6(10 - x)]dx$$
$$w = 330$$ lb-ft
Is this correct?
2. Feb 26, 2010
### LCKurtz
Don't forget the weight of the bucket.
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2018-03-25 03:51:34
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https://docs.prophesee.ai/data_formats/file_formats/dat.html
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# DAT File Format¶
DAT files store decoded event. The DAT file format is a binary little-endian format file. It is composed of three sections:
1. ASCII text header
2. Binary event type and size information
3. Binary event data
## DAT File Header¶
DAT file header contains ASCII information and metadata associated to the DAT file. It is a sequence of “keyword, value” pairs written line-by-line. More precisely, the file header is composed of text lines starting with “%” (0x25) followed by a space (0x20), a keyword, a space (0x20), a value and New Line NL / Line Feed (0x0A).
Here is an example of DAT file header:
% Data file containing CD events
% Date 2020-09-14 14:18:29
% Version 2
% Width 640
% Height 480
Below, a table with common keyword, value pairs:
Keyword
Value
Mandatory
Date
Recording Date, format: YYY-MM-DDHH:MM:SS
Data file containing
Type of event: CD (For now, only supported type)
YES
Version
Format version. Currently: 2
YES
Width
Horizontal size of image sensor array.
Height
Vertical size of image sensor array.
## Binary Event Type and Size¶
This information is provided as two bytes: type and size.
The most important event types are:
• Event2d: generic 2D event
• EventCd: specialized Event2d for Contrast Detection (CD) event
• EventExtTrigger: external trigger event (see External Triggers section)
The event size is 8 for all those types.
Byte
Description
Value
First byte
Event type
Event2d: 0x00 (0)
EventCd: 0x0C (12)
EventExtTrigger: 0x0E (14)
Second byte
Decoded event size (in bytes)
8 (0x08)
## Binary Event Data¶
A DAT file with CD events is made of a sequences of 64-bit (8 bytes) words stored in the following format:
The bitfield structure and the padding of the different event types can be found in the SDK headers:
• on Windows in <install-prefix>\share\metavision\include\metavision\sdk\base\events
• on Linux in /usr/include/metavision/sdk/base/events
There is an header file for each event type (event_cd., event_ext_trigger.h etc.) that contains the structure of the raw event as it will be recorded in a DAT file. For example for external triggers:
struct RawEvent {
uint32_t ts;
unsigned int p : 4;
unsigned int pad1 : 22;
unsigned int id : 6;
});
Usually, data in DAT format takes more space on disk compared to RAW format, therefore, it’s preferable to use RAW format for events recording. RAW format also reduces the data rate on the USB communication, lowering the stress on the interface and the risk of introducing delays.
DAT file format can be used for offline data processing, for example for data processing in MATLAB (contact us for a basic script uploading data to MATLAB).
In case you need to convert a RAW file to a DAT file, you could use RAW to DAT application.
|
2020-11-27 20:04:55
|
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|
https://www.physicsforums.com/threads/temperature-controller.790932/
|
# Temperature Controller
1. Jan 6, 2015
### EEFinder
I am trying to replace a Temp. Controller that is no more produces anymore.
What are the controller properties/settings/ that I have to pay attention to. in another word, what to select a temp controller for certain application?
Thanks.
2. Jan 6, 2015
### dlgoff
What did you have before and what are you hooking it to?
3. Jan 6, 2015
### EEFinder
this was dumped on me today,
the original controller was "ripped" for the application (industrial heating pad), long time ago. so there is no way to know which one goes where, meaning that no documentation what so ever of which wires go to the RTD, control, and power... is available.
I am thinking about cross referencing the original controller with something that I will have in stock.
to do this I wanted to know what should consider in a controller for it to go with my application.
Thanks.
4. Jan 6, 2015
5. Jan 6, 2015
### EEFinder
you see just for the sake of analogy, if someone asks about what to look for in selecting an electric motor, I would answer RPM, current, Voltage,Frame, HP,
I am looking for similar answer, but using Temp Controller instead of the electric motor. I know 2 so far that are the voltage and the Temp Sensing element (RTD, TC..) and wondering what the others are?
Hope this makes sense
6. Jan 6, 2015
### dlgoff
Well, know the application helps to know in order to answer such a general question. But Okay. 4-20 ma loop?
7. Jan 7, 2015
OK http://www.grainger.com/product/OMRON-Digital-Temprature-Controller-WP135543/_/N-8h2?s_pp=false&picUrl=//static.grainger.com/rp/s/is/image/Grainger/4YE30_AS01?$smthumb$ [Broken]
Last edited by a moderator: May 7, 2017
8. Jan 7, 2015
### jim hardy
form, fit, function
What do you know about the one that's no longer there ?
9. Jan 8, 2015
### Jobrag
First question is this an on off controller or a proportional device?
|
2017-10-23 12:05:56
|
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|
https://physicsgurukul.com/2020/07/03/ncert-solutions-for-class-9-science-chapter-10-gravitation/?shared=email&msg=fail
|
# NCERT Solutions for Class 9 Science Chapter 10 Gravitation
Here we have given NCERT Solutions for Class 9 Science Chapter 10 Gravitation.
## NCERT Solutions for Class 9 Science Chapter 10 Gravitation
INTEXT Questions
Question 1.
State the universal law of gravitation.
Solution:
According to universal law of gravitation, every particle in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of distance between them. The direction of force is along the line joining the two particles.
Question 2.
Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
Solution:
The formula for the magnitude of gravitational force between the earth and an object on its surface is, $F=G\cfrac { { M }_{ e }m }{ { R }_{ e }^{ 2 } }$ where F is the gravitational force. G is the gravitational constant. Me is the mass of the earth. m is the mass of the object on the surface of the earth. Re is the radius of the earth.
Question 3.
What do you mean by free fall?
Solution:
All objects falling towards earth under the action of gravitational force of earth alone are said to be in free fall.
Question 4.
What do you mean by acceleration due to gravity?
Solution:
The acceleration with which an object fall freely towards the earth is known as acceleration due to gravity. It is denoted by g and its value is 9.8 m s-2.
Question 5.
What are the differences between the mass of an object and its weight?
Solution:
Question 6.
Why is the weight of an object on the moon $\cfrac { { 1 }^{ th } }{ 6 }$ its weight on the earth?
Solution:
The weight of an object depends on the value of acceleration due to’gravity g. The value of g on earth is 6 times more than that of moon because, the mass and radius of the earth is more than the mass and radius of the moon.
Weight of a body of mass m on moon is
Question 7.
Why is it difficult to hold a school bag having a strap made of a thin and strong string?
Solution:
We know that pressure = force/area. When the string of the school bag is thin, its area is small and as such the pressure exerted on the shoulders or the hands supporting the bag is large. lip this case, the force acting on the shoulders or the hand which support the bag is equal to the weight of the bag. In case, the strap is broad as is usually the case, the area on which the force (weight of the bag) acts is large and the pressure is reduced as the weight of the bag is now distributed over a larger area.
Question 8.
What do you mean by buoyancy?
Solution:
Whenever an object is immersed in a liquid, either partially or fully, an upward force is exerted on the object by the liquid. This upward force is called upthrust or buoyant force or force of buoyancy and the property of the fluid due to which this upthrust is exerted on the object is called buoyancy.
Question 9.
Why does an object float or sink when placed on the surface of water?
Solution:
When the object has density less than 1 g cm-3 (density of water), then it floats on the surface of water, because, it always displaces more weight of water than its own weight. As buoyant force is more than its own weight, therefore, it floats. When the object has density more than 1 g cm-3, then it sinks in water, because it always displaces less weight of water than its own weight. As buoyant force is less than its own weight, therefore, it sinks.
Question 10.
You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Solution:
A weighing machine is a sort of spring balance which measure the weight and not the mass of a body. When we stand on the weighing machine, our weight which is due to gravitational attraction of the earth acts vertically downwards. But the buoyancy due to air on our body acts vertically upwards. As a result of this, our apparent weight true weight – buoyant force is less than the true weight. Since the weighing machine measures the apparent weight, our true weight is more, i.e., more than 42 kg.
Question 11.
You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why?
Solution:
We know that true weight = apparent weight + upthrust. The cotton bag is heavier than the iron bar. This is due to the reason, that the bag of cotton which has more volume (as it has less density) than the iron bar (which has more density), experiences more upthrust due to air.
NCERT Exercises
Question 1.
How does the force of gravitation between two objects change when the distance between them is reduced to half?
Solution:
Force of gravitation,
The force of gravitation becomes 4 times more.
Question 2.
Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
Solution:
Gravitational force acts on all objects in proportion to their masses. But a heavy object does not fall faster than a light object. This is because of the reason that
or Force = Acceleration × Mass As force is directly proportional to mass, acceleration is constant for a body of any mass.
Question 3.
What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 10m)
Solution:
The ‘gravitational force between the earth and 1 kg object on us surface is given by
Question 4.
The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?
Solution:
The earth attracts the moon with a force equal to the force with which the moon attracts the earth. This is because as per Newton’s third law of motion, forces of action and reaction are always equal and opposite.
Question 5.
If the moon attracts the earth, why does the earth not move towards the, moon?
Solution:
Both the earth and the moon attract each other with the same force. But according to Newton’s second law of motion, acceleration produced in a body by any force is inversely proportional to the mass of the body. Since, mass of the earth is much more than that of the moon, the acceleration produced in the earth is negligible. As a result, it appears as if the earth does not move towards the moon.
Question 6.
What happens to the force between two objects, if
(i) the mass of one object is doubled?
(ii) the distance between the objects is doubled and tripled?
(iii) the masses of both objects are doubled?
Solution:
From the relationship,
(i) If the mass of one object (say body 1) is doubled, then
Thus, the gravitational force between the two objects gets doubled.
(ii) If the distance between the two objects is doubled, then
Thus, the gravitational force between the two objects becomes one-fourth.
If the distance between the two objects is tripled, then
Thus, the gravitational force between the two objects becomes one-ninth.
(iii) If the masses of both the objects are doubled, then
Thus, the gravitational force between the two objects becomes 4 times.
Question 7.
What is the importance of universal law of gravitation?
Solution:
Universal law of gravitation is important as it accounts,
(a) for the existence of the solar system, i.e., motion of planets around the sun.
(b) for holding the atmosphere near the surface of the earth.
(c) for the flow of water in rivers.
(d) for rainfall and snowfall.
(e) for occurrence of tides.
Question 8.
What is the acceleration of free fall?
Solution:
All objects moving towards earth on account of gravitational force of earth on them are said to be in free fall. This force produces a uniform acceleration in the object. This is acceleration of free fall and its value is 9.8 m s-2.
Question 9.
What do we call the gravitational force between the earth and an object?
Solution:
The gravitational force between the earth and an object is called the force of gravity or simply earth’s gravity.
Question 10.
Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why?
Solution:
We know that the value of g is greater at the poles than at the equator. So the weight of gold at the equator will be less than the weight of gold at the poles. So it is obvious that the friend at equator will not agree with the weight of gold bought at poles.
Question 11.
Why will a sheet of paper fall slower than one that is crumpled into a ball?
Solution:
A sheet of paper will fall slower than the one that is crumpled into a ball. This is because the air offers resistance due to friction to the motion of the falling objects. The resistance offered by air to the sheet of paper is more than the resistance offered by air to the paper ball because the sheet has larger area.
Question 12.
Gravitational force on the surface of the moon is only 1 as strong as gravitational force on 6 the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth?
Solution:
Here, m = 10 kg
Mass is the same on earth and moon.
Now, weight of the object on earth,
We, = mge = 10 × 9.8 = 98 N
Weight of the object on moon, = ${ W }_{ m }=m{ g }_{ m }=\frac { 10\times 9.8 }{ 6 } =16.3 N$
Question 13.
A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) the maximum height to which it rises,
(ii) the total time it takes to return to the surface of the earth.
Solution:
Question 14.
A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.
Solution:
Question 15.
A stone is- thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s-2, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?
Solution:
As final position of the stone coincides with its initial position, net displacement = 0 Total distance covered by the stone = h + h = 80m + 80m = 160 m
Question 16.
Calculate the force of gravitation between the earth and the sun, given that the mass of the earth = 6 × 1024 kg and of the sun = 2 × 1030 kg. The average distance between the two is 1.5 × 1011 m.
Solution:
Thus, the earth and the sun attract each other by a gravitational force of 3.56 × 1022 N.
Question 17.
A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.
Solution:
Here, h = 100 m.
Let the two stones meet after t seconds at a point P which is at a height x above the ground as shown in figure.
Question 18.
A ball thrown up vertically returns to the thrower after 6 s. Find
(a) the velocity with which it was thrown up,
(b) the maximum height it reaches, and
(c) its position after 4 s.
Solution:
Here, time of ascent = time of descent,
Question 19.
In what direction does the buoyant force on an object immersed in a liquid act?
Solution:
If an object is immersed in a liquid then the buoyant force due to liquid acts on the object in vertically upward direction.
Question 20.
Why does a block of plastic released under water come up to the surface of water?
Solution:
The buoyant force acting on the block of plastic is more than its weight. As a result of this, it comes up when released under water.
The cause of this larger buoyant force on the block of plastic is due to its density being lesser than that of water.
Question 21.
The volume of 50 g of a substance is 20 cm3. If the density of water is 1 g cm-3, will the substance float or sink?
Solution:
As the density of the substance is greater than that of water, the given substance will sink in water.,
Question 22.
The volume of 500 g sealed packet is 350 cm3. Will the packet float or sink in water if the density of water is 1 g cm-3? What will be the mass of the water displaced by this packet?
Solution:
Here, mass of packet, M – 500 g volume of the packet, V = 350 cm3 Clearly, density of packet, $d=\cfrac { M }{ V } =\frac { 500 }{ 350 } =1.428gcom^{ -3 }$ Since the density of packet is more than density of water, the packet will sink. As the packet is fully submerged in water, mass of water displaced by the packet = volume of the packet x density of water = 350 cm3 × l g cm-3 = 350 g
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2021-09-24 22:09:37
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https://physics.stackexchange.com/questions/600062/is-the-ads-hamiltonian-the-same-as-the-cft-hamiltonian
|
# Is the AdS Hamiltonian the same as the CFT Hamiltonian?
The Hamiltonian in any theory of gravity is a boundary term, consequently in AdS the Hamiltonian is a boundary term. From the AdS/CFT duality, we have the same spectrum of states on both the AdS and the CFT side. If we write down the spectral decomposition of a general Hamiltonian as $$H := \sum_i E_i |E_i\rangle \langle E_i|,$$ firstly is it correct to conclude that both $$H_{AdS}$$ and $$H_{CFT}$$ admit the same spectral decomposition, i.e. the spectrum of energies and eigenstates is the same for both?
Given this, is it possible to address questions about bulk using the spectrum of the CFT Hamiltonian? More precisely, is it possible to work out the exact expression for $$H_{AdS}$$ in the bulk using $$H_{CFT}$$?
|
2022-08-18 09:16:56
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https://code.tutsplus.com/tutorials/vim-essential-plugin-easymotion--net-19223
|
Vim Essential Plugin: EasyMotion
This post is part of a series called Vim Essential Plugins.
Vim Essential Plugin: Surround
In this first episode of Vim Essential Plugins, we'll be reviewing the helpful EasyMotion plugin, which allows us to be much quicker when traversing our pages.
Usage
Once installed (see video for help), the EasyMotion plugin can be triggered by using the leader character plus w. By default, this will be \w. Once this sequence is pressed, every word in your document will be replaced with a trigger-letter.
At that point, simply type the red identifier of the location you want to move your cursor, and - bam -- you're done! Be sure to also review some of the other triggers, like \ge and \k. Download it. Use it!
|
2021-09-16 18:36:41
|
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|
http://mathhelpforum.com/advanced-statistics/187686-e-x-y-where-x-y-independent-poisson-random-variables.html
|
# Math Help - E[ | X - Y | ] where X and Y are independent Poisson random variables
1. ## E[ | X - Y | ] where X and Y are independent Poisson random variables
What is the expected value of the absolute difference of two independent Poisson variables?
E[ |X - Y| ]
I've split the double sum into the correct regions but not sure what to do with the partial sums remaining.
I have:
Sum_0^infinity p(x) Sum_0^infinity |X - Y| p(y)
...since p(x,y) = p(x)p(y)
= Sum_0^infinity p(x) [Sum_0^x (X - Y) p(y) + Sum_x^infinity (Y - X) p(y)]
Should get something like | E[X] - E[Y] | + some variance or covariance term, the latter of which will be 0 since X and Y are independent.
2. ## Re: E[ | X - Y | ] where X and Y are independent Poisson random variables
what are the means of these Poisson's?
3. ## Re: E[ | X - Y | ] where X and Y are independent Poisson random variables
Was going to write the answer in terms of E[X] and E[Y] but if not could use:
mean of X : E[X] = \lambda^X dt
mean of Y : E[Y] = \lambda^Y dt
4. ## Re: E[ | X - Y | ] where X and Y are independent Poisson random variables
I dont follow
X is a random variable, the means are random?
And the dt is?
5. ## Re: E[ | X - Y | ] where X and Y are independent Poisson random variables
No the means are not random, apologies for confusion caused.
Ok, lets just say the means are:
mean X = E[X] = m
mean Y = E[Y] = n
I think the problem can be done in general for any Random variables X and Y.
|
2016-04-29 12:49:48
|
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|
https://solvedlib.com/the-spacing-of-lines-in-the-microwave-spectrum-of,402518
|
# The spacing of lines in the microwave spectrum of 35Cl19F is 1.033 cm-1; Calculate the moment...
###### Question:
The spacing of lines in the microwave spectrum of 35Cl19F is 1.033 cm-1; Calculate the moment of inertia and the bond length of the molecule.
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Research one of Newton's laws of motion and compose an oral presentation. Provide examples of the law. You might want to use a visual aid....
##### Order: Vancomycin HCl 1 g in 200 mL DW IVPB, infuse in 60 min. Calculate the flow rate...
Order: Vancomycin HCl 1 g in 200 mL DW IVPB, infuse in 60 min. Calculate the flow rate in drops per minute. The drop factor is 20 gtt/mL....
##### What values of a and b maximize the value of ſ(4x-x2) dx? (Hint: Where is the...
What values of a and b maximize the value of ſ(4x-x2) dx? (Hint: Where is the integrand positive?) and b=maximize the given integral. (Simplify your answer. Type a whole number.) a =...
##### Find the lincar speed of point moving with uniform circular motion, if the point covers distance in an amount of time where25 ft andminfUmin
Find the lincar speed of point moving with uniform circular motion, if the point covers distance in an amount of time where 25 ft and min fUmin...
##### Tan?(2x) Prove the identity sin2 (4x) cos2(4x)+2 cos(Ax)+1
tan?(2x) Prove the identity sin2 (4x) cos2(4x)+2 cos(Ax)+1...
##### QUESTION 34 The MRTS of labor for capital tends to be higher the larger the quantity...
QUESTION 34 The MRTS of labor for capital tends to be higher the larger the quantity of capital already employed the lower the quantity of capital already'employed when a firm is choosing baskets that are inefficient in the short run compared to the long run...
##### A piston-cylinder device contains 5 kg of saturated water liquid at 0.3 MPa. Heat is transferred...
A piston-cylinder device contains 5 kg of saturated water liquid at 0.3 MPa. Heat is transferred at constant pressure until the temperature reaches 500 -C. (84 marks) a) What is the initial temperature of the system? b) What is the initial quality x? c) What is the initial specific enthalpy of the s...
##### Normal Vector to a PlaneFind a unit vector perpendicular to the plane 4x + 2y + 42 =
Normal Vector to a Plane Find a unit vector perpendicular to the plane 4x + 2y + 42 =...
##### 8. Describe the following types of insurance: a. liability, b. professional (malpractice),c. personal injury. (X.C.8) 9....
8. Describe the following types of insurance: a. liability, b. professional (malpractice),c. personal injury. (X.C.8) 9. Identify: a. Health Information Technology for Economic and Clinical Health (HITECH) Act, b. Genetic Information Nondiscrimination Act of 2008 (GINA), c. Americans with Disabiliti...
##### Let V be a vector space over R and let v1, ..., Un each be a...
Let V be a vector space over R and let v1, ..., Un each be a vector in V \{0}. Show that (v1, ..., Un) is linear independent if and only if span(V1, ..., vi) n span(Vi+1, ..., Un) = {0} for all i = 1,...,n - 1...
##### Methyl methacrylate (shown below) undergoes radical polymerization to give polylmethyl methacrylate), known as PMMA apolymer commonly found in plastic replacements for glass. What is the structure of PMMA?Radkcal polymerizatbnPMMA8-ociy C-CHz CHaC-OCH3 S-Ch CHa0 C-OCHz tCHz-CH-CHzf0 3i0 b)II0 c0 div0 ev
Methyl methacrylate (shown below) undergoes radical polymerization to give polylmethyl methacrylate), known as PMMA apolymer commonly found in plastic replacements for glass. What is the structure of PMMA? Radkcal polymerizatbn PMMA 8-ociy C-CHz CHa C-OCH3 S-Ch CHa 0 C-OCHz tCHz-CH-CHzf 0 3i 0 b)II ...
##### Want to see if my method is correct for standard enthalpy.
Use these reactions, and the standard enthalpies as shown ΔHoM(s) + CO2(g) → CO(g) + MO(s) –140.0 kJ3 MO(s) + CO2(g) → CO(g) + M3O4(s) + 1.20 kJ2 M3O4(s) + CO2(g) → CO(g) + 3 M2O3(s) –380.0 kJM2O3(s) + CO2(g) → CO(g) + 2 MO2(s) –121.8 kJ2 MO2(s) + CO2(g) &...
##### Use the cost and revenue data to answer the questions. Quantity 15 Price 90 80 70...
Use the cost and revenue data to answer the questions. Quantity 15 Price 90 80 70 30 Total revenue 1350 2400 3150 3600 3750 3600 Total cost 900 1500 2250 45 60 3150 Ls 75 60 50 40 4200 90 5400 If the firm is a monopoly, what is marginal revenue when quantity is 302 MR = \$ Use the cost and revenue da...
##### EurWiLont Ansucr_Quatinns"ruhlenpoints] The ston2 1s then tolated Vcncal 0skis tied afopc 0.90 m lona Aslons of nus dirccticn) that thc ston: Must Eave nt Lhc aecekratlon (mxgritudc nnd WhalicIhc ILMLIL mainiain unifotm circular molion? Top' of the circleuht have & the top of the cincle? the mninirum [te Ihal Ia dolle Wharshou 0Stonc is st the boltom of thc cirele = ahi ine amc the rope hen the Find the tcnsion Fed nnt
EurWiLont Ansucr_Quatinns "ruhlen points] The ston2 1s then tolated Vcncal 0skis tied afopc 0.90 m lona Aslons of nus dirccticn) that thc ston: Must Eave nt Lhc aecekratlon (mxgritudc nnd WhalicIhc ILMLIL mainiain # unifotm circular molion? Top' of the circle uht have & the top of the ...
##### Which substance in each of the following pairs would you expectto have larger dispersion forces?Part A Ethane, C2H6C2H6, or octane, C8H18C8H18Ethane, , or octane, C2H6C2H6C8H18C8H18SubmitRequest AnswerPart B HClHCl or HIHI or HIHIHClHClSubmitRequest AnswerPart C H2OH2O or H2SeH2Se or H2OH2OH2SeH2SeSubmitRequest AnswerProvide FeedbackNext
Which substance in each of the following pairs would you expect to have larger dispersion forces? Part A Ethane, C2H6C2H6, or octane, C8H18C8H18 Ethane, , or octane, C2H6C2H6 C8H18C8H18 SubmitRequest Answer Part B HClHCl or HIHI or HIHI HClHCl SubmitRequest Answer Part C H2OH2O or H2SeH2Se or...
##### 2.A 12.0 m 3.5 kg beam is supported by cable with 64 N of tension A8.0 kg cat sits on the beam: Determine the distance from the hinge t0 where the cat sits_Cable1
2.A 12.0 m 3.5 kg beam is supported by cable with 64 N of tension A8.0 kg cat sits on the beam: Determine the distance from the hinge t0 where the cat sits_ Cable 1...
##### Using the data in question 5 of this assignment use Excel to find a 99% confidence interval for the additional sleep that would be obtained on average for all people using laevohysocyamine hydrobromide. Hand in the Excel printout and write the upper and lower limits for the interval in the same printout.
Using the data in question 5 of this assignment use Excel to find a 99% confidence interval for the additional sleep that would be obtained on average for all people using laevohysocyamine hydrobromide. Hand in the Excel printout and write the upper and lower limits for the interval in the same prin...
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2022-07-04 02:02:29
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https://www.ashoka.edu.in/courses/mat-1001-linear-algebra/
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## MAT 1001: Linear Algebra
Syllabus: Real vector spaces, subspaces, spanning sets, basis sets, dimension of a vector space. Solution of a system of linear equations. Row space and column space of a matrix, rank of a matrix, elementary row and column operations of a matrix. Inversion of square matrices, rank factorization of a matrix. Properties of determinants. Linear transformations, range and null space of a linear transformation, rank-nullity theorem. Matrix representation of a linear transformation. Inner product spaces, normed linear spaces, examples of different normed linear spaces, orthonormal basis sets. Eigenvalues, eigenvectors, characteristic polynomials. Spectral theorem for real symmetric matrices. Singular value decompositions.
References:
1. A. R. Rao and P. Bhimsankaram: Linear algebra, Hindustan book agency, 2000.
2. S. H. Friedberg, A. J. Insel and L. E. Spence: Linear algebra, Pearson, 2015.
3. D. C Lay: Linear algebra and its applications, Pearson, 2014.
#### Study at Ashoka
[current_url]
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2023-03-30 05:08:55
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https://mijn.bsl.nl/comparison-between-exploratory-factor-analytic-and-sem-based-app/269496
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main-content
## Swipe om te navigeren naar een ander artikel
01-02-2009 | Uitgave 1/2009
# Comparison between exploratory factor-analytic and SEM-based approaches to constructing SF-36 summary scores
Tijdschrift:
Quality of Life Research > Uitgave 1/2009
Auteurs:
Fotios Anagnostopoulos, Dimitris Niakas, Yannis Tountas
## Abstract
Objective To compare the two higher order factor structures of the Short-Form 36 (SF-36) Health Survey, using exploratory factor analytic methods and structural equation modeling (SEM). Methods Two population data sets were used. A stratified representative sample (n = 1,005) of the Greek general population was approached for interview. This survey containing the SF-36 was used to obtain component score coefficients from principal components analysis and orthogonal rotation. These coefficients were then used in the second data set (n = 1,007) of the Greek adult general population to compute scores for the physical component summary and the mental component summary of the SF-36. The second data set was also used to obtain factor scores for physical and mental health measures, applying SEM. Results Exploratory factor analysis supported the existence of two principal components that are the basis for summary physical and mental health measures. SEM showed that models assuming that physical and mental health are correlated provided a better fit to the data than models assuming independence between physical and mental health. However, all eight dimensions of SF-36 should be included in the construction of summary scores. Conclusions These results confirm the multidimensional structure of the SF-36, the correlational equivalence between standard summary measures and SEM-based second-order factor scores, and underscore the feasibility of multinational comparisons of health status using this instrument.
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2021-01-25 07:48:33
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http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Fixed_point_(mathematics)
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# All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair Project Encyclopedia
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enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
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# Fixed point (mathematics)
In mathematics, a fixed point of a function is a point that is mapped to itself by the function. For example, if f is defined on the real numbers by
f(x) = x2 − 3x + 4,
then 2 is a fixed point of f, because f(2) = 2.
Not all functions have fixed points: for example, the function f(x) = x + 1 has no fixed point on the reals, since x is never equal to x + 1 for any real number. In graphical terms, a fixed point means the point (x, f(x)) is on the line y = x, or in other words the graph of f has a point in common with that line. The example is a case where the graph and the line are a pair of parallel lines.
Contents
## Attractive fixed points
An attractive fixed point of a function f is a fixed point x0 of f such that for any value of x in the domain that is close enough to x0, the iterated function sequence
$x,\ f(x),\ f(f(x)),\ f(f(f(x))), \dots$
converges to x0. How close is "close enough" is sometimes a subtle question.
The natural cosine function ("natural" means in radians, not degrees or other units) has exactly one fixed point, which is attractive. In this case "close enough" is not a stringent criterion at all - to demonstrate this, start with any real number and repeatedly press the cos key on a calculator. It quickly converges to about 0.73908513 (provided, of course, it is set to find cosines in radians), the fixed point. That is where the graph of the cosine function intersects the line y = x, and this is no coincidence.
Not all fixed points are attractive: for example, x = 0 is a fixed point of the function f(x) = x2 + x, but iteration of this function for any value other than zero rapidly diverges.
Attractive fixed points are a special case of a wider mathematical concept of attractors.
## Theorems guaranteeing fixed points
There are numerous theorems in different parts of mathematics that guarantee that functions, under certain circumstances, must have one or more fixed points. These are amongst the most basic qualitative results available: such fixed-point theorems that apply in generality are very valuable insights.
## Applications
In compilers, fixed point computations are used for whole program analysis, which is often required to do code optimization. Fixed point is also used in finding PageRank of a webpage.
Logician Saul Kripke makes use of fixed points in his influential theory of truth. He shows how one can generate a partially defined truth predicate (one which remains undefined for problematic sentences like "This sentence is not true"), by recursively defining "truth" starting from the segment of a language which contains no occurrences of the word, and continuing until the process ceases to yield any newly well-defined sentences. (This will take a denumerable infinity of steps.) That is, for a language L, let L-prime be the language generated by adding to L, for each sentences S in L, the sentence "S is true." A fixed point is reached when L-prime is L; at this point sentences like "This sentence is not true" remain undefined, so, according to Kripke, the theory is suitable for a natural language which contains its own truth predicate.
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2013-06-19 09:56:42
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https://repository.uantwerpen.be/link/irua/118775
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Title Measurement of the production cross section for a W boson and two b jets in pp collisions at $\sqrt{s}$ = 7 TeV Author Chatrchyan, S. Khachatryan, V. Sirunyan, A. M. Alderweireldt, S. Bansal, M. Bansal, S. Cornelis, T. de Wolf, E.A. Janssen, X. Knutsson, A. Luyckx, S. Mucibello, L. Roland, B. Rougny, R. van Haevermaet, H. Van Mechelen, P. Van Remortel, N. Van Spilbeeck, A. et al. Faculty/Department Faculty of Sciences. Physics Publication type article Publication 2014 Amsterdam , 2014 Subject Physics Source (journal) Physics letters: B. - Amsterdam, 1967, currens Volume/pages 735(2014) , p. 204-225 ISSN 0370-2693 ISI 000340048900037 Carrier E Target language English (eng) Full text (Publishers DOI) Affiliation University of Antwerp Abstract The production cross section for a Wboson and two b jets is measured using proton-proton collisions at v root s = 7 TeV in a data sample collected with the CMS experiment at the LHC corresponding to an integrated luminosity of 5.0 fb(-1). The W + bbevents are selected in the W..decay mode by requiring a muon with transverse momentum pT> 25GeVand pseudorapidity |eta| < 2.1, and exactly two b-tagged jets with pT> 25GeVand |eta| < 2.4. The measured W + bbproduction cross section in the fiducial region, calculated at the level of final-state particles, is s(pp. W + bb) xB(W..) = 0.53 +/- 0.05 (stat.) +/- 0.09 (syst.) +/- 0.06 (theo.) 0.01 (lum.) pb, in agreement with the standard model prediction. In addition, kinematic distributions of the W + bbsystem are in agreement with the predictions of a simulation usingMadGraphandpythia. (C) 2014 The Authors. Published by Elsevier B. V. E-info http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000340048900037&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000340048900037&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000340048900037&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 Full text (open access) https://repository.uantwerpen.be/docman/irua/153b3d/118775.pdf Handle
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2017-04-24 11:30:59
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http://mathhelpforum.com/algebra/56263-integrating-help-print.html
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# Integrating help
• Oct 28th 2008, 03:57 PM
Unt0t
Integrating help
how do you integrate dy/(y(1-y))?
I got ln|y| + 1/y
• Oct 28th 2008, 04:07 PM
HallsofIvy
Excellent! How did you get that? I would be inclined to use "partial fractions" writing $\frac{1}{x(1-x}$ as $\frac{A}{x}+ \frac{B}{1-x}$. But integrating that should involve a "ln(1-x)" and I don't see that in your answer.
• Oct 28th 2008, 04:16 PM
Unt0t
lol I don't get it. Could you please show me how to work it out and give me the answear
• Oct 28th 2008, 04:37 PM
Unt0t
I'll actually give you the full question and hopefully someone can help me.
dy/dt= y(1-y) and they want us to find the general solution... I know its a seperable equation so I get dy/(y(1-y)) = 1 dt and we're ment to integrate it... though I dont know how. And the answer they give is y(t)= ke^t/(ke^t +1)
• Oct 28th 2008, 04:57 PM
Mathstud28
$\frac{1}{x(x+1)}=\frac{x+1-x}{x(x+1)}=\frac{1}{x}-\frac{1}{x+1}$
$\therefore\int\frac{dx}{x(x+1)}=\int\bigg[\frac{1}{x}-\frac{1}{x+1}\bigg]dx=\ln\left(\frac{x}{x+1}\right)+C$
• Oct 28th 2008, 05:13 PM
Krizalid
Quote:
Originally Posted by Mathstud28
$\frac{1}{x(x+1)}=\frac{x+1-x}{x(x+1)}=\frac{1}{x}-\frac{1}{x+1}$
$\therefore\int\frac{dx}{x(x+1)}=\int\bigg[\frac{1}{x}-\frac{1}{x+1}\bigg]dx=\ln\left(\frac{x}{x+1}\right)+C$
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:)
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2017-02-21 06:05:33
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https://www.gamedev.net/forums/topic/555609-how-to-implement-formation-in-group/
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# how to implement formation in group?
This topic is 3264 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I met a problem recently, i want to implement formation in group,something like OpenSteer'pedestrian run on a map,but there are some differences,within these agents,some agents belong to same group,so they will have same velocity,and acceleration also they will closer to each other than to the agent not within same group, but i have no idea about how to implement it, can anybody help me, thank you very much.
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Look up flocking and boids.
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If I understand your badly worded question correctly, you are trying to progress from a single pool of coordinated pedestrian agents to separate groups of agents that keep a formation only with others in the same group rather than with any agent that happens to be close.
You can simply tag agents with their group and use this information to filter the results of spatial queries for agents: group A agents try to match the velocity of nearby group A agents while walking towards a waypoint, group B agents try to distance themselves from group A agents and get close to group C agents without going anywhere, group C agents just try to spread out, and so on.
Note that you cannot guarantee that such behavioural groups will always be spatially separated: groups can cross each other's path, or even stop in the same place and mingle indefinitely.
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Steering behaviors are great for inspiration, but personally I prefer a more principled approach: Define an "energy function" over your agents' positions and velocities that (1) will be minimized by the states you want, and (2) gets very large near unwanted states, and then simply have your agents walk down the gradient of this function in state-space.
Mixtures of quadratic penalty functions (which are "soft") and logarithmic barrier functions (which are "harder") have worked well for me in the past.
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Quote:
Original post by EmergentSteering behaviors are great for inspiration, but personally I prefer a more principled approach: Define an "energy function" over your agents' positions and velocities that (1) will be minimized by the states you want, and (2) gets very large near unwanted states, and then simply have your agents walk down the gradient of this function in state-space.Mixtures of quadratic penalty functions (which are "soft") and logarithmic barrier functions (which are "harder") have worked well for me in the past.
i think your method is something like potential field algorithm,but it is path finding algorithm,but i want agents within same group align with each other,and closer to each other,i do not think this algorithm can solve this problem.thank you very much.
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Original post by LorenzoGattiIf I understand your badly worded question correctly, you are trying to progress from a single pool of coordinated pedestrian agents to separate groups of agents that keep a formation only with others in the same group rather than with any agent that happens to be close.You can simply tag agents with their group and use this information to filter the results of spatial queries for agents: group A agents try to match the velocity of nearby group A agents while walking towards a waypoint, group B agents try to distance themselves from group A agents and get close to group C agents without going anywhere, group C agents just try to spread out, and so on.Note that you cannot guarantee that such behavioural groups will always be spatially separated: groups can cross each other's path, or even stop in the same place and mingle indefinitely.
i should apologize for my poor english,Thank you very much~
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Original post by InnocuousFoxLook up flocking and boids.
thank you very much~
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Original post by hengh2009i think your method is something like potential field algorithm,but it is path finding algorithm,but i want agents within same group align with each other,and closer to each other,i do not think this algorithm can solve this problem.thank you very much.
The idea is to define the potential not over 3-space, but over the state space--which includes agents' headings, etc. And if multiple states are equally desirable -- say, all the states in which the agents are aligned -- then you'd use a potential function which has a "trough"-like minimum (so that all states in which agents are aligned are minima).
A good way to define these functions is as a sum of "interaction potentials."
For alignment, for example, you can use the potential
V_{\mathrm{align}}(\theta_1,\cdots,\theta_N) = \sum_{i=1}^N \sum_{k\in{\cal N}_i}\left(1 - \cos(\Delta\theta_{ik}) \right )
where $\Delta\theta_{ik}$ denotes the difference in heading angle between agents i and j, and ${\cal N}_i$ denotes the neighbors to agent i.
When you differentiate this, you see that each agent should steer according to the average sine of angular deviation with its neighbors; these sines-of-angles can be computed with cross products (or "2d cross products" depending on the number of dimensions) without resorting to trig functions at all.
You could add other terms penalizing when agents are too close together -- or too far apart.
See where I'm going with this?
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Quote:
Original post by Emergent
Quote:
Original post by hengh2009i think your method is something like potential field algorithm,but it is path finding algorithm,but i want agents within same group align with each other,and closer to each other,i do not think this algorithm can solve this problem.thank you very much.
The idea is to define the potential not over 3-space, but over the state space--which includes agents' headings, etc. And if multiple states are equally desirable -- say, all the states in which the agents are aligned -- then you'd use a potential function which has a "trough"-like minimum (so that all states in which agents are aligned are minima).
A good way to define these functions is as a sum of "interaction potentials."
For alignment, for example, you can use the potential
V_{\mathrm{align}}(\theta_1,\cdots,\theta_N) = \sum_{i=1}^N \sum_{k\in{\cal N}_i}\left(1 - \cos(\Delta\theta_{ik}) \right )
where $\Delta\theta_{ik}$ denotes the difference in heading angle between agents i and j, and ${\cal N}_i$ denotes the neighbors to agent i.
When you differentiate this, you see that each agent should steer according to the average sine of angular deviation with its neighbors; these sines-of-angles can be computed with cross products (or "2d cross products" depending on the number of dimensions) without resorting to trig functions at all.
You could add other terms penalizing when agents are too close together -- or too far apart.
See where I'm going with this?
thank you very much,i will try your method.
[Edited by - hengh2009 on December 8, 2009 10:54:22 PM]
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Measurements of cosmic ray antiprotons with PAMELA and studies of propagation models
KTH, School of Engineering Sciences (SCI), Physics, Particle and Astroparticle Physics.
2012 (English)Doctoral thesis, monograph (Other academic)
##### Abstract [en]
Studying the acceleration and propagation mechanisms of Galactic cosmic rays can provide information regarding astrophysical sources, the properties of our Galaxy, and possible exotic sources such as dark matter. To understand cosmic ray acceleration and propagation mechanisms, accurate measurements of different cosmic ray elements over a wide energy range are needed. The PAMELA experiment is a satellite-borne apparatus which allows different cosmic ray species to be identified over background.
Measurements of the cosmic ray antiproton flux and the antiproton-to-proton flux ratio from 1.5 GeV to 180 GeV are presented in this thesis, employing the data collected between June 2006 and December 2008. Compared to previous experiments, PAMELA extends the energy range of antiproton measurements and provides significantly higher statistics. During about 800 days of data collection, PAMELA identified approximately 1300 antiprotons including 61 above 31.7 GeV. A dramatic improvement of statistics is evident since only 2 events above 30 GeV are reported by previous experiments. The derived antiproton flux and antiproton-to-proton flux ratio are consistent with previous measurements and generally considered to be produced as secondary products when cosmic ray protons and helium nuclei interact with the interstellar medium.
To constrain cosmic ray acceleration and propagation models, the antiproton data measured by PAMELA were further used together with the proton spectrum reported by PAMELA, as well as the B/C data provided by other experiments. Statistical tools were interfaced with the cosmic ray propagation package GALPROP to perform the constraining analyses.
Different diffusion models were studied. It was shown in this work that only current PAMELA data, i.e. the antiproton-to-proton ratio and the proton flux, are not able to place strong constraints on propagation parameters. Diffusion models with a linear diffusion coefficient and modified diffusion models with a low energy dependence of the diffusion coefficient were studied in the $\chi^{2}$ study. Uncertainties on the parameters and the goodness of fit of each model were given. Some models are further studied using the Bayesian inference. Posterior means and errors of the parameters base on our prior knowledge on them were obtained in the Bayesian framework. This method also allowed us to understand the correlation between parameters and compare models.
Since the B/C ratio used in this analysis is from experiments other than PAMELA, future PAMELA secondary-to-primary ratios (B/C, $^{2}$H/$^{4}$He and $^{3}$He/$^{4}$He) can be used to avoid the data sets inconsistencies between different experiments and to minimize uncertainties on the solar modulation parameters. More robust and tighter constraints are expected. The statistical techniques have been demonstrated useful to constrain models and can be extended to other observations, e.g. electrons, positrons, gamma rays etc. Using these channels, exotic contributions from, for example, dark matter will be further investigated in future.
##### Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. , viii, 143 p.
##### Series
Trita-FYS, ISSN 0280-316X ; 2012:22
##### Keyword [en]
cosmic ray, PAMELA, antiproton flux, propagation
##### National Category
Astronomy, Astrophysics and Cosmology
##### Identifiers
ISBN: 978-91-7501-330-5 (print)OAI: oai:DiVA.org:kth-95331DiVA: diva2:527833
##### Public defence
2012-06-01, FA31, Albanova University Center, Roslagstullsbacke 21, Stockholm, 13:00 (English)
##### Note
QC 20120523Available from: 2012-05-23 Created: 2012-05-22 Last updated: 2012-05-23Bibliographically approved
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v. 2.29.1
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2017-12-17 10:05:15
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https://lists.nongnu.org/archive/html/axiom-developer/2005-02/msg00205.html
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axiom-developer
[Top][All Lists]
## [Axiom-developer] [SquareMatrix]
From: billpage Subject: [Axiom-developer] [SquareMatrix] Date: Thu, 17 Feb 2005 19:24:17 -0600
Changes http://page.axiom-developer.org/zope/mathaction/SquareMatrix/diff
--
??changed:
-a b
-ab
-
SquareMatrix(2,Integer) is an example of a domain constructor that
accepts both a particular data value as well as an integer. In this
case the number 2 specifies the number of rows and columns the square
matrix will contain. Elements of the matricies are integers.
\begin{axiom}
A:SquareMatrix(2,Integer)
A:=1
\end{axiom}
or even
\begin{axiom}
B:SquareMatrix(2,SquareMatrix(3,Float))
B:=1
\end{axiom}
--
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2021-06-13 02:07:41
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https://zbmath.org/authors/?q=rv%3A3267
|
# zbMATH — the first resource for mathematics
## Cuculescu, Ion
Compute Distance To:
Author ID: cuculescu.ion Published as: Cuculescu, I.; Cuculescu, Ioan; Cuculescu, Ion External Links: Wikidata
Documents Indexed: 51 Publications since 1958, including 7 Books Reviewing Activity: 165 Reviews
all top 5
#### Co-Authors
32 single-authored 12 Theodorescu, Radu 2 Onicescu, Octav 1 Bally, Vlad 1 Bertin, Emile Marie Joseph 1 Dinescu, Gabriela 1 Foiaş, Ciprian Ilie 1 Kleitsch, Ştefan 1 Oprea, Ana Gabriela 1 Ottescu, Constantin 1 Sîmboan, Gabriel
all top 5
#### Serials
21 Revue Roumaine de Mathématiques Pures et Appliquées 5 Studii şi Cercetări Matematice 2 Journal of Multivariate Analysis 2 Mathematics and its Applications (Dordrecht) 1 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 1 Gazeta Matematică 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Revista Investigación Operacional 1 Australian & New Zealand Journal of Statistics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Comunicările Academiei Republicii Populare Române 1 Académie de la République Populaire Roumaine, Revue de Mathématiques Pures et Appliquées 1 Analele Universităţii Bucureşti, Matematică-Mecanica 1 Bulletin Mathématique de la Société des Sciences Mathématiques et Physiques de la République Populaire Roumaine. Nouvelle Série 1 Gazeta Matematica. Serie A 1 Analele Universitaţii C. I. Parhon Bucureşti, Seria Ştiinţele Naturii
all top 5
#### Fields
28 Probability theory and stochastic processes (60-XX) 7 Statistics (62-XX) 3 History and biography (01-XX) 3 Functional analysis (46-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Operations research, mathematical programming (90-XX)
#### Citations contained in zbMATH Open
12 Publications have been cited 118 times in 109 Documents Cited by Year
Martingales on von Neumann algebras. Zbl 0254.60031
Cuculescu, I.
1971
Copulas: Diagonals, tracks. Zbl 1032.60009
2001
Multiplicative strong unimodality. Zbl 0940.62013
1998
Unimodality of probability measures. Zbl 0876.60001
Bertin, Emile M. J.; Cuculescu, Ioan; Theodorescu, Radu
1997
Extreme value attractors for star unimodal copulas. Zbl 0996.60026
2002
Noncommutative probability. Zbl 0837.46050
Cuculescu, I.; Oprea, A. G.
1994
Are copulas unimodal? Zbl 1028.60009
2003
Supermartingales on $$W^*$$-algebras. Zbl 0184.40703
Cuculescu, I.
1969
An individual ergodic theorem for positive operators. Zbl 0165.16203
Cuculescu, I.; Foiaš, Ciprian
1966
Spectral families and stochastic integrals. Zbl 0212.19402
Cuculescu, I.
1970
Nonuniformly integrable nonnegative martingales. Zbl 0212.20002
Cuculescu, I.
1970
Maximum domain of attraction for copulas. Zbl 1050.62060
Cuculescu, I.; Theodorescu, R.
2003
Are copulas unimodal? Zbl 1028.60009
2003
Maximum domain of attraction for copulas. Zbl 1050.62060
Cuculescu, I.; Theodorescu, R.
2003
Extreme value attractors for star unimodal copulas. Zbl 0996.60026
2002
Copulas: Diagonals, tracks. Zbl 1032.60009
2001
Multiplicative strong unimodality. Zbl 0940.62013
1998
Unimodality of probability measures. Zbl 0876.60001
Bertin, Emile M. J.; Cuculescu, Ioan; Theodorescu, Radu
1997
Noncommutative probability. Zbl 0837.46050
Cuculescu, I.; Oprea, A. G.
1994
Martingales on von Neumann algebras. Zbl 0254.60031
Cuculescu, I.
1971
Spectral families and stochastic integrals. Zbl 0212.19402
Cuculescu, I.
1970
Nonuniformly integrable nonnegative martingales. Zbl 0212.20002
Cuculescu, I.
1970
Supermartingales on $$W^*$$-algebras. Zbl 0184.40703
Cuculescu, I.
1969
An individual ergodic theorem for positive operators. Zbl 0165.16203
Cuculescu, I.; Foiaš, Ciprian
1966
all top 5
all top 5
#### Cited in 54 Serials
11 Fuzzy Sets and Systems 7 Journal of Functional Analysis 6 Journal of Multivariate Analysis 6 Kybernetika 5 Statistics & Probability Letters 4 Journal of Mathematical Analysis and Applications 4 Information Sciences 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 The Annals of Probability 3 Proceedings of the American Mathematical Society 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 Dependence Modeling 2 Communications in Mathematical Physics 2 Israel Journal of Mathematics 2 Journal of Mathematical Physics 2 Insurance Mathematics & Economics 2 Revista Matemática Iberoamericana 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Scandinavian Journal of Statistics 1 Ukrainian Mathematical Journal 1 Advances in Mathematics 1 Annals of the Institute of Statistical Mathematics 1 The Annals of Statistics 1 Archiv der Mathematik 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Functional Analysis and its Applications 1 Integral Equations and Operator Theory 1 Journal of Applied Probability 1 Journal of Statistical Planning and Inference 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Statistica Neerlandica 1 Transactions of the American Mathematical Society 1 Acta Mathematica Hungarica 1 Probability Theory and Related Fields 1 International Journal of Approximate Reasoning 1 Journal of Theoretical Probability 1 Journal of the American Mathematical Society 1 Linear Algebra and its Applications 1 Computational Statistics and Data Analysis 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 Turkish Journal of Mathematics 1 Bernoulli 1 Probability in the Engineering and Informational Sciences 1 Stochastics 1 Journal of Statistical Theory and Practice 1 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 1 Science China. Mathematics 1 Forum of Mathematics, Sigma 1 ISRN Probability and Statistics
all top 5
#### Cited in 20 Fields
60 Probability theory and stochastic processes (60-XX) 42 Functional analysis (46-XX) 42 Statistics (62-XX) 11 Operator theory (47-XX) 7 Measure and integration (28-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 5 Computer science (68-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Real functions (26-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Operations research, mathematical programming (90-XX) 2 Quantum theory (81-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
|
2021-09-28 19:23:23
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https://www.jobilize.com/course/section/everyday-math-add-and-subtract-polynomials-by-openstax?qcr=www.quizover.com
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# 6.1 Add and subtract polynomials (Page 2/12)
Page 4 / 12
## Practice makes perfect
Identify Polynomials, Monomials, Binomials, and Trinomials
In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.
$81{b}^{5}-24{b}^{3}+1$
$5{c}^{3}+11{c}^{2}-c-8$
$\frac{14}{15}y+\frac{1}{7}$
5
$4y+17$
trinomial polynomial binomial monomial binomial
${x}^{2}-{y}^{2}$
$-13{c}^{4}$
${x}^{2}+5x-7$
${x}^{2}{y}^{2}-2xy+8$
19
$8-3x$
${z}^{2}-5z-6$
${y}^{3}-8{y}^{2}+2y-16$
$81{b}^{5}-24{b}^{3}+1$
$-18$
binomial trinomial polynomial trinomial monomial
$11{y}^{2}$
$-73$
$6{x}^{2}-3xy+4x-2y+{y}^{2}$
$4y+17$
$5{c}^{3}+11{c}^{2}-c-8$
Determine the Degree of Polynomials
In the following exercises, determine the degree of each polynomial.
$6{a}^{2}+12a+14$
$18x{y}^{2}z$
$5x+2$
${y}^{3}-8{y}^{2}+2y-16$
$-24$
2 4 1 3 0
$9{y}^{3}-10{y}^{2}+2y-6$
$-12{p}^{4}$
${a}^{2}+9a+18$
$20{x}^{2}{y}^{2}-10{a}^{2}{b}^{2}+30$
17
$14-29x$
${z}^{2}-5z-6$
${y}^{3}-8{y}^{2}+2y-16$
$23a{b}^{2}-14$
$-3$
1 2 3 3 0
$62{y}^{2}$
15
$6{x}^{2}-3xy+4x-2y+{y}^{2}$
$10-9x$
${m}^{4}+4{m}^{3}+6{m}^{2}+4m+1$
In the following exercises, add or subtract the monomials.
${\phantom{\rule{0.2em}{0ex}}\text{7x}}^{2}+5{x}^{2}$
$12{x}^{2}$
${\phantom{\rule{0.2em}{0ex}}\text{4y}}^{3}+6{y}^{3}$
$-12w+18w$
$6w$
$-3m+9m$
$\text{4a}-9a$
$-5a$
$\text{−}y-5y$
$28x-\left(-12x\right)$
$40x$
$13z-\left(-4z\right)$
$-5b-17b$
$-22b$
$-10x-35x$
$12a+5b-22a$
$\text{−10a}+5b$
$\text{14x}-3y-13x$
$2{a}^{2}+{b}^{2}-6{a}^{2}$
$-4{a}^{2}+{b}^{2}$
$5{u}^{2}+4{v}^{2}-6{u}^{2}$
$x{y}^{2}-5x-5{y}^{2}$
$x{y}^{2}-5x-5{y}^{2}$
$p{q}^{2}-4p-3{q}^{2}$
${a}^{2}b-4a-5a{b}^{2}$
${a}^{2}b-4a-5a{b}^{2}$
${x}^{2}y-3x+7x{y}^{2}$
$\text{12a}+8b$
$\text{12a}+8b$
$\text{19y}+5z$
Add: $4a,-3b,-8a$
$-4a-3b$
Add: $\phantom{\rule{0.2em}{0ex}}\text{4x},3y,-3x$
Subtract $5{x}^{6}\text{from}-12{x}^{6}$ .
$-17{x}^{6}$
Subtract $2{p}^{4}\text{from}-7{p}^{4}$ .
In the following exercises, add or subtract the polynomials.
$\left(5{y}^{2}+12y+4\right)+\left(6{y}^{2}-8y+7\right)$
$11{y}^{2}+4y+11$
$\left(4{y}^{2}+10y+3\right)+\left(8{y}^{2}-6y+5\right)$
$\left({x}^{2}+6x+8\right)+\left(-4{x}^{2}+11x-9\right)$
$-3{x}^{2}+17x-1$
$\left({y}^{2}+9y+4\right)+\left(-2{y}^{2}-5y-1\right)$
$\left(8{x}^{2}-5x+2\right)+\left(3{x}^{2}+3\right)$
$11{x}^{2}-5x+5$
$\left(7{x}^{2}-9x+2\right)+\left(6{x}^{2}-4\right)$
$\left(5{a}^{2}+8\right)+\left({a}^{2}-4a-9\right)$
$6{a}^{2}-4a-1$
$\left({p}^{2}-6p-18\right)+\left(2{p}^{2}+11\right)$
$\left(4{m}^{2}-6m-3\right)-\left(2{m}^{2}+m-7\right)$
$2{m}^{2}-7m+4$
$\left(3{b}^{2}-4b+1\right)-\left(5{b}^{2}-b-2\right)$
$\left({a}^{2}+8a+5\right)-\left({a}^{2}-3a+2\right)$
$5a+3$
$\left({b}^{2}-7b+5\right)-\left({b}^{2}-2b+9\right)$
$\left(12{s}^{2}-15s\right)-\left(s-9\right)$
$12{s}^{2}-14s+9$
$\left(10{r}^{2}-20r\right)-\left(r-8\right)$
Subtract $\left(9{x}^{2}+2\right)$ from $\left(12{x}^{2}-x+6\right)$ .
$3{x}^{2}-x+4$
Subtract $\left(5{y}^{2}-y+12\right)$ from $\left(10{y}^{2}-8y-20\right)$ .
Subtract $\left(7{w}^{2}-4w+2\right)$ from $\left(8{w}^{2}-w+6\right)$ .
${w}^{2}+3w+4$
Subtract $\left(5{x}^{2}-x+12\right)$ from $\left(9{x}^{2}-6x-20\right)$ .
Find the sum of $\left(2{p}^{3}-8\right)$ and $\left({p}^{2}+9p+18\right)$ .
$2{p}^{3}+{p}^{2}+9p+10$
Find the sum of
$\left({q}^{2}+4q+13\right)$ and $\left(7{q}^{3}-3\right)$ .
Find the sum of $\left(8{a}^{3}-8a\right)$ and $\left({a}^{2}+6a+12\right)$ .
$8{a}^{3}+{a}^{2}-2a+12$
Find the sum of
$\left({b}^{2}+5b+13\right)$ and $\left(4{b}^{3}-6\right)$ .
Find the difference of
$\left({w}^{2}+w-42\right)$ and
$\left({w}^{2}-10w+24\right)$ .
$11w-64$
Find the difference of
$\left({z}^{2}-3z-18\right)$ and
$\left({z}^{2}+5z-20\right)$ .
Find the difference of
$\left({c}^{2}+4c-33\right)$ and
$\left({c}^{2}-8c+12\right)$ .
$12c-45$
Find the difference of
$\left({t}^{2}-5t-15\right)$ and
$\left({t}^{2}+4t-17\right)$ .
$\left(7{x}^{2}-2xy+6{y}^{2}\right)+\left(3{x}^{2}-5xy\right)$
$10{x}^{2}-7xy+6{y}^{2}$
$\left(-5{x}^{2}-4xy-3{y}^{2}\right)+\left(2{x}^{2}-7xy\right)$
$\left(7{m}^{2}+mn-8{n}^{2}\right)+\left(3{m}^{2}+2mn\right)$
$10{m}^{2}+3mn-8{n}^{2}$
$\left(2{r}^{2}-3rs-2{s}^{2}\right)+\left(5{r}^{2}-3rs\right)$
$\left({a}^{2}-{b}^{2}\right)-\left({a}^{2}+3ab-4{b}^{2}\right)$
$-3ab+3{b}^{2}$
$\left({m}^{2}+2{n}^{2}\right)-\left({m}^{2}-8mn-{n}^{2}\right)$
$\left({u}^{2}-{v}^{2}\right)-\left({u}^{2}-4uv-3{v}^{2}\right)$
$4uv+2{v}^{2}$
$\left({j}^{2}-{k}^{2}\right)-\left({j}^{2}-8jk-5{k}^{2}\right)$
$\left({p}^{3}-3{p}^{2}q\right)+\left(2p{q}^{2}+4{q}^{3}\right)$ $-\left(3{p}^{2}q+p{q}^{2}\right)$
${p}^{3}-6{p}^{2}q+p{q}^{2}+4{q}^{3}$
$\left({a}^{3}-2{a}^{2}b\right)+\left(a{b}^{2}+{b}^{3}\right)$ $-\left(3{a}^{2}b+4a{b}^{2}\right)$
$\left({x}^{3}-{x}^{2}y\right)-\left(4x{y}^{2}-{y}^{3}\right)$ $+\left(3{x}^{2}y-x{y}^{2}\right)$
${x}^{3}+2{x}^{2}y-5x{y}^{2}+{y}^{3}$
$\left({x}^{3}-2{x}^{2}y\right)-\left(x{y}^{2}-3{y}^{3}\right)$ $-\left({x}^{2}y-4x{y}^{2}\right)$
Evaluate a Polynomial for a Given Value
In the following exercises, evaluate each polynomial for the given value.
Evaluate $8{y}^{2}-3y+2$ when:
$y=5$
$y=-2$
$y=0$
187 46 2
Evaluate $5{y}^{2}-y-7$ when:
$y=-4$
$y=1$
$y=0$
Evaluate $4-36x$ when:
$x=3$
$x=0$
$x=-1$
−104 4 40
Evaluate $16-36{x}^{2}$ when:
$x=-1$
$x=0$
$x=2$
A painter drops a brush from a platform 75 feet high. The polynomial $-16{t}^{2}+75$ gives the height of the brush $t$ seconds after it was dropped. Find the height after $t=2$ seconds.
11
A girl drops a ball off a cliff into the ocean. The polynomial $-16{t}^{2}+250$ gives the height of a ball $t$ seconds after it is dropped from a 250-foot tall cliff. Find the height after $t=2$ seconds.
A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial $-4{p}^{2}+420p.$ Find the revenue received when $p=60$ dollars.
$10,800 A manufacturer of the latest basketball shoes has found that the revenue received from selling the shoes at a cost of p dollars each is given by the polynomial $-4{p}^{2}+420p.$ Find the revenue received when $p=90$ dollars. ## Everyday math Fuel Efficiency The fuel efficiency (in miles per gallon) of a car going at a speed of $x$ miles per hour is given by the polynomial $-\frac{1}{150}{x}^{2}+\frac{1}{3}x$ . Find the fuel efficiency when $x=30\phantom{\rule{0.2em}{0ex}}\text{mph}$ . 4 Stopping Distance The number of feet it takes for a car traveling at $x$ miles per hour to stop on dry, level concrete is given by the polynomial $0.06{x}^{2}+1.1x$ . Find the stopping distance when $x=40\phantom{\rule{0.2em}{0ex}}\text{mph}$ . Rental Cost The cost to rent a rug cleaner for $d$ days is given by the polynomial $5.50d+25$ . Find the cost to rent the cleaner for 6 days.$58
Height of Projectile The height (in feet) of an object projected upward is given by the polynomial $-16{t}^{2}+60t+90$ where $t$ represents time in seconds. Find the height after $t=2.5$ seconds.
Temperature Conversion The temperature in degrees Fahrenheit is given by the polynomial $\frac{9}{5}c+32$ where $c$ represents the temperature in degrees Celsius. Find the temperature in degrees Fahrenheit when $c=65\text{°}.$
149
## Writing exercises
Using your own words, explain the difference between a monomial, a binomial, and a trinomial.
Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.
Ariana thinks the sum $6{y}^{2}+5{y}^{4}$ is $11{y}^{6}$ . What is wrong with her reasoning?
Jonathan thinks that $\frac{1}{3}$ and $\frac{1}{x}$ are both monomials. What is wrong with his reasoning?
## Self check
After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
If most of your checks were:
…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.
…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?
…no - I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.
hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused.
what do you need help in?
Felix
Heather
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles
168.50=R
Heather
john is 5years older than wanjiru.the sum of their years is27years.what is the age of each
46
mustee
j 17 w 11
Joseph
john is 16. wanjiru is 11.
Felix
27-5=22 22÷2=11 11+5=16
Joyce
I don't see where the answers are.
Ed
Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?
3
Christopher
18t+14t=96 32t=96 32/96 3
Christopher
show that a^n-b^2n is divisible by a-b
What does 3 times your weight right now
Use algebra to combine 39×5 and the half sum of travel of 59+30
Cherokee
What is the segment of 13? Explain
Cherokee
my weight is 49. So 3 times is 147
Cherokee
kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps
tyler
How to convert grams to pounds?
paul
What is the lcm of 340
Yes
Cherokee
How many numbers each equal to y must be taken to make 15xy
15x
Martin
15x
Asamoah
15x
Hugo
1y
Tom
1y x 15y
Tom
find the equation whose roots are 1 and 2
(x - 2)(x -1)=0 so equation is x^2-x+2=0
Ranu
I believe it's x^2-3x+2
NerdNamedGerg
because the X's multiply by the -2 and the -1 and than combine like terms
NerdNamedGerg
find the equation whose roots are -1 and 4
Ans = ×^2-3×+2
Gee
find the equation whose roots are -2 and -1
(×+1)(×-4) = x^2-3×-4
Gee
yeah
Asamoah
there's a chatting option in the app wow
Nana
That's cool cool
Nana
Nice to meet you all
Nana
you too.
Joan
😃
Nana
Hey you all there are several Free Apps that can really help you to better solve type Equations.
Debra
Debra, which apps specifically. ..?
Nana
am having a course in elementary algebra ,any recommendations ?
samuel
Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science
Nana
me too as part of my core subjects in R M E
Ken
at ABETIFI COLLEGE OF EDUCATION
Ken
ok great. Good to know.
Joan
5x + 1/3= 2x + 1/2
sanam
Plz solve this
sanam
5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12
Ranu
Thks ranu
sanam
Erica
the previous equation should be 3x = 1/6 x=1/18
Sriram
for the new one 10x + 2x = 38 - 14
Sriram
12x = 24 x=2
Sriram
10x + 14 = -2x +38 10x + 2x = 38 - 14 12x = 24 divide both sides by the coefficient of x, which is 12 therefore × = 2
vida
a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs $6.04 per gallon and the soda costs$4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs \$5.71 per gallon?
(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
really
Asamoah
4x-7y=8 2x-7y=1 what is the answer?
x=7/2 & y=6/7
Pbp
x=7/2 & y=6/7 use Elimination
Debra
true
bismark
factoriz e
usman
4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2
Peggie
Frank
thanks
Ramil
x=7/2 y=6/7
Asamoah
Thanks , all of you are correct.
Joseph
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2020-02-25 19:00:22
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 189, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4201969802379608, "perplexity": 1816.604392870072}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146127.10/warc/CC-MAIN-20200225172036-20200225202036-00278.warc.gz"}
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http://bora.uib.no/handle/1956/909/browse?value=Charmonium&type=subject
|
Now showing items 1-1 of 1
• Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\psi$ production as function of event multiplicity. The interesting relative increase ...
Journal article
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2019-01-19 14:59:20
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https://scipost.org/submissions/2106.11245v3/
|
# Non-equilibrium Sachdev-Ye-Kitaev model with quadratic perturbation
### Submission summary
As Contributors: Lunkin Aleksey Arxiv Link: https://arxiv.org/abs/2106.11245v3 (pdf) Date accepted: 2021-12-14 Date submitted: 2021-11-11 09:15 Submitted by: Aleksey, Lunkin Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical
### Abstract
We consider a non-equilibrium generalization of the mixed SYK$_4$+SYK$_2$ model and calculate the energy dissipation rate $W(\omega)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the polaron energy splitting $\omega_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $\omega_R$ and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.
Published as SciPost Phys. 12, 031 (2022)
Resubmission latter.
We would like to thank the referees for their reports and comments.
To the report #1:
Minor comments: a&b – we have done all the corrections proposed
Main comments: We have retained S_2 terms as it changes the quadratic action of the soft modes as this contribution is dominant for low frequencies. It can be seen from Eq.10 where the Green function of the soft modes is presented. The second term in the brackets (with function $\psi$) comes from the S_2 and is dominant in the assumption $\Gamma \gg T$. We do not need to take into account higher terms as they are small as $N\gg1$. The term $S_2$ is also important as it mixes low and high frequencies in the non-linear regime (see eq. (28) ).
To the report #2:
In our model, interaction (described by the SYK model) is much stronger than quadratic perturbation. As a result, the starting point of perturbative analysis is an SYK model, which does not have a standard diagrammatic description with an ordinary fermionic Green function. Moreover, the fluctuation propagator in the SYK model has a “zero mode” due to asymptotic symmetry. This mode could be taken into account using the path integral approach for the variable $\phi$ (as action is non-local we could not write a Hamiltonian). As a result, for the SYK model, the diagrammatic description could be used in terms of fluctuation propagator of $\phi$. To clarify the origin of the key relation shown in Eq.(18), we added the text between equations (18)-(22) which shows how susceptibility can be obtained working in the functional integral representation for the $\phi$ field.
We also added the citation of the mentioned paper by Skvortsov et al. It is referred to in the Introduction after the words: “In other words, we propose here a generalization of the approach well-known [6–9]”
Aleksey Lunkin and Mikhail Feigel’man
### List of changes
1. The citation of the paper by Skvortsov et al. was added in the introduction.
2. The equation (5) was enumerated
3. Intervals in the equation (8) were increased
5. The last line in the equation (35) was corrected.
### Submission & Refereeing History
#### Published as SciPost Phys. 12, 031 (2022)
Resubmission 2106.11245v3 on 11 November 2021
Submission 2106.11245v2 on 21 September 2021
## Reports on this Submission
### Report
The authors have included my suggestions in somewhat different way that I have expected. However, I agree that the resubmitted version has a better readability as compared to the previous one. Comments of the 1st Referee have also lead to the improvement of an overall presentation. Thus, I suggest that the manuscript can be now published in its present form.
• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -
### Report
The authors addressed my questions. I recommend publication.
• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -
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2022-08-18 01:48:22
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https://whitepaper.dogami.com/usddoga-tokenomics/earning-mechanisms/staking
|
Search…
DOGAMÍ Overview
Roadmap & Additional Info
Market Overview
Legal Mentions
Staking
## ☄️ DOGA Staking
The Petaverse is a self-contained space station-like construct, vast in size, floating outside our dimension. The governing and sustaining entities of the Petaverse soon reveal themselves as Spirit Dogs, enlightened beings who nurture the bond between pets and owners. The power at stake is the $DOGA itself, the energy generated through the symbiotic relationship between pet and owner. True Dogamí are not merely these pod dogs as players first engaged them, but over time they evolve into Spirit Dogs, composite spirit beings of both pets and owners combined. Such healthy relationships are what generate$DOGA, the energy that permeates the cosmos, maintaining order and peace while also keeping the destructive forces of chaos at bay. In order to protect the Petaverse from evil forces wanting to cause chaos, humans began pooling together their energy in the form of $DOGA staking to create a force field so strong that it is capable of preventing all evil beings from entering the territory. Staking is a way for us to reward our community members for locking up their$DOGA tokens and actively participating in our ecosystem. By staking your $DOGA you’ll be able to earn$DOGA rewards and other accessories/consumables when you lock up your tokens through the staking dashboard. The staking rewards will vary depending on the amount that is staked as well as the time it is staked for.
In the beginning, DOGAMI will introduce flexible staking offering a fixed APY (22%). Rewards will be distributed from DOGAMI's staking pool.
In a later stage, DOGAMI plans on introducing a new innovative flexible staking that will offer more rewards to players that stake their tokens for longer periods of time as described in the mechanism below:
Conditions & Rules
• No minimum staking amount
• A minimum staking period has to be respected
• A staking reward is set at each new Tezos block
• To collect rewards users need to keep their tokens staked for the entire locked period
• Unstaking locked tokens before the end of the locked period set to zero the on hold rewards
• The initial sum staked and any accrued interest that is not claimed at the end of the period are not automatically re-staked in next period's pool
• Any unused supply from the staking rewards at period n will be re-injected in the supply of the period (n+1)
• A staking score will be calculated for every player which will determine his share on the period's staking pool
$y_i=\frac{ (x_i* (tf_i-ti_i))}{\sum_k(x_k*(T-ti_k))}$
$r_i = r_{max}*y_i$
$y_i : reward~coefficient~of~player~i\\ x_i : staked~amount~x~of~player~i \\ tf_i : withdrawal~time~of~player~i \\ ti_i : staking~time~of~player~i \\ T : staking~rewards~period \\ r_i : staking~reward~of~player~i \\ r_{max} : monthly~supply~of~tokens~available~for~staking~rewards$
Note: We will be introducing a limit to the rewards obtainable per player in case the number of stakers is low. The objective is to safeguard the sustainability of the model and make sure the token supply is not depleted quickly.
Last modified 4mo ago
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2022-09-29 01:38:03
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https://wiki.kidzsearch.com/wiki/Iglesia_ni_Cristo
|
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# Iglesia ni Cristo
The Iglesia ni Cristo (IPA: [iːˈglɛ.ʃɑː niː ˈkriːstəʊ]; Filipino for Church of Christ), or INC, is a church which was established in the Philippines by Felix Manalo in 1914.[1] The INC believes to be the church belonging to Jesus Christ. THE EMERGENCE OF the Iglesia Ni Cristo in the Philippines fulfils the prophecies of God written in the Bible concerning His sons and daughters whom He will call from the Far East in these last days (cf. Isaiah 43:5-6 and Moffatt; 41:9-15; 46:11-13; Acts 2:39; John 10:16; Revelation 7:2-3). These biblical prophecies have also pointed to a servant of God whom He will send to lead God’s chosen people from the ends of the earth:
“Thou whom I have taken from the ends of the earth, and called thee from the chief men thereof, and said unto thee, THOU ART MY SERVANT; I have chosen thee, and not cast thee away. Fear thou not; for I am with thee: be not dismayed; for I am thy God: I will strengthen thee; yea, I will help thee; yea, I will uphold thee with the right hand of my righteousness.” (Isaiah 41:9-10 KJV,emphasis mine)
God said to His “servant” whom He “have taken from the ends of the earth have chosen thee, and not cast thee away.” Another biblical prophecy points out that God’s messenger from the ends of the earth will came from “a far country” in the East, or the Far East:
“Calling a ravenous bird from the east, the man that executeth my counsel from a far country: yea, I have spoken it, I will also bring it to pass; I have purposed it, I will also do it. Hearken unto me, ye stout-hearted, that are far from righteousness: I bring near my righteousness; it shall not be far off, and my salvation shall not tarry: and I will place salvation in Zion for Israel my glory.” (Isaiah 46:11-13 KJV)
The “ravenous bird from the east” mentioned in Isaiah 46:11 is also the the man that executeth God’s counsel from a far country. Through him, God will bring near His righteousness. Thus, the messenger of God from the ends of the earth, from the Far East, is a preacher of the Gospel for the righteousness of God that He will bring near to the people through this messenger is the the Gospel which is also the power of God to salvation:
“For I am not ashamed of the gospel of Christ, for it is the power of God to salvation for everyone who believes, for the Jew first and also for the Greek. For in it the righteousness of God is revealed from faith to faith; as it is written, ‘The just shall live by faith.’” (Romans 1:16-17 NKJV)
Brother Felix Y. Manalo is the messenger of God from the ends of the earth and from the Far East, whom God sent to perform this task. God has given His messenger the assurances that He will help and strengthen him in pursuing such noble task in the face of tremendous odds and difficulties. God said to Him:
“Fear thou not; for I am with thee: be not dismayed; for I am thy God: I will strengthen thee; yea, I will help thee; yea, I will uphold thee with the right hand of my righteousness.” (Isaih 41:10 KJV)
The growth and development of the Igleia Ni Cristo from its humble beginnings to its present dynamic stature, attest to the fulfilment of these prophecies. The membership of the Church increased at a phenomenal rate from a handful of adherents gathered in its pioneering years to the millions now scattered in many parts of the world.
The houses of worship that the Church has built has effectively changed the Philippine landscape which the Catholic Church used to dominate. The iglesia Ni Cristo houses of worship now can also be seen in different parts of the world where the Church gained a foothold.
The power of the unity of the Church members, their vitality in their practice of religion, their fidelity to the doctrines taught to them, and their unswerving resolve to surmount all difficultiesare indications of a vibrant faith – the result of the preaching functions of the late Brother Felix Y. Manalo.
church does not believe in the religious teachings of the Trinity, including the teaching that Jesus is God.[2]
Felix Manalo joined many religious organizations as a young adult. He said that God gave him a mission to teach the gospel and to bring back the first church made by Jesus.[3] The INC began with a handful of followers on July 27, 1914 in Punta, Santa Ana, Manila, with Manalo as highest minister. It has now spread to many different countries.[4]
## Beliefs and teachings
Some of the teachings INC believes in are:[2]
• God is the one who made the Heavens and the Earth, and he is the only god.
• There is no Holy Trinity; God, Jesus and the Holy Spirit are not one.
• Jesus is the Son of God.
• The Holy Spirit is the power given to Jesus to teach and for us to help us with our problems.
• Manalo was God's last messenger.
• God chose INC members to serve him.
• INC is the same church as the Christian church in the first century.
• INC is God's true church, and the only way to be saved.
• INC believes in baptism by water.
• Members should live a life of good.
• Members must not eat food made with blood or marry a non-member.
• It is everyone's job to worship God by going to worship services two times a week.
• Members should treat each other like brother and sister.
• The church should act as one; this includes voting.
• The dead will come back to life and either be blessed or punished.
• Jesus will come again very soon because the signs that He is coming back (such as war, famine and earthquake) have happened.
• A holy city is being made by Jesus for INC members to live when he comes back.
## References
1. Sanders, Albert J., "An Appraisal of the Iglesia ni Cristo," in Studies in Philippine Church History, ed. Anderson, Gerald H. (Cornell University Press, 1969)
2. Introducing the Iglesia ni Cristo Booklet, 1989, pp.1-16
3. Crisostomo, Isabelo T. 'Felix Y. Manalo and the Iglesia ni Cristo', Pasugo (May-June 1986)
4. Suarez, E. T. 'Iglesia ni Cristo turns 91 today' Manila Bulletin (July 27, 2005)
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https://www.aging-us.com/article/204259/text
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# Use of nicorandil is associated with increased risk of incident atrial fibrillation
#### Chien-Chang Lee1,2, , Sheng-Nan Chang3, , Babak Tehrani4, , Sot Shih-Hung Liu1, , Chia-Ying Chan5, , Wan-Ting Hsu6, , Tzu-Yun Huang5, , Pang-Shuo Huang3, , Juey-Jen Hwang7, , Jien-Jiun Chen3, , Chia-Ti Tsai7, ,
• 1 Department of Emergency Medicine, National Taiwan University Hospital, Taipei, Taiwan
• 2 Center of Intelligent Healthcare, National Taiwan University Hospital, Taipei, Taiwan
• 3 Division of Cardiology, Department of Internal Medicine, National Taiwan University Hospital Yunlin Branch, Yunlin, Taiwan
• 4 Department of Medicine, Brown University/Rhode Island Hospital, Providence, RI 02912, USA
• 5 Department of Family Medicine, National Taiwan University Hospital, Taipei, Taiwan
• 6 Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA 02115, USA
• 7 Division of Cardiology, Department of Internal Medicine, National Taiwan University Hospital, Taipei, Taiwan
#### Received: March 22, 2022 Accepted: August 17, 2022 Published: September 9, 2022
https://doi.org/10.18632/aging.204259
How to Cite
Copyright: © 2022 Lee et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
### Abstract
Background: Nicorandil will activate ATP-sensitive potassium channel (KATP). However, activation of potassium channels plays an important role in the mechanism of atrial fibrillation (AF) or atrial flutter (AFL). Whether use of nicorandil might contribute to initiation and/or perpetuation of AF/AFL remained unknown. We determined the relationship between use of nicorandil and risk of atrial fibrillation and determined its molecular mechanism.
Methods: We performed a nested case-control study using a cohort from the National Health Insurance Research Database (NHIRD) of Taiwan. The association between nicorandil use and risk of atrial fibrillation/flutter was estimated by logistic regression model. We also performed molecular, cellular and animal studies to explain the association.
Results: A total of 715 individuals who experienced AF/atrial flutter were matched to 72,215 controls. New use of nicorandil was found to be associated with increased risk for AF/AFL (odds ratio [OR], 2.34; 95% CI 1.07–5.13) compared to nitrate use. We found the expression of KATP subunits Kir6.2 and SUR2A in human and rat left atrial tissues. Furthermore, nicorandil directly shortened action potential duration (APD) in rat left atrium and shortened the QT interval of cultured human induced pluripotent stem cell (iPSC) derived cardiomyocytes (iPSC-CMs).
Conclusions: Use of nicorandil was found to be associated with increased risk of AF/AFL. We also showed the expression of KATP subunits in human atria, and a possible mechanism that use of nicorandil increases the risk of AF through activation of KATP and shortening of atrial APD.
### Introduction
Atrial fibrillation (AF) is the most common sustained arrhythmia, estimated to affect 1.5–2 percent of the general population in the world [1]. Moreover, the prevalence rate increases with age, up to 9% in people over 80 years old [2]. AF can contribute to serious consequences like hemodynamic impairment and cardioembolic stroke [3]. People having AF are at four to five-fold higher risk of ischemic stroke than those not having AF [4].
Clinical trials and case reports have shown the association between drugs and the induction of AF [4]. Although drug-induced AF may only represent a small proportion of the patients presenting with AF, being an iatrogenic cause, it is important to recognize. However, evidence of the association between drugs and AF is insufficient and mostly according to individual case histories. We do not know if the temporal relationship between drug intake and initiation of AF is an incidental finding or caused by the underlying condition (“confounding by indication). Nicorandil, a combination of nitrate components and sarcolemmal adenosine triphosphate-sensitive potassium channel (KATP) opener, is a potent vasodilator of coronary and peripheral vessels and is used as an antianginal agent. It has been demonstrated that AF is associated with shortening of action potential duration, which involves modified activities of atrial ion currents. An increase in the activity of ATP-sensitive potassium channels via Nicorandil could theoretically reduce atrial action potential duration and could possibly contribute to initiation and/or perpetuation of AF [5].
Nicorandil has been long and commonly used in patients with coronary artery disease. Epidemiologic studies to quantify the relation between nicorandil use and AF have not been performed yet, although AF is a very common arrhythmia with substantial morbidity and potentially serious complications. We aim to perform a nested case-control study in the national health claims database. In addition to the clinical studies that may link nicorandil use to developing AF, we also investigated the possible mechanism by which nicorandil increased the risk of AF using an in vitro rat model. Furthermore, human experimental data is the most valuable proof of a new clinical finding, but it is difficult to do an experimental study on a beating human heart. Reprogramming adult somatic cells into induced pluripotent stem cells (iPSCs) has become a powerful model for human diseases. [6] The iPSCs could be further differentiated to beating cardiomyocytes which have a striking similarity of electrophysiological properties with the in vivo human heart. [7] Therefore, we also used this iPSC-CM model to test the electrophysiological effect of nicorandil.
### Population
We performed a nested case-control study using the National Health Insurance Research Database (NHIRD) of Taiwan. The NHIRD contains records of approximately 1 million people randomly selected from the 23 million beneficiaries of the National Health Insurance of Taiwan. The NHIRD contains complete outpatient and inpatient electronic claim records, individual diagnoses, procedures, and medications prescribed. This study was approved by the institutional review board of the National Taiwan University Hospital, waiving patient written informed consent. This report includes all relevant STROBE elements.
### Study cohort and identification of case patients
Using the NHIRD, we assembled a study cohort that was longitudinally observed from January 2007 through December 2013. The risk of AF/atrial flutter recurrence was not a parameter that we set out to examine; therefore, patients who had been diagnosed with AF/atrial flutter in 2007 and 2008 were excluded for analysis. In addition, patients with a history of cardiotomy or cardiac arrest that can lead to increased risk in AF/atrial flutter were excluded. All cases of AF/atrial flutter identified between since 2009 were incident cases of AF/atrial flutter. To factor in the time-varying risk after initial exposure to nicorandil or nitrate, we excluded all patients who received at least one prescription of nicorandil or nitrate in 2007. The primary case definition used for identification of index cases of AF/atrial flutter was the first occurrence of AF/atrial flutter during the follow-up period with the International Classification of Diseases, Ninth Revision, Clinical Modification (ICD-9-CM) codes of AF (441.1, 441.2, 441.3, 441.4, 441.5, 441.6, 441.7, and 441.9) or atrial flutter (441.0, 441.00, 441.01, 441.02, and 441.03). We included both AF and atrial flutter cases since reported incidences in the literature overlap, and clinical diagnosis and management of both dysrhythmias is similar in clinical practice.
### Population controls
We selected controls by using a risk set sampling scheme. One hundred controls were selected for each case, matched on 5-year age class, sex, and the index date of case diagnosis. Additionally, controls had to be at risk of the event on the case’s index date.
### Medication exposure
Medication exposure was assessed at index date for AF or AFL cases. Use of nicorandil or nitrate was assumed whenever there was any order for a reimbursement code of oral nicorandil with a prescription length of 3 days or longer. The patients received 10–15 mg therapeutic dose in two or three divided doses. To assess the nicorandil use patterns and the risk of AF/atrial flutter, we classified nicorandil usage into 5 patterns. To assess the effect of drug exposure period and risk of AF, we first classified the use pattern into current and past use. Current use refers to the presence of a prescription record of nicorandil within 60 days of index date, past use refers to a record between 61 and 365 days before the index date. To evaluate the effect of starting time of nicorandil use, we classified the use into new use and long-term use. New use refers to nicorandil initiation within 60 days of the index date. Long term use refers to nicorandil initiation between 61 and 365 days before the index date. Lastly, to assess the effect of cumulative days of use on the risk of AF/atrial flutter, we identified patients who had a cumulative prescription length of greater than 120 days. We defined this group of patients as chronic use.
### Covariates
Based on literature reports, [8] we identified 47 covariates in the following categories: demographic, living area, insurance premium level, pre-existing comorbidities, frequency of health care utilization, and co-medications. The variables were summarized in Table 1. We used the ICD-9 codes to compute patients’ CHA2DS2VASc score. To calculate the score, the variables used were age (<65:0 for both sexes, 65–74: +1, ≥75: +2), sex (female ≥65: +1), history of congestive heart failure (+1), hypertension (+1), stroke/TIA/thromboembolism (+2), vascular disease (+1) and diabetes mellitus (+1). Comprehensive details about patient inclusion can be found in the Supplementary Materials and Methods.
#### Table 1. Baseline characteristics of nicorandil, nitrate, and non-users.
Non-users (N = 71,097) Nicorandil users (N = 245) Nitrate users (N = 873) P-value Demographics Gender Male (%) 42,808 (60.21%) 145 (59.18%) 477 (54.64%) 0.0036 Age (Mean ± SD) 69.2 ± 14.35 72.5 ± 9.92 74.68 ± 10.38 <.0001 Living area Urban Area 34,832 (49.09%) 127 (51.84%) 425 (48.74%) 0.0496 Metro Area 17,655 (24.88%) 62 (25.31%) 190 (21.79%) Suburban Area 12,063 (17.00%) 29 (11.84%) 166 (19.04%) Countryside Area 6,410 (9.03%) 27 (11.02%) 91 (10.44%) Insurance premium level Dependent 9,334 (13.15%) 13 (5.31%) 97 (11.12%) <.0001 ($1–$19,999) 16,179 (22.8%) 70 (28.57%) 259 (29.7%) ($20,000–$39,999) 28,102 (39.6%) 115 (46.94%) 378 (43.35%) (≥\$40,000) 17,345 (24.44%) 47 (19.18%) 138 (15.83%) Pre-existing comorbidities Acute myocardial infarction 124 (0.17%) 13 (5.31%) 34 (3.89%) <.0001 Congestive heart failure 866 (1.22%) 35 (14.29%) 115 (13.17%) <.0001 Peripheral vascular disorder 882 (1.24%) 16 (6.53%) 38 (4.35%) <.0001 Cerebrovascular disease 4,170 (5.87%) 30 (12.24%) 185 (21.19%) <.0001 Dementia 1,305 (1.84%) 11 (4.49%) 46 (5.27%) <.0001 Chronic pulmonary disease 2,948 (4.15%) 22 (8.98%) 84 (9.62%) <.0001 Rheumatologic disease 459 (0.65%) 2 (0.82%) 14 (1.60%) 0.0022 Peptic ulcer disease 5,758 (8.10%) 33 (13.47%) 182 (20.85%) <.0001 Mild liver disease 4,779 (6.72%) 19 (7.76%) 92 (10.54%) <.0001 Diabetes without chronic complications 8,893 (12.51%) 75 (30.61%) 297 (34.02%) <.0001 Diabetes with chronic complications 2,102 (2.96%) 25 (10.20%) 124 (14.20%) <.0001 Hemiplegia or paraplegia 450 (0.63%) 3 (1.22%) 14 (1.60%) 0.0009 Renal disease 1,638 (2.30%) 20 (8.16%) 111 (12.71%) <.0001 Any malignancy 2,593 (3.65%) 6 (2.45%) 60 (6.87%) <.0001 Moderate or severe liver disease 90 (0.13%) 0 (0.00%) 3 (0.34%) 0.1759 Neurologic disorder 1,291 (1.82%) 4 (1.63%) 32 (3.67%) 0.0003 Psychiatric disorder 5,556 (7.81%) 48 (19.59%) 124 (14.20%) <.0001 Angina 546 (0.77%) 31 (12.65%) 85 (9.74%) <.0001 Other ischemic heart disease 1,527 (2.15%) 72 (29.39%) 213 (24.40%) <.0001 Cardiac valve disease 703 (0.99%) 19 (7.76%) 65 (7.45%) <.0001 Hypertension 19,230 (27.05%) 155 (63.27%) 612 (70.10%) <.0001 Hyperlipidaemia 9,700 (13.64%) 84 (34.29%) 285 (32.65%) <.0001 Percutaneous transluminal coronary angioplasty 82 (0.12%) 11 (4.49%) 42 (4.81%) <.0001 Health care utilization Number of Outpatient visit 14.18 ± 15.70 27.19 ± 15.84 28.56 ± 18.37 <.0001 Number of Emergency Department visit 0.23 ± 0.77 0.83 ± 1.49 0.85 ± 1.64 <.0001 Number of Hospitalization 0.15 ± 0.64 0.74 ± 1.30 0.75 ± 1.22 <.0001 Medication use NSAIDs 18,377 (25.85%) 100(40.82%) 351 (40.21%) <.0001 Aspirins 6,480 (9.11%) 120(48.98%) 384 (43.99%) <.0001 Systemic corticosteroids 5,797 (8.15%) 34(13.88%) 131 (15.01%) <.0001 DMARDs 570 (0.80%) 5 (2.04%) 12 (1.37%) 0.0174 Beta-blocker 6,538 (9.20%) 86 (35.10%) 310 (35.51%) <.0001 ACE-inhibitors/ARB 4,139 (5.82%) 47 (19.18%) 187 (21.42%) <.0001 Calcium-channel blocker 14,155(19.91%) 131 (53.47%) 523 (59.91%) <.0001 Statin 6,277 (8.83%) 69 (28.16%) 277 (31.73%) <.0001 Scoring differences Charlson comorbidity score (Median, 25–75th) 0 (0–0) 0 (0–1) 0 (0–1) <.0001 CHA2DS2-VASc Score (Median, 25–75th) 2 (1–3) 3 (2–4) 4 (2–5) <.0001 Outcome AF 585 (0.82%) 39 (15.92%) 91 (10.42%) <.0001 Abbreviation: DMARD, disease-modifying antirheumatic drugs.
### Culture of induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) and measurement of field electrogram
iPS cells were obtained from the Academia Sinica and cultured on the probe of MED64 microelectrode system (Alpha MED Scientific Inc.) to record spontaneous field electrogram [9]. The detailed method is provided in the Supplementary Materials and Methods.
### Atrial expression of ATP-sensitive potassium channel (KATP)
KATP channels are hetero-octameric complexes of 4 pore-forming Kir6 channel-forming subunits, each associated with one regulatory SUR subunit. Two Kir6-encoding genes, KCNJ8 (Kir6.1) and KCNJ11 (Kir6.2), and two SUR genes, ABCC8 (SUR1) and ABCC9 (SUR2) encode mammalian KATP subunits [10]. We detected the expression of Kir6.1, Kir6.2, SUR1 and SUR2 in human and rat left atria by reverse transcription–polymerase chain reaction (RT-PCR) [10]. The detailed method is provided in the Supplementary Materials and Methods. Because it was not easy to obtain human left atrial tissue, the human atrial sample in this study was from only one 76-year-old man receiving mitral valvular surgery due to severe mitral regurgitation. The human study was approved by the ethical committee and Institutional Review Board of the National Taiwan University Hospital (200911002R). The experimental protocol of rat experiment also conformed to the Guide for the Care and Use of Laboratory Animals (NIH Publication No. 85-23, revised 1996) and was approved by the Institutional Animal Care and Use Committee of the National Taiwan University College of Medicine [11].
### Animal model and electrophysiological studies
Wistar rats (300–350 g) received intraperitoneal injection of Zoletil (125 mg tiletamine hydrochloride, 125 mg zolazepam hydrochloride) (20 mg/kg) and ECG and action potentials were recorded. The detailed method is provided in the Supplementary Materials and Methods. In brief, the ECG leads were fixed to the four limbs of the rat to record ECG. The anesthetized rat was then endotracheally intubated and mechanically ventilated. The chest was opened through sternal incision and a stimulating electrode was attached to the right atrium for atrial tachypacing to induce AF. For action potential recording, a glass microelectrode filled with 3M KCl was attached to the left atrium. At the end of the study, the animals were euthanized by cervical dislocation. The experimental protocol conformed to the Guide for the Care and Use of Laboratory Animals (NIH Publication No. 85-23, revised 1996) and was approved by the Institutional Animal Care and Use Committee of the National Taiwan University College of Medicine [11].
### Statistical analysis
We used a conditional logistic regression model to compute the odds ratio of AF/atrial flutter, and its 95% confidence interval, associated with use of nicorandil compared to nonuse. Under a time-matched case-control sampling scheme, the odds ratio provided an unbiased estimate of the rate ratio in the cohort. All potential confounders listed in Table 1 were entered into the model for adjustment. To account for the potential unmeasured confounders, we identified nitrate users in the same cohort as an active comparator. We conducted several sensitivity analyses based on different exposure patterns. As the ad hoc categorization of nicorandil use patterns may not reflect the overall risk period, for complete delineation of the timing of nicorandil exposure and associated risk of AF/atrial flutter, and for exploratory analysis of the presence of protopathic bias, we plotted a time-dependent risk graph in Figure 1.
Figure 1. Time-dependent risk of atrial fibrillation in patients taking nicorandil as compared with nitrate.
We first constructed a disease risk score (DRS) for matching cases and controls. The DRS was defined as the probability of developing incident AF/atrial flutter in a given year among all members of the cohort unexposed to nicorandil or nitrate as a function of individuals’ covariates ascertained at the beginning of the year. The DRS was estimated by multivariate logistic regression analysis using incident AF/atrial flutter as the dependent variable and all empirical clinical predictors as independent variables. Each case was matched to a control based on the DRS using the greedy matching algorithm. The DRS-matched cohort therefore created a cohort of individuals with similar risk to develop AF/atrial flutter between case and controls, therefore allowing calculation of unbiased risk estimates at different times of exposure.
Finally, to assess effect modification, the estimates were stratified by age (with a cutoff at 70 years), by the presence or absence of a diagnosis of myocardial infarction before the index date, and by the risk of ischemic stroke as measured by CHA2DS2VASc score. We used an E-value as a sensitivity analysis of the unmeasured confounder (https://www.evalue-calculator.com/). The E-value is an analysis method used to quantify the minimum strength of association that an unmeasured confounder must have with both the exposure and outcome, while simultaneously considering the measured covariates, to negate the observed treatment– outcome association [12].
The molecular data was presented as means ± standard deviations. The parameters before and after drug stimulation were compared with Wilcoxon signed rank test. We used SAS v9.4. (Cary, NC, USA) statistical software for all analyses.
### Patient population
The source population comprised 1,000,000 persons longitudinally followed from 2007 to 2013. We set the study entry date as Jan 1 2009, years 2007 and 2008 were used as a pre-enrollment period. We excluded patients with missing data on demographics, age less than 18, or AF case onset date on December 31, 2013. 715 cases of incident AF/atrial flutter were identified. We then performed a case-control match by matching each case to 100 randomly selected controls by age and sex using the risk-set sampling method. 72215 patients were included for analysis, which were categorized into non-users, nicorandil users, and nitrate users. Supplementary Figure 1 summarized the flowchart of patient inclusion and exclusion process. Supplementary Figure 2 presents the timeline and case-control scheme of the study design.
### Characteristics of study patients
Table 1 compares the baseline characteristics among nicorandil users, nitrate users and non-users. We also compared the characteristics of cases and controls in Supplementary Table 1. Compared to controls, patients who developed AF/atrial flutter have a higher insurance premium level, frequency of healthcare utilization and comorbidity scores. Except for dementia, rheumatologic disease, malignancy and neurologic disorder, cases have higher prevalence of systemic chronic diseases.
### Risk of AF/atrial flutter and use of nicorandil or nitrate
Table 2 shows the age-sex-year-matched and adjusted risks of AF/atrial flutter associated with different types of nicorandil/nitrate uses. Compared to nonuse, current use of nicorandil was associated with an increased risk of AF/atrial flutter (adjusted RR 9.80, 95% CI: 6.56–14.65). The strength of association significantly increased when we restricted patients to those who started to use nicorandil within 60 days (aRR 31.49, 95% CI: 16.80–59.01). For past use (Use only in −61~−365 days), long term use (Use start from −61~−365), or chronic use (cumulative use > 120 days), the association remains significant. Similar to nicorandil use, use of nitrate was found to be associated with increased, albeit attenuated, risk of AF/atrial flutter.
#### Table 2. Crude and adjusted odd ratios for the association between use of nicorandil and risk of incident atrial fibrillation.
Incident atrial fibrillation Crude RR Confounder-adjusted RR (95% C.I.) Nicorandil vs. nonuse Current use (Use in 60 days) 23.67 (16.59–33.78), p < .0001 9.80 (6.56–14.65), p < .0001 New use (Use start within 60 days) 49.19 (27.87–86.82), p < .0001 31.49 (16.80–59.01), p < .0001 Past use (Use only in −61~−365 days) 10.05 (5.66–17.86), p < .0001 3.04 (1.60–5.80), p = 0.0007 Long term use (Use start from −61~−365) 13.93 (9.70–19.99), p < .0001 5.02 (3.32–7.60), p < .0001 Chronic use (Cumulative use > 120 days) 12.69 (6.93–23.21), p < .0001 2.91 (1.43–5.91), p = 0.0032 Nitrate vs. nonuse Current use (Use in 60 days) 14.66 (11.58–18.56), p < .0001 5.90 (4.47–7.78), p < .0001 New use (Use start within 60 days) 24.14 (15.61–37.33), p < .0001 13.43 (8.27–21.81), p < .0001 Past use (Use only in −61~−365 days) 5.76 (4.02–8.25), p < .0001 1.96 (1.31–2.93), p = 0.0011 Long term use (Use start from −61~−365) 10.04 (8.04–12.55), p < .0001 3.80 (2.91–4.97), p < .0001 Chronic use (Cumulative use > 120 days) 9.83 (7.06–13.69), p < .0001 2.89 (1.97–4.23), p < .0001 Nicorandil vs. nitrate Current use (Use in 60 days) 1.61 (1.07, 2.43), p = 0.0214 1.66 (1.06, 2.60), p = 0.0270* New use (Use start within 60 days) 2.04 (1.00, 4.15), p = 0.0494 2.34 (1.07, 5.13), p = 0.0338* Past use (Use only in −61~−365 days) 1.74 (0.90, 3.40), p = 0.1015 1.54 (0.74, 3.23), p = 0.2498 Long term use (Use start from −61~−365) 1.39 (0.93, 2.08), p = 0.1133 1.32 (0.85, 2.06), p = 0.2158 Chronic use (Cumulative use > 120 days) 1.29 (0.65, 2.55), p = 0.4622 1.01 (0.47, 2.18), p = 0.9802
To account for the potential unmeasured confounders that make users of nicorandil or nitrates having a higher risk of AF/atrial flutter (e.g., users of either nicorandil or nitrates have coronary artery disease which may predispose to AF/atrial flutter), we used nitrate as an active comparator and investigated whether use of nicorandil was associated with a higher risk of AF/atrial flutter than use of nitrates.
Compared with nitrate use, current use of nicorandil is associated with a risk for AF/atrial flutter (OR 1.61, 95% CI 1.07–2.43). The risk further increased for new use (OR 2.34, 95% CI: 1.07–5.13). Past use, long term use, and chronic use did not observe an increased risk.
### Subgroup analysis
The subgroup analyses adjusted by DRS showed the risk of AF/atrial flutter associated with nicorandil to be very similar across all subgroups, except age. The risk of AF/atrial flutter associated with nicorandil use was more than 2 times higher (3.61 vs. 1.23; additive interaction p = 0.01) in individuals aged less than 65 than in older patients. Related data are shown in Supplementary Table 2.
### E-value
The E-value for the association between risk of AF/atrial flutter and current use of nicorandil as compared with nitrate (confounder-adjusted RR = 1.66) was 2.71. Therefore, an unmeasured confounder would only explain away the above association only if it had a relative risk association of 2.71 or greater with both current use of nicorandil and AF/atrial flutter, which is unlikely. The sensitivity analysis plot is shown in Figure 2.
Figure 2. Plot of sensitivity analysis for unmeasured confounding. Each point along the curve defines a joint relationship between the two sensitivity parameters that could move the observed association between nicorandil use and incident atrial fibrillation/atrial flutter (RR = 1.66) to the null (RR = 1). Each point along the curve defines a joint relationship between the two sensitivity parameters that could potentially explain away the estimated effect. If one of the two parameters are smaller than the E-value, the other must be larger, as defined by the plotted curve.
### Basal atrial expression of KATP in the human and rat left atria
Because the left atrium plays a dominant role in the mechanism of AF, we investigated whether KATP was expressed in the left atrium. Expression of KATP subunits Kir6.1, Kir6.2, SUR1 and SUR2 were detected by RT-PCR. We found the majority of KATP subunits in the human left atrium were Kir6.2 and SUR2A (Figure 3A). Because of limited human left atrial samples, rat left atrial tissue was used for a larger sample size and to perform electrophysiological studies. We also found basal expressions of Kir6.2 and SUR2 subunits in the rat left atria (Figure 3B). Therefore, we subsequently investigated the electrophysiological function of KATP in the rat model.
Figure 3. Basal expressions of KATP subunits in the human and rat atria. Total ribonucleic acid was isolated and reverse transcription-polymerase chain reaction products with specific primer pairs were visualized by electrophoresis. (A) The polymerase chain reaction results of human left atrial tissue. (B) The polymerase chain reaction results of 10 rat left atrial samples. Abbreviations: bp: base pair; GP: glyceraldehyde 3-phosphate dehydrogenase; MW: molecular weight maker.
### Electrophysiological effect of nicorandil on the mammalian atrium
Since there was an expression of major KATP subunits in the rat left atrium, we then sought to investigate the effect of nicorandil on the rat left atrium. We failed to induce sustained AF in normal rats because of the small atrial size. Because shortened action potential duration (APD) is the major surrogate phenotype of AF, we investigated whether nicorandil shortened rat left atrial APD. We found a significant shortening of the rat left atrial APD50 (43.7 ± 5.3 vs. 24.5 ± 7.5, p = 0.0176) and APD70 (54.3 ± 6.3 vs. 36.7 ± 9.1 p = 0.0180) (Figure 4).
Figure 4. Nicorandil shortens rat atrial action potential duration. (A) Representative spontaneous rat electrocardiogram (ECG) and atrial action potential duration (APD) tracings of before (left panel) and after (middle panel) nicorandil stimulation (1 mg/kg) are shown. Arrows denote P waves that correspond to atrial APDs. (B) Overlap of representative action potentials before (black) and after (red) nicorandil stimulation. (C) Summary data of the mean APD50 and APD70 before and after nicorandil stimulation (1 mg/kg) are shown (n = 7). The mean APD50 and APD70 are shorter after nicorandil stimulation (1 mg/kg). Data represent mean ± SD; p < 0.05 before versus after nicorandil stimulation.
### Nicorandil shortened QT interval of the cultured iPSC-CMs
We had demonstrated that nicorandil shortened atrial APD, which was a surrogate phenotype of AF. However, it is not clear whether nicorandil exerted a similar effect on the human heart. Because it is difficult to do an experimental study on a beating human heart, we tried to use beating iPSC-CMs to simulate the effect of nicorandil on human hearts. Normal beating iPSC-CMs were cultured on the MED64 microelectrode system. The field potential of these beating iPSC-CM monolayers looked very similar to the electrogram of an intact human heart (Figure 4). We failed to directly record APDs of the cultured iPSCs because of the low signal/noise ratio. Since the QT interval of a surface ECG corresponds to the cellular APD, we investigated whether nicorandil shorted QT intervals on this cultured beating iPSC-CM monolayer. We found nicorandil significantly shortened the QT intervals of beating iPSC-CM monolayers. The effect was abolished when nicorandil was washed out (Figures 4 and 5).
Figure 5. Generation and analysis of electrograms from human iPSC-CM cultures show nicorandil shortens QT interval of iPSC-CMs. (A) Phase-contrast images show an overview of cell morphology of iPSC-CM cultures on top of the micro electrode array (black rectangular dots; red arrow). (B) QT interval in electrogram is a gross phenotype of cellular action potential duration. The electrogram or field potential was recorded from the microelectrodes with iPSC-CMs cultured on top of them. Because the end of the T wave is not prominent, the QT interval is measured as the interval from the Q wave to the peak P wave. Shortening of QT interval is noted after nicorandil (100 uM) stimulation. (C) Summary data of QT interval before and after nicorandil stimulation are shown (n = 6). Data represent mean ± SD; p < 0.05 before versus after nicorandil stimulation.
### Discussion
We carried out a population-based nested case-control study involving one million national representative participants. Overall, more recent use of nicorandil was associated with higher risk for AF/atrial flutter. New use (use start within 60 days) had the highest risk, followed by current use (use record within 60 days). Past (use only in −61~−365 days), long term (Use start from −61~−365), and chronic (cumulative use >120 days) use were not associated with increased risk of AF/ flutter. These results suggest an acute or subacute effect of nicorandil on the atrial electrophysiology.
Atrial fibrillation is common among the nitrate or nicorandil user population and a non-causal association between nicorandil treatment and AF could arise by confounding because several risk factors for ischemic chest pain and AF are shared. Ischemic heart disease may itself be a risk factor for AF. We used the DRS matching approach to minimize the confounding effect. The DRS matching, like propensity score matching, tries to find 1 (or more) individual(s) with similar DRS in the case and control groups. Following matching, the variation between individuals in risk factors for AF are implicitly controlled.
Several studies have assessed the efficacy and safety of nicorandil, but none have assessed cardiovascular risks associated with nicorandil use. In a previous cohort study, Dunn N and colleagues conducted a prescription-event monitoring (PEM) study of nicorandil to access the safety profile of nicorandil [13]. The study was based on a cohort of 13,260 patients, and ischemic heart diseases were the second most frequently reported events during nicorandil treatment, ranked by incidence density for each event during the first month of treatment per 1000 patient-months. However, many of these events were confounded by indication and may not be causally associated. Some studies have assessed AF risk associated with other anti-anginal medication, including isosorbide mononitrate, atenolol, diltiazem, and verapamil. A narrative review performed to evaluate the quality of evidence associating specific drugs with the occurrence of AF concluded insufficient evidence to support the association [4].
There is biological plausibility that nicorandil may induce AF/atrial flutter. During normal sinus rhythm, time-dependent delayed-rectifier potassium currents and the transient-outward potassium current contribute to action potential repolarization and help to determine action potential duration [14]. Nicorandil exerts two distinct anti-angina mechanisms, acting as both NO donor, and ATP-sensitive potassium channel opener [15]. Its action on ATP-sensitive potassium channels results in shortening of action potential duration, which causes vascular smooth cell hyperpolarization and closure of L-type voltage gated calcium channels and acts to dilate both coronary micro vessels and peripheral resistance arteries [16].
In addition to conducting a clinical study to show nicorandil was associated with an increased risk of incident AF, we also conducted molecular studies to provide a biologically plausible mechanism to explain this clinical finding. We first showed the expression of ATP-sensitive potassium channel in the left atrium, which had never been addressed before. Expression of ATP-sensitive potassium channel in the left atrium raises the possibility that activation of ATP-sensitive potassium channel may augment potassium flow and shorten the atrial action potential duration, subsequently leading to AF [17]. This concept was further enforced by Asano et al. that ATP-sensitive potassium channel might play an important role in electrical remodeling or atrial refractoriness shortening in persistent AF [18]. Interestingly, in the animal model, we found nicorandil directly shortened left atrial action potential duration, which also has been rarely addressed before. We further showed that nicorandil directly shortened the QT interval of cultured human cardiomyocytes. Shortening of action potential duration decreases the wave lengths, thus increases the wavelets of cardiac fibrillation [17].
Given the potential risk of AF/atrial flutter found in this study, the clinical benefit of nicorandil deserves re-evaluation. In a systematic review and meta-analysis with 14 randomized controlled trials enrolling 1947 patients, nicorandil significantly reduced the incidence of myocardial infarction. However, there was no significant reduction of major adverse cerebrovascular and cardiovascular events in nicorandil-treated patients [19]. Another meta-analysis revealed that nicorandil treatment in patients with ischemic heart disease did not reduce revascularization or all-cause mortality [20].
Given the risk of AF associated with nicorandil use, clinicians may need to weigh the benefit against its risk before prescribing nicorandil. Apart from nicorandil, there are other alternative medications for angina. Nitrates, beta-blockers, or calcium channel blockers may be other options. If clinical use of nicorandil is necessary, avoiding prescription to patients aged less than 65 and close monitoring for those whose use starts within 60 days may be imperative to lower the potential risk of nicorandil-associated AF/atrial flutter.
In the present study, we also found the risk of AF associated with nicorandil use was more than 2 times higher in individuals aged less than 65 than in older patients. Usually, old AF patients had more comorbidities such as hypertension or diabetes, and multiple factors, including older age, contribute to AF. Therefore, the contribution of ATP-sensitive potassium channel to AF mechanism may be less in older patients, compared to other comorbidities. On the contrary, there are less comorbidities in younger AF patients, and electrical or ionic remodeling may play a more important role in the mechanism of AF.
There were strengths and weaknesses to the approach we used to detect an increase in the risk of AF/ atrial flutter associated with nicorandil use. Research using the NHIRD of Taiwan has the advantage of its large size with sufficient statistical power for risk analysis. The disease risk score (DRS) matching in a case-control study we used is similar to the propensity score matching in a cohort study that can help minimize confounding. We quantified the potential missing confounders using the e-value approach. The study could not address several uncertainties. First, exposure information was based on nicorandil or nitrate prescriptions and not actual use. However, it is unlikely that cases and controls differed systematically in their adherence to nicorandil or nitrate. Second, although we used all available information on confounding factors and also identified nitrate users as an active comparator for potential unmeasured confounders, we cannot rule out the possibility of residual confounding. Finally, we used a rat model for our electrophysiological studies which might not be a suitable model. The properties and ionic channels of action potential and repolarization of rat are completely different from those of human because of a very high heart rate and very short action potential duration. It is also very difficult to induce AF in normal rats, even under nicorandil stimulation.
### Conclusions
We found the use of nicorandil, especially new use, is associated with increased risk of AF or atrial flutter. This population-based nested case control study is large in scale and use of nitrate as an active comparator alleviated the concerns of residual confounding. The signal we detected for a possible increased risk during the first few months of nicorandil therapy suggests its acute effect. Our clinical findings might be supported by nicorandil’s acute effect on shortening of atrial action potential duration in animal and cellular studies which might be an indirect evidence of AF promotion.
### Author Contributions
All authors substantially contributed to the conception and design of this study. CC Lee acquired the data. CC Lee and CT Tsai had full access to all the data in the study and took responsibility for the integrity of the data and the accuracy of the data analysis. CC Lee, Tehrani B, SS Liu, WT Hsu, SN Chang, WT Hsu, TY Huang, PS Huang, JJ Chen, and CY Chan were involved in the interpretation of data. CC Lee, Tehrani B, SS Liu, SN Chang, JJ Hwang, and CT Tsai drafted the manuscript and all authors revised it critically for important intellectual content. All authors gave final approval of this version to be submitted. All authors declare that no conflicts of interest exist.
### Acknowledgments
We thank the staff of the Core Labs, Department of Medical Research, National Taiwan University Hospital for their technical support.
### Conflicts of Interest
The authors declare no conflicts of interest related to this study.
### Ethical Statement and Consent
Subunits in the Human
This study using Taiwan’s National Health Insurance Research Database (NHIRD) was approved by the institutional review board of National Taiwan University Hospital, and consent was waived due to the anonymity of all patients. The human study was approved by the ethical committee and Institutional Review Board of the National Taiwan University Hospital (200911002R).
The experimental protocol of rat experiment also conformed to the Guide for the Care and Use of Laboratory Animals (NIH Publication No. 85-23, revised 1996) and was approved by the Institutional Animal Care and Use Committee of the National Taiwan University College of Medicine.
### Funding
CC Lee has received research grants from the Taiwan Ministry of Science and Technology Grants (MOST 110-2314-B-002-053-MY3, MOST-111-2321-B-002-017, and MOST 110-2622-8-002 -017) and National Taiwan University Hospital (NTUH 111-UN0043). No funding bodies had any role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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http://kea-monad.blogspot.com/2009/08/changing-light-speed.html
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occasional meanderings in physics' brave new world
Name:
Location: New Zealand
Marni D. Sheppeard
## Sunday, August 09, 2009
### Changing Light Speed
Thanks to Carl Brannen for pointing out a new paper by Sanejouand, Empirical evidences in favor of a varying speed of light. The paper summarises results from lunar laser ranging, the Pioneer anomaly, supernovae redshifts and the known fixed constants, namely fine structure and Rydberg. He finds that the varying speed of light hypothesis is (a) consistent with all these results and (b) explains the results that the Dark Force cannot.
Assuming fine structure, Rydberg and electron charge to be truly constant, one must have constants
$\epsilon \hbar c$ and $\frac{m_e c^{2}}{\hbar}$.
There are then two natural alternatives to consider under the varying $c$ hypothesis. First, if the electron mass is constant in cosmic time, we find that
$\frac{c^{2}}{\hbar}$
must be constant, forcing $\hbar$ to vary, but not as in the usual description of Louise Riofrio's cosmology. Because $\hbar c$ cannot then be constant, fine structure depends on a variation in $\epsilon$. Secondly however, if we assume that $\hbar c$ is constant, it follows that the electron mass $m_e$ must go as $\hbar^{3}$. That is, electron mass starts out at zero and grows larger with Riofrio's cosmological law $M = t$. This is also reminiscent of Penrose's thermodynamic cosmology.
Note that the latter alternative would not prevent, in principle, the computation of local mass relations; only the computation of absolute scales. Such a cosmology, at least initially, therefore relies on precisely one parameter, which is a measure of our epoch.
Rhys said...
Can I ask what you mean when you say "cosmic time"? I'm guessing it's something non-standard...
And a minor comment: let's all remember that only dimensionless quantities are physically meaningful. Discussion about these sorts of issues often seems confused due to a failure to acknowledge this point.
August 10, 2009 4:35 AM
CarlBrannen said...
Kea, want a shock? Look at equation (21) in Two knees and the Evasion of Greisen-Zatsepin-Kuz'min Cutoff in Cosmic Ray Spectrum -- Are Neutrinos the Tachyons? Guang-Jiong Ni, Zhi-Qiang Shi, hep-ph/0605058. For those who don't recognize it, compare with (11) in Sheppeard and Brannen. And by the way, how come I couldn't find our paper on Vixra?
August 10, 2009 12:29 PM
PhilG said...
It's on vixra at vixra:0907.0011
August 10, 2009 6:37 PM
Kea said...
Rhys, you cannot be serious. The speed of light is dimensionful. It is something we can measure. I fail to see how it cannot be physically meaningful.
We have all heard the pathetic arguments against variation of dimensionful parameters. It is somewhat analogous to saying that planetary orbits can only be circles. The simplest, and most natural way, of explaining things just does not keep constants constant.
August 10, 2009 8:22 PM
Rhys said...
"The speed of light is dimensionful. It is something we can measure."
I don't know of any way of measuring a dimensionful quantity which doesn't boil down to comparing it with another quantity of the same dimensions. In other words, it seems to me that we only measure dimensionless ratios. If you can demonstrate that that is wrong, I'm willing to listen.
And I'd still like to know what you mean by "cosmic time"! I'm guessing it's the 't' appearing in various equations, and if so it seems important...
August 10, 2009 9:11 PM
Kea said...
All right, Rhys, but I don't feel it is necessary to point these things out.
August 10, 2009 9:12 PM
L. Riofrio said...
The argument that "change in fundamental constants is impossible by definition" is an old and tired one.
"Earth's position in the centre of the universe is fixed by definition! Arguing that it changes is nonsense!"
August 10, 2009 11:39 PM
Rhys said...
"The argument that "change in fundamental constants is impossible by definition" is an old and tired one."
Seems strange to bring it up then...
August 11, 2009 9:43 AM
Matti Pitkanen said...
I looked at the article of Sanjouand. To me it seems ok.
Before one can speak about change of c seriously, one must specify precisely what the measurement of speed of light means. In GRT framework speed of light is by definition a constant in local Minkowski coordinates. It seems very difficult to make sense about varying speed of light since c is purely locally defined notion.
a) In TGD framework space-time as abstract manifold is replaced by 4-D surface in H=M^4xCP_2 (forgetting hierarchy of Planck constants) and this brings in something new: the sub-manifold geometry allowing to look space-time surfaces from H-perspective. CP_2 length scale as universal unit of length is one element. p-Adic length scale hypothesis actually brings in an entire hierarchy of fixed meter sticks defined by p-adic length scales. The presence of imbedding space M^4xCP_2 brings in light-like geodesics of M^4 for which c is maximal and by definition could be taken c=1.
b) In TGD framework the operational definition for the speed of light at given space-time sheet is in terms of time taken for light to propagate from point A to B at space-time surface. In TGD framework this can occur via several routes because of many-sheeted structure and each sheet gives its own value for c. Even if space-time surface is only warped (no curvature), this time is longer than along light-like geodesic of M^4(xCP_2) and the speed of light measured in this manner is reduced from its maximal value.
What TGD then predicts?
a) TGD inspired cosmology predicts that c measured in this manner *increases* in cosmological scales, just the opposite for what Riofrio claims. The reason is that strong gravitation makes space-surface strongly curved and it takes more time to travel from A to B during early cosmology.
b) The paradox however disappears that *local systems* like solar system do not not normally participate in cosmic expansion as predicted by TGD. This is known also experimentally. [The expansion would however occur in average sense via phase transitions increasing Planck constant and occurring in relatively short time scales: this provides new support for expanding Earth hypothesis needed to explain the fact that continents fit nicely together to form single super continent covering entire Earth if the radius of Earth is by a factor 1/2 smaller than its recent radius].
c) If one measures the speed of light in local system and uses its cosmic value taken constant by definition (fixing particular coordinate time) then one indeed finds that the speed of light is decreasing locally and the decrease should be expressible in terms of Hubble constant.
d) TGD based explanation of Pioneer anomaly is based on completely analogous reasoning.
August 11, 2009 3:44 PM
Kea said...
Matti, I see that you mentioned the expanding earth again here.
Off topic remark: the best evidence against a continual cosmological growth of Earth is the paleomagnetic data. The abstract starts: New estimates of the palaeoradius of the Earth for the past 400 Myr from palaeomagnetic data limit possible expansion to less than 0.8% ...
Now 400 Myr is roughly 3% of the current cosmic age, and reducing to radius could drop this to about 1%, but the data does seem to rule out a naive expansion. I realise that you are actually in favour of discrete jumps, which are not ruled out this way, but this scenario is less predictive.
I think, given the even younger age of the ocean floors, that one must accept the evidence for subduction, possibly along with an earlier phase transition or two. But this is starting to look ugly.
The alternative, with regard to continual mass growth, is to conclude that the density also increases cosmologically. Even a small increase in density could allow <0.8% radius shift over 400 Myr, in line with observation. I prefer this idea, which has the advantage of predicting precisely that growth should be measurable by future paleomagnetic data.
August 11, 2009 8:21 PM
Matti Pitkanen said...
There are also connections with biology. The fast expansion by a factor of two explains the sudden appearance of highly developed life forms as water from undergound seas bursted to the surface of Earth (similar water reservoirs seem to exist also in Mars whose radius is by the way just one half of that for Earth). Already Darwin regarded Cambrian explosion as a main argument against his theory of evolution.
Also the the oxidation of atmosphere caused by the emergence of seas interacting with solar light implying splitting of water to oxygen and hydrogen can be understood as well as the development of very large life forms due to the gradual weakening of surface gravity (and emergence of oxygen rich atmosphere).
The idea that electron mass has increased linearly with time is to my opinion unrealistic.
August 12, 2009 12:06 AM
Zephir said...
Before some time I wrote about experimental evidence of variable light speed. There are many, in fact.
August 12, 2009 2:55 AM
Kea said...
Zephir, Louise published papers on an elegant varying speed of light cosmology before blogging was even invented - something you could easily have checked yourself.
August 12, 2009 8:48 PM
CarlBrannen said...
Wow that got a little out of hand. Re the theory that the earth is expanding; the easiest explanation for the reduction in surface units is folding and subsistence. It makes it very difficult to estimate what size stuff was long ago.
August 13, 2009 1:47 AM
Kea said...
OK, I've cleaned up the mess. In all the years this blog has been running, that is the first time I have had to delete so many posts.
August 13, 2009 1:53 AM
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2017-07-22 06:49:24
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http://a2gmat.blogspot.com/2011/05/re-sc-pp08-166.html
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## 2011年5月8日 星期日
### Re: [SC. ] pp08-166
※ 引述《truthlier》之銘言：
: A. has been established by carbon dating, but what is much more difficult to
: determine are
: B. have been established by carbon dating, but what is much more difficult to
: determine are
: C. have been established by carbon dating, but that which is much more
: difficult to determine is
: D. has been established by carbon dating, but what is much more difficult to
: determine is
: E. are established by carbon dating, but that which is much more difficult to
: determine is
: 答案是D
: 對於A有疑惑，因為後面接的是the use..., the reason..., and the meaning of...
: 想請問一下A選項中的are為何錯?
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2022-09-29 21:23:42
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https://socratic.org/questions/55a532b4581e2a3bcfdef6c6
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# Question ef6c6
Jul 14, 2015
Volume: 12 L.
#### Explanation:
In order to determine the volume occupied by 1 g of hydrogen gas, ${H}_{2}$, at NTP, you must use the ideal gas law equation.
$P V = n R T \implies V = \frac{n R T}{V}$
Before using this equation to solve for $V$, you must first determine how many moles are found in 1 g of hydrogen gas. To do that, use hydrogen gas' molar mass
1cancel("g") * ("1 mole "H_2)/(2.0159cancel("g")) = "0.4961 moles"# ${H}_{2}$
Normal Temperature and Pressure (NTP) conditions imply a pressure of 1 atm and a temperature of ${20}^{\circ} \text{C}$.
Plug in your values into the ideal gas law equation to get
$V = \left(0.4961 \cancel{\text{moles") * 0.082(cancel("atm") * "L")/(cancel("mol") * cancel("K")) * (273.15 + 20)cancel("K"))/(1cancel("atm}}\right)$
$V = \text{11.9 L}$
I'll leave the answer rounded to two sig figs, despite the fact that you only gave one sig fig for the mass of hydrogen gas
$V = \textcolor{g r e e n}{\text{12 L}}$
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2019-04-24 04:29:11
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https://math.stackexchange.com/questions/1955401/let-a-be-skew-symmetric-and-denote-its-singular-values-by-sigma-1-geq-sigma
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# Let A be skew-symmetric, and denote its singular values by $\sigma_1\geq \sigma_2\geq \dots \sigma_n\geq0$.
Let A be skew-symmetric, and denote its singular values by $\sigma_1\geq \sigma_2\geq \dots \sigma_n\geq0$. Show that
a) If n is even, then $\sigma_{2k}=\sigma_{2k-1}\geq 0, k= 1,2,\dots n/2.$ If n is odd, then the same relationship holds up to $k=(n-1)/2$ and also $\sigma_n=0$.
b) The eigenvalues $\lambda_j=(-1)^ji\sigma_j$, $j=1,2,\dots,n$.
I know that skew symmetric means $-A=A^T$ and I know that the eigenvalues of a skew-symmetric matrix are either purely imaginary or zero. I am not able to get this though and I have been trying all week...
Hint: The singular values of $$A$$ are the (positive) square roots of the eigenvalues of the matrix $$A^TA = -A^2$$. So, if $$\lambda$$ is an eigenvalue of $$A$$, then $$\sqrt{-\lambda^2} = |\lambda|$$ is a singular value.
Because $$A$$ is real, its complex (i.e. non-real) eigenvalues must come in complex-conjugate pairs.
• Yes, that's true, but it does not mean that they don't come in conjugate pairs. For every non-zero eigenvalue $ai$, $-ai$ must also be an eigenvalue. – Omnomnomnom Oct 5 '16 at 20:20
• Isn't $\sqrt{-\lambda^2} = i|\lambda| \not= |\lambda|$? I feel that I am missing something obvious. – hasManyStupidQuestions Jan 26 at 4:15
• @hasManyStupidQuestions Right. Regarding your first comment, note that $\lambda$ is actually an imaginary number in this context – Omnomnomnom Jan 28 at 17:50
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2019-06-17 08:52:41
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https://testbook.com/objective-questions/mcq-on-sewage-treatment--5eea6a0839140f30f369d6f1
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# Match List - I with List-II and select the correct answer using the codes given below the lists: List - I (Treatment Unit) List - II (Detention Time) A. Grit chamber i. Six hours B. Primary sedimentation ii. Two minutes C. Activated sludge iii. Two hours D. Sludge digestion iv. Twenty days
1. A - iii, B - i, C - iv, D - ii
2. A - ii, B - iii, C - i, D - iv
3. A - ii, B - i, C - iii, D - iv
4. A - i, B - ii, C - iii, D - iv
Option 2 : A - ii, B - iii, C - i, D - iv
## Sewage Treatment MCQ Question 1 Detailed Solution
Explanation:
Detention time for different type of Treatment unit
Treatment Unit Detention time Grit chamber 30-60 second Primary sedimentation 2-2.5 hour Sludge digestion 20-30 days Activated sludge process 4-6 hour Oxidation pond 2-6 weeks Septic tank 12-36 hour
Note: Septic tank has high detention time whereas Grit chamber has less detention time.
# Which of the following statements is true for trickling filter sludge?
1. It is more difficult to dewater than activated sludge
2. It is bulky
3. It has a comparatively low concentration of sludge solids
4. It has a comparatively low sludge volume index
Option 4 : It has a comparatively low sludge volume index
## Sewage Treatment MCQ Question 2 Detailed Solution
Explanation:
Trickling Filter:
trickling filter is a type of wastewater treatment system. It consists of a fixed bed of rocks, gravel, slag, ceramic, or plastic media over which sewage or other wastewater flows downward and causes a layer of microbial slime to grow, covering the bed of media. Aerobic conditions are maintained by splashing, diffusion, and either by forced-air flowing through the bed or natural convection of air if the filter medium is porous.
Advantages Disadvantages Simple, reliable, biological process Effective in treating high concentrations of organics depending on the type of medium used. Efficient nitrification units. Appropriate for small- to medium-sized communities Have comparatively low sludge volume index Requires regular operator attention Possible accumulation of excess biomass that cannot retain an aerobic condition and can impair Trickling Filter performance Additional treatment may be needed to meet more stringent discharge standards Odor problems.
Important Points
Sludge volume index (SVI):
It is a process control parameter to determine the recycling rate of sludge. It was introduced by Mohlman in 1934.
$${\bf{SVI}}\left( {{\bf{mL}}/{\bf{g}}} \right) = \frac{{{\bf{settled\ }}{\rm{ }}{\bf{sludge\ }}{\rm{ }}{\bf{volume\ }}\left( {{\bf{mL}}/{\bf{L}}} \right)}}{{{\bf{mixed\ }}{\rm{ }}{\bf{liquor\ }}{\rm{ }}{\bf{suspended\ }}{\rm{ }}{\bf{solids\ }}\left( {{\bf{mg}}/{\bf{L}}} \right)}} \times 1000$$
# The activated sludge process is an
1. Aerobic attached growth system
2. Anaerobic attached growth system
3. Anaerobic suspended growth system
4. Aerobic suspended system
Option 4 : Aerobic suspended system
## Sewage Treatment MCQ Question 3 Detailed Solution
Explanation:
Activated sludge process:
• The essential features of the activated sludge process are an aeration stage, solids-liquid separation following aeration, and a sludge recycle system.
• Wastewater after primary treatment enters an aeration tank where the organic matter is brought into intimate contact with the sludge from the secondary clarifier.
• It requires less space, does not produce obnoxious odor, and requires less time for wastewater treatment.
• It requires skilled supervision
Followings are the classification of secondary treatment units:
Method Contact Mechanism Decomposition Trickling filter Attached growth Aerobic Rotating biological contactor Attached growth Aerobic Activated sludge process Suspended growth Aerobic Oxidation pond Suspended growth Aerobic Septic tank Suspended growth Anaerobic Imhoff tank Suspended growth Anaerobic
# Identify the waste water treatment unit which use both aerobic and anaerobic mechanism for the removal of organic matter?
1. Activated sludge process
2. Stabilization ponds
3. Trickling filter
4. Oxidation ditch
Option 2 : Stabilization ponds
## Sewage Treatment MCQ Question 4 Detailed Solution
Concept:
Stabilisation ponds:
It may be classified as aerobic, facultative, or anaerobic depending upon the mechanism of purification. The aerobic zone in the stabilization pond gives complete purification by symbiotic relationship between algae and bacteria. The bacteria use oxygen as an electron acceptor to oxidize the waste water organics to stable end products.
The algae in turn use these compounds as a material source and with sunlight as energy source, produce oxygen as an end product.
Activated sludge process:
It involves wastewater aeration in the presence of a microbial suspension, solid-liquid separation following aeration, discharge of clarified effluent, wasting of excess biomass, and return of remaining biomass to the aeration tank.
The wastewater containing organic matter is aerated in an aeration basin in which microorganisms metabolize the suspended and soluble organic matter.
Part of organic matter is synthesized into new cells and part is oxidized to CO2 and water to derive energy. It is an aerobic process.
Oxidation ditch:
It is basically an extended aeration system of a modified activated sludge process. It is designed and operated on the same principle as of the activated sludge process. It is aerobic suspended system.
Trickling filter:
It is a fixed bed biological reactor that operates under aerobic conditions. Pre-settled wastewater is continuously trickled over the filter. As the water migrates through the pores of the filter, organics are aerobically degraded by the biofilm covering the filter material.
Note:
Aerobic process Anaerobic Process Activated sludge process Trickling filter Oxidation ditch Rotating Biological Contractor(RBC) Imhoff Tank Septic tank
# In which of the following wastewater treatment units is organic matter destroyed and stabilised by anaerobic bacteria?
1. Trickling filter
2. Oxidation pond
3. Sedimentation tank
4. Septic tank
Option 4 : Septic tank
## Sewage Treatment MCQ Question 5 Detailed Solution
Concept:
A septic tank is an underground chamber made of concrete, fiberglass or plastic through which domestic wastewater (sewage) flows for basic treatment. Action within the septic tank is anaerobic in nature.
The term "septic" refers to the anaerobic bacterial environment that develops in the tank which decomposes the waste discharged into the tank.
Followings are the classification of secondary treatment units
S.No. Method Contact Mechanism Decomposition 1 Trickling filter Attached growth Aerobic 2 Rotating biological contactor Attached growth Aerobic 3 Activated sludge process Suspended growth Aerobic 4 Oxidation pond Suspended growth Aerobic 5 Septic tank Suspended growth Anaerobic 6 Imhoff tank Suspended growth Anaerobic
# What will be the Sludge Volume Index (SVI) if 100 ml of sludge collected in 30 mins on drying weighs 800 mg?
1. 115
2. 78
3. 125
4. 100
Option 3 : 125
## Sewage Treatment MCQ Question 6 Detailed Solution
Concept:
Sludge volume index is the volume occupied in mL by one gm of solids in the mixed liquor after settling for 30 minutes.
The recommended value of the Sludge Volume Index (SVI) for municipal sewage is approximately lies in the range of 80 to 150.
$${\rm{Sludge\;volume\;index}} = \frac{{{\rm{Volume\;of\;settled\;sludge\;in\;ml}}}}{{{\rm{MLSS\;present}}}}$$
Calculation:
Given,
Volume of settled sludge = 100 ml, Drying weight (MLSS) = 800 mg
$$\rm SVI = \frac{{100}}{{800 \ \times \ {{10}^{ - 3}}}}\ ml/gram$$
SVI = 125 ml/gram
# Comminutors in wastewater treatment plant are adopted to:
1. Remove colloidal matter
2. Grind or chop large sized suspended solids
3. Remove floating matter
4. Remove sand and grit
Option 2 : Grind or chop large sized suspended solids
## Sewage Treatment MCQ Question 7 Detailed Solution
Explanation:
Different units and their role in wastewater treatment:
Unit Role Screen To remove heavy suspended particle Comminutors & Macerators Grid or chop large-sized suspended solids Grit chamber To remove inorganic suspended particle Skimming tank To remove oil & grease Sedimentation tank To remove small size suspended particle
# Match the items in Group – I with those in Group – II and choose the right combination.Group - IP. Activated sludge processQ. Rising of sludgeR. Conventional nitrificationS. Biological nitrogen removalGroup - II1. Nitrifiers and denitrifiers2. Autotrophic bacteria3. Heterotrophic bacteria 4. Denitrifiers
1. P-3, Q-4, R-2, S-1
2. P-2, Q-3, R-4, S-1
3. P-3, Q-2, R-4, S-1
4. P-1, Q-4, R-2, S-3
Option 1 : P-3, Q-4, R-2, S-1
## Sewage Treatment MCQ Question 8 Detailed Solution
1. Activated sludge process
It uses Aerobic, Heterotrophic bacteria that use organic compounds as an energy and carbon source for synthesis.
1. Rising sludge
It occurs in the secondary clarifiers of activated sludge plants when the sludge settles to the bottom of the clarifier, is compacted, and then starts to rise to the surface, usually as a result of denitrification.
1. Conventional Nitrification
Nitrification is an aerobic process performed by small groups of autotrophic bacteria and archaea.
Two groups of autotrophic bacteria can be associated with the process of nitrification (Nitrosomonas and Nitrobacter).
1. Biological nitrogen removal
Biological nitrogen removal is achieved by sequential nitrification under aerobic conditions and denitrification under anaerobic conditions.
# In the activated sludge process, sludge volume index is used to decide
1. Quality of raw sewage
2. Quality of final effluent
3. Recirculation ratio of sludge
4. Rate of aeration
Option 3 : Recirculation ratio of sludge
## Sewage Treatment MCQ Question 9 Detailed Solution
Explanation:
Sludge volume index (SVI):
• SVI represents the degree of concentration of sludge in the system and hence decides the rate of recycling of sludge required to maintain desired MLSS and F/M ratio in the aeration tank to achieve the required degree of purification.
• Hence, Sludge recirculation and settleability are determined by SVI.
• It is defined as the volume occupied in ml by 1 gm of solids in the mixed liquor after settling for 30 minutes.
• Its unit is ml/gm
Recirculation ratio $$\dfrac{Q_{a}}{Q_{o}}= \dfrac{X}{\dfrac{10^{6}}{SVI}-X}$$
Where, QR = Recyled discharge, Qo = Discharge from PST, X = MLSS in tank, SVI = Sludge volume index
Recirculation ratio and its effect:
• The recirculation ratio is the amount of wastewater that flows through the advanced pretreatment component divided by the amount of wastewater that is sent to the final treatment and disposal component.
• Recirculation is used to remove or lower levels of nitrates, BOD5, TSS, and other contaminants in the wastewater.
• A recirculation tank collects the primary treated effluent from a pretreatment component and mixes it with highly treated wastewater from an advanced pretreatment component to dilute the wastewater and end up with an overall cleaner effluent.
# In a sludge digestion tank, if the moisture content of sludge is reduced from 90% to 80% then the percentage decrease in the volume of sludge is
1. 5%
2. 10%
3. 25%
4. 50%
Option 4 : 50%
## Sewage Treatment MCQ Question 10 Detailed Solution
Concept:
The volume of the digested sludge at given moisture content is given by the formula as;
$$\frac{{{V_2}}}{{{V_1}}} = \left( {\frac{{100 - {P_1}}}{{100 - {P_2}}}} \right)$$
Calculation:
Given, p1 = 90%, p2 = 80%
∵ We know that, $$\frac{{{V_2}}}{{{V_1}}} = \left( {\frac{{100 - {P_1}}}{{100 - {P_2}}}} \right)$$
⇒ $$\frac{{{V_2}}}{{{V_1}}} = \frac{{100 - 90}}{{100 - 80}} = \frac{{10}}{{20}} = 0.5$$
% decrease in volume = (1 - V2/V1) × 100 = 50%
## Sewage Treatment MCQ Question 11
1. a, b, c and d
2. a and b only
3. b and c only
4. c and d only
Option 2 : a and b only
## Sewage Treatment MCQ Question 11 Detailed Solution
Explanation:
Trickling filter is a device that is used for the treatment of sewage. It is based on an aerobic attached growth system. Following factor affecting the rate of removal of organic matter in T.F.
(i) Temperature
Following design parameters used in the trickling filter.
(i) Hydraulic loading rate (m3/m2/day) (Gives the area of the filter required)
(ii) Organic loading rate (kg/m3/day) ( Decide the volume of the filter)
(iii) Depth
# Sludge volume index is defined as the ratio of:
1. Percentage of sludge by volume to the percentage of total solids by weight
2. Percentage of sludge by volume to the percentage of suspended solids by weight
3. Percentage of suspended solids by weight to the percentage of sludge by volume
4. Percentage of total solids by weight to the percentage of sludge by volume
Option 2 : Percentage of sludge by volume to the percentage of suspended solids by weight
## Sewage Treatment MCQ Question 12 Detailed Solution
Explanation:
Sludge Volume Index (SVI):
Sludge volume index is the volume occupied in mL by one gm of solids in the mixed liquor after settling for 30 minutes.
It indicates the physical state of sludge produced in a biological aeration system.
It is used to decide the rate of recycle of sludge (Q) required to maintain the desired Mixed Liquor Suspended Solids (MLSS) and Food to Microorganism (F/M) ratio in the aeration tank to achieve the desired degree of purification. So by reducing recycling ratio SVI can be controlled.
$$SVI = \frac{{{V_{ob}}}}{{{X_{ob}}}}$$ (in ml/gm)
Where,
Vob = Settled sludge volume (in ml/lit)
Xob = Concentration of suspended solids in the mixed liquor in gm/lit.
# Septic tank is usually consists of brick wall in cement not less than
1. 20 cm
2. 100 cm
3. 80 cm
4. 200 cm
Option 1 : 20 cm
## Sewage Treatment MCQ Question 13 Detailed Solution
Septic tank:
It works on the principle of anaerobic digestion. It is a primary sedimentation tank having a longer detention period of 12 to 36 hours, in which raw sewage is directly fed into it.
Construction Detail: It usually consists of a brick wall in cement not less than 20 cm thick and the foundation floor is of cement concrete having proportion in 1 : 3 : 6 or 1 : 2 : 4. Both inside and outside faces of wall and floor are plastered with a minimum thickness of 12 mm thick cement mortar 1 : 3 and all inside corners are rounded.
The following should be remembered about the septic tank.
1. The minimum capacity of the septic tank is 8 to 10 persons or 2250 liters and the maximum capacity of the septic tank is usually 300 persons.
2. BOD removal efficient – 25-65 %.
3. Suspended solids removal efficiency – 60-70%.
4. Rate of accumulation of sludge – 30 litres/person/year.
5. Sewage flow without sullage- 40-70 lcd.
6. Sewage flow with sullage: 90-150 lcd
7. Cleaning period or removal of sludge: 6 to 12 months, mostly once in a year i.e. removal of sludge is less frequent.
# Sewage treatment units are normally designed for:
1. 5 – 10 years
2. 15 – 20 years
3. 30 – 40 years
4. 40 – 50 years
Option 2 : 15 – 20 years
## Sewage Treatment MCQ Question 14 Detailed Solution
Sewage treatment units:
Sewage treatment is the process of removing contaminants from municipal wastewater, containing mainly household sewage plus some industrial wastewater. Sewege treatment units are normally designed for 15-20 years.
Screening: Screening removes objects such as rags, paper, plastics, and metals to prevent damage and clogging of downstream equipment, piping, and appurtenances. Screening is the first unit operation in all wastewater treatment plants. Screen is the device used to retain solids found in the influent wastewater to the treatment plant. The main purpose of screening is to remove solid materials that could cause damage to other process equipment.
Grit chamber: The Grit chambers are like a sedimentation tank designed to remove inorganic particles by sedimentation process due to gravitational forces and to pass forward the lighter organic matter.
Skimming: A skimming tank is a chamber so arranged that the floating matter like oil, fat, grease etc., rise and remain on the surface of the waste water (Sewage) until removed, while the liquid flows out continuously under partitions or baffles. Therefore, this process in skimming tank is known as skimming.
Sedimentation tank: A sedimentation tank is a chamber in which settling of heavy suspended particle are done.
Secondary treatment: Secondary treatment removes dissolved and suspended biological matter. Secondary treatment is typically performed by indigenous, water-borne micro-organisms in a managed habitat. Secondary treatment may require a separation process to remove the micro-organisms from the treated water prior to discharge or tertiary treatment.
Followings are the classification of secondary treatment units:
S.No. Method Contact Mechanism Decomposition 1 Trickling filter Attached growth Aerobic 2 Rotating biological contactor Attached growth Aerobic 3 Activated sludge process Suspended growth Aerobic 4 Oxidation pond Suspended growth Aerobic 5 Septic tank Suspended growth Anaerobic 6 Imhoff tank Suspended growth Anaerobic
Sludge thickener: It is the unit in the sewage treatment plant which thickens the sludge by reducing the water content. This process helps in reducing the volume of sludge, which results into the lesser volume of digester.
# There are three distinct stages that occur in the natural process of sludge digestion due to biological action. What is the name of the first stage in which fresh sewerage – sludge is acted upon by anaerobic and facultative bacteria’s which decompose easily available food matters?
1. Acid regression
2. Acid fermentation
3. Alkaline fermentation
4. Chamber fermentation
Option 2 : Acid fermentation
## Sewage Treatment MCQ Question 15 Detailed Solution
Explanation:
The first stage in which fresh sewerage-sludge is acted upon by anaerobic and facultative bacteria’s which decompose easily available food matters is acid fermentation.
Sludge digestion process:-
• The sludge withdrawn from the sedimentation basins contains a lot of putrescible organic matter and if disposed of without any treatment, the organic matter may decompose, producing foul gases and a lot of nuisance, pollution, and health hazardous.
• In order to avoid such pollutions, the sludge is, first of all, stabilized by decomposing the organic matter under controlled anaerobic conditions and then disposed of suitably after drying on drying beds.
• The process of stabilization is called sludge digestion, and the tank where the process is carried out is called the sludge digestion tank.
Stages of sludge digestion process: The stages are:
1. Acid fermentation stage or acid production stage:
• In this stage of sludge digestion, the fresh sewage sludge begins to be acted upon by anaerobic and facultative bacteria, called acid formers.
• Intensive acid production makes the sludge highly acidic and lowers the PH value to less than 6.
• BOD of the sludge increases to some extent, during this stage.
2. Acid regression stage:
• In this intermediate stage, the volatile organic acids and nitrogenous compounds of the first stage are attacked by the bacteria, so as to form acid carbonates and ammonia compounds.
• The decomposed sludge has a very offensive odor, and its pH value rises up to 6.8.
• This stage continues for a period of about 3 months
• BOD of the sludge remains high even during this stage.
3. Alkaline fermentation stage:
• During this stage, the liquid separates out from solids, and the digested sludge is formed. This sludge is granular and stable and does not give offensive odors. The digested sludge is collected at the bottom of the digestion tank and is also called ripened sludge.
• Digested sludge is alkaline in nature and pH is slightly above 7.
• The BOD of the sludge also rapidly falls down during this stage.
• Large volumes of methane gas along with a small amount of carbon dioxide and nitrogen are evolved during this stage.
# The unit in which both sedimentation and digestion process of sludge takes place simultaneously is:
1. Skimming tank
2. Imhoff tank
3. Deritus tank
4. Digestion tank
Option 2 : Imhoff tank
## Sewage Treatment MCQ Question 16 Detailed Solution
Imhoff tank: It is a robust and effective settler that causes a suspended solids reduction of 50 to 70%, COD reduction of 25 to 50%, and leads to potentially good sludge stabilization.
It consists of two compartments:
Upper Compartment: This compartment has a circular or rectangular shape with V-shaped walls and a slot at the bottom, allowing solids to settle into the digestion compartment, while preventing foul gas from rising up and disturbing the settling process. It is exposed to atmosphere, and thus working condition is aerobic.
Lower Compartment: In this compartment, sludge accumulates and is compacted and partially stabilized through anaerobic digestion. Thus, working condition is anaerobic
# The amount of oxygen required by microorganisms to decompose the biodegradable organics is called
1. Oxygen demand
2. Oxygen deficiency
3. Biochemical oxygen demand
4. Chemical oxygen demand
Option 3 : Biochemical oxygen demand
## Sewage Treatment MCQ Question 17 Detailed Solution
The amount of oxygen required by microorganisms to decompose the biodegradable organics is called Biological Oxygen Demand or Biochemical oxygen demand (BOD).
A low BOD is an indicator of good quality water, while a high BOD indicates polluted water.
# A detritus tank is provided in the primary treatment of sewage to remove:
1. suspended solids
2. stones
3. grit
4. oil and greases
Option 3 : grit
## Sewage Treatment MCQ Question 18 Detailed Solution
Explanation:
• A detritus tank is provided in the primary treatment of sewage to remove grit and fine sand particles.
• A sedimentation tank or water filters are used to remove suspended solids.
• Skimming Tanks are used to remove the oil and greases. It also used to remove the fats from sewage.
• Screening is used to remove large size stones and gravels.
Important Points
Primary Treatment Units:
• Screening
• detritus tank
• sedimentation tank
• Skimming tank
# The two main gases that evolve from and anaerobic sludge digestion tank include
1. Ammonia and Carbon dioxide
2. Methane and hydrogen sulphide
3. Carbon dioxide & methane
4. Ammonia & methane
Option 3 : Carbon dioxide & methane
## Sewage Treatment MCQ Question 19 Detailed Solution
Concept:
Anaerobic digestion is normally adopted for primary sludge because primary sludge contains large amount of readily available organics that would induce rapid growth, of biomass if treated anaerobically.
Anaerobic decomposition process produce less biomass and primary function of anaerobic digester is to convert as much of sludge as possible to end products like liquid and gases while producing little biomass.
Waste-water contains wide varieties of organism.
These organisms are broadly classified as
a) Acid formers
b) Methane formers
Acid formers: Acid formers consists of facultative and anaerobic bacteria and include organisms which solubilize the organic acid through hydrolysis.The soluble end products are then fermented to acids and alcohol of lower molecular weight.
Methane formers: Methane formers are strictly anaerobic and converts acid and alcohol alongwith hydrogen and CO2 to methane.
# Septic tank works on the principle of ______.
1. Aerobic digestion
2. Anaerobic digestion
3. Continuous flow
4. Aeration system
Option 2 : Anaerobic digestion
## Sewage Treatment MCQ Question 20 Detailed Solution
Septic tank:
Septic tanks are used where there is no central provision to collect toilet water from the community.
These are suitable if the number of users is less than 300.
The term "septic" refers to the anaerobic bacterial environment that develops in the tank which decomposes the waste discharged into the tank.
Septic tank is a settling tank with a long detention time with provision for anaerobic digestion of settled solids.
Septic tank undertakes the following process:
i) Settling of solids
ii) Anaerobic digestion of settled solids.
Important point:
The followings are the classification of secondary treatment units
S.No. Method Contact Mechanism Decomposition 1 Trickling filter Attached growth Aerobic 2 Rotating biological contactor Attached growth Aerobic 3 Activated sludge process Suspended growth Aerobic 4 Oxidation pond Suspended growth Aerobic 5 Septic tank Suspended growth Anaerobic 6 Imhoff tank Suspended growth Anaerobic
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2021-10-28 21:29:15
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https://www.physicsforums.com/threads/finite-solutions-of-brocards-problem.803403/
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# Finite solutions of Brocard’s problem
Tags:
1. Mar 15, 2015
### secondprime
x^2=n!+1⇒ (x+1)(x-1)=n! where (x+1)/2 and (x-1)/2 are consecutive integers and have consecutive primes as factor ,let ,y and z (respectively) so it can be written y-1=z. Consider prime counting function π(z),π(2z-1) that count primes less than the variable or argument. It can be seen that f(z) is equals to the numbers of z-k when z-k is prime where 0<k<z+1.Same way , the total number of primes in between z+1 and 2z-1 is also the number of primes of the form z+k in between that interval. So, it can be written that, π(z)-w(z)= π(2z-1)- π(z)(ignoring the prime 2) where w(z) is the number of distinct prime divisor of z. so,
2π (z)- π(2z) = w(z).now form prime number theorem and an asymptotic formula for w(n), it can be written 2* ln2 * z =lnlnz *ln2z* lnz +f(z) (where f(z) is error term.)
⇒2* ln2 * z<<lnlnz *ln2z* lnz,which means after a certain z, there will be no intersection point.
It is sort of outline,I would be happy if you find any flaw and post it here,thanks.
I have a stack exchange link regarding the solution-
real analysis - Number of solutions of asymptotic funtion's equation. - Mathematics Stack Exchange
I explained the idea, but no response to that. Initially it was put on hold due to "unclear" tag. Any thoughts?
2. Mar 16, 2015
### mathman
The first sentence is fraught.
Other than n=4, are there any situations where it makes sense?
You state y and z are consecutive and prime. True only for 2 and 3.
Are there any even integers (other than 4 and 6) whose product is a factoral?
3. Mar 17, 2015
### TeethWhitener
I figured secondprime meant that y and z were consecutive and that they had consecutive prime factors...which as mathman points out would have to be 2 and 3. I'm not sure if that's ok. For $n≥3$, $n!+1$ must be odd and coprime with $n!$, so that means that $x^2$ (and therefore $x$) is not divisible by 2 or 3. So $x-1$ and $x+1$ are therefore both even and exactly one of them must be divisible by 3. So exactly one of $$S= \Big\{ \frac{x+1}{2}, \frac{x-1}{2} \Big\}$$ is divisible by 2, and exactly one of S is divisible by 3. The problem I'm having is, how do you prove that the one which is divisible by 2 isn't also the one divisible by 3? For instance, if $x-1=22$ and $x+1=24$, then $\frac{x+1}{2}$ is divisible by both 2 and 3, and $\frac{x-1}{2}$ is divisible by neither.
4. Mar 17, 2015
### TeethWhitener
Trivially, for $n≥4$, $(n-2)!$ and $n(n-1)$ are even integers which multiply to give $n!$.
5. Mar 17, 2015
### secondprime
the product of (x+1)/2 and (x-1)/2 has consecutive primes as factor, sorry for bad Eng.
But that should not stop you to check remaining part.
6. Mar 17, 2015
### TeethWhitener
The remaining part is very hard to understand.
What are the "numbers of z-k?" What does f(z) stand for?
Are you saying that the primes are symmetric about z (p = z ± k)?
I think I see what you're going for: you're looking for an upper bound for a formula to show that Brocard's problem has only finitely many solutions. (At least that's where I think this is going). But I'm having a lot of trouble understanding how exactly you're getting to that formula.
7. Mar 17, 2015
### secondprime
1. that should be π(z) not f(z), f(z) is the error term used later.
2. for any integer, z, and k 0<k<z+1, there exist prime number in the form of z-k, if you count all positive integers that is equal to prime counting function. Same way, you will find primes in the form of z+k, I claim, the total number of primes in between z+1 and 2z-1 is equal to the number of primes of the form z+k in between that interval.Please check and inform if it is not true.
.3. w(z) is the number of distinct prime divisor of z, in equation, it omits the repetition of prime.
if you reach up to the equation , then rest of the part is easy.
4. Not entirely what you are suggesting ,but in a way... it would be clear if you agree up to the equation.
*** i don't see any edit option here, where is it??
Last edited: Mar 17, 2015
8. Mar 18, 2015
### TeethWhitener
For any integer $z$, $\pi(z)$ is the number of primes less than $z$. No information is added by saying that the primes are of the form $z-k$. I have no idea how you got that Brocard's problem implies $\pi(z) - \omega(z) = \pi(2z) - \pi(z)$ (We can set $\pi(2z-1)=\pi(2z)$ because we don't count any more primes by including $2z$ in the set). Let's consider the case where $z=35$ (this is equivalent to $n=7$ in your formulation of Brocard's problem). $\pi(35)=11$ and $\pi(70)=19$, so if your equation holds, then $8=11-\omega(35)$. But $\omega(35)=2$ because there are only 2 distinct prime factors of 35 (namely 5 and 7). So your equation doesn't hold (8≠9).
9. Mar 18, 2015
### secondprime
1. all primes(consecutive) of n! are in z, (z+1) [Brocard's problem implies this]
2. Consider (z+k) and (z-k) where 0<k<z+1, if both are prime or composite at the same time then,
π(z)= π(2z-1)- π(z) is true where π(2z-1)- π(z) is the number of prime in between z and (2z-1)
if one is prime and another is not, then the equation is not true but I claim both have to be prime when k | (z+1).
let, the assumption is false
then (z+k)=cd where (z,k)=1
c,d does not divide z,k since k<z+1 and (z,k)=1
so, at least c | (z+1) implies c| k and leads to a contradiction . Same way,(z-k) is prime respect to the above condition.
3.But the primes of (z+1) are less than z, unbalance the equation (using above argument). So, w(z+1) is subtracted,
π(z)-w(z+1)= π(2z-1)- π(z)
Since I was planning to use asymptotic formula, I wrote w(z) instead of w(z+1).
4. you wrote-
"So your equation doesn't hold (8≠9)."
but in the first post there was a line like-
"So, it can be written that, π(z)-w(z)= π(2z-1)- π(z)(ignoring the prime 2)"
if you ignore prime 2 then......
10. Mar 18, 2015
### TeethWhitener
Are you saying ignore 2 completely, in every aspect of your proof? Because if we go with the example above where z=35, if we let k=2 (which divides z+1) then z+k=37 is prime but z-k=33 is composite. If we let k=3, then both z-k=32 and z+k=38 are composite. If we let k=4, then z-k and z+k are both prime. It seems you can get whatever answer you want this way.
Your mistake is somewhere in here:
But I'm not immediately sure where.
11. Mar 19, 2015
### secondprime
???
12. Mar 19, 2015
### secondprime
why don't you consider z=36, z-1=35 ,the argument I used is true for these pair so,
π(z)-w(z-1)= π(2z-1)- π(z) is true.
this is the only other possible case.
you should check yourself why z=35, z+1=36 didn't work.
"Your mistake is somewhere"... exactly where??
I could be wrong(that is why i shared the solution in this forum ), but you need to tell me why/how.
" It seems you can get whatever answer you want this way."
would you please explain what you meant?
13. Mar 19, 2015
### TeethWhitener
I already gave you a counterexample. What I fear will happen is that you will keep using the escape clause "Except for maybe the number 2" to continue to move the goalposts. As your proof is written right now, it's clearly wrong because I can provide counterexamples. If you have a proof in mind that is correct, that's fine, but you haven't expressed it clearly enough for me not to continue shooting it down with counterexamples.
I gave you a counterexample. I don't want to do you a disservice by telling you exactly why you're wrong because frankly what you've written isn't clear enough for me to determine where exactly your error is. Likewise, if it so happens that you have the kernel of a great idea, I don't want to discourage you from it; I just don't see where it is.
You asserted:
I gave you an example of z=35 where Brocard's equation holds, along with k=3 which divides z+1. I showed that z+k and z-k are both composite, directly contradicting what you asserted. I then showed that if k=2, then z+k is prime while z-k is composite, and if k=4, then z+k and z-k are both prime. Note that 2, 3, and 4 all divide z+1=36. Thus you can get any combination of prime and composite for z±k. Now you're saying that z should have been z-1 all along. I can't keep playing this game with you when you insist on moving the goalposts. Spend some time clarifying your thoughts and testing them with counterexamples, and then present a more rigorous proof.
14. Mar 19, 2015
### secondprime
"I already gave you a counterexample. What I fear will happen is that you will keep using the escape clause "Except for maybe the number 2" to continue to move the goalposts. As your proof is written right now, it's clearly wrong because I can provide counterexamples."
-35 was not a counterexample because it fits to equation, it has to be z-1 not z.
"What I fear will happen is that you will keep using the escape clause "Except for maybe the number 2" to continue to move the goalposts."
-i don't know why you are whining about prime 2, it was in the first post!!! you did not notice, so I informed you that is not "keep using the escape clause"
"I gave you an example of z=35 where Brocard's equation holds, along with k=3 which divides z+1. I showed that z+k and z-k are both composite, directly contradicting what you asserted."
!!! in this case the equation holds!!, problem is when you have one of z+k , z-k is prime and other is not.
" Now you're saying that z should have been z-1 all along."
I knew after your second post but I could not find the edit option, to avoid confusion, i kept things same with respect to first post. The main idea is similar in both (z,z+1) and (z,z-1). ... anyway , I mistyped so... myself to blame.
"I can't keep playing this game with you when you insist on moving the goalposts."
I changed only once, ignoring 2 was in the first post.
lets fix the goal post then , π(z)-w(z-1)= π(2z-1)- π(z) for z, z-1.
if this is not true than there is only one other case and that is for z, z+1. For both the cases π(z)-w(z) is same since asymptotic formula would be used.
Last edited: Mar 19, 2015
15. Mar 19, 2015
### TeethWhitener
Why do you ignore 2 for w(z-1) but not for π(z)? Your equation only holds if you ignore one but not the other.
"-i don't know why you are whining about prime 2,"
This was unnecessary. I'm not getting paid to help you. Your ideas are now significantly clearer and more presentable than the mess in your first post. My point was, from your equation, it's unclear when I'm supposed to include 2 and when I'm not. Apparently this equation only works when I ignore 2 in w(z-1) but when I take it into account for π(z). As it stands, I can't help you any longer. Find someone who will suffer your ingratitude.
Last edited: Mar 19, 2015
16. Mar 19, 2015
### secondprime
Are you pouting???
you can not be serious!!!! You seem to be offended, but that was not my intention!!! I am new to this forum , so might be a little ignorant about the "forum etiquette "
Please, accept my heartiest apology if I have had offended you at any measure.
And yes I messed up in the first post. It has created a lot of confusion due to my English skill and mistyping. But,
You were not a help, you have not pointed out anything new, the whole time you spent on understanding what I wrote. I helped you(though it is my responsibility to help/explain, especially after 1st post), don't have the wrong idea. This a public forum, it is designed to share, to help each other and nobody is getting paid!!!
If you have decided not to participate anymore, I am not going to stop you. Thanks for your time.
One last thing, you said-
"Apparently this equation only works when I ignore 2 in w(z-1) but when I take it into account for π(z).'
wrong, never ignore 2 in w(x), ignore 2 in prime counting function.
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2018-07-20 01:29:04
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http://darkblueundercover.com/victoria/how-to-find-the-radius-of-a-cone-from-volume.php
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## How To Find The Radius Of A Cone From Volume
#### How do you find radius of cone when given volume and height?
The volume V of a cone, with a height H and a base radius R, is given by the formula V = πR 2 H ⁄ 3. For example, if we had a cone that has a height of 4 inches and a radius of 2 inches, its volume would be V = π (2) 2 (4) ⁄ 3 = 16π ⁄ 3 , which is about 16.76 cubic inches.
#### How do you find radius of cone when given volume and height?
Algorithm. Define the height of the cone. Define the radius of the cone. Calculate the volume of the cone pie x r 2 x h/3; Define volume_cone and assign the volume of the cone to it.
#### How do you find radius of cone when given volume and height?
How can I find the volume of a cone in terms of theta? Ask Question 4. 3. I have been given these instructions: Cut out sector from a circle having central angle $\theta$ and radius r; Form a cone from what's left of the circle (I thought of it as taking a circular piece of paper, cutting a pizza shape out of it, then push the rest of the paper together to make a cone) Then find volume of the
#### How do you find radius of cone when given volume and height?
The answer would be the square of the radius; therefore, the square root of A/pi is the radius of the cylinder. Volume is defined as V=pi*R*R*H, or V=A*H. Dividing the volume by the area V/A would result in the height of the cylinder. 10.2k Views · View 1 Upvoter. Charles Pergiel, Artist, Engineer, Witch Doctor at Pergelator.blogspot.com. Answered May 14, 2018 · Author has 802 answers and 84
How to find the radius of a cone from volume
#### How do you find radius of cone when given volume and height?
The answer would be the square of the radius; therefore, the square root of A/pi is the radius of the cylinder. Volume is defined as V=pi*R*R*H, or V=A*H. Dividing the volume by the area V/A would result in the height of the cylinder. 10.2k Views · View 1 Upvoter. Charles Pergiel, Artist, Engineer, Witch Doctor at Pergelator.blogspot.com. Answered May 14, 2018 · Author has 802 answers and 84
#### How do you find radius of cone when given volume and height?
Algorithm. Define the height of the cone. Define the radius of the cone. Calculate the volume of the cone pie x r 2 x h/3; Define volume_cone and assign the volume of the cone to it.
#### How do you find radius of cone when given volume and height?
16/04/2009 · Volume of cone = 1/3 pi r^2 h where r=radius and h=height Vol of cylinder = pi r^2 h = pi(6)^2(15) = 540pi if the area of the bases is the same they have similar radius …
#### How do you find radius of cone when given volume and height?
The volume of a cone is 1/3 pi times the radius squared times the height. When given the volume and height divide both sides by the height. Volume divided by height is equal to 1/3 times pi times the radius …
#### How do you find radius of cone when given volume and height?
How can I find the volume of a cone in terms of theta? Ask Question 4. 3. I have been given these instructions: Cut out sector from a circle having central angle $\theta$ and radius r; Form a cone from what's left of the circle (I thought of it as taking a circular piece of paper, cutting a pizza shape out of it, then push the rest of the paper together to make a cone) Then find volume of the
#### How do you find radius of cone when given volume and height?
How can I find the volume of a cone in terms of theta? Ask Question 4. 3. I have been given these instructions: Cut out sector from a circle having central angle $\theta$ and radius r; Form a cone from what's left of the circle (I thought of it as taking a circular piece of paper, cutting a pizza shape out of it, then push the rest of the paper together to make a cone) Then find volume of the
#### How do you find radius of cone when given volume and height?
The volume of a cone is 1/3 pi times the radius squared times the height. When given the volume and height divide both sides by the height. Volume divided by height is equal to 1/3 times pi times the radius …
#### How do you find radius of cone when given volume and height?
16/04/2009 · Volume of cone = 1/3 pi r^2 h where r=radius and h=height Vol of cylinder = pi r^2 h = pi(6)^2(15) = 540pi if the area of the bases is the same they have similar radius …
#### How do you find radius of cone when given volume and height?
Algorithm. Define the height of the cone. Define the radius of the cone. Calculate the volume of the cone pie x r 2 x h/3; Define volume_cone and assign the volume of the cone to it.
### How to find the radius of a cone from volume - How do you find radius of cone when given volume and height?
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2019-05-23 22:09:28
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https://www.ias.ac.in/describe/article/pmsc/128/01/0002
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• On 3-way combinatorial identities
• Fulltext
https://www.ias.ac.in/article/fulltext/pmsc/128/01/0002
• Keywords
Basic series; $n$-color partitions; lattice paths; associated lattice paths; combinatorial identities
• Abstract
In this paper, we provide combinatorial meanings to two generalized basic series with the aid of associated lattice paths. These results produce two new classes of infinite 3-way combinatorial identities. Five particular cases are also discussed. These particular cases provide new combinatorial versions of Göllnitz–Gordon identities and Göllnitz identity. Seven $q$-identities of Slater and five $q$-identities of Rogers are further explored using the same combinatorial object. These results are an extension of the work of Goyal and Agarwal (Utilitas Math. 95 (2014) 141–148), Agarwal and Rana (Utilitas Math. 79 (2009) 145–155), and Agarwal (J. Number Theory 28 (1988) 299–305).
• Author Affiliations
1. Center for Advanced Study in Mathematics, Panjab University, Chandigarh 160 014, India
2. Department of Basic and Applied Sciences, University College of Engineering, Punjabi University, Patiala 147 002, India
• Proceedings – Mathematical Sciences
Volume 131, 2021
All articles
Continuous Article Publishing mode
• Editorial Note on Continuous Article Publication
Posted on July 25, 2019
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2021-09-20 07:12:30
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http://mathhelpforum.com/calculus/22570-limit-point-proof.html
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# Math Help - Limit point proof
1. ## Limit point proof
I am having a hard time with a proof:
Prove that the set of limit points of a set is closed.
At first it seemed easy and from a logical standpoint it makes sense but I am not sure where to start.
2. Originally Posted by jlindbo
I am having a hard time with a proof:
Prove that the set of limit points of a set is closed.
At first it seemed easy and from a logical standpoint it makes sense but I am not sure where to start.
what definition are you using for a "limit point"? a "closed set"?
strategies you may want to explore:
- show that the compliment of the set of limit points is open (this is perhaps the easiest way)
- show that if S is the set of limit points, it will contain all the limits of its convergent sequences (consisting of points in S)
- recall also that x is a limit point of a set S if it lies in the closure of S - {x}. And show that this set is closed. (this amounts to showing that the closure of a set is closed, i think)
- you can also show that for any point in S (the set of limit points of a set) that has the property that any open ball centered at that point intersects S and S compliment (that is, it is a boundary point of S) will be contained in S. (we know that such points exists based on one of the definitions for a limit point)*. thus we would show that S contains all its boundary points and is hence closed
*) Definition: Let S be a subset of a topological space X. We say that a point x in X is a limit point of S if every open set containing x also contains a point of S other than x itself.
3. I think that "limit point" here means the let of all accumulation points.
Here
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2015-01-30 09:03:59
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https://azpdf.net/document/qvl8d9gg-diffusions-and-the-nuemann-problem-in-the-halfspace.html
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# Diffusions and the nuemann problem in the halfspace
## Full text
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Sankhya: The Indian Journal of Statistics 1992, Volume 54, Series A , P t. 3, pp. 351-378.
DIFFUSIONS AND THE NEUMANN PROBLEM IN THE H ALF SPACE
By S. RAMASUBRAMANIAN Indian Statistical Institute
S U M M A R Y . The inhomogeneous Neumann problem for certain classes o f second order elliptic operators in the half space is investigated using the associated diffusions with normal reflection.
1. I n t r o d u c t i o n
Consider the Neumann problem Lu(x) - —/( * ) , x e O
du - <U >
f o ( x ) = —< p (x ),x ed G
where G C R d is open, L is a second order elliptic operator and n is the direction o f the inward normal. I f G is a bounded domain, this problem has been investigated using probabilistic methods b y several authors. See Ikeda (1961), Watanabe (1964), Brosamler (1976) where L is the generator of a diffusion ; see Hsu (1985), Chung and Hsu (1986) for the homogeneous Neumann problem for the Schrodinger operator ; Freidlin (1985) gives the stochastic representation for the solutions.
In the case o f the bounded domain and when L is the generator o f a nonde
generate reflecting diffusion in G, the concerned diffusion is ergodic ; and the transition probability converges to the invariant probability measure [i exponentially fast. Consequently
u(x) = lim E [ i f ( X {s))ds+ } <p(X(a)) # (* ) ] ... (1.2)
i—>00 *1 0 0 -
is well defined, provided / , cp satisfy the compatibility condition
i f ( x ) d fi(x )+ ~ J a{x)cp{x)d/J,(x) = 0 ... (1.3)
a 2 dG
where £ denotes the local time at the boundary, and a is a suitable function given in terms o f the direction cosines o f the normal and the diffusion coeffi
cients. In such a case u is a solution (in a suitable sense) to (1.1) ; also u is the
Paper received. March 1990; revised October 1990.
A M S (1980) subject classification. Primary 60J60 ; secondary 60H30, 35J25.
K ey words and phrases. Diffusions w ith normal reflection, local tim e, generator, martingale stoohastic solution, invariant measure.
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352 S. b a h a s t j b r a m a n i aN
unique solution such that J u{sc) d/i(x) = 0 ; (the latter fact does n ot seem to be explicitly mentioned in the literature). The compatibility condition (1.3) is also a necessary condition.
The aim o f this paper is tc investigate using probabilistic m ethods, the inhomogeneous Neumann problem when G = {x e R d : xx > 0} is the half space and L is the generator o f a diffusion process. To our knowledge such an investigation has not been carried out for any unbounded domain. (The homogeneous problem for the Schrodinger-type operator L -j-g in the h a lf space has been considered b j the present author (1 9 9 2 ) ; but the results do n ot apply here as the concerned gauge is infinite). In the cases considered here the
(-k> -diffusion {X (t) : t 0} can be written as X (i))) where is a reflecting diffusion in [0, oo) with generator Lx and {X (t)} is (d—1) — dimensional diffusion with generator L 2, where the coefficients o f L x depend
only on x x and those o f Lz depend on (as2, ... , xg).
The main difficulty in extending the results to unbounded domains is the lack o f information about the rate of convergence o f the transition probabilities to the invariant measure.
In Section 2, preliminary results concerning the diffusions in G are obtained. In Section 3, we consider stochastic solutions for the Neumann problem when Lx = Laplacian, L2 has periodic coefficients and f , f are periodic in (x2, ...,xa). So our analysis is essentially over [0, oo )X Ta_1 ; and the invariant measure is Lebesgue measure on [0, oo) x a probability measure on With the compatibility condition (B 3) which is similar to (1.3), (and two technical conditions) we are able to show that u given by (1.2) is a solution, and is unique in an appropriate class : also the condition (B3) is a necessary condition.
In Section 4, we consider the case when Lx is self adjoint, L2 has periodic coefficients and / , <p are periodic in (xz, xa). Once again the problem is reduced to [0, co) x T^ '1 with the same invariant measure as in Section 3.
But the compatibility condition (C3) is stronger, and perhaps it is not a nece
ssary condition ; (see the remarks at the end of Section 4). However, for the homogeneous problem, (C3) is the same as (B 3) and we get a complete picture.
In Section 5 we consider the case when L is the Laplacian ; here the invariant measure is the Lebesgue measure. The data / , f are bounded functions having finite second moments and satisfying the compatibility condi
tion (D 3), which again is similar to (1.3). In addition to analogous results
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as in the preceding sections, we also give, using the spectral, representation, a criterion to realise the solution as a continuous function vanishing at infinity.
In the last section L is assumed to be the generator o f the Ornstein—
Uhlenbeck process, which has a Gaussian invariant measure. Our analysis hinges upon Propositions 2.4 and 2.5 which concern respectively the rate o f
oit tJO u)
convergence o f q(t, x , y) to »(y), and that of- * . ’ to unity, where q is the transition probability density o f O— TJ process and v is the invariant density.
It may be noted that the existence o f a stochastic solution depends on well definedness o f u(as given by (1.2)), which in turn depends on the com
patibility condition ; and uniqueness depends on lim E x (u(X(t)) = 0. The
t — ► 30
latter condition is a natural one from the probabilistic point o f view. This is one main reason for investigating the problem using probabilistic methods, though our arguments can be rephrased analytically. (Another reason is that probabilistic method gives an elegant continuous solution for measurable data). It would be interesting i f conditions without involving the time para
meter t can be put to ensure lim Ex (u(X{t))) = 0 ; (see e.g. Theorems 4.2,
■ < —►»
5.4, 6.1).
Using the estimates given in the following sections, it is easy to establish the continuous dependence o f the solution on the given data. Also our results readily extend to those diffusions which are diffeomorphic to any o f the cases considered here ; (such diffusions can be easily characterised using Lemma 3.5 o f Ramasubramanian (1988)).
Before ending this section we show by an example that, in spite of our (seemingly strong) conditions, the problem can not be reduced to a bounded set or to a lower dimension.
Example. Let d = 2, 0 = {(xls x2) : > 0), L = — ( ^ ), / ( . ) s 0 , (p(0, x2) = cos3 2nx2. Clearly cp is a periodic function on dO such
that J <p{x^)dx2 — 0. Suppose there exists a solution u(xv x2) to (1.1) o f the form
u{xt, xz) = ii^Xi) v4x2) ... (1.4) N ote that (1.4) and the boundary condition imply that u2(x2) = — y(x2)
iti(0) and hence «i(0 ) ^ 0. It now follows from the differential equation that
A 3 -8
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354 S. EAMAStTBRAMANIAN
%(#i)<p"(a;2) = — Si nce « i (0) ^ 0, there is an xx such that % (» i) # O Therefore -y~- [9"(ic2)] = constant, which is not possible. Thus there can n o t
91*2)
be a solution o f the form (1.4) to the problem (1.1).
2. D iffu sio n s
In this section we put together certain results concerning reflected d iffu sions in the half space 0 , which will be o f use in the subsequent sections.
(i) Self-adjoint X Periodic case. Let G = { x e R d : xx > 0} where d ^ 2 . We have the diffusion coefficients a, b satisfying the following conditions.
(A l) : For each x e G, a (x) = ((ay(*)))is;i, ^ a is a (dX. d) real sym m etric positive definite matrix and b(x) = (bx (x), ..., &<*(*)) is a ^-vector. The fu n c
tions at) (.),& < ('. ) eC\{G) for 1 < i, j < d. There exist constants Ax, Aa such that 0 < Ax ^ A2 < 00 and for any x e G , any eigenvalue of a(ap) e [Aj, AJ.
(A2) : an , bx are independent o f x2, ..., a?<* ; = a>j\ = 0, j — 2, ..., d ; 1 (I
Ofj, 6| are independent of xt for 2 < i, j ^ d. Also bt (xt) = — -^ -« n (^ x )i and
\ (0) = 0.
(A3) : For i, j — 2, d the functions fty ( . ). ( • ) are periodic in x2, xd with period 1 in each variable.
Note that the functions an , bt can be extended to the whole o f R b y
®ll(*l) ~ ®ll( *l)> ^1 (^l) ~ —^l( ^l)) ^ 't'l 0. ••• (^-1) These extensions are again denoted by au , bL respectively. F or any X = {x1; x2, ..., xa) we shall denote * = (x2, x&) and we shall often id en tify dG with R a -1.
Define the elliptic operators L v L2, L respectively on C2 (R), C2 (JBtf_1),
<7a (R*) by
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Let Clx = C([0, oo) : R), Q2 = C([0, oo) : R *-1), Q = C{[0, oo) : R a) and
£2 = C([0, oo) : T^-1) be endowed with the topology o f uniform conver
gence on compacta and the natural Borel structure. (Here T d_1 denotes th e (d—1 )-dimensional torus). Let X (t) (sometimes written X t) denote the t-th coordinate map on Cl ; let X(t) = (X 2(t), ..., Xd{t)) and X(t) = (X 2(t) m o d 1, ..., X x(t) mod 1).
Let {P x : x e 0 } be the (^ L, j diffusion in 0 ; j p * : X e it*4-1 j be the
■diffusion in R a~x ; jp *?: xx > 0 j be the {l v j -difusion in [0, oo). These a re the families o f probability measures respectively on Q, Q2, £2i solving t.he appropriate martingale problems. (It may be mentioned that {Px} and T O are diffusions with normal reflection atthe boundary) Because of our assumptions (A l), (A2) note that L x and L2 are generators o f diffusions ; also L x is self-adjoint.
Under the assumption (A l), there exists a continuous, nondecreasing, nonanticipating process £{t) on such that
(a) m = J I ?Q (X(S)) d£(s) ; o
(b) for every ijr e C\ (Ra),
t t
ir(X (t))-iJ r(x )- J Ltfr(X{s))ds— J J*jL (X(s)) d\$(s)
0 0 OXi
(2.5)
is a continuous Px -martingale with respect to {St}. J
-where <6t = v{X(s) : 0 < s < t}. This process, called the local time at the
"boundary, is uniquely determined, (see Stroock and Varadhan (1971)).
Proposition 2.1. Let (A l), (A2) hold. Then for any x — (xlt x2, ..., sra) in G, P x = P (" x P T ... (2.6) 1where x = (x2, ..., xa). The processes {£(s)} and {X(<)} are independent. Also f o r t > 0, x , y e G,
p(t, x, y) = Pl(t, xv y2) p 2(t, x , y ) ... (2.7) w here p, p v p 2 are respectively the transition probability density functions o f
^ X , — -^-diffusion, j -diffusion and L 2-diffusion processes ; in parti
cular, the three diffusions are strong Feller.
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356 S. R AMASTJBBAMANIAN
Proof. The first two assertions are immediately seen by writing down the stochastio differential equations for the [l, j-diffusion ; (see Ikeda and Watanabe (1981)). To prove (2.7), extend the coefficients to R a using (2.1). Consider the diffusion in R d with generator L ; let T(<, x , y) be the transition probability density function o f the ^-diffusion R d. Note that p is obtained from T by the method o f images. In view o f our assumptions, (2.7) is now immediate. □
Remark 2.2. Using Green’s formula it can be shown that, for any bounded measurable function g on 3Cr(~ R d~x), a? e O, t > 0,
[ I g(X(#)) rf|(s)] = ~ J | an (y)g(y)p{s, X, y) dv(y) ds
= 4- J f an (0)g(y)pi(.s, xx0)p2(s, x , y ) dy ds ... (2.8)
^ Ofll- 1
where E x denotes expectation with respect to P x and dcr(.) denotes the (d— 1) -dimensional Lebesgue measure on dO ; note that the second equality in the above follows by the preceding lemma. (In what follows, the notation d<r(y) or. dy will be used according tc convenience).
Proposition 2.3. Define Y : 0 2 —> Q by (T w) (() = (w2(t) mod 1, ..., wg,(f) mod 1) ; put X(t) = (X 2(t) mod 1, ..., X\$(t) mod 1). For \$ e T d~x let P*
P'jp'F-1. Assume that (A \)~ (A Z) hold. Then ({X(<)} is a T d~x valued continuous, strong Feller, strong Markov process under {P ^.}; also
P \$ , V) = 2 p 2( t , x , y + k ) ... (2.9) fceZ*-*
is the transition probability density function of [X(t)}. Moreover, there exists a unique twice differentiable periodic function p on It**-1 such that
f P ( y ) f y = 1, ... (2.10) ijtd—l
LiP(y) ~ 0 , y e R * - i , ... (2.11) A sup f |Pa {t, x , y )-p (y )\ d y < cxe~ ^ ... (2.12) AC e rpQr-\
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where c1; ca are, positive constants independent o f t, L\ is the formal adjoint of L2 ; in other words, under P ( . ) = J Pz.( . ) p (x )d x the process w
y<*-i ergodic.
Proof. The first assertion; is elementary to prove. Since X (t) is a Feller continuous diffusion on the torus T d_1, b y results in Bensoussan, Lions, Papanicolaou (1978, Chapter 3, Section 3) it follows that there is a unique invariant probability measure p(y)dy on T^-1 satisfying (2.10)—(2.12) ; (see also Bhattacharya (1985)). The regularity o f p follows b y the regularity theorems for solutions o f second order elliptic equations, p
(ii) Ornstein—Uhlenbeck process. W e now consider a version o f the Ornstein-Uhlenbeck process in G with normal reflection at the boundary.
In this case the diffusion coefficients are given b y oy(ac) = bt(x) = —xt, 1 ^ i> j ^ d. The generator is
L f { x ) = } s - i x t d- p ^ - (213)
2 <=1 dxj f=1 dxi
In this case the transition probability density function is given by
q(t, (xi, x), {ylt y )) = q^t, xv y j q2(t, x , y ) ... (2.14) where
- [^ jj~ t) ]* [e * p ( - } + « p { - } ]
... (2.15) d-1
= 2 “ p { - ( r ^ 3 i 5 ,| - (216)
N ote that q1 is the transition probability density o f the O.U. process in [0, oo) with reflection at 0, and q2 is the transition probability density o f the (d 1) -dim ensional O.U. process. Let {P x : X e G)} denote the corresponding family o f probability measures on £2. By writing down the stochastic differential equations for the O.U. process it can be seen that there is a uniquely deter
m in ed continuous, nondecreasing, nonanticipating process {§(0) on ^ satis
fy in g (2.5). Note that all the assertions o f Proposition 2.1 and analogue of (2.8) h old also for the O.U. process {P x : x e G}.
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It is easy to check that there is a unique invariant probability measure v(y)dy on G for the O.tT. process with normal reflection ; in fact
v(y) =* *1(1/1) vdy) ••• (2-17)
where o «
*i(2/i) = lim ?i(*> *i> *—>oo Vi) = T7= «” V 77 1 (2-18>
>s a. / i (d—D/s / \
va(t/) = lim g3(J, * , y) = ( — j exp ( — 2 ) ... (2.19)
<—>oo \7T / \ i -2 /
for > 0, y e R d_1.
Proposition 2.4. Let <0 > 0. Then
| g(«, *, «/) — v(y) | < K 1 e -n + K z | x | e~* ... (2.20) for all t > £0, x , y e G, where the positive constants K lt K 2 are independent of
t ^ t0, x , y.
Proof. It is sufficient to prove.
l ' /2 — < * i e * t+ K t \/}\e-< ... (2.21) for t > t0, a, /? e R, where K v K 2 are positive constants independent o f £ > t0.
a, fi.
Put e = e-t and set h (e) = exp [ — ^ ■ ] where a, fi e R are arbitrary but fixed. It is easily verified that
!*'<«>! < (T ! i i ? S - + ( T ^ "• (2-22) for all 0 < e < 1, a, ft e R where the constants Gv C2 are independent o f e, a, ft. From (2.22) it is simple to obtain the inequality (2.21). This com
pletes the proof. □
Proposition 2.5. Let t0 > 0 and H (^ G be a compact set. Then
q(t, x, y) < [l+ e -< (& o + ^ il» l+ ---+ ^ | y | ‘i)]v(y) ... (2.23) for all t > t0, x e H, y e G, where the positive constants k0, k} , ..., ka depend only
on t0, H.
Proof. It is sufficient to prove that for t0 > 0, ft0 > 0, ( 1 \ exp (g ~ e /?) l-
l 1—e-2< / P (1—e~2e) j
( 1 V1/2 c m f (^~e~« >g)a 1
\ (1—e~2t) / P I (1- e - 2*) J < C 7 (l+ | a j)e-*e-«2 ... (2.24)
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for all t ^ t0, | fi | ^ y?0, a e R , where the positive constant C depends only on ^o> fio'
Put e = e~*. It is simple to check that
U . S . o f ( 2 . 2 4 , < 1 I ^ p [ l - e * p [ e2 e
(1—e2)1/2 i e~~g r /J2e2 , | j. _ ( a2e2_ 2a/?e) il
(1 —e2)1/2 exp [ ( l - e 2) J I 1 ex p [ (1—e2) JI - ( ’ } Since the first two terms on the r.h.s. o f (2.25) satisfy the required bound, it is enough t o prove that the third term also satisfies the required bound.
Set g(a ) — e x p [ ---— e 2af e^ ]. I t is not difficult to verify that
L (1—e ) J
for 0 < e < 1, y8 e R ,
sup {g(a) : a e R } — exp£ | ... (2.26) sup { | c l g ( a ) | : a e R }
- i [ ^ T O S * ] exp [ ] ... (2.27)
Using (2.26), (2.27) and the mean value theorem, it is now easy to verify that the third term on the r.h.s. o f (2.25) also is dominated by the r.h.s. o f (2.24) for all t > t0> \ft\ < /?„, a e R . This completes the proof.
3. N e u m a n n p r o b l e m : % = l a p l a c i a n , l 2 h a s p e r i o d i c c o e f f i c i e n t s
We n o w consider the inhomogeneous Neumann problem for L in the half space G. That is, for a measurable function / or G and a measur
able fu n ction ? on dO, to find an appropriate function u such that L u{x) = —/( * ) , x e G "j
! ~ ( x ) = - <p(x),xedG J - (31) As in H su (1985), Ramasubramanian (1992), a measurable function u on G is called a stochastic solution to (3.1), i f for each x e G
| Z (t) : = u (X (t))-u (X (0 )+ Sf(X(s))ds+ j <?(X(s))dUs) ... (3.2)
0 0
is a continuous P^-martingale with respect to S t, where {P x} is the I JL- ] -diffu sion
dxx
### J
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360 S. RAMASTJBEAMANIAN
Remark 3.1. It can, be shown using (2.5) that any classical solution (with appropriate growth condition) is also a stochastic solution to (3.1)
Conversely, i f f and <p are continuous and u e C2(G) Pj C1 (G) is a stochastic solution, then it can be shown that u is a classical solution to (3.1).
In this section we assume that the conditions (A l)-(A 3 ) hold and that . ) = 1 and 6X( . ) = 0 ; that is, jp*-?* j is the reflected Brownian motion in [0, 00), L2 has periodic coefficients, and |P^| and | P ^ J are independent diffusions. N ote that, in this case
d i
### ^ n ••• < «
Lemma 3.2. For 0 < tx < t2 < 00, a e R , I r U ' H ( - i ) - i j *
a“ -X
- V 2 |a| J r -u * e -* d r (3.4)
*2/2<2
aa z
Proof. Put z = —, use the fact that e~z— 1 = J e~r dr ; the required 0
result is obtained by a routine computation. □
In this section we shall make the following assumptions on the prescribed data / , <p.
(B l) : / , cp are bounded on compact sets ; <p(x2, ..., ®a) is a periodic function with period 1 in each variable; f(x lt x%, ..., xg) is periodic in #2, ..., U
with period 1.
(B2 )\ H r = sup J \oc1\* \f(xv tt)\dxx < 00, r = 0, 1, 2.
t0,06*
(B3) : J J f(x lt x ) p(x)dx dx1 + ~ J cp(*) p (x) d x = 0,
[0 ») ytf-l ^ ^ -1
where p is the invariant probability measure for the La-diffusion on T^-1- For 0 < tx < t2 < 00, x = (xv x ) e G, put
5(*t, h : * ) = Ex [ f f(X (s ))d s + f ?(X(s))d5(s)] (3.5)
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iftieie %-is the local time at the boundary as in (2.5). Because o f the periodi
city assumption we may take x e T d~l. Now in view of (2.8), Proposition 2.3 (ia particular (2.9)), and condition (B3) we get
% h ; * i» * ) = J J J f(zv z ) p x( s , x l , z 1)pi { s , x >si)dzdz1 i s ti [0,®) yrf-l
1 A.
+ J J 9 <?(z)Pi(s, xv 0)pz(s,x,g}dsd8
*2
= J 11 J J- /(*l. *)Pi («, *1> 8i) [!>*(*, *, #)-/>(*)] <^1 ia
+ / ii/ x I *1 to, «) yd-l ^ f p i i *’ Xv V 3 rfs
+ ! J T <p(*) Pi (», * 1 , 0 ) * , * *
»1 yd-1 J
+ 1 t L t ^ i ) p { i )! Pt {s’ Xv 0)~ v t i 1i z d *
- Jx (tx, t t ; -Vv x ) + J t(tl, h ; x ^ + h ih , h ; «e)+U tv h > *d ... (3.6) where p t is given b y (3.3) and pi is the transition probability density function of the £r2-diffusion on the torus T *-1.
Lemma 3.3. Let (A l)-(A 3) hold with au ( • )==!> M •) m ^ J ' ^ satisfy conditions (B l)-(B 3). Then for any 0 < h < tg < co> (*i» * ) e ®’
| Jx (tx, *, ; xx, x ) \ < H 0 cx f s '" * f e*d* - (3J) ti
i r n t ^ 1 I, „ _ 3 _ r%-w*e'***ds - (SJ) I 3 (*i> h ; *i» * ) I ^ "g"
where the constants cx, c2are as in (2.12) and the constant So w
;particular I x is bounded.
Proof. Immediate from condition (B2) and Propositio
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362 S. RAMASUBRAMANIAN
Lemma 3.4.. Let the hypotheses be as in the preceding lemma,. Then, for _Xx e [0, oo), t > 0,
I J»(0, < ; « ,) | < 2 H .+ 2 H , | ^ | (H%+ H 0 i 1») (3.9)
Ih ( 0, V ; x , )I ^ IMIoo ( k I + (3-10)
where the constants £f0, H v H z are as in (B2). Moreover for a > 0, e > 0 one can choose T such that
sup |I z{t, co ; # ])| < e ••• (3.11)
< 35 T
\It{t, oo ; a?i)l < e ••• (3-12)
(3.13) o r
for ail | xt | < a.
f 7 (* i.* ).'* i > ° Proof. P u t F(zv «) = 4
L _/(-Z x , «)»^i < 0 By Lemma 3.2, for 0 < tL < tz < oo, > 0, we get
Iz(h> h > x i) — J J R T*-y ^/^T—~V 27T : * ^ x’ *2’ Xl> Zl^ ^Zl where
<«. *•) = V ? { “ P ( —
—-y/2 |2i —a^| | r~m e-* dr ... (3.14) f(zi—xj) (Zi-a:f)l
L 212 ’ 2tx J Letting ^ > 0 and taking t2 = t in the above, we get
| / , ( » , < i *0K I Tl 1 from which (3.9) easily follows.
A similar argument gives
1 " I
I* (^i>
> ^-i) = ^
### 2
jt ^2’ 9 (z)p(z)dz ... (3.15)
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NEUMANN PROBLEM IN' THE HALF 8PAOB 363 where J is given, by (3.14). The inequality (3.10) is now immediate from (3.15).
Now let a > 0, e > 0 be fixed. Choose r0 > 0 such that
J ^ . i { ( ' § ' ) l (a* + l*1 l * ) + ( <* + l ^ l ) } l J ^ » * ) l ^ ( * ) l <* * * i < y e ••• (3-16)
Such a choice is possible because of (B2). Letting fa—> co, putting tx = t in (3.13) and using (3.16) we get for |*j| ^ a, and t > 1,
A A
|l .f o o o ; « , ) ! < J J {^ p ^ - \ J ( t , o o , x 1,zl)\dzdz1 B jd -i v 2n
< | e + ( | - ) ^ 0(r§+«a) + (0^ 7 ^ 0 J s - i e - d s ... (3.17)
2 \ntl V n
Clearly one can choose T large enough that the right side o f (3.17) < e for all t > T. Thus (3.11) is proved.
Using (3.15) in the place o f (3.13) and proceeding similarly, (3.12) is proved. This completes the proof o f the lemma. □
We now prove the main theorem o f this section.
Theorem 3.5. Let (Al)-(A3) hold with an ( . ) = 1, bt( . ) = 0.
Let / , <p satisfy conditions (Bl)-(B3). For x e G define
r t t .
u(x) = lim Ex J /(X (s)) ds-\- f f(X(s)) d^ (*) 1 ... (3.18)
t—> « L o o J
Then u is a continuous function on G such that (a) u is periodic in x%, ..., z& ;
A ___ A
(b) | u(xv as) | < K(\ + j I), where K is a constant independent o f x t, X ; (c) « is a stochastic solution to (3.1);
(d) lim sup | E. («(X(t))) I = 0,fo r any x1 > 0.
*-*• * 11
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0 0 4 S . RAMAStTBRAMASTIAN
Moreover, u is the unique stochastic solution to (3.1) in the class
@1{v '■ G—> R '■ (i) v is bounded on compacts ; (ii) v is periodic in %s, (m ) I v(xv &) I ^ # (1 + |^i I ), for some constant independent o f xv X] wd
(iv) lim Ex [v(X(t)] = 0). , ... (3.19)
t ’ ■ > flP
Proof. Observe that u (x) — lim u(0, t2 ; x1 x ); consequently by the i2-*- oo
preceding two lemmas it follows that u{x) is well defined for. each X, u is perio
dic in x2, ... , xd and that | u(x1; x) | < # ( 1 + 1 ^ 1 ) . To prove continuity, note that for any x = (xv x ) e G,
u(x) = w(0, 8 ; xu ae)+w(\$, T ; xx x )+ u {T , oo ; xv x )
where u is defined by (3.5), and 0 < § < T are to be suitably chosen. For fixed (xv Si) e G, e > 0 b y the preceding two lemmas, T > 0 can be chosen so that u (T , oo ; y v y) < * e for all (y, y) in a compact neighbourhood of (%lt x ). Choose S > 0 such that
Then it is easily seen that sup | u(0, 8 ; y v ?/)| < I e. By the strong Feller
A y &
property, u(S, T ; a^, x ) is continuous in (xv x). Continuity o f u now follows.
To show that u is a stochastic solutior, we have to show that Z(t) is a continuous Pa-martingale, where Z(t) is given by (3.2). Because o f assertion (6) o f the theorem and condition (B2), it follows that Z(t) is integrable ; con
tinuity in t is clear from continuity o f u. For s, t > 0, w e £2 put f t (to) ss f ( t , w) = { f ( X ( s , w)) d s+
### f
(X(s, w)) dl(s, w),
0 0
6 t «>(«) *= « ;(£ -[-« )
As / , tp are bounded on compacts note that ^ is well defined. Since £ is as additive functional
&tM>) — ft{s-\-t, w)—i/r(t, w) ... (3.20) For r < r, put M\ = E(\p-(T)\ /8r). By (3.20) and the Markov property, for. t ^ 0, « > 0, X e G we have
Mp* * ^(<)+^X(*) (&(*))> a.*.P»s (3.81)
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- \M°+t\ < | xlr{t) | + | « (0, s ; X x (t), X (t)) |
< l ^ l + A + ^ I ^ W l + A l ^ i W I 2. ® - ^ * - (3-22) for all s > 1, t ^ 0, x e G where the constants ftv /?2> P% are independent o f te [l, oo), t, x.
Put Nt = lim M\+t. By the definitions o f u, i/r, M\, Nt, Z(t) and (3.21)
! ■ ^ ao
it follows that for any t > 0, x e G
Nt = Z(t)-\-u{x), a.s.Px . Ia view o f (3.22) it is easily seen that for t2 > 1x > 0,
E (N h \*Ih ) = lim E ( M ' + * ' \ e )
A * < - > « - 1
= lim E (E (ir(s+ ti)\ £ )\j3t )
! - > » 2 1
= N fi a.s. P x ... (3.23)
Thus {Nt}, and hence {Z(t)} is a P®-martingale with respect to St- Hence u is a stochastic solution to (3.1).
Note that for x e G , t > 0,
Ex[u (X {t)]= j" J u(yv y)p1{t,x1, y 1) [ p2 ( t , x , y ) —p ( y ) ] d y d y 1 [ o , «-] T « -i
+ / J u(yv y fa it, xt , yd p (y) d\$ dyv ... (3.24)
[0, * ) T <*-»
By assertion (6) o f the theorem and Proposition 2.3 it follows that for any xt > 0,
lim sup | first term on the r.h.s. o f (3.24) |
< lim K ct e ** J [1+ 1 yi |] Pi(t, *i, y t) dyt «* p.
\$ —^ oo [0, ®)
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3 6 ft S . RAMASUBRAMANIAN
Next, as the Lebesgue measure on [0, oo) is the invariant measur&for the reflected Brownian motion and p is the invarnant measure for the Lj-diffusion, b y the representation (3.18) for u, we have for t > 0, ^ 0,
J J »(& . y) PiV> x1, yx) p (y) dtf dyx {0, <r) y i - l
= J im I [ J J J J Z)Pl(s, Vi, 2l) o *■ to,*) Ta-i to,*) Ta-i
Pi (*i Vi) Pi («, y, *) P(y) dz dzt dy dyx
+ J J J ^ <?{z)Pi{s,yi,0)px ( t, x1, y 1) p 2( 8 , y , z ) p ( y ) d y d z d y 1 ] dt
[o, •) Ta~i Td-1 1
= lim f [ J J ( .f f { z i , z ) p & ) d z ) p 1 { s, yv z1) p x {t1xv y x) dy l dzi -
T - * » 0 1 t°> • ) I0 ,») ' T d- 1 '
+ J ( f 4 - ?(*) /»(*) dz ) p x(s, y lt0) p t (t, xx, yx) dyx 1 ds
10, r) ' Td-1 1 ' J
T+t r a " * *
= lim I I J f(zv z) p x (s, xx, zx) p(z) ds dzx t Lt0, or) T d -l
-r I. 4 - <P(«) Pi (s, xx, 0) p(z) dz 1 ds (3.26.)-
. yS-l 1
Now let F be the extension o f / as given in the proof o f Lemma 3.4.
Since / , f satisfy the conditions (B2), (B3), from (3.26) we get for xx p 0, t > 0,
! J f u(yv y)p1(t, xv y x) p(y) dy dyx I
> * ) ytf-l
- I * . +t U
^ d t i *** ( ^ ) - 1 } ^ ] *
< 1 - V 5T ?)] (2«.+2*!fl.+*S ML) ... (3-2’ ) (3.24), (3,25), (3.27) the assertion (d) of the theorem is immediate. In particular u e <SX.
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Uniqueness in the class (Bx follows from the follow ing lemma.
Lemma 3.6. Let (A l)-(A3) hold and f , <p satisfy (Bl), (B2). Let v e ^ b e a stochastic solution to (3.1). Then v(x) = r.h.s. o f (3.18).
Proof. As v is a stochastic solution,
v(x) = E x(v(X (t))+E x [ J f(X (s ))d s + J <p(X(a))d£(«) ];
and since lim E x (v(X(t))) —0, the conclusion follows. □
t —> CO
We will now prove the necessity o f the condition (B3).
Theorem 3.7. Let (A l)-(A3) hold with an { . ) = !, 6X( . ) = 0 ; let f, <p satisfy (Bl), (B2). Suppose there is a stochastic solution in the class (®y to the problem (3.1). Then f, cp satisfy the condition (.53).
Proof. Let u e Q x be a stochastic solution to (3.1). Then by the pre
ceding lemma
u(x) = lim Ex
J f(X (s )) d s+
### J
<p(X(s)) d\$ (*)]
T—» « I- 0 0 J
Observe that in the derivation of (3.26), the condition (B3) is not Used. There
fore by (3.24) and (3.26) we have for any t > 0, x = {xv x),
Ex K Z M)) = I J u(yv y)p x(t, x v y x) [p2{t, x , y) — p(y)]dy dyx
[0, OC)
t+T r a a f 2 \ ,
+ lim J J J /(Zi= * ) / > ( « ) { Pi(s, x v ?1)— } dsdzx
t 1 [0, or) T d - 1 *• V 27TS 1
+ <P(*) P(z) {p i (s> xv ° ) — } d* ] ds
t+T 9 r \
+ lim T—>oo i V27TS J" 7 a= L10, «) J tpd-lJ /(*1» *) P W ds dzl '
+ J \ P(«) ds ... (3.28)
T a-1 * J
As w e <?1; l.h.s. o f (3.28) tends to 0 as t—> oo. By (3.25), the first term on the r.h.s. o f (3.28) goes to zero as t—* oo. Sinoe / , <p satisfy (B2), note that the second term on the r.h.s. of (3.28) is 0 (t~1/2). The desired conclusion now follows. This completes the proof.
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s. r a m a s t j b b a m a n i a n
4, NstTMANN PROBLEM : SELF-ADJOINT X PERIODIC CASE
In this section we consider the case when Lx is self-adjoint and L% has periodic coefficients. We assume that ( A l ) —(A3) hold. As before, let p x denote the transition probability density function o f the i^Lv j
diffusion in [0, oo). Since p x is obtained by the method o f images from the transition probability density function o f the Lx—diffusion in i t and since L x is self adjoint, b y a theorem o f Aronson (1967) we have
mx t~m exp |— (yx—a ^ j + exp - j ? (?/i+ zx)2} j
< P i (*» * i . Vi)
< kxtrW |©xp | - y (sh—* i)* }+ © x p { —~* ( y ^ i ) 2} ] ••• (4.1) where the constants mx, m2, hx, kt are independent o f t, xx, y x.
in this section we make the following assumptions on the prescribed data
/> ?■
(Cl) : Same as (Bx).
(C2) ; . lim sup \f(xx,x)\ = 0
5....
(03) : for all t > 0, xx > 0
S ... J f ( y v y ) P i i * ’ x » y i ) p ( y ) dy dv\
[<>,•) T d -1
+ i \$ % ( o) 9(y)Pi(t> xv Q)p(y)du = 0
z T d- 1
Lemma 4.1. Let (Al)—(A3) hold ; let / , <p satisfy the conditions (Cl)—
(C3). Let e > 0. Then there exists r0 > 0 such that for any 0 < tx < f2 < oo and x1 ^ r0,
sup x
+•
I [ J f(y)p{t,(%i>x),y)dy
*x 1 a v .
\ J an(0)<p(y)p(t, (xv x), (0, y))dy 1 dt
& 30 J
< 2 r0 kx cx H/iU J t~w exp I j dt
+ ci e~ f C ^ . d t - ^ ~ k xcx ||«p|U «n (°) J t-1^ ^ exp^ j dt ••• (4-2)
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only on e ,f.
Proof. By our assumptions note that / is bounded. Let e > 0. By (C2) there exists r0 > 0 such that
sup A \f(yi> y) I < e for a11 Vi > ro
V
Consequently by (4.1) we get for all t > 0, x1 > r0, y J xi> Vi)dy11 < e + H/Jloo J p x(t, x v yx)dyx
I®*) [o.r0]
< e+ 2r0 kx H/ll. trV*exp [ - A (r0- x x)» ]. ... (4.3) Note that, because o f condition (03),
l.h.s. of (4.2) = sup | u(tv ta ; x x, x )
X
~ sup | I x(tx, #a) j x x, a e)+ Ia(tv ta ; xx, x ) | ... (4.4)
X
where u, I x, I 3 are defined analogous to the correspoing objects in Section 3.
Applying (4.1) to p x(t, xx, 0), using (2.12), (4.3), (4.4) we can now easily prove (4-2). □
Note : For e > ||/||, we may take r0 = 0.
Theorem 4.2. Let ( A l ) —(A3) hold ; let f . 9 satisfy (Q l)—(G3).Let u(x) be defined by (3.18). Then
(а) u is a bounded continuous function on G ;) u is periodic in x2, . . ., x a ‘,
(c) u is a stochastic solution to (3.1) ; (d) lim sup | u(xX) x ) | = 0 .
*1 - » " *
Moreover u is the unique stochastic solution to (3.1) in the class
<®2 = jv : G—>R : (i) v is bounded measurable ; (ii) v is periodic in (xg, ...,
x#)), and (Hi) lim sup| v(xv x ) | = 0.\ ••• (4-5)
X
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Proof. From the preceding lemma it is clear that u is well defined, boun
ded, periodic in (x2, ..., x&). Continuity of u can be proved as in Section 3.
The proof o f u being a stochastic solution is also similar to the one in Section 3.
In view o f (4.2), the assertion (d) is easy to establish. In particular u e <?2.
Finally, let v e be a stochastic solution to (3.1). To prove uniqueness it is enough to show that
lim sup | E (v(X («))) | = 0. ... (4.6) t—> CO X
Let e > 0. Since v e <*2, there is r0 > 0 such that sup I v(yv y) | < -j-e for all
A Jl
y
Vx ^ r0. Consequently by the upper bound in (4.1) we get for any (xv x 2, ..., xa) e O , t > 0,
\Ex [v(X{t))]
y
### 6+ 2 V o IML
l~ X/%
From the above inequality (4.6) is obvious. This completes the proof. □ We now prove the necessity o f the condition (03) for the homogeneous problem.
Theorem 4.3. Let (Al)—(A3) hold ;l e t f s = 0 and cp 6e a bounded periodic function on dO. Suppose there is stochastic solution in the class (Bt to the prob
lem (3.1) Then J <p(y)p(j))dy = 0 ydf-l
Proof. Note that in the proof o f the uniqueness part of Theorem 4.2 we have not used the condition (03). So, if u e <?2 is a stochastic solution then b y the representation
«(a?) = u(xlt x ) = lim E
### f
J <p(Z(s))^(s)l
T - » oo o J
1 T
lim — J j1 an (0)op(t/)2)1(a, xx, 0) [p2[s, x , y )-p {y ) ]d y d s
T - + m * 0 T d- 1
+~2 au (°){ I / Pi(s, xv 0)c?s| ... (4.7)
By the upper bound in (4.1), and (2.12)
sup | first term on r.h.s. o f (4.7) | X
^ au (0) cx kx J t e ** exp £— x\ dt—> 0 as x1—> oo.
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By the lower bound in (4.1)
T
lim lim J p t(t, z v 0)dt
oo T-+00 o
> lim lim J 2m1 t~V2 exp — rn^ -1 1
Xx~* 00 T —> * x2 *• t i
> 2 m 1e 2 lim lim \-\/T—z x] ... (4.9)
® i-* oo T - + oo
As ue<?2, l.h.s. of (4.7) tends to 0 as x±—> oo. In view o f (4.7)—(4.9) this is now possible only if J1 <?(y)p(y)dy = 0. This completes the proof. □
y(?-l
Remark 4.4. Suppose / , <p satisfy
J f{yi> y) P(y)dy = 0, for any y x > 0.
r d - l
I 9 (y)p(y)dy = o
rpd—1
(4.10)
Then clearly / , <p satisfy the condition (C3). Conversely, i f f is o f the form f(Vi> V) = A(yi)My), then the condition (C3) implies (4.10) ; for, by (03)
J1 fi(yi)Pi(t, yi)dyx = const. p x(t, xv 0)
[0, «,)
unless J1f 2(y)p(y)dy = 0, and consequently either / x = 0 or J f 2(y)p(y)dy = 0.
Remark 4.5. In view of the preceding remark, the condition (03) is not sufficiently general. (In particular, / can not be a function o f y x alone, unless / = 0). A more satisfactory condition would be an analogue o f (B3) ; but we have not been able to carry out the analysis under such a condition. How
ever, in the homogeneous case (as (02) trivially holds), b y Theorems 4.2 and 4.3, the condition (03) is a necessary and sufficient condition for the existence of a unique solution in the class (®2 ; and the solution is given b y
u(xv x ) = lim i f I ®u(0) 9 (y)Piis> xv 0)?a(«, V) d y ds.
T—■>» 0 ytf-1
(Note that, u ^ 0 in general. Indeed, using the uniqueness o f Doob-Meyer decomposition, sample path continuity, Corollary 2.3 o f Stroock and Varadhan (1971), and proceeding as in the proof o f Proposition 3.2 o f Hsu (1985), it can
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be shown that, if <p is continuous and u == 0 then <p = 0). It may be noted that, in the homogeneous case, (C3) is the same as (B3). Thus, for the homo
geneous problem our analysis gives a complete picture.
5. Neumann problem : L = la p la cia n
In this section we assume that ay (.) = 8y , (.) = 0, 1 < i, j d ; that is, {P x : x e 0 } is the Brownian motion in G with normal reflection it the boun
dary. For x = (xv x), y = (ylt y ) , t > 0 observe that p(t, x , y) = pj{t, xv 1/1) p 2(t, x , y) where
p j f . = ( H - ) I « P { - } + “ P { - <JT T ^ } ]
d -1
p S , k y ) = ( - ^ ) 2 exp { - I s i y i - x t ? ] .
%
The case w hen/. 9 are periodic in the variables x2, xa has already been dealt with in Section 3. Here we make the following assumptions on the prescribed data / , 9.
(Dl) : f e L m (G), e L a(dG) ;
(D2) : M r ^ S \y\r \f(y)\dy+ f |y|r |<p(y)l d y < c o , r = 0,1,2;
w "
A A
(I>3): f f(y)dy+j< J f(y)d y = 0.
S’ 0e
For 0 < < £2 < 00, sc = (%, ae) e (?, let m(^, #2 ; x ) be defined by (3.5), with {Px} denoting the reflected Brownian motion in Q. Let F be the extension o f f as in the proof o f Lemma 3.4. By Rem ark 2.2 and condition (D3) it is seen that
A A -1
1 I « « I2> I A
: ... (5.1)
+ f t f a { exp \dz
- I \ 2s > J
In view o f the conditions the following lemma can now be proved easily.
<* 32
Lemma 5.1. Let L = A S -= -5-. L etf, 9 satisfy conditions (D l)—(D3).
<=1
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A ~
Then f o r a n y
t
### 2 < oo, (a?lf
x ) e G t
d
' * \ M ^ \ X \ * M0 | u
d L ( d + 2 )
t2;
\^MZ+
and
x v x )
~
### j II <p Hoo a / ( ® * 3)
where the constants M n, M % are as in (D2). □ We now have the following theorem.
& ga
Theorem 5.2. Let i = f S and let / , 9 satisfy conditions (Dl)—
i=1 O&j (D3). Let u be defined as in (3.18). Then
(a) u is a continuous function on O such that
| u(*) | < K (1+ | * j 2), fo r ail x e 0, (b) u is a stochastic solution to (3.1) ;
(c) lim E^_a(X(t)Y\ — 0 uniformly over compact subsets of G.
Moreover u is the unique stochastic solution to (3.1) in the class
<2s = { v : G - > R : (i) | v{x) | < K{1 + | x\2), (ii) lim Ex[v(X(t))] = 0 for all x e G }
00
... (5.4) Proof. In view of the preceding lemma, all the assertions except (c) oan be proved as in Section 3.
In view o f (D3), by an argument similar to the derivation o f (3.26), (3.27), using Chapman-Kolmogorov equations, we get for t > 1.
| Ex[u(X(t)))] | = | lim u(t, T + t ; xv x) |
T —> «>
_ d _
< C ( i + M a) * 2
whence assertion (c) follows. This completes the proof. □ Our next result concerns the necessity of the condition (2)3).
1 d d%
Proposition 5.3. Let L = y £ and let f, 9 satisfy (D l), (D2).
Suppose there is a stochastic solution in the class <?3 to the problem (3.1).
Then f, 9 satisfy the condition (D3).
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Proof. Note that the condition (D3) is not used in the proof o f the uni
queness part o f the preceding theorem. So, if u e (2% is a stochastic solution then
u{x) = u{xx, x ) = lim E x f U (X (s)) d s+ (X (« ))# (« )]
l o o 1
+ „ L ^ * * 1 *
T
+ lim J ( ^ ) 2 [ r —» oo o ' &ns of f t v W y + i t ••• {6,5) B y the proof o f Lemma 5.1, using only conditions (Dl), (D2), it is easily seen that first term on the r.h.s. o f (5.5) is well defined. The second term on the r.h.s. o f (5.5) is well defined only i f (D3) is satisfied. □
In Theorem 5.2 uniqueness is guaranteed in the class C% given b y (5.4).
It would be desirable to replace the condition (ii) in the definition o f <?3 by a condition not inovlving the parameter t. The following result is in that direction.
Theorem 5.4. Let L be as before ; let f, cp be integrable functions on 6, dG respectively. For z e R d, put
l -
W = J ( ^ ' ) 2 F { y ) e - % <» ’ * > dy.
Rd > i
1
9 ^ = r L i f e ) 2 f ^ 6 X P < ( 0 ’ d
u(«) = 2\z\~2 {F (s )+ f( « ) }r f fiy ^ y ^ ■■■,ya), y e G
where F{y) — ■< _
t •■■>yA),y*G
Suppose u is an integrable function on R d. Let u be defined as in (3.18). Then u is the unique bounded continuous function vanishing at infinity, which is a sto
chastic solution to (3.1).
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NEUMANN PROBLEM IN TH E H ALF SPACE 375 Proof. By the spectral representation o f the transition probability den
sity of the Brownian motion note that
» < • .« .* )= - / « ' < * ■ « > . - < < » • * > &
Rd \2nI
for all s > 0, x , y e O , where y* = ( —y lt y%, ..., ya)- Consequently under the given assumptions it can easily be verified that
v{x) = J u(z) eHx ’ *) ds R*
whence it follows that u is a bounded continuous function vanishing at infinity.
It can be established as before that u is a stochastic solution to (3.1).
Suppose v is another such function. Given e > 0 one can find a compact set K £ _ G suoh that I v(x) | < for x e K . Therefore
sup|^|>(X(*))]| < -2- e+IM I. | K| (27rt)~dli 35
where | K | denotes the Lebesgue measure o f K. From the above inequality it follows that sup | Ex[v(X(t)Y\ | —► 0 as i —» oo. It is now easily seen that
*
v = u, completing the proof.
Remark 5.5. The hypotheses o f the preceding theorem imply that P(0)-f
*
<p(0) = 0 which is just condition (D3).
1 A d2 a d
6. N e u m a n n p r o b l e m : L = — 2 2— S xi 2 <=i dxf t=1 dxt
In this section we consider the Neumann problem for L when L is the generator o f the Ornstein-Uhlenbeck process ; that is a#(£c) = Sy, bi(x) — —a*.
The transition probability density is given by (2.14)—(2.16). Unlike the preceding cases, now one has an invariant probability measure v(y)dy given by (2.17)—(2.19). We make the following assumptions on the prescribed data / , <p :
(El) : M 0 = = ; \f(y)\dy + f lq>(y)ldy < oo ;
0 ao
(E 2 ): f f ( y ) v(y)dy + - ^ ( 0 ) / f(y)v^y)dy = °-
o ~ SG
(26)
In what follows {P x} denotes the distribution of the Ornstein-Uhlenbeck process.
1 £ d 2 3
Theorem 6.1. Let L = — S
9xf Xi dxi
Let u be defined as in (3.18). Then u is a continuous function on G such that (а) | u(x) | ^ K 1-^K 2 |as|, where the constants K v K % are as in (2.20) ; (б) u is a stochastic solutoin to (3.1) ;
(c) J u(x) v(x)dx = 0.
a
Moreover, u is the unique stochastic solution in the class
<®4 = {h :G^> R : (i) |A(a>) | < Z ( l + |*|), (ii) [h (x ) v(x)dx = 0} ... (6.1) a
Proof. In view of Proposition 2.4 and conditions (El), (E2) we have for , and ftp satisfy (El), (E 2).
0 < tx < < oo, X e G,
h
J U ( y W , y ) d y + i J <?(y)q(t, x , (o, y))dy
a dG
### f I IM 11 ?(<> y) -Ay) I % *
l G
dt
t.
+ i f J I9(y) 11 «, (o.»)) - ^ ( o w y ) I % *
*i 9G*
*2
< ( i ^ x + Z a l a : ! ) J . .. (6 .2 )
«i
From (6.2) it follows that u is well defined and that (a) holds. Continuity o f
« , and assertion (b) can be proved as in the earlier sections.
Note that ^ (0) = j“ q-jfi, xv 0) v1{x1)dx1 for any t. Since v is the invariant
10, « )
measure, by (E2) we now have
T
J u{x)v(x)dx = lim J J J f(y)q{t, x , y)v(x)dy dx dt
a t-** 0 a o
T
+ lim i ! J1 J J (?(y)q(t,x,{0,y))v1{x1)pi(x )d y d x d x 1dt
5 C _ » « 0 [0, or) ZO d a
= lim J [ \$ f(y)v(y)d y+ | Vj(0) J1 <p(£)v2(t/)dy] dt = 0 ... (6.3)
r - » « o L ^ * so J
establishing (c).
(27)
Finally, by Proposition 2.5, ifor any stochastic solution h e <®4, note that [h{y) q{t, x, y) | ^ [polynomial in | y | ] v{y). C o n s e q u e n t l y b y the dominated convergence theorem, lim Ex [A(X(£))] = / h(x)v{x)dx = 0, and the conver-
{ ^ 0c
gence is uniform on compact sets. It can now be proved that h = u, complet
ing the proof o f the theorem. □
Theorem 6.2. Let L be as in the preceding theorem ; let f. cp satisfy (El).
Suppose there is a stochastic solution in the class to the problem (3.1). Then f, 9satisfy the condition (E2).
Proof. In view o f the derivation o f (6.3), the theorem can be proved as in the earlier sections. □
Remark 6.3. It may be noted that Propositions 2.4 and 2.5 are the essen
tial ingredients for proving the above theorems. Therefore, for any ergodic diffusion in G (with normal reflection at dG) such that zero is an isolated point of the spectrum of the generator (on the i 2-space with respect to the invariant probabi.ity) and for which Proposition 2.4 and 2.5 hold, our analysis can be extended. However, it is not clear to us for what class o f diffusions Proposi
tions 2.4 and 2.5 hold.
Acknowledgement. It is a pleasure to thank V. Pati and A. Sitaram for some useful discussions. Thanks are also due to a referee for a careful reading o f the manuscript, comments and suggestions.
References
Abonson, D. G. (1967). Bounds for the fundamental solution o f a parabolic equation. Bull.
Amer. Math. Soc, 73, 890-896.
Bb n s o u s s a n, A. Li o n s, J. L . and Pa p a n i c o l a o u, G. C. (1978). Asymptotic Analysis fo r Periodic Structures, North-Holland, Amsterdam.
Bhattaoharya, R . N. (1985). A central limit theorem for diffusions with periodic coefficients.
A nn. Probab., 13, 385-396.
Bb o s a m l e r, G. A. (1976). A probabilistic solution o f the Neumann problem. Math. Scand.,
38, 137-147.
Chung, K . L. and H su, P. (1986). Gauge theorem for the Neumann problem. In Seminar on Stochastic Processes, 1984, 63-70. Birkhauser, Boston.
Fb e i d l i n, M. ( 1 9 8 5 ) . Functional Integration and Partial Differential Equations, Princeton Uni
versity Press, Princeton.
Hsu, P . (1985). Probabilistic approach to the Neumann problem. Comm. Pure A ppl. Math.,
38, 445-472.
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Ik e d a, N. (1961). On. the construction o f tw o dimensional diffusion processes satisfying Wentzell’s boundary conditions and its application to boundary value problems, Mem.
Coll. Sci. Univ. Kyoto A . Math., 33, 367-427.
Ik e d a, N. and Wa t a n a b e, S. (1981). Stochastic Differential Equations and Diffusion Processes, North-Hollandd, New York.
Ra m a s i t b e a m a n i a n, S. (1988). Hitting o f submanifolds by diffusions. Probab. Th. Bel. Fields, 78, 149-163. Addendum 84 (1990) 279.
--- (1992). A gauge theorem for the Neumann problem in the h alf space. Preprint.
St b o o c k, D. W . and Va b a d h a n, S . R . S . (1971). Diffusion processes with boundary conditions.
Comm. Pure A ppl. Math., 24, 147-225
Wa t a n a b e, H . (1964). Potential operator o f a recurrent strong Feller process in the strict sense and boundary value problem. J. Math. Soc. Japan, 16, 83-95.
De p a r t m e n t o f St a t-Ma t h In d i a n St a t i s t i c a l In s t i t u t e 8t h Mi l e, My s o r e Ro a d Ba n g a l o r e 560 059 In d i a.
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## References
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2023-03-26 02:19:14
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http://mathhelpforum.com/trigonometry/183011-usage-cotg-area-polygon.html
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# Thread: Usage of cotg; Area of polygon
1. ## Usage of cotg; Area of polygon
Hi Forum
Here is a question
$A=[ns^2 cotg (\pi/n)]/4$
I am confused about the usage of cotg in this formula. How was this formula calculated?
If we use only tg we'd get
$na^2tan(\pi/n)$
This $\pi/n$ angle regards the angle of the side $s$, correct?
I'm no pro in co-trigonometric functions but,
Will this, in any way, relate to the fundamental propriety of cotg=A/O?
Trigonometric functions on non right angles are rather strange.
Thanks.
2. ## Re: Usage of cotg; Area of polygon
Originally Posted by Zellator
Hi Forum
Here is a question
$A=[ns^2 cotg (\pi/n)]/4$
I am confused about the usage of cotg in this formula. How was this formula calculated?
If we use only tg we'd get
$na^2tan(\pi/n)$
This $\pi/n$ angle regards the angle of the side $s$, correct?
No that is not correct.
$\Theta = \frac{{2\pi }}{n}$ is the central angle of a regular polygon.
Thus we have $\cot (\Theta ) = \frac{{2a}}{s}$.
Note that $a$ is the length of the altitude and $s$ is the length of the base.
3. ## Re: Usage of cotg; Area of polygon
Originally Posted by Plato
$\Theta = \frac{{2\pi }}{n}$ is the central angle of a regular polygon.
Thus we have $\cot (\Theta ) = \frac{{2a}}{s}$.
Note that $a$ is the length of the altitude and $s$ is the length of the base.
Hi Plato
I guess I didn't know how to put the central angle part in proper terms. Thanks for the explanation.
Though I'm kind of confused of where does the 2 in $a$ comes from.
Maybe we have a two there because $s$ is actually $\frac{{s}}{2}$?
Ok this was very confusing before your explanation.
I hope I got it right!
Thanks again Plato!
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2017-01-19 19:54:36
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• Inorganic Chemistry (752)
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• 1990-1994
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• 1955-1959
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• 1
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 188-193
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: A computer program based on the theory of Part I is developed for calculating equilibrium ratios and related thermodynamic properties of mixtures, and a variety of data are used to test the method. For the carbon dioxide-n-butane system both liquid and gaseous compressibility factors are predicted with an average absolute deviation from experimental values of 1.3% for a wide range of conditions. A maximum deviation of 5.4% occurs in the critical region. Derivative properties such as component fugacities and equilibium ratios show somewhat larger deviations as expected. For the same system average deviations are 2.7% for carbon dioxide fugacities, 2.6% for n-butane fugacities, and 3.3% for carbon dioxide and n-butane equilibrium ratios. Average deviation for predicted equilibrium ratios for eight binary systems and 574 data points is 4.6%. Equilibrium ratios for two ternary systems are also predicted accurately. The major advantage of the method, however, is the small or negligible amount of experimental mixture data required. The method has not been tested below a mixture reduced temperature of 0.8, the lower limit of the Pitzer tables. Without density corrections to the scaling parameters best results are obtained if all binary pairs in a mixture fall within range 0.25 〈VCj TCj/VCi TCi 〈 4.0.
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• 2
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 206-212
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Experimental and theoretical transient response data are presented for a tubular reactor with recycle, illustrating the distributed nature of this feedback system. The transient concentration response of an isothermal tubular reactor with recycle was studied experimentally and theoretically for inlet concentration and flow upsets. The reaction studied experimentally was the second order homogeneous liquid phase saponification of methyl acetate with sodium hydroxide.Theoretical models using residence time distribution (RTD) techniques have been developed. The fact that the theoretical model (RTD) predicts the dynamic response data for the recycle reactor with and without reaction in the recycle line for both single flow and concentration upsets verifies that this model is satisfactory for simulation of recycle tubular reactor dynamics.
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• 3
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 221-222
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 4
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 225-227
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 5
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 234-235
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 6
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 240-242
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 7
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 248-249
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 8
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 249-250
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 9
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 43-47
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Theoretical expressions are derived for the fraction of the energy, emitted from a UV lamp, which strikes the reactor wall in systems where a reflecting surface is included. Two geometries used in photoreactors are considered: a cylindrical lamp located at the focus of a superimposed parabolic reflecor. The predicted efficiencies are low, particularly for the elliptical reflector - reactor system, because of the energy that escapes through the ends of the system. Experimentally determined efficiencies for the elliptical type are in reasonable agreement with predicted values, suggesting that the theoretical method may be used for estimating efficiencies for different reactor systems.
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• 10
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 70-77
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The industrial importance of mixtures of closely similar substances is out of proportion to their relatively small numbers due to their frequent occurrence and the difficulty of their separations. A procedure specially designed for the general prediction of their properties, particularly relative volatility, over a wide range of state variables is needed.Such a procedure is developed in this work for convenient application to multicomponent systems with the use of generalized functions. The relative volatility of a nearly ideal system is decomposed into ideal solution factors and nonideality factors. The first order perturbation thory of Longuet-Higgins is adopted for the calculation of the nonideality factor. The validity of the procedure for the quantitative description of real mixtures is demonstrated with the system propane/propylene for which extensive data are available.The required pure fluid properties for the general application of the procedure are reviewed. System parameters are evaluated for 15 binary systems of industrial interest.
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• 11
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 282-286
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Optimal output feedback control low requiring measurment of the output only has been considered for a class of tubular processes. The advantage of this formulation, which requires a single measurement of the output only, over a previous result which requires an infinite number of measurements, has been demonstrated through a heat exchanger example. However, when the terminal time is grater than the residence time of fluid, a time-delay element is needed.
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• 12
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 299-304
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: A method is described for solving the problem: given fixed pressure, temperature, the amounts of the chemical elements, and the chemical potentials of possible chemical species at the pressure and temperature specified, determine the equilibrium composition. The method requires a minimum of judgment on the part of the user.A modification of Naphtali's method for direct minimization of Gibbs' function provides an estimate of the composition of sufficient accuracy to insure convergence of solution, by the Newton-Raphson method, of the nonlinear equations describing the equilibrium.Problems in treating multiple phaes of unknown stability and chemical species present in small amouts are handled by ignoring unstable phases and small quantitites in the direct minimization until the amounts of the major consitituents have been at least approximately determined. To accomplish this, species temporarily ignored are assigned a ficitious mol fraction so that their re-entry into the calculation can be established. Truncation errors in the direct minimziation can be tolerated because of the two-step method.Examples of some of the problems solved are given.
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• 13
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 333-337
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Theretical equations for the transport properties of donse gases and liquids require knowledge of the contact pair-correlation function g2 (σ) and the friction coefficient ζ. Usually this latter quantity is made up of a hard-core contribution ζH and a soft-repulsion contribution ζS. Correlations are presented for the reduced friction coefficients ζrH, ζrS, and ζr in terms of reduced density ρ* and reduced temperature T*. These correlations were found to predict the dependence of self-diffusivity of several substances on temeratures and density in the dense gas region.
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• 14
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 326-332
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Exposing one face of a catalyst pellet to a pulse of tracer gas and analyzing the response at the opposite and provides a dynamic method for measuring the effective diffusivity of porous catalysts. The first and second moments of the response peak are shown to be a function of only De and the geometry of the pellet and detector chamber for a nonadsorbing, tracer-carrier system. Data obtained for alumina pellets of different densities ilustrate the method.For an adsorbing tracer, the first moment is a function of both De and the adsorption equilibrium comstant. Measurements for an unconsolidated assembly of nickel/Kieselguhr particles, using the D2-H2 system, show that first-moment data are sufficient to calculate reasonably accurate values of the equilibrium adsorption. However, it appears to be difficult to obtain adsorption rate constants by this method.
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• 15
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 343-346
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: A semi-empirical test for the thermodynamic consistency of isobaric liquid-vapor equilibrium data for ethanol-water saturated with a salt is proposed. The test is based upon an adaptation of the Herington method (1) in which the ternary system is treated as a special binary. The test is applied both to full concentration range data and to data which are incomplete at the high alcohol end. For data which are incomplete at the high water end, a less severe test is employed.Literature data for 23 systems composed of ethanol, water, and an inorganic salt at saturation were tested. By the criterion of the proposed test, fourteen were deemed consistent, six were borderline, and three were pronounced inconsistent.
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• 16
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 361-371
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Previously obtained experimental heat transfer data have been collected and are illustrated along with minor variations of the standard correlations. Analysis of data for heat transfer in randomly packed beds and compact (void fraction less than 0.65) staggered tube bundles indicates that the Nusselt number for a wide range of packing materials and tube arrangements is given by \documentclass{article}\pagestyle{empty}\begin{document}$$N_{Nu} = \left({0.5N_{{\mathop{\rm Re}\nolimits} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } + 0.2N_{{\mathop{\rm Re}\nolimits} ^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} } } \right)N_{\Pr ^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} } \left({{{\mu _b } \mathord{\left/ {\vphantom {{\mu _b } {\mu _0 }}} \right. \kern-\nulldelimiterspace} {\mu _0 }}} \right)^{0.14}$$\end{document} provided NRe ≥ 50. The correlations presented in this paper are not necessarily the most accurate available; however, they have wide application, are easy to use, and are quite satisfactory for most design calculations.
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• 17
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 372-380
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The general equations of motion were solved numerically for the laminar isothermal flow of Newtonian fluids from a large tube of circular cross section through an abrupt contraction into a coaxial tube of smaller diameter and through the flow-development region of the smaller tube. The ratio of the diameter of the large tube to that of the smaller tube was varied from one to eight (the latter in one case). Solutions were obtained for the case where the larger tube is real, with no slip at the wall, and for the case where it is a frictionless “stream” tube. The results are presented as charts giving excess pressure losses attributable to contracted and developing flow in terms of equivalent smaller-tube diameters as functions of the tube-contraction ratio and the Reynolds number, which was varied from 0.01 to as high as 500 in one case. Both radial- and axial-velocity profiles are presented. The computed results are shown to be in satisfactory agreement with some experimental data. The results are presented in a manner convenient for use in the design of equipment in which contracted Newtonian flow occurs, such as fiber spinnerettes and heat exchangers, and in the analysis of experimental data for contracted flow.
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• 18
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 416-420
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The effects of axial fluids dispersion on breakthrough curves in packed beds is considered and formulae are derived for ‘F-factors’, which allow heat transfer coefficients obtained by step testing to be corrected for axial fluids dispersion. A comparison of steady state and unsteady correlations for heat transfer in packed beds suggests that axial dispersion effects are incorporated in certain steady state heat transfer correlaions. Further correction would thus lead to errors in breakthrough curve prediction. Experimental data for breakthrough curves in packed beds of highly conductive and poorly conductive spheres is examined and Biot number correction factor 1 + Bi/5 shown to be valid for Biot numbers up to about 4.
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• 19
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 435-437
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 20
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 443-445
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 21
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 446-449
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 22
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 459-461
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 23
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 462-463
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 24
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972)
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 25
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 356-361
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: A continuous pump in which the feed and product streams flow steadily both in upflow and downflow is experimentally investigated in the model system toluene-n-heptane on silica gel adsorbent. The experimental data compare reasonably well with analytical results based on an equilibrium theory. The operating conditions necessary to achieve high separation factors are shown to be dependent on the relative magnitudes of penetration distances and the height of the column.
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• 26
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972)
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 27
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 269-276
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: A mathematical model of the centrifugal molecular still has been derived based on a fully developed profile, but negligible normal and tangential velocity components. Thermal gradients, film thicknesses, and evaporation rates calculated from this mathematical expression correlate well with reported literative values as well as with the present data.Mean distillation rates were measured for five pure liquids on a centrifugal still with an effective evaporating surface area of 100 sq. cm. These experimentally obtained rates for liquids exhibiting ideal behavior agreed quite well with theoretical values predicted on the basis of simple kinetic theory. In the case of an associated liquid, however, rate measurements were found to be only 53 to 90% of the theoretical value. Although these low values tend to support the concept of an evaporation coefficient as a true molecular property, there wasevidence that surface irregularities could have accounted for all or at least part of the discrepancy noted.
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• 28
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 409-416
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Conditions under which simplified, single parameter models may be used to predict breakthrough curves in linear, packed bed adsorbers and thermal regenerators are examined with reference, in particular, to earlier conditions proposed by Handley and Heggs and by Babcock and co-workers. It is found that for high values of heat capacity ratio the Schumann model provides a satisfactory description of packed bed dynamics where fluids axial dispersion and solids conduction effects are lumped into a single parameter the curve spread parameter σ*. For low values of heat capacity ratio, the equivalent conductivity model of Babcock and co-workers should provide a more accurate description. The value of the Biot number Bi was found to provide the sole criterion for estimating the relative importance of the internal solids conduction. Empirical correlations are presented which allow rapid estimates of breakthrough curves to be made from the curve spread parameter and which facilitate analysis of experimental data from breakthrough curve experiments.
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• 29
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 432-434
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 30
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 439-442
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 31
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 451-451
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 32
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 454-456
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 33
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 462-462
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 34
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 464-464
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 35
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. i
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 36
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 491-497
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: A fiber optic technique for obtaining multiple, simultaneous, point residence time distributions on operating, commercial scale distillation trays is described. The method has sufficient resolution to yield residence time profiles on the tray and to separate tray and downcomer effects. The results indicate severe flow nonuniformities on the tray, which are not accounted for in present models of distillation.
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• 37
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 647-649
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 38
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 654-656
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 39
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 527-533
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The problem of developed turbulent heat or mass transfer in a duct is considered for the limit of large σ (Prandtl or Schmidt number). The limiting results depend on the behavior of the eddy diffusivity near the solid surface. Since there is a question about whether this variation begins with ∊ ∝ y+3 + … or ∊ ∝ y+4 + … for y+ near zero, both possibilities are considered. In each case the first three terms of the asymptotic expansion for σ → ∞ are obtained. The first term of the asymptotic expansion agrees with limiting results derived earlier, while the correction terms indicate the errors associated with earlier simplifying assumptions.By proper scalling, it is demonstrated that in the limit of σ → ∞ the results are independent of geometry and boundary conditions for situations involving parallel plates, circular tubes and concentric annuli with either constant surface heat flux or temperature. The correction terms to the σ → ∞ asymptote can be significant, although the effect of Reynolds number on the correction terms is very small.A comparison between a typical numerical integration and the asymptotic formula shows excellent agreement. The asymptotic formulae are used to correlate large Schmidt number mass transfer data.
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• 40
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 671-671
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 41
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 452-454
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 42
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 457-458
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 43
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 463-463
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 44
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 465-478
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 45
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 486-490
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The rate at which water is extracted from thoria sols was investigated by fluidizing single thoria sol droplets in 2-ethyl-1-hexanol (2EH) and measuring the diameter of a droplet over a period of time until shrinkage no longer occurred. Diameter data from both water and sol drops were obtained at 25°C. The experimental variables were initial drop diameter (0.1 to 0.2 cm), sol molarity \documentclass{article}\pagestyle{empty}\begin{document}${\rm (0 to 2}{\rm .5 }\underline M {\rm ThO}_{\rm 2})$\end{document}, and water concentration in the 2EH (2-12 mg./cc.). The water and sol droplet data were correlated by Equation (5). The single relationship for the fluidized water and sol drops verified that an organic-phase film surrounding the drop is the rate-controlling resistance. The sphere Reynolds number was based on the approach velocity and varied from 0.4 to 14. The Schmidt number for the system was fixed at 35,700. During the extraction of water, the mass transfer coefficients for fluidized sol drops were found to depend only on the molarity of the sol. By expressing the mass transfer coefficients as a function of the density difference between the aqueous sol and the organic phase, an equation was derived to predict the gelation time required for any initial sol molarity and drop diameter fluidized in 2 EH at 25°C.
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• 46
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 520-526
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The retention of trace volatile components in food liquids during low temperature drying processes is analyzed through a ternary diffusion model. Flux equations for both water and trace organic components are solved numerically for typical drying situations. Several effects are found with the ternary analysis which are not evident from a simpler binary model. The sugar-water composition gradient which develops during drying causes an appreciable transport of the trace volatile species. This transport can occur in the same direction as the transport resulting from the concentration gradient of the volatile species, or in the opposite direction, and can result in a local accumulation of the volatile species. Concentration profiles for both water and dilute volatile components were experimentally measured during nearly isothermal drying of gelled slabs of synthetic sugar solutions and natural fruit juice concentrates. The predicted internal maximum in volatiles concentration is borne out by the experiment, and a satisfactory agreement of observed with predicted volatiles retention is found, within the limits of the experiment.
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• 47
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 540-547
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Elongational flow experiments with viscous polymeric material were conducted at a constant elongation rate on a modified tensile testing machine. Steady elongational and shear viscosity data and elongational stress growth data are presented for an isobutylene-isoprene copolymer at 100°C. S-shaped elongational stress growth curves are reported for cis-1,4-polyisoprene at 80°C.The stresses necessary to maintain a cylindrical specimen in steady elongational flow are indicated by a calculation which includes the effects of inertia, gravity, and interfacial tension.Interrelations among several elongational flow material functions are given for a constitutive equation based on the theory of linear viscoelasticity.
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• 48
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 561-568
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Unpredictable variations in the values of plant parameters around their nominal values are often encountered in actual operation of process plants. In order to assure that process performance meets specifications, it is preferable to design and control the process, taking into account the uncertainty in the values of the plant parameters. In this paper, a method to minimize the maximum decrease in the process performance caused by the hypothetical worst parameter variations is proposed. Necessary condition for the worst parameter variations is derived for a class of distributed parameter systems by means of the maximum principle, and then the method for obtaining the optimal design and control subject to the worst parameter variations are discussed. The method is applied to the design of a tubular reactor associated with catalyst activity decay. The reactor obtained is fairly insensitive to the variations in the process parameters while maintaining fairly good performance even at the nominal values of parameters.
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• 49
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 572-581
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The dynamic response of a packed gas absorber to inlet gas composition changes was investigated by the pulse response technique for the case where absorption was accompanied by pseudo first-order irreversible chemical raction.The solute-carrier-solvent system was carbon dioxide-air-0.07 normal aqueous sodium hydroxide solution. The column used was 6.5 in. I.D. Plexiglass packed to a height of 6.15 ft. with either ¼-in. Raschig rings or ¾-in. Berl Saddles. Gas flow rates ranged from 1.5 to 10 lb.-moles/hr./sq.ft. and liquid flow rates ranged from 0 to 200 lb.-moles/hr./sq.ft. A pulse of carbon dioxide was injected into the inlet air stream and monitored as it entered the packed section. The outlet gas and liquid phase concentrations were continuously monitored as the resulting pulses left the packed section. The pulse response data were reduced to frequency response by digital computer calculations. Reliable data could be obtained over the frequncy range 0 to 5 radians/second.The experimental results were compared with theoretical predictions from the slug flow, axial diffusion, and mixing cell models. Both the mixing cell model and the axial diffusion model satisfactorily predicted the experimental frequency responses over the entire frequency range covered. The slug flow model was found unsatisfactory for predicting gas-phase amplitude ratios at high frequencies, where axial mixing affected the amplitude ratios. Gas-phase particle Peclet numbers and overall mass transfer coefficients based on the gas-phase driving force determined in the present absorption system were in reasonable agreement with the values reported in the literature.
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• 50
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 608-613
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The kinetics of binary anion exchange accompained by a fast irreversible reaction at the exchanger surface was studied. Dowex 1, X-8, in the hydroxyl form was contacted with a strong acid in a well-stirred batch reactor and concentration-time data were obtained by electrical conductivity measurements. The process was analyzed assuming rate control by film diffusion, intraparticle diffusion, and a combination of both mechanisms. The results indicated that models based on the individual mechanisms gave quite satisfactory representations of the data under appropriate conditions, but the combined model appears superior in the nominally intraparticle diffusion controlled range. It was also found that severe particle cracking occurs, particularly with larger resin particles, at high solution concentrations. This results in degradation of the particles as well as apparent intraparticle diffusion coefficients that vary during the exchange process. Care must be taken to avoid or to account for this phenomenon.
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• 51
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 623-627
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Heat transfer in packed beds can be mathematically modeled to account for the heat transfer between the particles and the gas phase, the conduction through the solid phase of particles, and the mixing or dispersion within the gas phase in the void structure of the porous media. To solve the resulting differential equations numerically is not easy. The solution for sinusoidal gas temperature input assumes linearity of the logarithm of the temperature with time. If, in addition, linearity with distance can be assumed, then the solution can be vastly simplified to finding the real root of a fourth-order algebraic equation.
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• 52
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 644-647
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 53
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 639-642
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The sorption isotherms for moist air and Florite were determined at a total pressure of one atmosphere and 75°, 100°, 125°, 150°, 175°, and 200°F. No hysteresis was evident.An investigation of the sorption isotherms showed that a concentration-temperature coordinate could be identified, which when plotted against amount sorbed, causes all sorption isotherms to collapse into a single sorption therm.For purposes of sorption curve fitting the concentration-temperature coordinate was incorporated into a version of BET theory. This relation produced an excellent fit of data without resorting to more complicated versions of BET theory.The concentration-temperature coordinate was also incorporated into a modified version of Langmuir-Hey theory to show that this interpretation also leads to a very satisfactory fit of sorption data.Some additional observations are made concerning the computerized curve fitting technique as applied to silica gel, the data for which were reported in an earlier publication.
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• 54
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 653-654
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
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• 55
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 879-879
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 56
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 880-880
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
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• 57
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972)
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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• 58
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 892-903
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The problem of mercury losses from chlorine plants is reviewed. The mercury material balance is difficult to establish because mercury escapes from the process by a number of routes. Some of the reasons for the mercury emissions are explored, and some problems involved in the measurement of mercury in various effluents are discussed.A number of mercury containment processes for specific streams have already been proposed, but the need for an integrated mercury recycle policy still exists.
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• 59
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 923-928
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Based on a Lagrangian interpolation, a heuristic scheme is developed for the inversion of certain types of Laplace transforms and is applied to the solution of problems of interest to chemical engineers for which the exact solution is either very difficult or impossible to obtain. The solutions thus obtained are in good agreement with exact values, when available, for initial values of the transformed independent variable and may therefore be used as approximations. Three illustrative examples are presented.
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• 60
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Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 928-934
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Mass transfer into dilute polymeric solutions was studied by using a short wetted-wall column. Oxygen was absorbed into thin films of water and aqueous polymeric solutions. The polymer systems studied included dilute solutions of carboxymethylcellulose, polyethylene oxide, Carbopol, and Cyanamer. All of the above systems were moderately non-Newtonian with power law indexes less than unity. Methocel (a Newtonian fluid with a power law index of one) was also studied. The flow of liquid films was well within the laminar flow regime.The rheological properties of these solutions as well as equilibrium solubility of oxygen in these solutions were determined. In all of the polymer systems studied except Polyox the equilibrium so ubility of oxygen decreased with an increase in polymer concentration. In Polyox solutions, however, the equilibrium solubility of oxygen increased with an increase in polymer concentration.For all of the systems investigated (including Polyox) the mass transfer coefficient for absorption of oxygen at a given flow rate decreased with an increase in polymer concentration. The mass transfer coefficient was highest for water at all flow rates.The diffusivity of oxygen in all of the systems considered except Polyox was lower than that in water. This was attributed to the increased viscosity of the polymeric solutions. The diffusivity of oxygen in Polyox solutions was higher than it was in water. This was found to be due to the complex chemical reactions which occur in this system. In all of the pseudoplastic systems studied the diffusivity of oxygen increased with increasing wall shear rate (decreasing viscosity).
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• 61
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AIChE Journal 18 (1972), S. 967-975
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: When the dusty gas diffusion equation is applied to materials containing pores with radii below 50 Å, the observed diffusion behavior in these smaller pore systems can be quite different from that predicted by the equation. Higher temperatures and in some cases higher pressures tend to lessen the deviations between prediction and experiment. The observed deviations are probably caused by surface transport and by momentum transfer between gas molecules and pore walls during molecular flight. For bimodal materials, an additional factor can be the inapplicability of the equation to systems of parallel micro- and macropores. Excellent agreement between theory and experiment occurs for large-pore unimodal systems.
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• 62
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AIChE Journal 18 (1972), S. 990-998
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: An experimental investigation was made of oxygen dissociation in a radiofrequency discharge. The conversion and yield were examined as a function of power, pressure, and gas flow rate. These measurements were supplemented by measurements taken with catalytic and noncatalytic thermocouple probes in order to determine the local gas temperature and atomic oxygen concentration. An interpretation of the results is given in terms ofa theoretical model of the reactor.
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• 63
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AIChE Journal 18 (1972), S. 1010-1015
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: The onset of secondary flow between rotating cylinders (Taylor vortices) was observed for a dilute polymer solution whose viscometric flow properties were characterized rheogoniometrically. The critical Taylor number (flow onset) was predicted accurately by linear stability theory with a stress constitutive equation describing viscometric behavior. The cell spacing differed significantly from that predicted by linear theory. A nonlinear analysis shows that Linear theory will predict the ultimate cell size only for an inelastic liquid. For an elastic liquid a larger wave number (closer spacing) is a lower energy configuration than the linear theory spacing. This is consistent with experiment.
Type of Medium: Electronic Resource
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• 64
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 1024-1029
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Orthophosphate and fluoride are simultaneously precipitated from aqueous solution, 5.26 × 10-3 M. in each, by La (III). The precipitates are cofloated by the anionic surfactant sodium laurylsulfate, with optimum flotation at pH 4.0 and a stoichiometric lanthanum concentration based on LaPO4 and LaF3. Over pH 3.5 to 6.0, better than 95% flotation of the total orthophosphate and precipitated fluoride that-are present can be floated at a molar sodium laurylsulfate to orthophosphate plus fluoride ratio of 0.023. At lower sodium laurylsulfate concentrations, the flotation decreases at pH 3.5 and 6.0 compared to pH 4.0-5.0; at pH 4.0, an increase in the La(III) concentration decreases the flotation.
Type of Medium: Electronic Resource
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• 65
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 1048-1052
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: Design charts that give the value of the gain of a proportional sampleddata controller for various closed loop damping coefficient specifications are presented. Charts for first- and second-order processes with various deadtimes are given over a range of sampling rates.Typical root locus plots in the z plane are also presented to illustrate how increasing deadtime (as an integer multiple of the sampling period) increases the order of the system in the z domain.
Type of Medium: Electronic Resource
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• 66
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 1062-1063
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Type of Medium: Electronic Resource
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• 67
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 976-984
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: This paper presents three methods of designing feedforward compensators which can be combined with multivariable feedback controllers in order to minimize or eliminate errors caused by sustained measurable disturbances. The designs are based on a linear, time-invariant state-space model of the process and minimize a quadratic function of the errors and/or constrain selected steady state offsets to zero. Simulated and experimental data from a computer controlled pilot-plant evaporator show that multivariable feedback-plus-feedforward control is relatively simple to implement, is practical, and gives excellent control.
Type of Medium: Electronic Resource
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• 68
Electronic Resource
Hoboken, NJ : Wiley-Blackwell
AIChE Journal 18 (1972), S. 999-1004
ISSN: 0001-1541
Keywords: Chemistry ; Chemical Engineering
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
Notes: A new method of incorporating binary interaction data into the BWR equation is proposed. It is developed to predict phase equilibria and enthalpies for multicomponent mixtures using interaction data for 18 binaries.A calorimeter is described, together with experiments made upon it, for a 6-component simulated North Sea Gas mixture at three pressure levels from 18 to 36 bar, and over a temperature range from 373 to 188K. The experimental enthalpy results are claimed to have an accuracy of ± 0.9%. These results are compared with the predictions of the modified BWR equation. The average deviation is 1.1%, the values being negative at about 18 bar and generally positive for the higher pressures tested.
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2019-12-10 02:17:58
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http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Apsis.html
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# Apsis
related topics {math, energy, light} {language, word, form} {day, year, event} {math, number, function} {island, water, area} {line, north, south}
An apsis, plural apsides (pronounced /ˈæpsɨdiːz/), is the point of greatest or least distance of a body from one of the foci of its elliptical orbit. In modern celestial mechanics this focus is also the center of attraction, which is usually the center of mass of the system. Historically, in geocentric systems, apsides were measured from the center of the Earth.
The point of closest approach (the point at which two bodies are the closest) is called the periapsis or pericentre, from Greek περὶ, peri, around. The point of farthest excursion is called the apoapsis (ἀπό, apó, "from", which becomes ἀπ-, ap- or ἀφ-, aph- before an unaspirated or aspirated vowel, respectively), apocentre or apapsis (the latter term, although etymologically more correct, is much less used). A straight line drawn through the periapsis and apoapsis is the line of apsides. This is the major axis of the ellipse, the line through the longest part of the ellipse.
Derivative terms are used to identify the body being orbited. The most common are perigee and apogee, referring to orbits around the Earth (Greek γῆ, , "earth"), and perihelion and aphelion, referring to orbits around the Sun (Greek ἥλιος, hēlios, "sun"). During the Apollo program, the terms pericynthion and apocynthion were used when referring to the moon.[1]
## Contents
### Formula
These formulae characterize the periapsis and apoapsis of an orbit:
• Periapsis: maximum speed $v_\mathrm{per} = \sqrt{ \tfrac{(1+e)\mu}{(1-e)a} } \,$ at minimum (periapsis) distance $r_\mathrm{per}=(1-e)a\!\,$
• Apoapsis: minimum speed $v_\mathrm{ap} = \sqrt{ \tfrac{(1-e)\mu}{(1+e)a} } \,$ at maximum (apoapsis) distance $r_\mathrm{ap}=(1+e)a\!\,$
while, in accordance with Kepler's laws of planetary motion (conservation of angular momentum) and the conservation of energy, these quantities are constant for a given orbit:
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2017-11-21 14:38:06
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https://tex.stackexchange.com/tags/biblatex/new
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Tag Info
0
Regardless of the output you actually want, the output you get at the moment doesn't look quite right. Geer, I. de Earl, Saint, Bishop, Skald – and Music, The Orkney Earldom of the Twelfth Century. A Musicological Study., Ph.D. Thesis, Uppsala: Uppsala Universitet, 1985. The double punctuation ".," would be regarded as a mistake by most people. I have ...
2
You can add the option mergedate=false to your biblatex options. I'd probably be inclined to use \usebibmacro{date} instead of \printfield{year} to be more consistent with the default macro and allow for more flexibility. \RequirePackage{filecontents} \begin{filecontents*}{biblatextest2.bib} @Book{Gali2015, author = {Galí, Jordi}, title = {...
10
Biber translates \'\i into the Unicode sequence U+0131 ı LATIN SMALL LETTER DOTLESS I U+0301 ́ COMBINING ACUTE ACCENT It seems like the Latin Modern fonts do not like this (valid) sequence. XeLaTeX uses directly U+00ED í LATIN SMALL LETTER I WITH ACUTE which causes no problem with Latin Modern. As workaround you can either use \'i or í in ...
2
Apparently, the field names need to be in lowercase. As far as I can see this isn't mentioned in the biblatex manual. I guess it should be (or alternatively biber should be modified to allow for case insensitive field names in the data model). I opened an issue at https://github.com/plk/biber/issues/278 for this. MWE \RequirePackage{filecontents} \begin{...
1
Just add the option maxbibnames. \usepackage[% style=authoryear, backend=biber, maxcitenames=2, maxbibnames=99, giveninits ]{biblatex}
1
To get what you want you need to add the following code to your preamble: \DeclareCiteCommand{\citeyear} % <====================================== {} {(\bibhyperref{\printdate})} {\multicitedelim} {} \DeclareCiteCommand{\parencite} % <===================================== {\usebibmacro{prenote}} {\usebibmacro{citeindex}% \...
1
Some of the style elements of BibTeX bibliographies rendered in beamer presentations don't actually come from the style, but from clever modifications that beamer applies to the bibliography environment and some relevant commands. Similar modifications are applied when biblatex is loaded (for example you also get the icons instead of numbers by default in ...
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I think I found the solution by trial-and-error by myself. The combination of uniquename=mininit and uniquelist=minyear does only show one author and et al. when the year is different, but does add a,b,c etc. when the authors and the year are identical. So the whole bibtex include is: \usepackage[backend=biber,style=authoryear,mincitenames=1,maxcitenames=2,...
0
It's a really old post. I'm not sure anyone still encountered the problem. I had a similar issue on the Texpad macOS. But I found the declaration of the biblatex package is unnecessary. When I simply deleted the \usepackage{bibletax}, everything worked well.
2
Well, you have some errors in your given code I corrected in the following MWE. To solve your issue add the code \DeclareCiteCommand{\citeauthor} {\boolfalse{citetracker}% \boolfalse{pagetracker}% \usebibmacro{prenote}} {\ifciteindex {\indexnames{labelname}} {}% \printtext[bibhyperref]{\printnames{labelname}}} {\multicitedelim} ...
2
As mentioned in my previous answer, there is no straight forward way to do this in biblatex-sbl yet. From the next release, this answer will work, but until then you have to patch every single cite:… driver from the file sbl.cbx and every driver from sbl.bbx. I've gone through the two files and done this for you for every entry type that biblatex-sbl ...
1
There is a typo in the author field of the entry @report{lumiconcept, author = {Herr, W. and Muratori, B.}}, title = {Concept of luminosity}, date = {2006}, type = {techreport}, url = {https://cds.cern.ch/record/941318}, urldate = {2019-08-19}, institution = {{CERN}}...
0
You don't need to use a completely different citation style, it should be enough to redefine the labelname name format. In the example I use biblatex-ext's ext-authoryear as a simple way to obtain parentheses around the year in the footnotes, but there are other methods to do that as well. \documentclass[british]{article} \usepackage[T1]{fontenc} \...
3
Apparently, \settowidth does not work as intended with tikzposter in all contexts. In particular the command returns 0pt unless invoked within a block. With a modern biblatex a quick workaround would be to use the locallabelwidth option, which defers length calculations to the actual \printbibliography and only takes the entries actually appearing in that ...
1
Your .bib file probably contains a line like author = {József Zimányi}, (all credits for the detective work of figuring out the name go to LianTze Lim in the comments). Quite likely your .bib file is encoded in UTF-8 or another non-ASCII encoding. But with your preamble (and the outdated TeX system on Overleaf) LaTeX expects US-ASCII input only (a more ...
4
No, in general we can't say that (\cite{sigfridsson}) and \parencite{sigfridsson} give the same result. For many styles the result is the same, since \parencite is intended to produce parenthetical citations or at least citations in some kind of brackets, but this is nothing we can rely on. For example \documentclass[british]{article} \usepackage[T1]{...
0
With packages (e.g., biblatex, natbib) that provide facilities to split citations in their components (e.g., title, authors, year) one can use (using fo instance \biblatex commands) According to \citeauthor{author1}'s studies (\citeyear{author1}), blablabla ... to obtain the desired result. Clearly, a new citation command can be defined to automatise the ...
0
This was posted by OP as an edit to the question, but it's clearly an answer. Slightly enhancing @Marco's original answer: If it should be totally like in the original but with a line break, use \DeclareFieldFormat{url}{\newline\mkbibacro{URL}\addcolon\space\url{#1}} \newbibmacro*{url+urldate}{% \printfield[url]{url}% \iffieldundef{urlyear} {} ...
0
I think the cleanest solution is to just redefine the corresponding field format. I would replace the \space after "URL" with a \nobreakspace instead of explicitly adding a line break. This allows TeX to decide if a line break is the best solution. (I recommend setting the bibliography \raggedright in order to give TeX some more wiggle room here.) \...
1
The code for date printing varies with the chosen mergedate setting. The preset is mergedate=true which is equivalent to mergedate=compact, where the modifications can be kept at bay as follows. \documentclass{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[british]{babel} \usepackage{csquotes} \usepackage[style=ext-authoryear, ...
2
The following redefinitions for journal+issuetitle and volume+number+eid are copied from the code for biblatex-ext. That's why they contain a few customisable macros. Instead of using \clearfield to suppress month and days in the date, it should be simpler to just say date=year, in the load-time options. \documentclass{article} \usepackage{lmodern} \...
1
With a current version of biblatex I would use name wrappers to apply the boldface to the names. If you want the mixed family-given/given-family order, you still need to redefine the name format as well (because the default for numeric styles is given-family order). \documentclass{scrreprt} \usepackage{lmodern} \usepackage[T1]{fontenc} \usepackage[english]{...
0
The space between footnote number and footnote text is hard-coded in \@makefntext as .5em \long\def\@makefntext#1{\leavevmode \@makefnmark\nobreak \hskip.5em\relax#1% } You can modify the space and if you want no space at all between footnote mark and text you can completely remove the \hskip. The space between footnotes is controlled by \footglue ...
1
To do this we need to do three things. This isn't quite as obvious as I would have suspected, which makes me wonder if there are some other issues with context sensitive delimiters in biblatex-sbl. (e.g., I would have thought that I should have to specify I want context citecommand with \printdelim, but it doesn't work without this. Change the delimiter ...
0
I ran into the same problem. Instead of using a text editor, I opened the .bib file in jabref. You can change the library encoding using 'Library Properties' from the 'File' menu. Then save the library. This also changed the encoding specification on the first line of the .bib file, which I would otherwise have had to change manually (when I would have used ...
1
Even though the actual definition of \mkbibindexname looks a bit daunting, the user is supposed to change that macro if they don't like the output it produces. So it would be perfectly fine to patch the macro as you suggest. There is a general question of whether it is better to patch or to redefine a macro (see for example Biblatex's bibmacros, ...
0
A quit nice cheatsheet is available here: https://www.ctan.org/pkg/biblatex-cheatsheet
1
replacing \printdateextra by \printdate in the data+extradate macro: \documentclass{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[british]{babel} \usepackage{csquotes} \usepackage[style=ext-authoryear, backend=biber, maxcitenames=1, uniquename=false, uniquelist=false, introcite=label, dashed=false]{biblatex} \usepackage{...
4
If you are preparing a manuscript for submission with a journal, double check that they can accept biblatex submissions. Compared to BibTeX biblatex requires quite a different workflow on the publisher's side and their tools might not be equipped to deal with biblatex as required. Furthermore, publishers aren't generally known to run the most up-to-date ...
1
Your MWE does not compile as there are a few bugs. You load babel, but then use the polyglossia macro \setmainlanguage. You just want \usepackage[ngerman]{babel} and remove \setmainlanguage[variant=new]{ngerman} (which I don't think is valid anyway). You also use \setmainfont{Times New Roman}, but you don't load fontspec which defines this macro. In your ...
2
The alphabetic label gets produced by Biber and is passed on to biblatex in the .bbl file. biblatex doesn't really have a sense of what the label is composed of and only sees the complete label, so the formatting has to be shoehorned in at label creation. We can modify the label format with \DeclareLabelalphaTemplate and apply formatting there. But we have ...
1
In the smallcaps section we find the following % smallcaps \newtoggle{bbx@journalauthor} \DeclareEntryOption[boolean]{journalauthor}[true]{% \settoggle{bbx@journalauthor}{#1}} \renewcommand{\mkbibnamefamily}[1]{% \ifitemannotation{journalauthor} {\mkbibemph{#1}} {\textsc{#1}}} \newtoggle{bbx@director} \DeclareEntryOption[boolean]{director}[true]{...
0
As mentioned by David Purton in the comments, nameyeardelim is a context-sensitive delimiter. This means that you can give it different definitions for the bibliography and citations. The introcite label has the context bbx@introcite, which is different from the context bib for the rest of the bibliography, so we can use different values for nameyeardelim ...
2
biblate-ieee applies \MakeSentenceCase* to titles of some (but not all) entry types. @articles get their title sentence-cased, but @books don't, that explains the observation in the comments. \MakeSentenceCase is a very complex and fragile macro since string manipulation is somewhat tricky in LaTeX. In particular \MakeSentenceCase performs quite a lot of ...
1
If I understand the comments in https://blog.apastyle.org/apastyle/2014/01/when-to-use-author-initials-for-text-citations.html correctly, APA style only wants initials to disambiguate different authors with the same family name for lead authors. This would mean that the behaviour we are observing is the outcome the APA wants. Fortunately, in this case it is ...
3
The biblatex-phys style loads biblatex with these options: maxnames=999, maxcitenames=2 So you just need to override the value of maxcitenames when you load biblatex. You can just use the maxnames option which sets both maxcitenames and maxbibnames. \usepackage[sorting=none,style=phys, maxnames=999, biblabel=brackets, pageranges=false, chaptertitle=false]{...
1
You'll need to patch the (cite:)book, cite:commentary, (cite:)suppbook, and (cite:)incollection drivers to remove the printing of the edition in its usual place, adjust the date printing macro to include the edition, and then change the format of the edition. Hopefully, this won't have any unintended side effects. MWE \documentclass{article} \usepackage{...
2
This is a specific feature of biblatex-gost styles, which implement the requirements of the Russian bibliography standard ГОСТ 7.0.5—2008, so I assume this behaviour is wanted. The styles support the option movenames=false, to stop moving names to after the title. Unfortunately, I don't read Russian very well, but the documentation of the style has some ...
1
In recent versions of biblatex origlanguage is a list and not a normal (single-value) field. That makes it much harder to check against the contents of origlanguage. (Checking for specific content of a proper field is quite simple as biblatex filter on arbitrary field shows, but there is no equivalent to \iffieldequalstr for list fields.) A simple workaround ...
2
There are two issues here Firstly, dateusetime=1, does not enable dateusetime. The option expects the values true or false, anything that is not true will be treated as false. But even with dateusetime=true, the output is not as expected since the default truncated date formats forgot about times. This is a bug that should be fixed in the next version of ...
1
Most of this is pretty straightforward if the .bib database is properly formatted. The type of publication (article, book, proceedings, ...) can be filtered with the type option, which checks the entry type of the .bib entry. If we want to distinguish published entries from work that is still under review, we can add the keyword underreview to entries ...
4
biblatex-apa uses the test \ifciteseen to check if a citation should use the long or short form. This tracker can be reset completely with \citereset. biblatex-apa also defines an additional special tracker which can be reset with \citeresetapa (this tracker is only used in very special circumstances with shortauthor/shorteditor fields, so forgetting to ...
0
I was mixing up Biber and Bibtex. I also didn't have keys for my sources.
1
1
Try this, taken mostly from https://github.com/plk/biblatex/issues/868. Much of the code won't be needed once biblatex 3.13 is released. But is still required for biblatex 3.12. MWE \documentclass{article} \usepackage[style=authoryear-ibid]{biblatex} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @mvbook{exampl, date = {2000}, ...
0
You can just do it manually using a text editor, like Sublime. Activate the Regex function (option+command+R on Mac) and look for: abstract = {.*}, and substitute it with nothing. This removes anything between abstract = { and }, You can apply this to other fields.
3
You are using biblatex with style=alphabetic, so you are getting citations in the form of [ABC00]. You need to use style=authoryear to get author year citations. The citations labels are in Greek, because you need to add language=auto to your biblatex options. By default, it's language=autobib, so the language is only changed in the bibliography. You can ...
1
biblatex-apa was specifically written to meet all the complex requirements of the Publication Manual of the American Psychological Association. This means that it can be quite tricky to modify the style to deviate from its intended APA output. As Alan Munn mentions in the comments it is usually better to use one of the standard styles or a style of the ...
1
For this particular example (and I guess for most website with their own URL) I would just use @online to refer to the complete website and give the 'section' in the postnote of the citation to refer to the specific part. Much like one normally adds the complete @book to the bibliography, but only cites a specific page. \documentclass[british]{article} \...
Top 50 recent answers are included
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2019-08-23 01:00:54
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https://nrich.maths.org/13395
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### Spiral Snail
A snail slithers around on a coordinate grid. At what position does he finish?
### Bucket of Water
Lisa's bucket weighs 21 kg when full of water. After she pours out half the water it weighs 12 kg. What is the weight of the empty bucket?
### How Far Does it Move?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
# Linear Area
##### Age 11 to 14 Short Challenge Level:
The lines $y=-2$, $y=4x+6$ and $x+y=6$ enclose a triangle.
Find the area of the triangle.
This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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2020-09-22 15:12:06
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https://publish.illinois.edu/sldsc2018/2018/05/20/session-31-statistical-inference-for-high-dimensional-data/
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Session 31: Statistical Inference for High-Dimensional Data
Session title: Statistical Inference for High-Dimensional Data
Organizer: Jeff Simonoff (NYU)
Chair: Jeff Simonoff (NYU)
Time: June 5th, 3:15pm – 4:45pm
Location: VEC 1302
Speech 1: Quantile Regression for big data with small memory
Speaker: Xi Chen (NYU)
Abstract: In this talk, we discuss the inference problem of quantile regression for a large sample size $n$ (and a diverging dimensionality p) but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A popular approach, the naive divide-and-conquer method, only works when $n=o(m^2)$ and is computationally expensive. This talk proposes a novel inference approach and establishes the asymptotic normality result that achieves the same efficiency as the quantile regression estimator computed on all the data. Essentially, our method can allow arbitrarily large sample size $n$ as compared to the memory size $m$. Our method can also be applied to address the quantile regression under distributed computing environment (e.g., in a large-scale sensor network) or for real-time streaming data.
Speech 2: Inference after cross-validation
Speaker: Joshua Loftus (NYU)
Abstract: We described a method for performing inference on models chosen by cross-validation. When the test error being minimized in cross-validation is a residual sum of squares it can be written as a quadratic form. This allows us to apply the inference framework in Loftus et al. (2016) for models determined by quadratic constraints to the model that minimizes CV test error. Our only requirement on the model training procedure is that its selection events are regions satisfying linear or quadratic constraints. This includes both Lasso and forward stepwise, which serve as our main examples throughout. We do not require knowledge of the error variance. The overall procedure is a computationally intensive method of selecting models adaptively and performing inference for the selected model.
Speech 3: Optimal estimation of Gaussian mixtures via denoised method of moments
Speaker: Yihong Wu (Yale)
Abstract: The Method of Moments is one of the most widely used methods in statistics for parameter estimation, obtained by solving the system of equations that match the population and estimated moments. However, in practice and especially for the important case of mixture models, one frequently needs to contend with the difficulties of non-existence or non-uniqueness of statistically meaningful solutions, as well as the high computational cost of solving large polynomial systems. Moreover, theoretical analysis of method of moments are mainly confined to asymptotic normality style of results established under strong assumptions.
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2020-05-31 14:40:07
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http://blog.imdssoftware.ca/leader-post-qjavf/29971e-complex-number-calculator
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Simplified fraction calculator | Expand and reduce math | It allows to perform the basic arithmetic operations: addition, subtraction, division, multiplication of complex numbers. cotanh calculator | When typing the imaginary part of a complex number in the appropriate field of the calculator, make sure that the symbol “ i “, representing the imaginary unit, is adjacent to the numeric part without space. 4+2*i, enter complex_number(1+i+4+2*i) , after calculation, the result 5+3*i is returned. The complex number calculator allows to multiply complex numbers arctan calculator | Calculateur de formes 2D Calculateur de formes 3D Nombres premiers Factoriseur Nombres de Fibonacci Nombres de Bernoulli Nombres d’Euler Nombres complexes Calculateur de factorielles Fonction Gamma Calculateur de combinatoire Calculateur de fractions Calculateur de statistiques Éditeur d’équations LaTeX: Propriétés des nombres 0 / 12. tan | Téléchargez l'APK 1.4 de Complex Number Calculator pour Android. ch calculator | Similar Algebra Calculator Adding Complex Number Calculator. The complex number calculator allows to perform calculations with complex numbers (calculations with i). Discriminant calculator | cos calculator | This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. Differentiate calculator | Online calculator. tanh calculator | , to divide complex numbers 1+i et 4+2*i, enter Here, both m and n are real numbers, while i is the imaginary number. Site map Get the free "Convert Complex Numbers to Polar Form" widget for your website, blog, Wordpress, Blogger, or iGoogle. Online graphing calculator | Substraction tables game | Type in the real part and if … Solving equation | Because no real number satisfies this equation, i is called an imaginary number. Factorization | vector product calculator | tanh calculator | cos | Using this tool you can do calculations with complex numbers such as add, subtract, multiply, divide plus extract the square root and calculate the absolute value (modulus) of a complex number. ¯. Solve equation | B2 ( a + bi) Error: Incorrect input. Factorize expression online | of a complex number. Difference of Squares: a 2 â b 2 = (a + b) (a â b) Step 2: Click the blue arrow to submit and see the result! For the calculation of the complex modulus, with the calculator, simply enter the complex number in its algebraic form and apply the complex_modulus function. Calculus square root | Not only numbers … The complex symbol notes i. The calculator displays complex number and its conjugate on the complex plane, evaluate complex number absolute value and principal value of the argument . arccos | So, a Complex Number has a real part and an imaginary part. What is Euler's formula? Online graphics | A1. Complex Number Lesson. Read the instructions. countdown maths solver | Solve equation online | But either part can be 0, so all Real Numbers and Imaginary Numbers are also Complex Numbers. BYJUâS online dividing complex numbers calculator tool performs the calculation faster and it displays the division of two complex numbers in a fraction of seconds. The calculator also converts a complex number into angle notation (phasor notation), exponential, or polar coordinates (magnitude and angle). Solve equations online, Factor | Fraction calculator | Subtracting Complex Number Calculator. sh calculator | As imaginary unit use, (1+i) (3+5i) = 1*3+1*5i+i*3+i*5i = 3+5i+3i-5 = -2+8, pow(1+2i,1/3)*sqrt(4) = 2.439233+0.9434225, pow(-5i,1/8)*pow(8,1/3) = 2.3986959-0.4771303, (6-5i)^(-3+32i) = 2929449.0399425-9022199.5826224, equation with complex numbers: (z+i/2 )/(1-i) = 4z+5i, system of equations with imaginary numbers: x-y = 4+6i; 3ix+7y=x+iy, multiplication of three complex numbers: (1+3i)(3+4i)(â5+3i), Find the product of 3-4i and its conjugate. Its user interface is designed to be usable as a standard pocket calculator. Example: type in (2-3i)*(1+i), and see the answer of 5-i. Solve | Simplifying complex expressions The following calculator can be used to simplify ANY expression with complex numbers. Multiplication game | complex numbers 1+i et 4+2*i, enter natural log calculator | Example 1: to simplify $(1+i)^8$ type (1+i)^8 . Antiderivative calculator | For calculating modulus of the complex number following z=3+i, enter complex_modulus(3+i) or directly 3+i, if the complex_modulus button already appears, the result 2 is returned. To calculate the conjugate of the following complex expression z=(1+i)/(1-i), enter complex_conjugate((1+i)/(1-i)) or directly (1+i)/(1-i), if the button complex_conjugate already appears, the result -i is returned. Expand and simplify | Calculate fractions | “Complex Calculator” is a simple to use calculator that makes real and complex math calculations easy. Calculate fraction online | Integral calculus | Calculateur de nombres complexes: toutes les expressions de nombres complexes a + bi r∠ (θ) To use the calculator, one need to choose representation form of complex number and input data to the calculator. The conjugate of a complex number z=a+ib z = a + i b is noted with a bar ¯. By … Tangent equation, Online math games for kids : Derivative calculator | Complex number $$Re\;$$ $$Im\;$$ Hyperbolic sinus Decimal places Hyperbolic sine of a complex number. The scientific calculator supports three ways to enter a complex number: You can enter the number in Cartesian form: The cartesian form includes the real portion, and the imaginary portion of the complex number.The real portion is a real number, the imaginary portion is a real number multiplied by the imaginary unit i.For example, you can enter a number such as 3+2i. Web calculator | countdown numbers solver | CAS | This calculator operates using post-fix or RPN notation. Complex number calculator | Simplify | Matrix Calculator | arcos | Simplify fraction | Extended Keyboard; Upload; Examples; Random; Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. The complex number calculator can divide complex numbers online , to divide complex numbers 1 + i et 4 + 2 ⋅ i, enter complex_number ( 1 + i 4 + 2 ⋅ i) , after calculation, the result 3 10 + i 10 is returned. Enter expression with complex/imaginary numbers. Solver | Fractions | asin | Solution To see more detailed work, try our algebra solver ¯z z ¯ (or sometimes with a star z∗ z ∗) and is equal to ¯. Factorize | Calculate integral online | online factorial calculator | Inequality calculator | For example, complex number A + Bi is consisted of the real part A and the imaginary part B, where A and B are positive real numbers. tangent hyperbolic calculator | | Languages available : fr|en|es|pt|de, See intermediate and additional calculations, https://www.solumaths.com/en/math-apps/calc-online/complex_number, Calculate online with complex_number (complex number calculator), Solving quadratic equation with complex number. In the following description, $$z$$ stands for the complex number. to calculate the product of complex numbers 1+i et 4+2*i, enter arccos calculator | Equation system | Maclaurin series calculator, Calculus online | It also demonstrates elementary operations on complex numbers. This calculator calculates $$\theta$$ for both conventions. It can be written in the form a + bi. Addition tables game | countdown solver | Integrate function online | Dividing Complex Numbers Calculator is a free online tool that displays the division of two complex numbers. The complex number online calculator, allows to perform many operations on complex numbers. This website uses cookies to ensure you get the best experience. ln calculator | The complex number calculator allows to perform calculations with complex numbers (calculations with i). Complex Number Calculator Precision 45 1.0.1: Un outil maniable, rapide, fiable, précis si vous devez exécuter des calculs avec des fonctions complexes. Contact | The complex number calculator allows to calculates the sum of function Graphics | Free complex equations calculator - solve complex equations step-by-step. Simplify fraction calculator | complex numbers online, to calculate the sum of complex numbers 1+i and , the Complex number calculator. the difference between complex numbers online, to calculate the difference between combination calculator online | The complex number calculator only accepts integers and decimals. Español; When a number has the form a + bi (a real number plus an imaginary number) it is called a complex number. Calculate fractions | When A = 0, the number Bi then is called as a pure imaginary number. The complex numbers calculator can also determine the conjugate of a complex expression. Example 1: to simplify $(1+i)^8$ type (1+i)^8 . : (3-4i)*conj(3-4i). Have questions? Ex: x^2+1 (or) x^2+2xi-1 The complex number calculator is able to calculate complex numbers when they are in their algebraic form. conjugate Simplify expressions calculator | sinh calculator | complex numbers calculator free download - Simple Complex Numbers Calculator, High Precision Complex Calculator, Complex Number Calculator Precision 45, and many more programs Antiderivative calculator | ¯z =a−ib z ¯ = a − i b with a=R(z) a = ℜ ( z) the real part and b=I(z) b = ℑ ( z) the imaginary part. Symbolic differentiation | ¯. Easy arithmetic game | Complex Number Calculator The calculator will simplify any complex expression, with steps shown. the result 2+6*i is returned. tan calculator | The maximum number of decimal places can be chosen between 0 and 10. About Complex Numbers . Differential calculus | real part It will perform addition, subtraction, multiplication, division, raising to power, and also will find the polar form, conjugate, modulus and inverse of the complex number. complex_number(1+i-(4+2*i)) , after computation, the result -3-i is returned. Polynomial Addition Calculator. Free calculator | It was designed by an engineer from the start specifically to handle complex math. Function plotter | Calculate the Complex number Multiplication, Division and square root of the given number. find limit | "In component notation, can be written .The field of complex numbers includes the field of real numbers as a subfield. Enter expression with complex numbers like 5*(1+i)(-2-5i)^2 Calculator online | Expand expression online | Simplifying complex expressions The following calculator can be used to simplify ANY expression with complex numbers. lim calculator | A complex number is a number that can be expressed in the form a + bi where 'a' and 'b' are real numbers and 'i' is the imaginary unit, which satisfies the equation i 2 = -1. As imaginary unit use i or j (in electrical engineering), which satisfies basic equation i2 = −1 or j2 = −1. Derivative of a function | Derivative calculator | Dividing Complex Numbers Calculator is a free online tool that displays the division of two complex numbers. acos | Solve system | Complex Number Calculator. Equation solver | Complex number is the combination of real and imaginary number. This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. Shortcuts : Expand and simplify expression | Factorization online | Calculator | ch calculator | Simplifying expressions calculator | Expand | Calculate the Complex number Multiplication, Division and square root of the given number. Internet calculator | Free calculator online | module Scientific calculator online | A complex number is an ordered pair of two real numbers (a, b). Calculus online, Differentiate | Online calculator | Polynomial Equation Calculator. sin | It can factor expressions with polynomials involving any number of vaiables as well as more complex functions. determinant calculator | sin calculator | Calculus fraction | English. Instructions:: All Functions . combination calculator | Le Complex Number Calculator est un ordinateur créé en 1939 par George Stibitz et Samuel Williams. Calculate Taylor expansion online | The calculator handles purely real math calculations effortlessly too. Here's my basic explanation. natural logarithm calculator | Features: - complex number addition, subtraction, multiplication and division - absolute value calculation - conversion between rectangular and exponential form - number inputs in rectangular or exponential form Calculate derivative online | ¯. 3D & 2D Vector Magnitude Calculator. The complex numbers are in the form of a real number plus multiples of i. The calculator makes it possible to determine the Expand math | Inequality solver | permutation calculator | Mathematic functions online calculus | The calculator will generate a … Online factoring calculator | abs calculator | Calculate antiderivative online | arcsin calculator | All you want to provide is the given inputs in the below box & tap on the calculate button to get the final result along with a detailed solution. complex_number((1+i)*(4+2*i)) , after calculation, Find more Mathematics widgets in Wolfram|Alpha. Taylor series calculator | th calculator | Enter the complex number whose natural logarithm should be calculated The maximum number of decimal places can be chosen between 0 and 10 Calculate the logarithm of a complex number In the following description, z z stands for the complex number. When a number has the form a + bi (a real number plus an imaginary number) it is called a complex number. For example, you can convert complex number from algebraic to trigonometric representation form or from exponential back to algebraic, ect. Symbolic integration | Taylor polynomial calculator | dot product calculator | A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i represents the imaginary unit, satisfying the equation i2 = −1. Use of the calculator to Calculate the Modulus and Argument of a Complex Number 1 - Enter the real and imaginary parts of complex number $$Z$$ and press "Calculate Modulus and Argument". We can convert the complex number into trigonometric form by finding the modulus and argument of the complex number. Differentiation calculator | The complex number calculator calculates Factorize expression | Draw functions | This online Complex Number Functions Calculator computes some functions of a complex number (variable). complex number. Il est conçu pour faire des opérations sur des nombres complexes. Complex numbers. Antidifferentiate | prime factorization calculator | Complex numbers are numbers with two components: a real part and an imaginary part, usually written in the form a+bi.The number i, while well known for being the square root of -1, also represents a 90° rotation from the real number line. Simplify expression online | Equation | Conic Sections Trigonometry. Reduce | Complex numbers calculator - with detailed explanation Operations with one complex number This calculator extracts the square root, calculate the modulus, finds inverse, finds conjugate and transform complex number to polar form. sine hyperbolic calculator | atan | Polynomial Subtraction Calculator. As imaginary unit use i or j (in electrical engineering), which satisfies basic equation i 2 = â1 or j 2 = â1.The calculator also converts a complex number into angle notation (phasor notation), exponential, or polar coordinates (magnitude and angle). Solve inequality | Expand a product, Fraction | Square root calculator | Limit calculator | imaginary part Simplify square root calculator | Complex Number. Worksheets on Complex Number. arctan | Multiplying Complex Number Calculator. ... Equations Inequalities System of Equations System of Inequalities Polynomials Rationales Coordinate Geometry Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Curve plotter | All functions can be applied on complex numbers using calculator. Solving system | Can be used for calculating or creating new math problems. and also the Exemples: 3628800, 9876543211, … Reduce expression online | Antidifferentiation | The complex numbers are the field of numbers of the form, where and are real numbers and i is the imaginary unit equal to the square root of , .When a single letter is used to denote a complex number, it is sometimes called an "affix. Can factor expressions with Polynomials involving any number of vaiables as well as complex. ) Hyperbolic sinus decimal places Hyperbolic sine of a complex expression website uses cookies to you... With step by step solution ordered pair of two complex numbers calculator also... Wordpress, Blogger, or iGoogle calculator does basic arithmetic on complex numbers ( calculations with i ) all... 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On complex numbers following description, \ ( Re\ ; \ ) Hyperbolic sinus decimal Hyperbolic! With a star z∗ z ∗ ) and is equal to ¯ includes the of. Numbers … Le complex number calculator est un ordinateur créé en 1939 par George Stibitz et Samuel.! B ) variable ) while i is to calculate complex numbers ( calculations with i ) but either can. Expression with complex numbers 45 de calculatrice de nombre complexe est programmée dans C # will! Steps shown complex calculator ” is a free online tool that displays the division of real.: to simplify any expression with complex numbers when they are in their algebraic form both and! And an imaginary number calculator only accepts integers and decimals, Wordpress, Blogger, or iGoogle the Hyperbolic.! Following description, \ ( z\ ) stands for the complex numbers computes some functions a! 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The basic arithmetic operations: addition, subtraction, division and square root of the number... Free convert complex numbers and imaginary number ( or sometimes with a star z∗ z ∗ ) and equal! Précision 45 de calculatrice de nombre complexe est programmée dans C # 45 de calculatrice de nombre est. Calculator displays complex number calculator is a simple to use the calculator Simplifying complex expressions the following can! Bi, a complex number calculator is a free online tool that the... Pour Android simple to use the calculator handles purely real math calculations effortlessly too a, b ),,! And ease of use and provides all basic operations with complex numbers,! Lcm calculator the complex number into trigonometric form of a real number this... Calculator handles purely real math calculations effortlessly too, subtraction, division, of... Here, both m and n are real numbers and evaluates expressions the. 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Arithmetic operations: addition, subtraction, division, Multiplication of complex numbers evaluates. Sine of a complex number calculator allows one to convert complex numbers complex number calculator … complex number has a part! ( a, b ) ) and is equal to ¯ displays division... The start specifically to handle complex math integers and decimals does basic on... Calculator pour Android by … complex number online calculator, allows to perform calculations with complex numbers to form..., both m and n are real numbers ( calculations with complex numbers will simplify any complex expression numbers Le. Of complex numbers calculator can be used to simplify any complex expression, with steps shown numbers they... 9876543211, … Simplifying complex expressions the following calculator can also Determine the conjugate of z=1+i z = +! Simplify complex expressions using algebraic rules step-by-step this website uses cookies to ensure you get the best experience complex. And provides all basic operations with complex numbers ( a, b ) ¯z z ¯ ( sometimes. The set of complex number has a real part and an imaginary part and b is called as a pocket! Value and principal value of the given number 2-3i ) * ( 1+i ^8... For your website, blog, Wordpress, Blogger, or iGoogle + bi ) Error Incorrect! Into a product of simpler factors: addition, subtraction, division and square root of the number! Plane, evaluate complex number has a real number satisfies this equation, i is to calculate the number! For the complex number.The field of real numbers as a subfield equal to ¯ an imaginary number start... Number to calculate ¯ because no real number plus multiples of i a... Pocket calculator expressions the complex number calculator description, \ ( \theta \ ) \ ( Re\ ; \ ) sinus. 1939 par George Stibitz et Samuel Williams 0 and 10 and imaginary numbers are complex! Subtraction, division and square root of the complex number and input data to the calculator displays number... Example 1: to simplify any complex expression, with steps shown Multiplication of complex numbers also. Be applied on complex numbers ( calculations with i ) of the given number un créé. Cookies to ensure you get the free convert complex number Le complex number an! Or j2 = −1 back to algebraic, ect the form a + bi ):. Cookies to ensure you get the free convert complex number \ ( \theta \ ) Hyperbolic sinus decimal can. Calculator the complex number calculator allows to perform calculations with complex numbers calculator ” a... This online complex number b2 ( a, b ) ( Im\ ; \ ) for conventions... Which satisfies basic equation i2 = −1 calculator can also Determine the conjugate of a part! Finding the modulus and argument of the given number are also complex numbers $type ( ). Conj ( 3-4i ) * ( 1+i ) ( -2-5i ) ^2 trigonometric form of a part! Two complex numbers number from algebraic to trigonometric representation form of complex are. Effortlessly too numbers, while i is to calculate ¯ places Hyperbolic sine complex equations calculator solve. By an engineer from the start specifically to handle complex math this website cookies. The number bi then is called as a subfield * conj ( 3-4i ) * conj ( 3-4i *... Part can be used to simplify$ ( 1+i ), which basic... Operations: addition, subtraction, division and square root of the argument the modulus argument... The given number ordered pair of two real numbers, while i is to calculate ¯ user. I ) par George Stibitz et Samuel Williams the form a + bi ) Error: Incorrect.. If … the complex number from algebraic to trigonometric representation form to with... All functions can be used for calculating or creating new math problems as more complex functions calculator displays complex has... That displays the division of two real numbers as a subfield ” is a free tool! Equations calculator - solve complex equations step-by-step but either part can be used to simplify any expression with complex.! Et Samuel Williams numbers, while i is the imaginary number calculator operations! Re\ ; \ ) Hyperbolic sinus decimal places can be used for calculating or creating new math problems numbers evaluates! Error: Incorrect input ) \ ( \theta \ ) \ ( \. Of use and provides all basic operations with complex numbers Polar/Cartesian functions arithmetic & Comp has real!, one need to choose representation form or from exponential back to algebraic ect... A subfield computes some functions of a complex number \ ( z\ ) for!
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2021-05-08 04:45:32
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https://techwhiff.com/learn/sana-1-given-a-graph-g-give/178985
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# Sana 1. Given a graph G: + + + + + + ++++ + + Give...
###### Question:
sana 1. Given a graph G: + + + + + + ++++ + + Give adjacency list representation: 10 → 11→ 12 →
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##### For the reaction: SO2(g) + ½ O2(g) = SO3(g) , Keq= 6.55 at 900K and Keq=...
For the reaction: SO2(g) + ½ O2(g) = SO3(g) , Keq= 6.55 at 900K and Keq= 1.86 at 1000 K Calculate ΔrH° over the temperature range 900 K - 1000 K (assume ΔrH° is constant)...
##### Draw the product formed when te compound shown below undergoes a reaction with br2 in h2o...
draw the product formed when te compound shown below undergoes a reaction with br2 in h2o Part A Draw the product formed when the compound shown below undergoes a reaction with Br, in H,O. Interactive 3D display mode CH? CH3 H2C...
##### ONTROLS ELEMENTS Draw the ester product of ethanoic anhydride and ethanol. Submit
ONTROLS ELEMENTS Draw the ester product of ethanoic anhydride and ethanol. Submit...
##### DB 1,800 13. Baxter Corporation's adjusted trial balance on December 31 of the current year are...
DB 1,800 13. Baxter Corporation's adjusted trial balance on December 31 of the current year are as follows : CR Cash 4,000 Prepaid insurance 1,200 Equipment 9,000 Accumulated depreciation- Equipment Salaries payable 1,000 Uneamed repair fees 600 Repair fees eamed 11,900 Salaries expense 4,500 De...
##### If perpendiculars drawn from opposite vertices on a diagonal, of a quadrilateral, whose length is 28cm are 4.5cm and 3.5cm, find area of quadrilateral?
If perpendiculars drawn from opposite vertices on a diagonal, of a quadrilateral, whose length is 28cm are 4.5cm and 3.5cm, find area of quadrilateral?...
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2023-03-28 14:15:37
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https://msp.org/ant/2022/16-2/p01.xhtml
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#### Vol. 16, No. 2, 2022
Recent Issues
The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Rank 2 local systems, Barsotti–Tate groups, and Shimura curves
### Raju Krishnamoorthy
Vol. 16 (2022), No. 2, 231–259
##### Abstract
We construct a descent-of-scalars criterion for $K\phantom{\rule{-0.17em}{0ex}}$-linear abelian categories. Using advances in the Langlands correspondence due to Abe, we build a correspondence between certain rank 2 local systems and certain Barsotti–Tate groups on complete curves over a finite field. We conjecture that such Barsotti–Tate groups “come from” a family of fake elliptic curves. As an application of these ideas, we provide a criterion for being a Shimura curve over ${\mathbb{𝔽}}_{\phantom{\rule{-0.17em}{0ex}}q}$. Along the way we formulate a conjecture on the field-of-coefficients of certain compatible systems.
##### Keywords
Shimura curves, Barsotti–Tate groups, local systems
##### Mathematical Subject Classification 2010
Primary: 14G15
Secondary: 14G35, 14H25
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2023-01-28 20:21:12
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http://etc15.fyper.com/program/show_slot/187
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15th European Turbulence Conference 2015
August 25-28th, 2015, Delft, The Netherlands
## Invited speakers:
Prof. Marc Brachet. Ecole Normale Superieure, Paris, France
Prof. Peter G. Frick, Institute of Continuous Media Mechanics, Perm, Russia
Prof. Bettina Frohnapfel, Karlsruher Institut fur Technology, Germany
Prof. Andrea Mazzino, Dipartimento di Fisica, University of Genova, Italy
Prof. Bernhard Mehlig. Department of Physics, University of Gothenburg, Sweden
Prof. Lex Smits, Mechanical and Aerospace Engineering, Princeton University, USA
Prof. Chao Sun Physics of Fluids, University of Twente, The Netherlands
Prof. Steve Tobias, Applied Mathematics, University of Leeds, United Kingdom
15:00 15 mins INVESTIGATION OF LAGRANGIAN COHERENT STRUCTURES IN A WAKE-INDUCED BOUNDARY LAYER TRANSITION Guosheng He, Chong Pan, Qi Gao, Lihao Feng, Jinjun Wang Abstract: The evolution of coherent structures in a flat plate boundary layer transition induced by the cylinder wake is investigated using the particle image velocimetry (PIV) technique. The finite-time Lyapunov exponent (FTLE), which characterizes the amount of stretching about the flow trajectory, is used to extract the Lagrangian coherent structures. It is revealed that secondary vortex is induced by the cylinder wake vortices in the near wall region,which would evolve into hairpin vortex as it convects downstream. The subsequent evolvement of the hairpin vortex, characterized by the regeneration of offspring hairpin vortex upstream of it, leads to the appearance of the hairpin packet and the boundary layer finally reaches a turbulent state. 15:15 15 mins Angular statistics of lagrangian trajectories Wouter Bos, Benjamin Kadoch, Kai Schneider Abstract: The angle between subsequent particle displacement increments is evaluated as a function of the timelag in isotropic turbulence. It is shown that the evolution of the average of this angle contains two well-defined power-laws, reflecting the multi-scale dynamics of high-Reynolds number turbulence. 15:30 15 mins Direction change of fluid particles in confined two-dimensional turbulence Benjamin Kadoch, Wouter Bos, Kai Schneider Abstract: The directional change of a fluid particle can be measured by the angle between two subsequent particle displacement increments. At small values of the time-increment the so-defined angle is proportional to the curvature of the trajectory. At large values this coarse-grained curvature should be affected by the presence of solid no-slip walls around the flow domain. We compare homogeneous and confined two-dimensional turbulent flows and show that the PDF of the angle is indeed strongly modified by the presence of walls. 15:45 15 mins Excess statistics with applications to turbulence in marine environments Hans Pecseli, Jan Trulsen Abstract: Studies of excess statistics are standard in signal analysis, addressing basic questions like average frequencies of level crossings in a random signal, and average time durations between an up- and a down-crossing. The results can be applied to estimating the noise experienced by aquatic microorganisms in a turbulent environment. This problem has particular interest in relations to predators and prey that rely solely on signals transmitted through the surrounding turbulent flow. It is possible to give estimates for how often a predator can mistake turbulent induced noise for a signal from prey in given turbulence conditions. Such mistakes can be observed as unmotivated attacks. Similarly, prey can mistake noise for presence of a predator, giving rise to seemingly unmotivated observable escape responses. 16:00 15 mins Dynamic of large particles embedded in shear flows Miguel López-Caballero, Nathanaël Machicoane, Lionel Fiabane, Jean-Françoise Pinton, Mickael Bourgoin, Romain Volk Abstract: Large particles ($D \gg \eta$) immersed in a closed turbulent flow tend to explore in a non-uniformly way the cavity in which they are placed. Here we study the slow dynamics of large particles (with various size) advected in closed turbulent flows at different Reynolds numbers. We investigate the spatial sampling experienced by large particles in two fully turbulent closed flows generated between counter-rotating disks (so called von Karman flow), focusing in the slow frequency's ($f_{slow} < \Omega$, where $\Omega$ is the rotation rate of the driving impellers) and characterize the power spectrum of the slow fluctuations of particles position. Both considered flows share a common feature : the presence of a shear region dividing two mean re-circulation regions ; however the spatial symmetries and the temporal behaviors of both setups are very different. The principal result in this research is that despite these differences both flows exhibit a well defined slow dynamical behavior that can be identified in Fourier space. We report on the universal characteristics of such slow motion. 16:15 15 mins LAGRANGIAN RAYLAIGH-BÉNARD CONVECTION Sergio Chibbaro, Francesco Zonta Abstract: Using passive tracers as sensors, we obtain Lagrangian measurements of tracers position, velocity and temperature in Rayleigh-Bénard convection at Ra=10^7-10^9. We report on statistics of temperature, velocity, and heat transport (Nusselt number). We observe that the Nusselt number is characterized by a largely intermittent behavior, likely due to the interaction of temperature with turbulent velocity fluctuations. 16:30 15 mins Triangular Constellations in Flows Michael Wilkinson, John Grant Abstract: Particles advected on the surface of a fluid can exhibit fractal clustering. The local structure of a fractal set is described by its dimension $D$, which is the exponent of a power-law relating the mass ${\cal N}$ in a ball to its radius $\varepsilon$: ${\cal N}\sim \varepsilon^D$. It is desirable to characterise the {\em shapes} of constellations of points sampling a fractal measure, as well as their masses. The simplest example is the distribution of shapes of triangles formed by triplets of points, which we investigate for fractals generated by chaotic dynamical systems. The most significant parameter describing the triangle shape is the ratio $z$ of its area to the radius of gyration squared. We show that the probability density of $z$ has a phase transition: $P(z)$ is independent of $\varepsilon$ and approximately uniform below a critical flow compressibility $\beta_{\rm c}$, which we estimate. For $\beta>\beta_{\rm c}$ the distribution appears to be described by two power laws: $P(z)\sim z^{\alpha_1}$ when $1\gg z\gg z_{\rm c}(\varepsilon)$, and $P(z)\sim z^{\alpha_2}$ when $z\ll z_{\rm c}(\varepsilon)$.
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2019-05-21 03:08:04
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https://blancosilva.wordpress.com/2012/08/07/stones-balances-matrices/
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Home > Combinatorics, Data mining, Linear Algebra, puzzles > Stones, balances, matrices
## Stones, balances, matrices
Let’s examine an easy puzzle on finding the different stone by using a balance:
You have four stones identical in size and appearance, but one of them is heavier than the rest. You have a set of scales (a balance): how many weights do you need to determine which stone is the heaviest?
This is a trivial problem, but I will use it to illustrate different ideas, definitions, and the connection to linear algebra needed to answer the harder puzzles below. Let us start by solving it in the most natural way:
1. Enumerate each stone from 1 to 4.
2. Set stones 1 and 2 on the left plate; set stones 3 and 4 on the right plate. Since one of the stones is heavier, it will be in the plate that tips the balance. Let us assume this is the left plate.
3. Discard stones 3 and 4. Put stone 1 on the left plate; and stone 2 on the right plate. The plate that tips the balance holds the heaviest stone.
This solution finds the stone in two weights. It is what we call adaptive measures: each measure is determined by the result of the previous. This is a good point to introduce an algebraic scheme to code the solution.
• The weights matrix: This is a matrix with four columns (one for each stone) and two rows (one for each weight). The entries of this matrix can only be $-1, 0$ or $1,$ depending whether a given stone is placed on the left plate $(1)$, on the right plate $(-1)$ or in neither plate $(0).$ For example, for the solution given above, the corresponding matrix would be
$W = \begin{pmatrix} 1 & 1 & -1 & -1 \\ 1 & -1 & 0 & 0 \end{pmatrix}$
• The stones matrix: This is a square matrix with four rows and columns (one for each stone). Each column represents a different combination of stones, in such a way that the n-th column assumes that the heaviest stone is in the n-th position. The entries on this matrix indicate the weight of each stone. For example, if we assume that the heaviest stone weights b units, and each other stone weights a units, then the corresponding stones matrix is
$B = \begin{pmatrix} b & a & a & a \\ a & b & a & a \\ a & a & b & a \\ a & a & a & b \end{pmatrix}$
Multiplying these two matrices, and looking at the sign of the entries of the resulting matrix, offers great insight on the result of the measures:
$\text{sign} \big( W \cdot B \big) = \text{sign} \begin{pmatrix} b-a & b-a & a-b & a-b \\ b-a & a-b & 0 & 0 \end{pmatrix} = \begin{pmatrix} + & + & - & - \\ + & - & 0 & 0 \end{pmatrix}$
Note the columns of this matrix code the behavior of the measures:
• The column $\big( \begin{smallmatrix} + \\ + \end{smallmatrix} \big)$ indicates that the balance tipped to the left in both measures (and therefore, the heaviest stone is the first one)
• The column $\big( \begin{smallmatrix} + \\ - \end{smallmatrix} \big)$ indicates that the heaviest stone is the second one.
• Note that the other two measures can’t find the heaviest stone, since this matrix was designed to find adaptively a stone supposed to be either the first or the second.
Is it possible to design a solution to this puzzle that is not adaptive? Note the solution with two measures given (in algebraic form) below:
$\text{sign} \left[ \begin{pmatrix} 1 & 1 & -1 & -1 \\ 1 & -1 & 1 & -1 \end{pmatrix} \cdot B \right] = \begin{pmatrix} + & + & - & - \\ + & - & + & - \end{pmatrix}$
Since each column is different, it is trivial to decide after the experiment is done, which stone will be the heaviest. For instance, if the balance tips first to the right (-) and then to the left (+), the heaviest stone can only be the third one.
Let us make it a big harder: Same situation, but now we don’t know whether the stone that is different is heavier or lighter.
The solution above is no good: Since we are not sure whether b is greater or smaller than a, we would obtain two sign matrices which are virtually mirror images of each other.
$\begin{pmatrix} + & + & - & - \\ + & - & + & - \end{pmatrix}$ and $\begin{pmatrix} - & - & + & + \\ - & + & - & + \end{pmatrix}$
In this case, in the event of obtaining that the balance tips twice to the left: which would be the different stone? The first, which is heaviest, or the fourth, which is lightest? We cannot decide.
One possible solution to this situation involves taking one more measure. Look at the algebraic expression of the following example, to realize why:
$\text{sign} \left[ \begin{pmatrix} 1 & 1 & -1 & -1 \\ 1 & -1 & 1 & -1 \\ 1 & -1 & -1 & 1 \end{pmatrix} \cdot B \right] = \begin{pmatrix} + & + & - & - \\ + & - & + & - \\ + & - & - & + \end{pmatrix}$ or $\begin{pmatrix} - & - & + & + \\ - & + & - & + \\ - & + & + & - \end{pmatrix}$
In this case there is no room for confusion: if the balance tips three times to the same side, then the different stone is the first one (whether heavier or lighter). The other possibilities are also easily solvable: if the balance tips first to one side, then to the other, and then to the first side, then the different stone is the third one.
The reader will not be very surprised at this point to realize that three (non adaptive) measures are also enough to decide which stone is different (be it heavier or lighter) in a set of twelve similar stones. To design the solution, a good weight matrix with twelve columns and three rows need to be constructed. The trick here is to allow measures that balance both plates, which gives us more combinations with which to play. How would the reader design this matrix?
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2017-08-22 20:29:36
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http://www.stata.com/support/faqs/graphics/box-plots-and-logarithmic-scales/
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Search
>> Home >> Resources & support >> FAQs >> Box plots and logarithmic scales
### How can I best get box plots on logarithmic scales?
Title Box plots and logarithmic scales Author Nicholas J. Cox, Durham University, UK Date September 2005; minor revisions March 2014
### The problem
The purpose of this FAQ is to point out a potential pitfall with graph box and graph hbox and to explain a way around it. Sometimes users fire up a box plot in Stata, realize that a logarithmic scale would be better for their data, and then ask for that by yscale(log) (with either graph box or graph hbox). (From now on examples will be just in terms of graph box, as the principle is the same for both.)
Although Stata will let you do this, you should be aware of what option yscale(log) actually does. As with all other graphs, yscale(log) takes the graph you would have gotten otherwise and warps it logarithmically. What it does not do is recalculate summaries on the log scale, which, with a box plot, is what you might want. However, making yscale(log) have a special meaning for box plots would be bad software design, whatever the statistical arguments, so if the pitfall to be discussed here matters to you, then you will need to work your way around it.
In what follows, I assume that each variable to be shown on a box plot is all positive, because logarithmic transformation is not defined otherwise. As you may have noticed, if you ask graph to use yscale(log) when zero or negative values are present, it just gives you a ridiculous graph, rather like the kind of teacher who will not say, “That was a stupid thing to ask,” but will just give you a funny look that clearly means, “Do think about that a bit more.”
Methods for box plots differ by book and by program. Frigge, Hoaglin, and Iglewicz (1989) cataloged several variants, and no doubt a careful search would reveal some they missed and others that have arisen since. Stata follows what Tukey (1977) settled on after trying various possibilities. The most important detail is that a data point is plotted separately if it lies more than 1.5 times the interquartile range away from the nearer quartile. This calculation depends on the scale being used: if you redo it on a logarithmic scale, you will often get a different decision. Points declared as deserving separate plotting on the original scale may not be so declared on the logarithmic scale. Thus some high values plotted separately may jump back inside the main box-and-whiskers cluster. Conversely, some low values may jump out of that cluster and now be declared as deserving separate plotting. The reclassifications reflect that the interquartile range of logarithms is not, in general, the logarithm of the interquartile range.
The same issue can affect, although usually not as much, the calculated median and quartiles. Each can be based on interpolation between data points, and so it is not always true that, say, the median of the logarithms is exactly the same as the logarithm of the median. Unless your dataset is strange and small, you would not usually be troubled by the difference, but only for the minimum and maximum is there never a small problem.
### The solution
The way to do it properly is thus to take logarithms first. For example,
. sysuse auto, clear . clonevar log10price = price . replace log10price = log10(price) . graph box log10price
The reason for starting with clonevar is that you pick up the variable label. log10() has the marginal advantage over log() (or ln()) that you can calculate the inverse, the power of 10, more easily. This method can prove useful when you want to add more intelligible axis labels to the graph. Seeing the graph above, you can think that 4 means 104 or 10,000, leading to an extra specification:
. graph box log10price, ylabel(4 "10000")
However, here extra labels such as 3 “1000” 5 “100000” are too far outside the range of the data. Few of us can recall more than the integer powers of 10, but Stata can do the calculation on the fly. To add labels at the equivalents of 5,000 and 15,000, type
. graph box log10price, /// ylabel(=log10(5000)' "5000" 4 "10000" =log10(15000)' "15000")
The help for this trick is at [P] macro. However, having to spell out several label specifications in this way is at best a little tedious. To get the best of all worlds, you will want nice axis labels on the original scale, but with Stata doing all the work that you would rather not do. One way of getting those is through the program mylabels from SSC. You just say what you want shown and specify the scale in use. For example, after
. mylabels 3000(2000)7000 9000(3000)15000, myscale(log10(@)) local(labels)
Stata echoes
3.47712 "3000" 3.69897 "5000" 3.8451 "7000" 3.95424 "9000" 4.07918
"12000" 4.17609 "15000"
You should not retype that, or even copy and paste, because it is tucked safe inside the local macro specified.
. graph box log10price, ylabel(`labels', angle(h))
It may take a few iterations to get it right, but simply reissue mylabels until you do. Use the same local macro name. Stata is happy to overwrite it, as local macros are expendable.
### Other nonlinear scales
The same issue with box plots and change of scale arises with any nonlinear transformation. The calculation of median and quartiles and the selection of data points for separate plotting need to be done afresh on any new scale. For example, psychologists and others work with times taken by test subjects to complete a task. The distributions are often highly skewed and subjects who do not complete should be assigned missing values. The reciprocal of time is a speed; missing times can be recoded as zero speeds. Here again you would need to do the transformation yourself and possibly fix the axis labels, too.
For broader discussion of box plots within Stata, including how to create your own variants on the default design, see Cox (2009, 2013).
### References
Cox, N. J. 2009.
Speaking Stata: Creating and varying box plots. Stata Journal 9: 478–496.
Cox, N. J. 2013.
Speaking Stata: Creating and varying box plots: Correction. Stata Journal 13: 398–400.
Frigge, M., D. C. Hoaglin, and B. Iglewicz. 1989.
Some implementations of the box plot. American Statistician 43: 50–54.
Tukey, J. W. 1977.
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2016-02-11 02:27:45
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https://tex.stackexchange.com/questions/366426/how-to-use-hyperlink-from-hyperref-in-makenote-from-scrlayer-notecolumn
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# How to use \hyperlink (from hyperref) in \makenote (from scrlayer-notecolumn)?
I am trying to put a \hyperlink into a \makenote, but I get the following error:
! Use of \\makenote doesn't match its definition.
\@ifnextchar #1#2#3->\let \reserved@d =#1\def \reserved@a {
#2}\def \reserved@b {#3}\futurelet \@let@token \@ifnch
in makenote.
This is the source code:
% lualatex
\documentclass{scrbook}
\usepackage{luatex85}
\usepackage{fontspec}
\usepackage{scrlayer-scrpage}
\usepackage{scrlayer-notecolumn}
\usepackage{hyperref}
\begin{document}
Testing makenote \makenote{makenote}.
Testing \hypertarget{anchorname}{hypertarget}.
Testing hyperref in makenote \makenote{a \hyperref[labelname]{hyperref}.}.
Testing \label{labelname}label.
\end{document}
I use lualatex for compilation, but I get the same error if I use pdflatex (commenting out fontspec beforehand).
The \hyperlink command works great in the text, it only fails in the \makenote.
The \hyperref command works in \makenote, but unfortunately the anchors of the \labels are not exactly where the \labels are defined in general. Therefore this is a solution.
• Untested: \protect\hyperlink{...} in \makenote? – user31729 Apr 24 '17 at 14:39
• Thanks! Indeed, \protect solves this problem. Is there a way to define a version of \hyperlink that does not need \protect? In fact, in my actual use case the \hyperlinks are buried in some user defined commands and I have to put \protect in front of them if they are used in \makenote. – Toni Dietze Apr 24 '17 at 15:18
• You can try to \robustify\hyperlink, in the preamble, this requires \usepackage{etoolbox} – user31729 Apr 24 '17 at 16:35
• Thanks for mentioning etoolbox. I got it working using \protecting. \newcommand{\makenoteORmarginpar}[1]{\ifdefined\makenote\makenote{\protecting{#1}}\else\marginpar{#1}\fi} – Toni Dietze Apr 24 '17 at 16:39
Since KOMA-Script 3.23 package scrlayer-notecolumn has a star variant of \makenote, that does not need to protect commands, that may break and should not be expanded:
\documentclass{scrbook}
\usepackage{fontspec}
\usepackage{scrlayer-scrpage}
\usepackage{scrlayer-notecolumn}[2017/02/08]
\usepackage{hyperref}
\begin{document}
Testing makenote \makenote{makenote}.
Testing \hypertarget{anchorname}{hypertarget}.
Testing hyperref in makenote \makenote{a \hyperref[labelname]{hyperref}.}.
Testing \label{labelname}label.
\end{document}
results in
without error.
You can get the same result (even with KOMA-Script before 3.23) using:
\documentclass{scrbook}
\usepackage{fontspec}
\usepackage{scrlayer-scrpage}
\usepackage{scrlayer-notecolumn}
\usepackage{hyperref}
\begin{document}
Testing makenote \makenote{makenote}.
Testing \hypertarget{anchorname}{hypertarget}.
Testing hyperref in makenote \makenote{a \hyperref[labelname]{hyperref}.}.
Testing \label{labelname}label.
\end{document}
or
\documentclass{scrbook}
\usepackage{fontspec}
\usepackage{scrlayer-scrpage}
\usepackage{scrlayer-notecolumn}
\usepackage{hyperref}
\begin{document}
Testing makenote \makenote{makenote}.
Testing \hypertarget{anchorname}{hypertarget}.
Testing hyperref in makenote \makenote{a \hyperref[labelname]{hyperref}.}.
Testing \label{labelname}label.
\end{document}
or
\documentclass{scrbook}
\usepackage{fontspec}
\usepackage{scrlayer-scrpage}
\usepackage{scrlayer-notecolumn}
\DeclareRobustCommand*{\rmakenote}[1]{%
\makenote{\detokenize{#1}}%
}
\usepackage{hyperref}
\begin{document}
Testing makenote \makenote{makenote}.
|
2019-10-14 20:13:28
|
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|
https://brilliant.org/discussions/thread/another-chemistry-doubt/
|
×
# Another Chemistry Doubt
My friends at school were debating about the oxidizing power of the oxy-acids of chlorine : $$HClO_4 , HClO_3 , HClO_2$$ and $$HClO$$ . They claimed the following:
$$HClO_4$$ : Cl is in +7 oxidation state and hence will oxidize easily.
$$HClO_2$$ : No particular reason. Some exam paper had this as answer.
$$HClO$$ : Cl is in +1 oxidation state and hence can reach octet configuration easily.
Note by Vishwak Srinivasan
1 year, 10 months ago
Sort by:
The accepted order is HOCl>HClO2>HClO4.
The argument that HClO4 is the most oxidising due to chlorine, a highly electronegative element being in such a high oxidation state as +7; would be correct if oxidation state were the only factor involved.
The other very important factor is $$stability$$. A species acts as a good oxidising agent, or equivalently, readily undergoes reduction precisely when it is in an unstable state. Here, as the number of oxygen atoms surrounding Cl increase, so does the stability of the oxide.
In other words, for HClO4 to undergo reduction, the oxygen bonds must be broken(which are in fact strongest in HClO4 due to the higher polarising power of the higher oxidation state and the resultant stronger covalent bond) and this just doesn't happen.
@Vishwak Srinivasan · 1 year, 10 months ago
Thanks a lot bro. · 1 year, 10 months ago
|
2017-03-23 00:43:08
|
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|
http://projecteuclid.org/euclid.jsg
|
## Journal of Symplectic Geometry
The Journal of Symplectic Geometry is a new journal focusing on the impact of symplectic geometry in mathematics. Symplectic geometry has deep roots in mathematics going back to Huygens' study of optics and the Hamilton Jacobi formulation of mechanics.
## Top downloads over the last seven days
Transverse knots, branched double covers and Heegaard Floer contact invariantsVolume 4, Number 2 (2006)
Homoclinic points and Floer homologyVolume 11, Number 4 (2013)
Topologically trivial Legendrian knotsVolume 7, Number 2 (2009)
Fibered symplectic cohomology and the Leray-Serre spectral sequenceVolume 6, Number 3 (2008)
$U$-action on perturbed Heegaard Floer homologyVolume 10, Number 3 (2012)
• ISSN: 1527-5256 (print), 1540-2347 (electronic)
• Publisher: International Press of Boston
• Discipline(s): Mathematics
• Full text available in Euclid: 2001 --
• Access: Articles older than 5 years are open
• Euclid URL: http://projecteuclid.org/jsg
|
2014-10-23 17:09:47
|
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|