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Post TOPIC: Inflation RE: Inflation Permalink Title: Initial conditions for inflation Author: Konstantinos Dimopoulos, Michal Artymowski A novel proposal is presented, which manages to overcome the initial conditions problem of inflation with a plateau. An earlier period of proto-inflation, beginning at Planck scale, accounts for the Universe expansion and arranges the required initial conditions for inflation on the plateu to commence. We show that, if proto-inflation is power-law, it does not suffer from any eternal inflationary stage. A simple model realisation is constructed in the context of alpha-attractors, which can both generate the inflationary plateau and the exponential slopes around it, necessary for the two inflation stages. Our mechanism allows to assume chaotic initial conditions at the Planck scale for proto-inflation, it is generic and it is shown to work without fine-tunings. Read more (906kb, PDF) Title: Supersymmetry and Inflation Author: S. Ferrara, A. Sagnotti Theories with elementary scalar degrees of freedom seem nowadays required for simple descriptions of the Standard Model and of the Early Universe. It is then natural to embed theories of inflation in supergravity, also in view of their possible ultraviolet completion in String Theory. After some general remarks on inflation in supergravity, we describe examples of minimal inflaton dynamics which are compatible with recent observations, including higher-curvature ones inspired by the Starobinsky model. We also discuss different scenarios for supersymmetry breaking during and after inflation, which include a revived role for non-linear realizations. In this spirit, we conclude with a discussion of the link, in four dimensions, between "brane supersymmetry breaking" and the super--Higgs effect in supergravity. Read more (27kb, PDF) Title: Irruption of massive particle species during inflation Author: Michael A. Fedderke, Edward W. Kolb, Mark Wyman (Version v2) All species of (non-conformally-coupled) particles are produced during inflation so long as their mass M is not too much larger than H, the expansion rate during inflation. It has been shown that if a particle species that is normally massive (M \gg H) couples to the inflaton field in such a way that its mass vanishes, or at least becomes small (M<H), for a particular value of the inflaton field, then not only are such particles produced, but an irruption of that particle species can occur during inflation. In this paper we analyse creation of a massive particle species during inflation in a variety of settings, paying particular attention to models which realize such an irruptive production mechanism. Read more (4229kb, PDF) Title: Planck 2015. XX. Constraints on inflation Author: Planck Collaboration: P. A. R. Ade, N. Aghanim, M. Arnaud, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, E. Battaner, K. Benabed, A. Benoit, A. Benoit-Levy, J.-P. Bernard, M. Bersanelli, P. Bielewicz, A. Bonaldi, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J.-F. Cardoso, A. Catalano, A. Challinor, A. Chamballu, R.-R. Chary, H. C. Chiang, P. R. Christensen, S. Church, D. L. Clements, S. Colombi, L. P. L. Colombo, C. Combet, D. Contreras, F. Couchot, A. Coulais, B. P. Crill, A. Curto, F. Cuttaia, L. Danese, R. D. Davies, R. J. Davis, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, F.-X. Desert, J. M. Diego, H. Dole, S. Donzelli, O. Dore, M. Douspis, et al. (186 additional authors not shown) We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarisation data on large angular scales measure the spectral index of curvature perturbations to be ns=0.968±0.006 and tightly constrain its scale dependence to dn[s]/dlnk=-0.003±0.007 when combined with the Planck lensing likelihood. When the high-l polarisation data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is r0.002<0.11 (95% CL), consistent with the B-mode polarisation constraint r<0.12 (95% CL) obtained from a joint BICEP2/ Keck Array and Planck analysis. These results imply that V(\phi) \propto \phi² and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R² inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalised models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data. Read more (14756kb, PDF) Title: Higgs inflation at the critical point Author: Fedor Bezrukov, Mikhail Shaposhnikov Higgs inflation can occur if the Standard Model (SM) is a self-consistent effective field theory up to inflationary scale. This leads to a lower bound on the Higgs boson mass, M_h \geq M_{\text {crit}}. If Mh is more than a few hundreds of MeV above the critical value, the Higgs inflation predicts the universal values of inflationary indexes, r\simeq 0.003 and n_s\simeq 0.97, independently on the Standard Model parameters. We show that in the vicinity of the critical point Mcrit the inflationary indexes acquire an essential dependence on the mass of the top quark m_t and M_h. Thus the cosmological measurements of r and n_s different from the universal values lead to precise prediction of M_h and m_t. Read more (203kb, PDF) Title: Multifield Inflation after Planck: Isocurvature Modes from Nonminimal Couplings Author: Katelin Schutz, Evangelos I. Sfakianakis, David I. Kaiser Recent measurements by the Planck experiment of the power spectrum of temperature anisotropies in the cosmic microwave background radiation (CMB) reveal a deficit of power in low multipoles compared to the predictions from best-fit deltaCDM cosmology. The low-l anomaly may be explained by the presence of primordial isocurvature perturbations in addition to the usual adiabatic spectrum, and hence may provide the first robust evidence that early-universe inflation involved more than one scalar field. In this paper we explore the production of isocurvature perturbations in nonminimally coupled two-field inflation. We find that this class of models readily produces enough power in the isocurvature modes to account for the Planck low-l anomaly, while also providing excellent agreement with the other Planck results. Read more (960kb, PDF) Title: Loop corrections and a new test of inflation Authors: Gianmassimo Tasinato, Christian T. Byrnes, Sami Nurmi, David Wands Inflation is the leading paradigm for explaining the origin of primordial density perturbations and the observed temperature fluctuations of the cosmic microwave background. However many open questions remain, in particular whether one or more scalar fields were present during inflation and how they contributed to the primordial density perturbation. We propose a new observational test of whether multiple fields, or only one (not necessarily the inflaton) generated the perturbations. We show that our test, relating the bispectrum and trispectrum, is protected against loop corrections at all orders, unlike previous relations. Read more (25kb, PDF) Title: The R_h=ct Universe Without Inflation Authors: Fulvio Melia The horizon problem in the standard model of cosmology (LDCM) arises from the observed uniformity of the cosmic microwave background radiation, which has the same temperature everywhere (except for tiny, stochastic fluctuations), even in regions on opposite sides of the sky, which appear to lie outside of each other's causal horizon. Since no physical process propagating at or below lightspeed could have brought them into thermal equilibrium, it appears that the universe in its infancy required highly improbable initial conditions. In this paper, we examine this well-known problem by considering photon propagation through a Friedmann-Robertson-Walker (FRW) spacetime at a more fundamental level than has been attempted before, demonstrating that the horizon problem only emerges for a subset of FRW cosmologies, such as LCDM, that include an early phase of rapid deceleration. We show that the horizon problem is nonexistent for the recently introduced R_h=ct universe, obviating the principal motivation for the inclusion of inflation. We demonstrate through direct calculation that, in the R_h=ct universe, even opposite sides of the cosmos have remained causally connected to us - and to each other - from the very first moments in the universe's expansion. Therefore, within the context of the R_h=ct universe, the hypothesized inflationary epoch from t=10^{-35} seconds to 10^{-32} seconds was not needed to fix this particular "problem", though it may still provide benefits to cosmology for other reasons. Read more (1284kb, PDF) Title: Alchemical Inflation: inflaton turns into Higgs Authors: Kazunori Nakayama, Fuminobu Takahashi We propose a new inflation model in which a gauge singlet inflaton turns into the Higgs condensate after inflation. The inflationary path is characterised by a moduli space of supersymmetric vacua spanned by the inflaton and Higgs field. The inflation energy scale is related to the soft supersymmetry breaking, and the Hubble parameter during inflation is smaller than the gravitino mass. The initial condition for the successful inflation is naturally realised by the pre-inflation in which the Higgs plays a role of the waterfall field. Read more (2103kb, PDF) Title: Observable Spectra of Induced Gravitational Waves from Inflation Authors: Laila Alabidi, Kazunori Kohri, Misao Sasaki, Yuuiti Sendouda Measuring the primordial power spectrum on small scales is a powerful tool in inflation model building, yet constraints from Cosmic Microwave Background measurements alone are insufficient to place bounds stringent enough to be appreciably effective. For the very small scale spectrum, those which subtend angles of less than 0.3 degrees on the sky, an upper bound can be extracted from the astrophysical constraints on the possible production of primordial black holes in the early universe. A recently discovered observational by-product of an enhanced power spectrum on small scales, induced gravitational waves, have been shown to be within the range of proposed space based gravitational wave detectors; such as NASA's LISA and BBO detectors, and the Japanese DECIGO detector. In this paper we explore the impact such a detection would have on models of inflation known to lead to an enhanced power spectrum on small scales, namely the Hilltop-type and running mass models. We find that the Hilltop-type model can produce observable induced gravitational waves within the range of BBO and DECIGO for integral and fractional powers of the potential within a reasonable number of e-folds. We also find that the running mass model can produce a spectrum within the range of these detectors, but require that inflation terminates after an unreasonably small number of e-folds. Finally, we argue that if the thermal history of the Universe were to accommodate such a small number of e-folds the Running Mass Model can produce Primordial Black Holes within a mass range compatible with Dark Matter, i.e. within a mass range 10^{20} g< M_{BH}<10^{27} g. 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Circular draw Circular draw --- Introduction --- Circular draw is a graphical exercise that asks you to draw an inscribed or circumscribed circle of a triangle, etc. You will have a score according to the precision of your drawing. The most recent This page is not in its usual appearance because WIMS is unable to recognize your web browser. Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program. • Description: draw the circumscribed circle (cinscribed circle , circumcircle, incircle) of a triangle. interactive exercises, online calculators and plotters, mathematical recreation and games • Keywords: interactive mathematics, interactive math, server side interactivity, geometry, triangles, circle, jsxgraph,circle_equation	{"url":"https://wims.divingeek.com/wims/wims.cgi?lang=en&+module=H4%2Fgeometry%2Fcircdraw.en","timestamp":"2024-11-07T13:47:42Z","content_type":"text/html","content_length":"8044","record_id":"<urn:uuid:389edf47-97da-46f1-9084-793d623cb51a>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00045.warc.gz"}
How can vaccines be effective vs. COVID hospitalization if most hospitalized are vaccinated and vaccinated percentages are similar in those hospitalized for flu or COVID? Jeffrey Morris Kirsch, et al. have published a preprint providing commentary on a JAMA paper that compared death rates after hospitalization for COVID-19 or influenza, respectively, from a large Veteran's Administration database. The paper used propensity score weighting to balance confounders between the influenza and COVID-19 cohorts, and found that COVID-19 hospitalization led to higher death risk than Influenza hospitalization in the core of the 2022-23 influenza season (October 2022 through January 2023). Further, they found this death risk in the COVID-19 cohort was highest in the unvaccinated and lowest in the boosted individuals. The study does not focus on or look at vaccine effectiveness vs. hospitalization, and does not even look at risk of hospitalization but conditions on a cohort of individuals, all of which have been hospitalized. Additionally, note that the propensity score weighting is done to balance the COVID-19 and influenza hospitalized cohort, not to balance vaccinated and unvaccinated, so again is not designed to assess vaccine effectiveness. It would be possible to use the large VA database to estimate vaccine effectiveness of SARS-CoV-2 vaccines and influenza vaccines against COVID-19 and influenza hospitalization, respectively, but this would require a completely different design and analytical approach. Kirsch et al.'s claims and argument However, in spite of this, the Kirsch et al. preprint claims that they can determine from this paper that neither the SARS-CoV-2 vaccines nor the Influenza vaccines had any effectiveness whatsoever based on Table 1 of the JAMA paper: Their objection is based on the percent of COVID-19 and Influenza hospitalized in the various COVID-19 and Influenza vaccinated subgroups, thinking that if there was any vaccine effectiveness vs. hospitalization at all for the two vaccines that: 1. there should be lower % vaccinated if there was any vaccine effectiveness 2. the percentages for influenza and COVID-19 hospitalized should be very different. They extract this part out of the table and present in their preprint: The crux of their argument is that the fact that these two columns in the table are close to one another implies neither vaccine had any effectiveness vs. infection. From this table they assert: Had the vaccines been even minimally effective, significant differences in vaccination percentages would be expected. They then proceed to compute what they expect this table would look like under assumptions of vaccine effectiveness (VE) of 90% for COVID-19 vaccines vs. COVID-19 hospitalization and VE=50% for Influenza vaccination vs. Influenza hospitalization, presenting the following table: 1. The actual VA data from the JAMA paper had a much higher percentage of COVID-19 hospitalized patients who were COVID-19 vaccinated (81.11% vs. 30.04% in their expected table) 2. The actual VA data had a much higher percentage of Influenza hospitalized patients who were Influenza vaccinated (61.88% vs. 46.89% in their expected table) 3. The actual VA data had similar percent COVID-19 vaccinated and percent Influenza vaccinated in both the COVID-19 hospitalized and Influenza hosptalized groups, while their expected table had them vastly difference. We are not aware of any viable alternative explanation for the observed data other than that neither vaccine provided any protection against hospitalization They are extremely bold and confident in these conclusions: In conclusion, our assessment indicates that neither the influenza vaccine nor the COVID-19 vaccines provided any measurable difference in risk reduction of hospitalization for the very diseases they were designed to protect against. They suggest that their paper introduces a much better way to assess vaccine effectiveness than the current design and analyses approaches that they complain "rely on complex models" Since we observed minimal differences in vaccination percentages, this approach may offer a simpler and more expeditious way to assess vaccine efficacy of two or more vaccines without having to rely on complex models They go further and suggest the vaccines be pulled from the market all over the world (and suggesting the "method" they introduce in this paper be an essential part of the regulatory approval process) We propose that health authorities worldwide should reconsider the decision to approve both of these vaccines until such time as a real public health benefit can be demonstrated from the data using the method described in this paper, along with other complementary analytic methods. These findings reinforce recommendations to halt the global distribution of both the influenza vaccine and the COVID-19 vaccines Very bold claims to make on the basis of the simple fact that they cannot understand how the vaccination percentages in Table 1 in the JAMA article could occur if the vaccines had nonzero Basic evaluation of the claims First of all, fundamentally, it is not possible to estimate or make any direct inferences about vaccine effectiveness vs. hospitalized infection from a simple table summarizing percent vaccinated for COVID-19 or Influenza in COVID-19 or Influenza hospitalized cohorts. It may be interesting to think about what a table like Table 1 in the JAMA paper would look like under various assumed states of reality, but if one is to undertake this exercise, it is important for them to be aware of all of the assumptions they are making, and for it to have any value or validity whatsoever, needs to reflect the key basic realities of the situation. In their preprint, they do not provide any details about how they arrive at this table based on their 90%/50% VE assumptions, but from personal correspondence with the lead author, I have learned 1. They assumed independence between COVID-19 and Influenza vaccination, assuming that someone getting a COVID-19 vaccine was not more likely to get an Influenza vaccine than someone not getting a COVID-19 vaccine, and vice versa. It is extremely unlikely that these are independent, as propensity to get one vaccine increases the likelihood of receiving the other 2. They did not consider age confounding the age dynamics of the population, including the age distribution of the VA cohort, the stark differences across age groups in terms of both (1) propensity to get COVID-19 and/or Influenza vaccines and boosters and (2) risk of hospitalization if infected. They treated the entire population as a homogeneous group with identical hospitalization risks and vaccination rates, so ignores the massive age confounding present in this data set. There may be other assumptions they made, as well, but again are not clear because they are not described in the preprint. First, if their preprint is to be considered a legitimate scientific publication, it needs to provide the specific details of how they get such an "expected" table, including all assumptions and calculations, especially given it is the entire crux of their argument that there is no vaccine effectiveness that is the primary goal of their paper. However, it is clear that some of assumptions they made are grossly oversimplified and inaccurate, enough so as to make their "expected" table they compute irrelevant for the situation at hand. In terms of independence of COVID-19 and influenza vaccination, the literature (and common sense) are very clear that those receiving influenza vaccines are more likely to have received a COVID-19 vaccine, and vice versa. For example, this study found those receiving influenza vaccines were 5.18x more likely to receive COVID-19 vaccines. This fact alone would make the percent influenza and COVID-19 vaccinated in the influenza and COVID-19 hospitalization cohorts more similar than random chance, providing some explanation for why these were much more similar in Table 1 of the JAMA paper than the simple expected Table 2 of the preprint. Second, and even more fundamentally, the age confounding that is by far the dominant feature of this data set, and is completely ignored in the authors' Table 2 of expected vaccination percentages. This confounding plays a major role in the percent vaccinated in the hospitalized cohorts and the structure of Table 1 of the JAMA paper, and as I will show is sufficient to produce much of the structure evident in that table. In the remainder of this article, I will compute an "expected" table of % COVID-19 and influenza vaccinated for the VA cohort in the 2022-23 flu season based on the actual VA population numbers and age distribution, and the actual age group specific rates of influenza and COVID-19 vaccination and boosting, and the actual age group specific rates of influenza and COVID-19 hospitalization in the USA under the assumption of COVID-19 vaccines have VE=60% and influenza vaccines have VE=20% vs. hospitalization. Even though my calculation of this expected table assumes independence of influenza and COVID-19 vaccination, only roughly accounts for age confounding, and does not accounting for any other important confounders in the population including sex and comorbidities, I will show that under these assumptions one can obtain a table with features similar to Table 1 of the JAMA article, and the authors of the preprint have absolutely no basis for claiming zero vaccine effectiveness on the basis of this table. I provide full transparency on all my assumptions, sources, and calculations. Basic Assumptions for Calculations I based my calculations on the actual age group specific population, vaccination, and hospitalization numbers as documented from various resources -- and provide a hyperlink from the source in each I started with the actual VA population numbers, specifically taking the veteran population on 9/30/2022 for 5 year age groups and aggregating into 3 age groups: 18-49yr, 50-64yr, and 65yr+ for further consideration. and the proportion of each age group unvaccinated, receiving 1-2 doses, or receiving 3+ doses: Unvaccinated 1-2 Doses 3+ Doses For the same age groups, I found data on the hospitalization rate (per 100k) for each age group for Influenza and for COVID-19 for the 2022-2023 flu season (10/1/2022-9/30/2023): Hospitalization Rate (per 100k) For vaccine effectiveness, for the sake of this simulation I assumed: Vaccine Effectiveness vs. Hospitalization Notes on vaccine effectivenss assumptions: • The preprint authors used VE=90% for COVID-19. This would be a reasonable value for 2021 after initial rollouts, but not for end of 2022 and beginning of 2023 with Omicron and with many vaccinated many months or years beforehand. None of the literature from late 2022 and early 2023 has VE vs. hospitalization anywhere near 90%. • For the sake of this simulation, we use VE=60% and have it the same for 1-2 or 3+ doses. One could propose different VE for 1-2, 3, and 4+ doses and see how results change if they'd like • The preprint authors used VE=50% for Influenza. This is close to the estimates in the literature for Influenza A (best matching the vaccine for 2022-23) that ranged from 30%-70%, but considering other influenza clades not matching the vaccine as well we assume a VE=20% here (and again, one could propose different VE and see how results change) • I assume constant relative VE across all age groups. Calculation of Percent Vaccinated Table On the basis of these numbers, assuming homogeneity within age groups, independence of COVID-19 and influenza vaccination status within age groups, and no additional confounders, I followed the following steps to estimate/simulate the number hospitalized for COVID-19 and Influenza in the 2022-2023 flu season: 1. From the assumed vaccination rates, I computed the actual number of the VA population for each of the 3 age groups (18-49, 50-64, 65+) in fall 2022 in each COVID-19 vaccination group (unvaccinated, 1-2 doses, 3+ doses) and influenza vaccination group (vaccinated or unvaccinated in fall 2022) 2. From the assumed VE, I computed the hospitalization rates for Influenza and for COVID-19 for each vaccination/age group, assuming the baseline hospitalization rates mentioned above, denoted by h, are for unvaccinated, and assuming the hospitalization rate is h x (1-VE/100) for the vaccinated. 3. I then multiply the age/vaccine-group specific VA population numbers by age/vaccine-group specific hospitalization rates for influenza and for COVID-19 to get number hospitalized for influenza and for COVID-19 for each age/vaccine group. 4. Taking the cohort of COVID-19 hospitalized, I compute % unvaccinated, 1-2 doses, and 3+ doses for COVID, and % unvaccinated or vaccinated for influenza. 5. Taking the cohort of influenza hospitalized, I compute % unvaccinated, 1-2 doses, and 3+ doses for COVID, and % unvaccinated or vaccinated for influenza. 6. Combining #4-#5 together gives me an "expected" table similar to table 2 of the preprint. Based on those assumptions, following are the results I obtain for the COVID-19 hospitalized alongside the Table 1 from the JAMA paper and the Table 2 from Kirsch preprint: • Looking at the COVID-19 hospitalization results, our results assuming a straight VE=60% yields a table similar to Table 1 in the JAMA table. • We see that in spite of the fact that VE=60% by simulation, 80% of the COVID-19 hospitalized were vaccinated. This is a result of the age confounding, and a phenomenon seen during the entire pandemic. At first glance it seems impossible to have 80% of hospitalized be vaccinated under a scenario of 60% VE, but as can be seen by these calculations the age dynamics when taken into account make a higher proportion of hospitalized vaccinated than one would think. • The percent of COVID-19 hospitalized who were flu vaccinated was close to what was seen in the JAMA paper, and recall we did not account for the known high concordance of influenza and COVID-19 vaccination nor did we account for other confounders like sex and comorbidities. • The Kirsch simulation that ignores the age dynamics and assuming VE=90% obtains results wildly different from those of our simulation that are based on more reasonable VE and the age dynamics of the population. Based on those assumptions, following are the results I obtain for the Influenze hospitalized alongside the Table 1 from the JAMA paper and the Table 2 from Kirsch preprint: • First, note that my simulation found that the percent receiving flu vaccine (61.4%) close to the JAMA paper (61.9%). At first glance it seems impossible that 61.4% of the influenza hospitalized were influenza vaccinated when 55% of the total VA population was influenza hospitalized under an assumption of VE=20%, but this is what we obtain given the age distributions of the VA population, and is a function of the known age confounding. • Kirsch's simulation that did not account for the population age distribution or age confounding found a much lower % influenza vaccinated (46.9%) than the JAMA paper our our simulation (61.9% and • My simulation had a higher % boosted (65.0% vs. 54.9%) and lower % unvaccinated (7.2% vs. 18.9%) in the influenza hospitalized cohort. This suggests those who were COVID-19 vaccinated had lower influenza hospitalization rates than expected based on the assumptions of the simulation. So, we see that by simply accounting for the basic age dynamics of the VA population and accounting for some of the age confounding (by stratifying hospitalization rates and vaccination rates across 18-49yr, 50-64yr, and 65yr+ age groups), a simple simulation obtained results similar to the Table 1 of the JAMA paper under a scenario of nonzero vaccine effectiveness assumptions (60% for COVID-19 and 20% for influenza vaccine). There is no basis for the argument that the structure of Table 1 in the JAMA paper impies the COVID-19 and influenza vaccines have zero effectiveness vs. cause specific hospitalization, and certainly not sufficient support for the notion that the approval for the vaccines should be reversed and vaccines removed from the market. The assertion that the preprint introduces a new method for estimating vaccine effectiveness that is superior to existing methods for estimating vaccine effectivenss (based on "complex models") is also completely unsubstantiated. It is not even clear what their "method" is as they do not delineate any methodology. The simulation I conducted, although simplistic, gave results much more similar to the real world data from the JAMA study than the simulation conducted by Kirsch et al. given it used actual figures from the 2022-23 flu season, and at least partially adjusted for the age confounding by computing these quantities within broad age groups 18-49yr, 50-64yr, and 65yr+. The age confounding has major effects on the vaccination proportions in hospitalized cohorts, and so must be taken into account in any simulation. In spite of these advantages and the fact that our simulation was able to obtain results similar to the Table 1 of the JAMA paper, it also makes many simplifying (and false assumptions), including: • Independence of COVID-19 and influenza vaccination, when we know that they are highliy dependent (e.g. influenza vaccinated >5x more likely to be COVID-19 vaccinated than influenza unvaccinated). • Constant hospitalization rates and vaccination rates within age groups, when we know that there is still major variability across the ages within each age group. For example, an 18 year old is much less likely to be COVID-19 or influenza hospitalized and much less likely to be vaccinated than a 49 year old. Thus, my simulation only partially adjusts for age confounding, and the remaining confounding can strongly affect the results. • No other confounding, when we know that sex and comorbidity status and other factors are major confounders affecting both risk of hospitalization and vaccination status, as well as other residual confounding contributing to healthy vaccinee effect (especially immediately after vaccination), and these will also impact the types of tables computed. Because these limitations exist no matter how rigorously one tries to simulate, one cannot make firm causal inference about vaccine effects by simply conducting such a simulation. It may be interesting to shed light on various aspects of the data, but is not a primary tool for estimating vaccine effectiveness. Because of this, I would NEVER claim that COVID-19 vaccines have VE=60% or influenza vaccines have VE=20% just because this simulation gave reasonably similar results to the actual table from the VA data. This was simply chosen as an illustration to prove the point that one can obtain tables like seen in the JAMA paper even with substantial vaccine effectiveness. The best way we have to estimate vaccine effectiveness vs. rare events like COVID-19 or Influenza hospitalization from currently available data is observational studies, which must account for key known confounders as well as possible, and assess potential residual confounding and robustness to modeling assumptions through transparently described design and analysis techniques and rigorous sensitivity analyses. This could be done with the VA cohort from the JAMA paper using appropriate design and analysis techniques, but it is ill advised to try to infer vaccine effectiveness from a study designed for a completely different purpose without the required data to directly estimate vaccine effects on hospitalization. 21 comentários There are many popular video games, but this one may not be. Try it to see how great it is! retro games Kirsch et al. critique a JAMA study revealing that COVID-19 hospitalizations resulted in higher death rates compared to influenza, particularly among the unvaccinated. Their argument overlooks the study’s design, which isn't focused on vaccine effectiveness. Interestingly, just like navigating the slope game , understanding the complexities in these datasets requires careful maneuvering. The VA database could yield insights on vaccine efficacy with a different approach. https://www.gevezeyeri.com/chat.html Chat topluluğumuz size yeni arkadaşlar edinme ve diğer insanlarla güzel anları paylaşma fırsatı verir. https://www.gevezeyeri.com/mobil-sohbet.html Android uyumlu dokunmatik ekran akıllı cep telefonları, tablet, ipad, iphone gibi Mobil cihazlarla tek bir tıkla Mobil Sohbet’e katılabilırsıniz.	{"url":"https://www.covid-datascience.com/post/how-can-vaccines-be-effective-vs-covid-hospitalization-if-most-hospitalized-are-vaccinated-and-vacc","timestamp":"2024-11-04T17:16:45Z","content_type":"text/html","content_length":"1050490","record_id":"<urn:uuid:781ba2af-510a-40ef-8d76-1eb07d96cb08>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00032.warc.gz"}
Lesson 4 Using Function Notation to Describe Rules (Part 1) 4.1: Notice and Wonder: Two Functions (5 minutes) This warm-up familiarizes students with a new way of using function notation and gives them a preview of the work in this lesson. The prompt also gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is how the values in the $f(x)$ and the $g(x)$ columns in each table correspond to the expression describing each function. When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first use less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly. Display the tables for all to see. Tell students that their job is to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their partner, followed by a whole-class discussion. Student Facing What do you notice? What do you wonder? │$x$ │$f(x)=10-2x$ │ │1 │8 │ │1.5 │7 │ │5 │0 │ │-2 │14 │ │$x$ │$g(x)=x^3$ │ │-2 │-8 │ │0 │0 │ │1 │1 │ │3 │27 │ Activity Synthesis Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the tables. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information. 4.2: Four Functions (10 minutes) In this activity, students are introduced to the idea that some functions can be defined by a rule, and the rule can be described in words or with expressions and equations. Students examine some simple rules and make connections between their verbal and algebraic representations. Doing so prompts them to look for and make use of structure (MP7). The algebraic statements are written in function notation, so the work also reinforces students’ understanding of the notation and expands their capacity to use it to describe functions. Display an image of a “function machine” with “cube the input” as the rule. Tell students that a function takes any input and cubes it to generate the output. Ask students to • Find the output when the inputs are 0, 1, 3, and $x$. • Write the input-output relationship using function notation and name the function $g$. $g(0)=0\\ g(1)=1\\ g(3)=27\\ g(x)=x^3$ If not mentioned by students, point out that these equations describe the same function as that shown by the second table in the warm-up. Explain to students that some functions have a specific rule for getting its output. The rule can be described in words (like “cube the input”) or with expressions (such as $x^3$). Tell students that they’ll now look at some rules expressed in both ways. Representation: Internalize Comprehension. Chunk this task into more manageable parts to differentiate the degree of difficulty or complexity. Give students a subset of the expressions and descriptions to start with and hold a brief small-group or whole-class discussion once students have completed the first match. Invite 1–2 students to share their strategies for finding a match before introducing the remaining expressions and descriptions. Supports accessibility for: Conceptual processing; Organization Student Facing Here are descriptions and equations that represent four functions. A. To get the output, subtract 7 from the input, then divide the result by 3. B. To get the output, subtract 7 from the input, then multiply the result by 3. C. To get the output, multiply the input by 3, then subtract 7 from the result. D. To get the output, divide the input by 3, and then subtract 7 from the result. 1. Match each equation with a verbal description that represents the same function. Record your results. 2. For one of the functions, when the input is 6, the output is -3. Which is that function: $f, g$, $h$, or $k$? Explain how you know. 3. Which function value—$f(x), g(x), h(x)$, or $k(x)$—is the greatest when the input is 0? What about when the input is 10? Student Facing Are you ready for more? Mai says $f(x)$ is always greater than $g(x)$ for the same value of $x$. Is this true? Explain how you know. Activity Synthesis Invite students to briefly share how they matched the equations and verbal descriptions in the first question. Discuss questions such as: • “The expressions for functions $f$ and $g$ both involve multiplying by 3 and subtracting 7. How are they different?” (The order in which the operations happen is different. Function $f$ first multiplies the input by 3, and then 7 is subtracted from the result. Function $g$ first subtracts 7, then multiplies the result by 3.) • “The expressions for $h$ and $k$ both involve subtracting 7 and dividing by 3. How did you decide which one corresponds to description A and which one corresponds to D?” (By looking at what is done to $x$ first. In $h$, $x$ is divided by 3 before 7 is subtracted, so it must correspond to D.) Next, ask students how they determined which function has $(6, \text-3)$ as an input-output pair and which function has the greatest output when $x$ is 0 and when $x$ is 10. Highlight explanations that mention evaluating each function at those input values and seeing which one generates -3 for the output or gives the greatest output. The functions in this activity are given without a context. Tell students that they will now look at rules that describe relationships between quantities in situations. Speaking, Representing: MLR8 Discussion Supports. Use this routine to support whole-class discussion as students explain how they matched the descriptions to the equations. Display the following sentence frames for all to see: “The equation _____ matches _____ because . . .” and “I noticed _____, so . . . .” Encourage students to challenge each other when they disagree. If necessary, revoice student ideas to demonstrate using mathematical language such as input and output. This will help students use the structure of equations to make connections between equations and descriptions of Design Principle(s): Support sense-making 4.3: Rules for Area and Perimeter (20 minutes) Previously, students interpreted rules of functions only in terms of the operations performed on the input to lead to the output. In this activity, students analyze functions that relate two quantities in a situation and work to define the relationship between the quantities with a rule. They do so by creating a table of values and generalizing the process of finding one quantity given the other. Students also plot the values in each table to see the graphical representation of the functions. The mathematical reasoning here is not new. Students have done similar work earlier in the course, when investigating expressions and equations. What is new is seeing these relationships as functions and using function notation to describe them. Students are likely to graph the functions by plotting the values in the tables and then connecting the points with a curve. As students work on the second set of questions about a perimeter function, which is linear, look for those who relate $P(\ell)=2\ell + 6$ to a linear equation, namely $y=2x+6$, and then graph a line with a vertical intercept of $(0,6)$ and a slope of 2. Invite them to share their thinking during the whole-class discussion. Arrange students in groups of 2. Give students a few minutes of quiet time to work on the first set of questions, and then a moment to discuss their responses with their partner. Then, pause for a brief discussion before students proceed to the second set of questions. Invite students to share their rule for the area function. Some students may have written $A = s^2$, while others $A(s)=s^2$. Ask students who wrote each way to explain their reasoning. Highlight explanations that point out that $A$ is the name of the function and that function notation requires specifying the input, which is $s$. Clarify that in the past, we may have used a variable like $A$ to represent the area, but in this case, $A$ is used to name a function to help us talk about its input and output. If we wish to also use a variable to represent the output of this function (instead of using function notation), it would be helpful to use a different letter. Student Facing 1. A square that has a side length of 9 cm has an area of 81 cm^2. The relationship between the side length and the area of the square is a function. 1. Complete the table with the area for each given side length. Then, write a rule for a function, $A$, that gives the area of the square in cm^2 when the side length is $s$ cm. Use function notation. │side length (cm) │area (cm^2) │ │1 │ │ │2 │ │ │4 │ │ │6 │ │ │$s$ │ │ 2. What does $A(2)$ represent in this situation? What is its value? 3. On the coordinate plane, sketch a graph of this function. 2. A roll of paper that is 3 feet wide can be cut to any length. 1. If we cut a length of 2.5 feet, what is the perimeter of the paper? 2. Complete the table with the perimeter for each given side length. Then, write a rule for a function, $P$, that gives the perimeter of the paper in feet when the side length in feet is $\ell$. Use function notation. │side length (feet) │perimeter (feet) │ │1 │ │ │2 │ │ │6.3 │ │ │11 │ │ │$\ell$ │ │ 3. What does $P(11)$ represent in this situation? What is its value? 4. On the coordinate plane, sketch a graph of this function. Anticipated Misconceptions If students struggle to graph the functions, suggest that they use the coordinate pairs in the tables to help them. Activity Synthesis Select students to share the rule they wrote for the perimeter function (from the second set of questions) and how they determined the rule. Students may have written expressions of different forms for $P(\ell)$: Record and display the variations for all to see and discuss whether they all give the value of $P(\ell)$. Ask students to explain how they know these expressions are equivalent and define the same Next, discuss how students sketched the graph of the function. If no students made a connection between the slope and vertical intercept of the graph of $P$ to the parameters in their equation, ask them about it. For example, display the graph of $P$ and ask students to use it to write an equation for the line. Lesson Synthesis Display for all to see the equations $f(x) = 5x + 3$ and $g(x)=10x-4$. Ask students, • “How would you describe to a classmate who is absent today what each equation means? What would you say to help them make sense of these?” (Each equation gives the rule of a function. The rule for $f$ says that, to get the output, we multiply the input by 5 and add 3. The rule for $g$ says that the output is 10 times the input, minus 4.) • “How do the rules help us find the value of $f(10)$ or $g(10)$?” (If we substitute 10 for $x$ in each equation and evaluate the expression, we would have the value of $f$ or $g$ at $x= 10$, which are 53 and 96, respectively.) • “Is it possible to graph a function described this way? How?” (We could create a table of values and find the coordinate pairs at different $x$-values. Or, if a rule is expressed as a linear equation, we could use it to identify the slope and vertical intercept of the graph.) 4.4: Cool-down - Perimeter of a Square (5 minutes) Student Facing Some functions are defined by rules that specify how to compute the output from the input. These rules can be verbal descriptions or expressions and equations. For example: Rules in words: • To get the output of function $f$, add 2 to the input, then multiply the result by 5. • To get the output of function $m$, multiply the input by $\frac12$ and subtract the result from 3. Rules in function notation: • $f(x) = (x + 2) \boldcdot 5$ or $5(x+2)$ • $m(x) = 3 - \frac12x$ Some functions that relate two quantities in a situation can also be defined by rules and can therefore be expressed algebraically, using function notation. Suppose function $c$ gives the cost of buying $n$ pounds of apples at \$1.49 per pound. We can write the rule $c(n) = 1.49n$ to define function $c$. To see how the cost changes when $n$ changes, we can create a table of values. │pounds of apples, $n$ │cost in dollars, $c(n)$ │ │0 │0 │ │1 │1.49 │ │2 │2.98 │ │3 │4.47 │ │$n$ │$1.49n$ │ Plotting the pairs of values in the table gives us a graphical representation of $c$.	{"url":"https://curriculum.illustrativemathematics.org/HS/teachers/1/4/4/index.html","timestamp":"2024-11-03T06:56:04Z","content_type":"text/html","content_length":"121006","record_id":"<urn:uuid:624cc4c2-b8a2-49f7-a57c-04f9b3fa627d>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00243.warc.gz"}
Repeated Games with Incomplete Information over Predictable Systems Consider a stationary process taking values in a finite state space. Each state is associated with a finite one-shot zero-sum game. We investigate the infinitely repeated zero-sum game with incomplete information on one side in which the state of the game evolves according to the stationary process. Two players, named the observer and the adversary, play the following game. At the beginning of any stage, only the observer is informed of the state ξ[n] and is therefore the only one who knows the identity of the forthcoming one-shot game. Then, both players take actions, which become publicly known. The paper shows the existence of a uniform value in a new class of stationary processes: ergodic Kronecker systems. Techniques from ergodic theory, probability theory, and game theory are employed to describe the optimal strategies of the two players. Funders Funder number Deutsche Forschungsgemeinschaft KA 5609/1-1 Israel Science Foundation 591/21 • Kronecker systems • incomplete information on one side • irrational rotation of the unit circle • odometers • repeated games • stationary processes • uniform value Dive into the research topics of 'Repeated Games with Incomplete Information over Predictable Systems'. Together they form a unique fingerprint.	{"url":"https://cris.tau.ac.il/en/publications/repeated-games-with-incomplete-information-over-predictable-syste","timestamp":"2024-11-04T00:57:12Z","content_type":"text/html","content_length":"49623","record_id":"<urn:uuid:46b41c35-cc3c-4a00-b52f-fa23e48e8939>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00618.warc.gz"}
Scalar mesons in radiative phi ->(KK-0)-K-0 gamma decay We study the radiative phi -> K-0(K) over bar (0)gamma decay within a phenomenological framework by considering the contributions of the f(0)(980) and a(0)(980) scalar resonances. We calculate the branching ratio B(phi -> K-0(K) over bar (0)gamma) by employing the coupling constants g(f0)K(+)K(-) and g(a0)K(+)K(-) as determined by different experimental groups. A. Gokalp, C. S. Korkmaz, and O. Yılmaz, “Scalar mesons in radiative phi ->(KK-0)-K-0 gamma decay,” PHYSICAL REVIEW D, pp. 0–0, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/	{"url":"https://open.metu.edu.tr/handle/11511/63291","timestamp":"2024-11-03T13:04:15Z","content_type":"application/xhtml+xml","content_length":"53882","record_id":"<urn:uuid:2b33bf25-d546-44c1-ba84-45d60a5fcc02>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00648.warc.gz"}
Five Minute Lessons How to check if a cell contains a valid number When writing a formula that references other cells, it can sometimes be useful to check that those cells contain a valid value. In this lesson, we'll look at Excel's ISNUMBER function as a way of doing this. I was recently asked by a reader to provide a formula that would return the result of a calculation if a certain value cell contained a number, and leave the cell blank if that value cell contained anything that wasn't a valid number. There are various ways to check for errors in an Excel formula. In this example, the best function to use is the ISNUMBER function. ISNUMBER Syntax ISNUMBER has a very simple syntax: The ISNUMBER function will return either TRUE or FALSE. For the purposes of writing additional formulas, you can consider TRUE = 1 and FALSE = 0. I'll show you an example later in this lesson. The value you provide to ISNUMBER can be a reference to another cell, such as: It can also be a direct value: • =ISNUMBER(3) returns TRUE Here are some examples: • =ISNUMBER(1) returns TRUE • =ISNUMBER("1") returns FALSE • =ISNUMBER(five) returns FALSE • =ISNUMBER(3) * 30 returns 30 (remember that TRUE = 1, so TRUE * 30 is the same as 1 * 30) • =ISNUMBER(happy) * 30 returns 0 (remember that FALSE = 0, so FALSE * 30 is the same as 0 * 30) A worked example for the ISNUMBER function. As I mentioned earlier, this lesson was inspired by someone who asked how to return the results of a calculation if a certain cell contained a number, and leave the cell blank if the cell did not contain a number. This scenario is preferable to seeing #VALUE! if the cell doesn't contain a number. In this case, I'll use Excel's IF function combined with the ISNUMBER function to get the right outcome. Suppose we have this example (it's a simple calculation simply to illustrate the point). We need to calculate the Result in column C, but only when column A contains a valid number. Here is the formula to use in C2: • =IF(ISNUMBER(A2),A2B2,"") Here's what this formula does: • First, it checks the contents of A2. • If A2 contains a number, the formula calculates A2B2 and returns the result. • If A2 doesn't contain a number, the formula simply returns "" - quote marks with nothing between them. In doing so, cell C2 appears to be empty. Note that you could, if you prefer, put something between the quote marks to warn other users that there is an invalid value in A2. For example: • =IF(ISNUMBER(A2),A2*B2,"Not valid") Here's the finished version of our example: Note that although C4 and C5 appear to be empty, they are not - they still contain our formula. Changing the values in A4 or A5 would change the values in those cells so they are no longer blank. The ISNUMBER function is a quick, easy way to check if a cell contains a number. Our example used the IF function to illustrate how ISNUMBER can be used. If you haven't used IF in a formula before, you can read our lesson on the IF function here. Finally, If you have any questions about this lesson, please post them in the comments below. Our Comment Policy. We welcome your comments and questions about this lesson. We don't welcome spam. Our readers get a lot of value out of the comments and answers on our lessons and spam hurts that experience. Our spam filter is pretty good at stopping bots from posting spam, and our admins are quick to delete spam that does get through. We know that bots don't read messages like this, but there are people out there who manually post spam. I repeat - we delete all spam, and if we see repeated posts from a given IP address, we'll block the IP address. So don't waste your time, or ours. One other point to note - if you post a link in your comment, it will automatically be deleted. Comments on this lesson while using formula ISNUMBER return value shows false. how can convert it in number	{"url":"https://fiveminutelessons.com/learn-microsoft-excel/how-check-if-cell-contains-valid-number","timestamp":"2024-11-11T10:49:56Z","content_type":"text/html","content_length":"408905","record_id":"<urn:uuid:33b20457-4d71-4b0c-9969-85442c253676>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00072.warc.gz"}
How to get the y coordinate of a point based on the x and z coordinates So basically I am working on a game at the moment and I have a random object spawner which spawns the object randomly on the plane, this worked before as I had a simple plane set at a y of 3, now I received a new plane .obj which is sloped and has different y values at different points, and so the spawner does not work any more. My question is how can I get the y position of a point based on the x and z coordinates and based on the returned y position spawn the object. I was thinking of raycasting but from what I can tell it does not return the Y value when it hits something. Is there any way to do this or would I have to change the terrain and set a specified Y pos for each section of the terrain. Thank you. What’s wrong with raycast? The point property of the raycasthit gives you a Vector 3 in world space, so you can take the y coordinate straight from that: Unity - Scripting API: RaycastHit.point If you think about it abstractly, an x-coordinate specifies “some distance to the right”, and a z-coordinate specifies “some distance forward”. So this: Vector3 v = new Vector3(x, 0, z); Is the same as: Vector3 v = Vector3.right * x + Vector3.forward * z; The above uses “world space”. Every object in Unity has a transform component, which keeps track of its position, rotation, and scale. The transform also allows you to convert between world space and “local space” (relative to that specific transform). So you could use something like this: Vector3 v = transform.TransformPoint(x, 0, z); Vector3 v = transform.position + transform.right * x + transform.forward * z; All of this assumes that the transform’s opinion of “right” and “forward” agrees with what you’re expecting. If they don’t, it’s simple enough to switch around the axes: Vector3 v1 = new Vector3(0, x, z); //for example Vector3 v2 = transform.TransformPoint(v1); You’ll also need a reference to the plane’s very own transform. Maybe that’s the same transform your script is attached to, or maybe you need to set up a reference in the inspector. There are plenty of tutorials to help with that bit, if you need.	{"url":"https://discussions.unity.com/t/how-to-get-the-y-coordinate-of-a-point-based-on-the-x-and-z-coordinates/111286","timestamp":"2024-11-12T08:57:52Z","content_type":"text/html","content_length":"31326","record_id":"<urn:uuid:96da6465-07e2-454d-9647-787fcc8cb4df>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00412.warc.gz"}
3.06 Division with larger numbers \| Grade 5 Math \| Florida BEST 5 - 2022 Edition Are you ready? Do you remember how to perform long division when dividing large numbers by a single digit? Let's try this problem to practice. Find the value of $951$951$\div$÷$4$4. 1. $951$951$\div$÷$4$4$=$=$\editable{}$ remainder $\editable{}$. We can use long division to divide by $2$2 digit numbers in the same way that we would divide by a single digit. This video looks at how we set out our work when using long division to divide by a 2 digit number. Find the value of $5016\div57$5016÷57 Question 2 Find the value of $379\div29$379÷29. 1. $379\div29=\editable{}$379÷29= with remainder $\editable{}$ When we solve division, if we cannot share the total (dividend) equally, we end up with a remainder.	{"url":"https://mathspace.co/textbooks/syllabuses/Syllabus-1115/topics/Topic-21486/subtopics/Subtopic-276586/?ref=blog.mathspace.co","timestamp":"2024-11-04T07:46:22Z","content_type":"text/html","content_length":"370481","record_id":"<urn:uuid:5d980f2c-3949-4031-a188-dfebc695bda0>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00628.warc.gz"}
Welcome to Theodore Chu's Docs \| Theo Chu's Docs Welcome to Theodore Chu's Docs Hello! Thanks for stopping by. My name is Theodore, and I'm a human being. This website is a place for me to document my personal projects and products, favorite tools, and fun explorations. I hope it can help you learn, think, and feel. 🤓 🤔 🥺 Everything is a work in progress. You can read more about me on my about page. Be sure to read the disclaimer. Please contact me if you have any questions or need help with anything. 🙂 If there's one idea that I'd offer you right now, it's that if you apply your mind, body, and heart over time, you can grow and learn to be and do anything. This is the power of compounding 1% every Day 1: $1.00 \times 1.01 = 1.01$ Day 2: $1.01 \times 1.01 = 1.0201$ Day 3: $1.0201 \times 1.01 = 1.030301$ $\cdot \cdot \cdot$ Day 100: $1 \times \left(1 + \frac{1}{100}\right)^{100} = \left(1.01\right)^{100} = 2.70$ After just 100 days, you will have grown by 170% from where you started. Who will you be? What will you do? See the docs for my open-source products: Technical Docs See my technical notes:	{"url":"https://theochu.com/","timestamp":"2024-11-08T20:55:38Z","content_type":"text/html","content_length":"28516","record_id":"<urn:uuid:de90529c-ef2e-44aa-bdbc-5279e88e0a3e>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00782.warc.gz"}
For what values of x, if any, does f(x) = 1/((x-1)(x-7)) have vertical asymptotes? \| HIX Tutor For what values of x, if any, does #f(x) = 1/((x-1)(x-7)) # have vertical asymptotes? Answer 1 The denominator of the rational function cannot equal zero as this would lead to division by zero which is undefined. Setting the denominator equal to zero and solving for x will give the values that x cannot be and if the numerator is non-zero for these values of x then they must be vertical asymptotes. solve: (x-1)(x-7) = 0 → x = 1 , x = 7 #rArrx=1,x=7" are the asymptotes"# graph{1/((x-1)(x-7)) [-10, 10, -5, 5]} Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer 2 Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer 3 The function ( f(x) = \frac{1}{(x-1)(x-7)} ) will have vertical asymptotes where the denominator, ( (x-1)(x-7) ), equals zero. Setting each factor equal to zero and solving for ( x ) gives us the values where vertical asymptotes occur: 1. ( x - 1 = 0 ) gives ( x = 1 ). 2. ( x - 7 = 0 ) gives ( x = 7 ). Thus, the function has vertical asymptotes at ( x = 1 ) and ( x = 7 ). Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer from HIX Tutor When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some Not the question you need? HIX Tutor Solve ANY homework problem with a smart AI • 98% accuracy study help • Covers math, physics, chemistry, biology, and more • Step-by-step, in-depth guides • Readily available 24/7	{"url":"https://tutor.hix.ai/question/for-what-values-of-x-if-any-does-f-x-1-x-1-x-7-have-vertical-asymptotes-8f9af9cd0a","timestamp":"2024-11-01T23:48:47Z","content_type":"text/html","content_length":"574771","record_id":"<urn:uuid:ce89d22b-2b1e-4c96-8c17-f6c42253a8b0>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00774.warc.gz"}
Suggested Curriculum for Physical Chemistry - Quantum Chemistry Copyright (c) RDMCHEM LLC 2019,2021,2022,2023 Computational chemistry is a powerful tool for introducing, exploring, and applying concepts encountered throughout the chemistry curriculum. The aim of these lessons is to provide students and/or instructors ways to interact with selected topics using the QuantumChemistry package exclusively within Maple with no need to collate multiple software packages! Lessons are written to emphasize learning objectives rather than Maple coding. However, in order to show students and instructors how the calculations are set up, each lesson contains the Maple syntax and coding required to interact with the selected topic. In some cases, questions are asked of the student with the answer provided as a subsection. As such, each lesson can be used 'as-is' or modified as desired to be used by students in a classroom setting, laboratory setting, or as an out of class guided inquiry assignment. While lessons are largely independent of each other and may be done in any order, the following suggestion corresponds to the ordering of topics typically encountered in a Physical Chemistry - Quantum Chemistry course. Lessons 1 and 2 (Blackbody Radiation and Photoelectric Effect) correspond to early experiments related to the quantization of energy. Lessons 3 and 4 (Particle in a Box (H chain) and Particle in a Box (Dyes) ) involve the Schr\303\266dinger equation and its solutions with applications to a chain of hydrogen atoms and absorption spectra of conjugated dyes (a common undergraduate physical chemistry experiment), respectively. Lesson 5 (Vibrational Motion and the Harmonic Oscillator) explores vibrational motion and the harmonic oscillator approximation for several diatomic molecules. Lesson 6 (Variational Theorem) introduces the variational theorem and related basis set / matrix methods for the particle in a box and fir the Morse oscillator for hydrogen chloride. Lesson 7 (Molecular Orbitals) focuses on molecular orbital (MO) theory as applied to hydrogen fluoride. Lesson 8 (Huckel Theory and Conjugated Molecules) explores Huckel MO theory for the description of conjugated molecules, comparing its predictions with those from an ab initio electronic structure method. Lesson 9 (Koopman's Theorem and Drug Activities) introduces Koopman's theorem for approximating ionization energies with applications to small isoelectronic binary compounds and to non-steroidal anti-inflammatory drug (NSAID) activities. Lesson 10 (Geometry Optimization and Normal Modes) explores a very common quantum mechanical calculation, geometry optimization, and the subsequent normal mode analysis of the vibrational modes in the molecule. Lesson 11 (Vibrational Spectroscopy) uses basis set / matrix methods introduced in Lesson 6 to calculate a potential energy surface for a diatomic and then calculates the rovibrational energy levels and associated Q- and R-branches. Lesson 12 (Fermi's Golden Rule) derives Fermi's Golden Rule for transition rates and present an application to a fluorescent molecule in the presence of a mirror. 1. Blackbody Radiation This lesson compares Rayleigh-Jeans and Planck distributions for blackbody radiation and applies Planck's distribution to calculate the temperature of the universe. 2. Photoelectric Effect This lesson uses the photoelectric effect to find an 'empirical' fit to Planck's constant. 3. Particle in a Box (H-atoms) This lesson explores solutions (energies and wavefunctions) to the Schr\303\266dinger equation for a particle in a symmetric box and applies the particle in a box model to a chain of hydrogen atoms. 4. Particle in a Box (Dyes) Similar to Lesson 3, this lesson focuses on the solutions to the Schr\303\266dinger equation for a particle in a box with an application to absorption spectra of conjugated dye molecules. 5. Vibrational Motion and the Harmonic Oscillator This lesson explores vibrational motion and the harmonic oscillator approximation for several diatomic molecules. 6. Variational Theorem This lesson explores the variational theorem using particle in a box and the Morse oscillator for hydrogen chloride. 7. Molecular Orbitals This lesson emphasizes the linear combination of atomic orbitals (LCAO) approach to calculating molecular orbitals for hydrogen fluoride. 8. Huckel Theory and Conjugated Molecules This lesson explores Huckel MO theory for the description of conjugated molecules, comparing its predictions with those from an ab initio electronic structure method. 9. Koopman's Theorem and Drug Activities This lesson uses Koopman's theorem to approximate ionization energies of small binary compounds. 10. Geometry Optimization and Normal ModesJSFH This lesson involves finding the optimum geometry for a triatomic and the associated vibrational normal modes. 11. Vibrational Spectroscopy This lesson allows students to go beyond a normal mode analysis to calculate ab initio potential energy surface and associated rovibrational energies of a diatomic using a variational matrix method. 12. Fermi's Golden Rule This lesson derives Fermi's Golden Rule for transition rates and present an application to a fluorescent molecule in the presence of a mirror. JSFH	{"url":"https://fr.maplesoft.com/support/help/content/11929/QuantumChemistry-PhysicalChemistry-Quantum.mw","timestamp":"2024-11-04T01:32:07Z","content_type":"application/xml","content_length":"30162","record_id":"<urn:uuid:0d9c7f12-5872-491c-aa9b-ca9c325e3299>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00501.warc.gz"}
Related Queries: Data science interview questions \| Typical questions asked in a data science interview \| Data Science skills test \| Technical tests for Data Scientist \| Data Science Questions \| Interview questions of data science for freshers What does t-SNE stand for in dimensionality reduction? Temporal Sequence Numerical Embedding t-distributed Stochastic Neighbor Embedding Time Series Network Estimation Transformed Spatial Neighborhood Evaluation What is the diff. between lin. and log. regression? Linear: predicts continuous output Logistic: predicts binary outcome Logistic: uses sigmoid function All of the above What is the main purpose of curriculum learning? To design school curricula To train models on progressively harder tasks To speed up convergence To reduce model complexity What is the difference between a statistic and a parameter? There is no difference Statistic describes sample, parameter describes population Parameter describes sample, statistic describes population They are the same concept What programming languages/tools are used in data science? Python, R, SQL Pandas, Numpy, Matplotlib Spark, Hadoop All of the above Which of these is NOT a common technique for handling missing data? Mean imputation Median imputation Mode imputation Random imputation What does ANOVA stand for? Analysis of Variance Analysis of Variables Advanced Notice of Variable Alteration Assessment of Numerous Variable Attributes What does API stand for in web development? Advanced Programming Interface Application Programming Interface Automated Process Integration Analytical Protocol Implementation What does CORS stand for in web development? Cross-Origin Resource Sharing Centralized Object Retrieval Service Compiled Output Rendering System Controlled Origin Reference Standard What does the standard deviation measure? The average distance of data points from the mean The spread or variability of the data The most frequent value in the data The middle value in the data Score: 0/10 What is the purpose of early stopping in neural network training? To speed up training To prevent overfitting To increase model complexity To reduce memory usage What is the probability that Karen's second child is a girl, given that one child is a girl? What does RDBMS stand for in database systems? Rapid Database Management System Relational Database Management System Recursive Data Backup and Monitoring Service Remote Digital Business Modeling Strategy What is the primary goal of t-SNE? Dimensionality reduction and visualization Feature selection Which of these is not a measure of model performance? What does GBM stand for in ensemble learning? General Boosting Method Gradient Boosting Machine Grouped Binary Model Global Benchmark Mechanism What is a statistical model? A statistical model is a mathematical representation of a real-world process A statistical model is a type of database A statistical model is a tool for data visualization A statistical model is a type of machine learning algorithm How is AUC different from ROC? AUC is a curve, ROC is a value ROC is a curve, AUC is a value They are the same thing They are unrelated concepts What is the primary goal of sentiment analysis? To classify emotions To predict stock prices To cluster documents To reduce dimensionality How does machine learning differ from large language models? ML is broader and includes various types of models, while LLMs are specialized for language tasks LLMs are broader and include various types of models, while ML is specialized for image tasks Both are identical in scope and application LLMs do not use machine learning techniques Score: 0/10 What is the main purpose of feature engineering? To remove all features To create new informative features To compress existing features To encrypt feature data What is the purpose of the Durbin-Watson test? To check for multicollinearity To check for autocorrelation in residuals To assess normality To test for heteroscedasticity What is the primary goal of data archiving? To increase data accessibility To preserve data for long-term retention To visualize data To encrypt data What is the purpose of the Earth Mover's Distance (EMD) in machine learning? To perform classification To measure the distance between probability distributions To reduce dimensionality To generate synthetic data What assumption does Naive Bayes make about the relationship between features? Strong dependence Conditional independence Linear relationship Polynomial relationship What does LRP stand for in neural network interpretation? Layer-wise Relevance Propagation Linear Regression Prediction Logarithmic Response Processing Localized Random Projection What is the purpose of the Levenshtein distance in natural language processing? To perform sentiment analysis To measure the similarity between two strings To generate word embeddings To perform named entity recognition What is the main purpose of data archiving? To delete old data To store historical data for long-term retention To compress archived data To encrypt old records What type of kernel is typically used in support vector regression for non-linear relationships? Linear kernel Polynomial kernel RBF kernel Sigmoid kernel Which algorithm is best for multi-modal learning? Neural Networks Decision Trees Linear Regression Score: 0/10 Which of these is NOT a common method for collaborative filtering? Matrix factorization Random filtering What does ROC stand for in model evaluation? Rate of Change Receiver Operating Characteristic Return on Computing Range of Correlation What is the diff. between K-means and K-medoids? K-means: assigns data to nearest centroid K-medoids: assigns data to nearest data point K-medoids: more robust to outliers All of the above What is the main advantage of using Neural Architecture Search over manual architecture design? Faster training Automatic discovery of optimal architectures Lower memory usage Simpler hyperparameter tuning How is the random forest algorithm typically used in time series forecasting? To decompose time series To classify time series To generate ensemble forecasts To test for stationarity What does the Kendall's tau coefficient measure? Linear correlation Rank correlation Partial correlation Multiple correlation What is the main difference between a decision tree and a random forest? Decision trees are unsupervised Random forests combine multiple decision trees Decision trees are only for regression There is no difference What does MDM stand for in data management? Master Data Management Multiple Database Merging Metadata Driven Modeling Modular Data Mining Which method is commonly used to choose the optimal number of clusters? Elbow method Grid search Backward elimination What are some common challenges in data science? Data quality, data quantity, and model interpretability Data quality, data quantity, and building machine learning models Model interpretability, visualizing data, and storing and managing data None of the above Score: 0/10	{"url":"https://coolgenerativeai.com/data-science-analytics-interview-questions/","timestamp":"2024-11-06T18:08:31Z","content_type":"text/html","content_length":"192507","record_id":"<urn:uuid:2a12f9a2-74ce-42ca-a767-5419d81596e8>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00494.warc.gz"}
Export Reviews, Discussions, Author Feedback and Meta-Reviews Submitted by Assigned_Reviewer_1 Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http: This paper develops a new method of performing blind source separation, by formulating the problem as an additive factorial HMM (AFHMM), and then applying signal aggregate constraints (SACs). The motivation behind this is that additional domain knowledge can be incorporated to improve the separation of the time series into components. The example used throughout the paper is energy disaggregation, where the components of domestic energy use (relating to individual appliances) can be better separated, when information relating to total (expected) usage of each appliance in a time period is incorporated. The objective function that is maximized to perform the separation (which is the log of the posterior distribution of the hidden chains given the observed data) is then transformed into a convex optimization problem. The efficacy of the method is demonstrated in practice with both a toy data set, and with real data from domestic energy output readings. The paper is technically sound with a strong simulation section. The method, as expected, performs favorably in contrast to regular AFMM and also AFAMAP (a recently developed alternative method) - neither of which incorporate the SACs. The improvements are shown to be significant using t-tests. The author(s) also show that the speed of optimization is comparable to AFAMAP. My only question on the results section is why the author(s) used such a low noise variance in their toy example - is this to make the illustration of Figure 2 clear that they can separate the signal very well and other methods cannot? Some clarification would be good here otherwise the problem setup seems "overly" toy and rather easy. Or are these signal to noise ratios common in real data? On this note, the authors could also comment on the signal/noise ratio between the mains readings and the aggregate appliance output in the energy application. The theoretical aspects of the paper are overall well presented and structured. The paper would perhaps benefit from a proof that the final procedure in equation (6) is indeed convex, as it is not quite clear to me using the reasoning provided. In addition, theoretical scaling arguments (with respect to data length and number of hidden states) would benefit the paper, and compliment the simulation findings. Are the methods tractable if used for much larger data sets and state spaces, and how would this contrast with AFAMAP? The paper is well written and structured. The problem is nicely motivated in the introduction, with a clear description of relevant literature, though I am not that familiar with this problem, so cannot definitively state that nothing has been omitted here. I point to a small (potential) error on page 4 (line 202), in the unnumbered equation before (6), where I believe there should be no commas in the subscripts proceeding the object p, to be consistent with earlier notation on page 3 (unless new notation has been introduced here?) To my knowledge the work is novel and original, though I am not an expert so cannot comment on the significance of these results to the HMM community and to the energy application studied. Addendum: The authors satisfactorily answered my questions in the feedback phase, and I encourage them to make similar clarifications in the next version of the paper. Q2: Please summarize your review in 1-2 sentences This paper proposed a method of performing blind source separation using Additive Factorial HMMs with Signal Aggregate Constraints. The method performs very well, when compared with the state-of-the-art, particularly with real data from an energy disaggregation problem. Submitted by Assigned_Reviewer_18 Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http: An additive factorial hidden Markov model is developed to model electricity usage. The model incorporates the so-called signal aggegate constraint. The quality of the paper is good, but it is really hard to read. There are too many acronyms, and some of them are really log (even 11 letters!) Q2: Please summarize your review in 1-2 sentences It seems that the Authors are looking for a constraint to be placed on the posterior density and so they place a constraint on a prior density. They should state they have an a priori constraint and hence the posterior is constrained. Submitted by Assigned_Reviewer_26 Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http: The paper proposes additive factorial HMM (AFHMM) with signal aggregate constraints (SAC) to deal with blind source separation problem. Authors propose convex quadratic problem for relaxed AFHMM with SAC. The technique shows promising results on both synthetic and real world data. - Paper is well written and has good mathematical foundation. - Problem motivation is good - Evaluation results indicate good boost in performance metrics, NDE and SAE Areas of improvement: - Results are shown as an improvement over AFHMM without SAC and AFAMAP. Both these use less data than SACAFHMM which seems unfair comparison. Are there any other approaches that could use SAC but are not as efficient in computation? - Results in Figure 1 are not clear. It seems like for distance more than 10^4 AFAMAP beats SACAFHMM. Does this indicate that bad constraints can result in much poorer performance? Discussion seem to indicate that results are always better which seems misleading. - I was expecting to see more complex constraints incorporated in the algorithm. For e.g. Person cannot use the heater and cooler at the same time. What about having no more than 3 out of 10 bulbs in the house active at the same time. Things like grinders having time constraints of less than 10 mins. To summarize, there could various kinds of constraints that could be specified. Is it possible to extend the algorithm to other kinds of constraints as well? Q2: Please summarize your review in 1-2 sentences Paper is well written and provides good motivation into the problem. Future work involves extending the model further to other kinds of constraints. Submitted by Assigned_Reviewer_40 Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http: The paper proposes an extension to the additive factorial HMM model where additional constraints are added to require that the sum of individual chain outputs to be close to some reasonable (known) aggregate value. The authors propose a convex relaxation to MAP inference and apply the algorithm to real-world data sets involves energy disaggregation, both across 100 UK homes with low frequency readings, and 10 homes with higher frequency readings (but without each appliance monitored). The ideas presented here are fairly straightforward, and the authors use a relatively simple optimization formulation to solve these problems, but overall the work is still compelling. The authors are applying these methods to relatively large real-world data sets, and as a paper that combines both applied and algorithmic elements, I think that it is a success. The comments below could help to improve the paper in my view: A motivation for AFAMAP to enforce the constraint that one chain stages state at a time is that this can improve the relaxation to achieve integer solutions more often. Does the SACAFHMM optimization formulation also accomplish a similar thing, or do the resulting solutions still have lower error despite have non-integral solutions? Some discussion of these points would be very helpful as it would also further elucidate the distinctions. Fundamentally, it seems like the AFAMAP and SACAFHMM ideas are orthogonal: one could just as easily include the SACAFHMM contraints in the optimization formulation for AFAMAP. While I don't expect feedback on this during the author response, I would strongly encourage them to try this for a final version. The authors do seem to conflate models and optimization procedures a few times. For instance, comparing the results of "AFHMM" versus "AFAMAP" isn't being very precise: AFAMAP is an algorithm for (approximately) computing MAP solutions to the AFHMM, and I believe by AFHMM here they really mean alternating Viterbi optimization. Is this correct? This also gets to the point above, where the strategies of the different algorithms presented here could easily be combined and might in fact perform better than the current approaches. Q2: Please summarize your review in 1-2 sentences The paper proposes a simple extension and optimization to solve a variant of the AFHMM, but the results on real world data is compelling here, and overall the paper looks reasonable. Q1:Author rebuttal: Please respond to any concerns raised in the reviews. There are no constraints on how you want to argue your case, except for the fact that your text should be limited to a maximum of 6000 characters. Note however, that reviewers and area chairs are busy and may not read long vague rebuttals. It is in your own interest to be concise and to the point. We thank all reviewers for their very helpful comments. The only question on the results is our use of a low noise variance in the toy data. We will provide an analysis of sensitivity of results to noise variance in the final paper, including calculation of signal/noise ratio in the real data and how that relates to the toy data results. * Convexity: This is observed by noting that the objective function in (6) has a linear component and a quadratic component, and the constraint is linear, so this is a convex quadratic programming problem (and hence convex). * Scaling: Both AFAMAP and SACAFHMM are convex quadratic programming (CQP) problems. CQP has known computational bounds (polynomial in the number of time steps times the total number of states of the appliances, which we will note in the final paper.) In practice our implementations of SACAFHMM and AFAMAP scale similarly, since the optimization problem for SACAFHMM has the same number of variables as AFAMAP, although AFAMAP actually has more constraints. REVIEWER 18: We thank the reviewer's positive comments. REVIEWER 26 * Fairness of our comparison: We are unaware of any previous research that uses SAC. The point of our method is to provide a way to incorporate prior knowledge (i.e., the SAC) into the separation problem. Therefore, our experiments were specifically designed to compare the effect of having prior knowledge to not having it. * Figure 1: Yes, this is correct, this experiment indicates that extremely inaccurate constraints are worse than no constraints at all. We would argue that this is an expected result. The results on the energy data indicate that in real-world scenarios, it is possible to obtain constraint values that are reliable enough to improve performance. * More complex constraints: This is an interesting idea, but the tradeoff is how complex they make the corresponding optimization problem. This is an interesting avenue for future work. REVIEWER 40 * Non-integral solutions: The AFAMAP does help to improve the relaxation to achieve integer solutions more often. Indeed, in our experiments, we observed that SACAFHMM also prefers integer and sparse solutions, which actually does improve the results over AFHMM and AFAMAP as shown in the paper. * AFAMAP and SACAFHMM ideas are orthogonal: We agree. We will try this and report the results in the final paper. * "AFAMAP is an algorithm for (approximately) computing MAP solutions to the AFHMM": In our view, the models for AFAMAP and AFHMM are also different, as we would view the one-at-a-time constraint as an additional modelling assumption within AFAMAP. Yes, the AFHMM results in our paper use alternating Viterbi.	{"url":"https://papers.nips.cc/paper_files/paper/2014/file/2d1b2a5ff364606ff041650887723470-Reviews.html","timestamp":"2024-11-11T21:42:53Z","content_type":"application/xhtml+xml","content_length":"19638","record_id":"<urn:uuid:8725948f-e9c1-4a2f-b777-998f36d1e382>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00064.warc.gz"}
How To Calculate Square Feet 2024 How to Calculate Square Feet Understanding how to calculate square feet is an essential skill, whether you’re measuring a room for new furniture, planning a home renovation, or involved in real estate. Square footage helps you gauge how much space you have available and can influence decisions in various situations. This comprehensive guide will walk you through everything you need to know about calculating square feet. How to Calculate Square Feet Definition of Square Feet Square feet is a unit of area measurement used in the United States and some other countries. It represents the area of a square with sides that measure one foot each. When you calculate square feet, you’re essentially determining how much flat space an area occupies. How to Calculate Square Feet Importance of Knowing How to Calculate Square Feet Knowing how to calculate square feet is important for several reasons: • Real Estate Pricing: Square footage is often a key factor in determining the value of a property. • Renovation and Design: When planning renovations, you need to know the square footage to estimate material costs, such as flooring or paint. • Space Planning: Understanding the area helps you decide if furniture or fixtures will fit in a given space. How to Calculate Square Feet Calculating square feet is a simple mathematical process. The method can vary slightly depending on the shape of the area you are measuring. Here, we break it down by shape type. How to Calculate Square Feet 1. Calculating Square Feet for Rectangles and Squares Step 1: Measure the Length and Width To calculate square feet for rectangular and square areas, you first need to measure the length and width. • Use a measuring tape and ensure both measurements are in feet. How to Calculate Square Feet Step 2: Apply the Formula The formula to calculate square feet is: Square Feet=Length (in feet)×Width (in feet) Example Calculation If a room is 10 feet long and 12 feet wide, the calculation would look like this: Square Feet=10,ft×12,ft=120,sq ft How to Calculate Square Feet 2. Calculating Square Feet for Irregular Shapes For spaces that are not perfectly rectangular or square (such as L-shaped areas), you’ll need to break the area down into smaller sections. Step 1: Divide the Area into Regular Shapes Identify how you can split the shape into smaller rectangles or squares. Step 2: Measure Each Section Measure the length and width of each section individually. Step 3: Calculate Each Section’s Area Use the formula for square feet on each section. Square Feet for Section=Length (in feet)×Width (in feet) Step 4: Sum the Areas Add the square footage from all sections together to get the total square footage. Example Calculation for Irregular Shapes Let’s say you have an L-shaped room that consists of two rectangles: • Section 1: 10 feet by 12 feet • Section 2: 6 feet by 8 feet Calculating each: Section 1=10,ft×12,ft=120,sq ft Section 2=6,ft×8,ft=48,sq ft Total square footage: Total=120,sq ft+48,sq ft=168,sq ft How to Calculate Square Feet Calculating Square Feet for Special Shapes Sometimes you may encounter circular or triangular areas. Here’s how to calculate square footage for those shapes. How to Calculate Square Feet 1. Calculating Square Feet of Triangles The formula for the area of a triangle is: • Base: The length of one side of the triangle. • Height: The perpendicular distance from the base to the opposite vertex. If a triangle has a base of 8 feet and a height of 5 feet: Area=12×8,ft×5,ft=20,sq ft How to Calculate Square Feet 2. Calculating Square Feet of Circles For circular areas, you need the radius (the distance from the center of the circle to the edge). The formula is: If a circular area has a radius of 3 feet: Area≈3.14×(3,ft)2≈28.26,sq ft How to Calculate Square Feet Tools Needed for Measuring Square Feet 1. Measuring Tape A standard measuring tape is essential for measuring lengths and widths, especially in smaller rooms. 2. Laser Measuring Device For larger areas, a laser measuring device can provide quick and accurate results without the hassle of long tape measures. 3. Calculator Keep a calculator handy for quick multiplication and addition as you calculate the square footage of different areas. 4. Sketching Tools Having a paper and pencil to sketch out the space can help visualize how to break it down into manageable sections. How to Calculate Square Feet Current Trends and Innovations in Calculating Square Feet As of 2024, technology is greatly influencing how to calculate square feet. Here are some trends: 1. Digital Measuring Tools Increasingly, homeowners and professionals are using digital tools that can calculate square footage automatically. These devices can measure, calculate, and even create a digital blueprint of a space in seconds. 2. Mobile Apps There are numerous apps available today that allow you to calculate square footage directly from your smartphone. Many of these apps enable you to take pictures of the area and input dimensions, automating calculations. 3. Real Estate Technology In real estate, more listings now showcase detailed square footage calculations using innovative software, allowing potential buyers to compare properties more effectively. 4. Sustainable Materials Planning As awareness of environmental sustainability grows, understanding square footage is crucial for estimating resources needed—such as paint or flooring—encouraging efficient use of sustainable How to Calculate Square Feet What is Usable Square Footage? Usable square footage refers to the amount of space in a home or office that is functional and can be used effectively. It excludes common areas such as hallways and stairwells. How to Calculate Square Feet Importance of Usable Square Footage • Space Planning: Knowing usable square footage helps you plan how best to utilize the available space. • Real Estate Listings: Agents often highlight usable square footage to attract buyers looking for efficient spaces. How to Calculate Square Feet Measuring Square Footage for Different Rooms 1. Bedrooms Measuring bedrooms involves calculating length and width. Pay attention to any alcoves or built-in closets and account for these in your total measurement. 2. Living Rooms For living rooms, measure length and width, considering furniture placement to understand how much usable space remains. 3. Kitchens Kitchens often have many features. Measure areas around appliances and counters while ensuring to capture odd-shaped parts, if any. How to Calculate Square Feet Final Tips for Measuring Square Feet 1. Double-Check Measurements Always double-check your measurements to avoid mistakes. Measure twice, especially in larger spaces. 2. Use the Right Units Make sure you’re using feet for your calculations. If you measured in inches or yards, convert your measurements before plugging them into equations. 3. Be Methodical Approach measuring methodically to avoid missed areas. A careful and organized approach can prevent errors and save time. Calculating square feet is a practical skill that can aid in numerous situations, from home improvement projects to real estate decisions. Whether you’re measuring a simple square or an irregular shape, understanding how to calculate square footage empowers you to make informed choices. By utilizing the formulas provided, tools mentioned, and current trends, you can enhance your knowledge and ensure accuracy in your measurements. Knowing how to calculate square feet can serve not only your daily needs but can also assist in achieving long-term goals related to space optimization and resource allocation. Common Problem Solving blogs: Best Support for Hip Joint Pain Fatty Liver Disease Drug: Live Pure Are Teeth Bones: Unraveling the Mystery 2 hours of sun a day lowering blood sugar Knowing Fat Burner —A Voyage to a Healthier You. AI-Powered Video And Content Creation CelluCare: New Breakthrough In Blood Sugar Science The Ultimate Guide to Dolphin Tattoos Learning to draw is supposed to be difficult Get Paid To Use Facebook, Twitter and YouTube How to Series How to Cancel Kindle Unlimited How to Buy Bitcoin on eToro App How to Deactivate Facebook: A Simple Guide for Everyone How to Delete Instagram Account: A Simple Guide for Everyone How to Screenshot on Windows: A Complete Guide for Everyone How to Screenshot on Mac: A Complete Guide for Everyone How to Change Your Name on Facebook How to Block Someone on TikTok How to Delete Your Facebook Account How Long to Boil Corn on the Cob How Long Does It Take to Get a Passport How to Screen Record on iPhone	{"url":"https://dailybreez.com/how-to-calculate-square-feet/","timestamp":"2024-11-11T06:07:01Z","content_type":"text/html","content_length":"109893","record_id":"<urn:uuid:c7564a3a-54c6-416f-a81f-6c3f9e4d5182>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00518.warc.gz"}
Control Chart Thresholds - Data360_DQ+ - Latest Western Electric Rules and Nelson Rules are process control rule sets invented by statisticians. You can select these rules only for a Control Chart, when plotting measures against time. Western Electric and Nelson rules do not need to be configured. Western Electric Rules This rule set was invented by the Western Electric Company and was first published in 1956. It was first applied to achieve statistical control of manufacturing processes. The rule set consists of the four rules described below. Each rule evaluates how points on the control chart fall within three chart zones. Western Electric Chart Zones Zone A - Between 2 and 3 standard deviations from the center line mean. Zone B - Between 1 and 2 standard deviations from the center line mean. Zone C - Within 1 standard deviation of the center line mean. UCL - Upper Control Limit LCL - Lower Control Limit The 4 Western Electric Rules Western Electric Rule 1 Any single point falls outside the Upper Control Limit (UCL) or Lower Control Limit (LCL). A point at such a position is over 3 standard deviations away from the center line mean, i.e. beyond Zone A. Western Electric Rule 2 Two consecutive points out of three, on the same side of the center line, fall beyond Zone B, i.e. beyond two standard deviations from the mean. These points can fall within Zone A or beyond. Note: This point also breaks Western Electric Rule 1. Western Electric Rule 3 Four consecutive points out of five, on the same side of the center line, fall beyond Zone C, i.e. beyond one standard deviation from the mean. These points can fall in Zone B, Zone A, or beyond. Western Electric Rule 4 Nine consecutive points fall on the same side of the center line mean, in any Zone. Nelson Rules This rule set was first published in the October 1984 issue of the Journal of Quality Technology in an article by Lloyd S. Nelson. Like Western Electric, the Nelson rules are a process control rule set that can be applied to a measure over time. The Nelson rules feature the 8 rules described below, each of which are designed to find trends in a data set. Unlike the Western Electric Rules, Nelson rules do not use the Zone terminology; instead, only standard deviation lines are used. The 8 Nelson Rules Nelson Rule 1 Any single point falls outside the Upper Control Limit (UCL) or Lower Control Limit (LCL). A point at such a position is over 3 standard deviations away from the center line mean. This is the same as Western Electric Rule 1. Nelson Rule 2 Nine or more consecutive points fall on the same side of the center line mean. This is similar to Western Electric Rule 4. Nelson Rule 3 Six or more consecutive points are continually increasing or continually decreasing. Nelson Rule 4 Fourteen or more consecutive points continuously alternate in direction, i.e. extended oscillation. Nelson Rule 5 Two or three consecutive points out of three, on the same side of the center line, fall beyond two standard deviations from the mean. This is similar to Western Electric Rule 2. Nelson Rule 6 Four or five consecutive points out of five, on the same side of the center line, fall beyond one standard deviation from the mean. This is similar to Western Electric Rule 3. Nelson Rule 7 Fifteen consecutive points are all within one standard deviation from the mean. Nelson Rule 8 Eight consecutive points where no point is within one standard deviation from the mean. These points can be found above the mean and below the mean. Tooltips and overlapping threshold rules violation When using either the Western Electric or the Nelson rules sets, multiple rules within these sets can be violated at the same time. For example, see the chart above which depicts Western Electric Rule 2 (but also depicts Rule 1). This situation can also occur when multiple rule sets are used at the same time. For example, if you were using both Western Electric and Nelson on the same chart, Rule 1 from each rule set would always be applied whenever any point beyond 3 standard deviations from the mean occurred. Depending on the data set, a Multipoint or Expression rule could also simultaneously be broken. To account for this behavior, Control Charts have a tool tip functionality that shows all rules that are broken at highlighted points. To activate this functionality, make sure the Toggle data tooltips option is on and then hover over a highlighted point. Standard deviation date filter override for control charts When using control charts, standard deviation lines are drawn based on the standard deviation of the entire date range present in the visualization. This can be overridden, however, by using the Standard Deviation Date Filter Override option. Like other measure options, this option is available by clicking on the measure tab that is being used in your control chart. Once configured, the override redraws standard deviation lines based on the standard deviation of measured values within the specified date range. At the same time, all measured points will still be plotted on your control chart, allowing you to compare points both inside and outside of the override date range to that date range's standard deviation lines.	{"url":"https://help.precisely.com/r/Data360-DQ/Latest/en-US/Data360-DQ-Help/User-guide/Dashboards/Dashboard-elements/Charts-and-tables/Thresholds/Control-Chart-Thresholds","timestamp":"2024-11-13T11:57:48Z","content_type":"text/html","content_length":"763226","record_id":"<urn:uuid:dd96e768-df02-446a-ac8b-e7f69ef3ca3b>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00721.warc.gz"}
Scientists Explain And Improve Upon 'Enigmatic' Probability Formula Science News from research organizations Scientists Explain And Improve Upon 'Enigmatic' Probability Formula October 21, 2003 University Of California, San Diego Scientists at the University of California, San Diego (UCSD) have developed new insight into a formula that helped British cryptanalysts crack the German Enigma code in World War II. Scientists at the University of California, San Diego (UCSD) have developed new insight into a formula that helped British cryptanalysts crack the German Enigma code in World War II. Writing in the Oct. 17 edition of the journal Science, UCSD Jacobs School of Engineering professor Alon Orlitsky and graduate students Narayana P. Santhanam and Junan Zhang shed light on a lingering mathematical mystery and propose a new solution that could help improve automatic speech recognition, natural language processing, and other machine learning software. In the article, Orlitsky and his colleagues unlock some of the secrets of the "Good-Turing estimator," a formula for estimating the probability of elements based on observed data. The formula is named after famed mathematicians I.J. Good and Alan Turing who, during WWII, were among a group of cryptanalysts charged with breaking the Enigma cipher -- the code used to encrypt German military communications. Working at Bletchley Park outside of London, their work has been credited by some with shortening the war by several years. (It also led to the development of the first modern computer, and was documented in a number of books and movies.) The cryptanalysts were greatly aided by their possession of the Kengruppenbuch, the German cipher book that contained all possible secret keys to Enigma, and had been previously captured by British Intelligence. They documented the keys used by various U-boat commanders in previously decrypted messages and used this information to estimate the distributions of pages from which commanders picked their secret keys. The prevailing technique at the time estimated the likelihood of each page by simply using its empirical frequency, the fraction of the time it had been picked in the past. But Good and Turing developed an unintuitive formula that bore little resemblance to conventional estimators. Surprisingly, this Good-Turing estimator outperformed the more intuitive approaches. Following the war, Good published the formula, mentioning that Turing had an "intuitive demonstration" for its power, but not describing what that demonstration entailed. Since then, Good-Turing has been incorporated into a variety of applications such as information retrieval, spell-checking, and speech recognition software, where it is used to learn automatically the underlying structure of the language. But despite its usefulness, "its performance has remained something of an enigma itself," said Orlitsky, a professor in the Electrical and Computer Engineering department. While some partial explanations were given as to why Good-Turing may work well, no objective evaluation or results have been established for its optimality. Additionally, scientists observed that while it worked well under many circumstances, at times, its performance was lacking. Now, Orlitsky, Santhanam, and Zhang believe they have unraveled some of the mystery surrounding Good-Turing, and constructed a new estimator that, unlike the historic formula, is reliable under all conditions. Motivated by information-theoretic and machine-learning considerations, they propose a natural measure for the performance of an estimator. Called attenuation, it evaluates the highest possible ratio between the probability assigned to each symbol in a sequence by any distribution, and the corresponding probability assigned by the estimator. The UCSD researchers show that intuitive estimators, such as empirical frequency, can attenuate the probability of a symbol by an arbitrary amount. They also prove that Good-Turing performs well in general. While it can attenuate the probability of symbols by a factor of 1.39, it never attenuates by a factor of more than 2. Motivated by these observations, they derived an estimator whose attenuation is 1. This means that as the length of any sequence increases, the probability assigned to each symbol by the new estimator is as high as that assigned to it by any distribution. "While there is a considerable amount of work to be done in simplifying and further improving the new estimator," concluded Orlitsky, "we hope that this new framework will eventually improve language modeling and hence lead to better speech recognition and data mining software." Story Source: Materials provided by University Of California, San Diego. Note: Content may be edited for style and length. Cite This Page: University Of California, San Diego. "Scientists Explain And Improve Upon 'Enigmatic' Probability Formula." ScienceDaily. ScienceDaily, 21 October 2003. <www.sciencedaily.com/releases/2003/10/ University Of California, San Diego. (2003, October 21). Scientists Explain And Improve Upon 'Enigmatic' Probability Formula. ScienceDaily. Retrieved November 1, 2024 from www.sciencedaily.com/ University Of California, San Diego. "Scientists Explain And Improve Upon 'Enigmatic' Probability Formula." ScienceDaily. www.sciencedaily.com/releases/2003/10/031020055436.htm (accessed November 1, Explore More from ScienceDaily	{"url":"https://www.sciencedaily.com/releases/2003/10/031020055436.htm","timestamp":"2024-11-02T20:42:29Z","content_type":"text/html","content_length":"47066","record_id":"<urn:uuid:5dd0f041-f7ae-4eba-be27-a796a1f2ee8a>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00827.warc.gz"}
Real-Life Application of LinkedList Data structure; A Secret VAL Match-Making App If you are a software engineer or studying to become a software engineer, then you have probably come across these Computer Science concepts - Data Structures and Algorithms. What are Data Structures and Algorithms? Data Structures and Algorithms called DSA for short, are two important related concepts in Computer Science and Software Engineering. Data Structures are simply methods of organizing or holding data in a virtual system. Algorithms are step-by-step instructions given to a computer to execute by collecting some input in order to produce a targeted output. While certain software engineers have a theory that studying DSAs is not so important as they believe there are only a little or no applications of DSAs in real-life software, understanding DSAs will improve your ability to solve coding problems more efficiently as we will see in this application. What is a LinkedList? A LinkedList is a data structure that holds a collection of nodes that are connected to each other. A node in a LinkedList is an independent object that holds two important values at the least; the value of the node and a pointer that connects it to another node. A Basic LinkedList starts with a node, called HEAD node, that is connected to the next node by a pointer value except the last node, whose pointer value is null. There are 3 basic types of LinkedLists: • Singly LinkedList • Doubly LinkedList • Circular LinkedList In this application, we will use the Doubly and Circular LinkedLists. Background of the Secret VAL Match-Making Website. This program is a secret VAL matching website. The aim of the software was to match my college students to exchange gifts on valentine’s day. The website is aimed at matching opposite genders (male and female). The caveat to that plan is that there would most likely be an unequal amount of males and females. That was exactly what happened. The website got a total of 1292 registrations, 991 of the registrations were males and only 301 were females. Match-Making Algorithm with LinkedList: Before thinking about the algorithm, we need to have a representation of the students. So, let’s create a model like this: • fullname: string • phoneNumber: string • department: string • gender: string • year: string • matchedFrom: Student • matchedTo: Student. With a model like that, the basic algorithm to match males to females is quite straightforward. With the matchedTo and matchedFrom fields, one male can connect to a female and the same female can connect to the same male. And we can do that with the Circular LinkedList Data Structure. In a Circular LinkedList, the last node points back to a previously reached node in the LinkedList, most times it points back to the first node, hence the name, CIRCULAR. See how that looks like a Circular, Doubly LinkedList? Cross Gender Algorithm: • FILTER ALL students that are males • FILTER ALL students that are females • LET len_males be the length of all males • LET len_females be the length of all females • LET min_length be the minimum length between len_males and len_females • LET i = 0 • WHILE i < len_males; • UPDATE females[I].matchedTo to males[i] • UPDATE females[I].matchedFrom to males[i] • UPDATE males[I].matchedTo to females[i] • UPDATE males[I].matchedFrom to females[i] • UPDATE i to (i+1) • END WHILE With this algorithm, we can successfully match all 301 females to 301 males. Here's an implementation example in Python/Django: However, this creates a problem for the remaining 691 males. We can decide to match them to each other as well, match one male to another male. That would have worked if it was an even number but with this odd number of males remaining using the same algorithm above, will always leave one male unmatched. We need to look for a better algorithm to make sure that every student is matched, even if we have to match them to the same gender. It’s only a gift-exchanging program so, why not? So, with the matchedTo and matchedFrom fields, we can connect every male to the next male and then connect the last male back to the first male. Same Gender Algorithm: • FILTER ALL remaining unmatched students • CREATE variable “prev_student” and initialize to null • CREATE variable “first_student” and initialize to null • FOR student in unmatched students • IF first_student is null • UPDATE first_student to student • END IF • IF prev_student is not null • UPDATE prev_student.matchedTo to student • UPDATE student.matchedFrom to prev_student • END IF • UPDATE prev_student to student • END FOR • UPDATE prev_student.matchedTo to first_student • UPDATE first_student.matchedFrom to prev_student This part of the algorithm is only needed after all the available females have been matched with males, that way it will always leave only students of one gender left to match. An Implementation in code: Testing the Algorithm 5 females and 2 males: The first algorithm will match 2 males to 2 females. The second algorithm can match all the remaining 3 females to themselves. Everyone gets a gift, the algorithm works! 23 males and 10 females: The first algorithm will match 10 males to 10 females. The second algorithm can match all the remaining 13 males to themselves. Everyone gets a gift, the algorithm works! 40 males and 39 females: The first algorithm will match 39 males to 39 females. But how can we cater to just 1 person in the second algorithm? Well, we know that every other student has been matched with an opposite gender, so, unfortunately, we will have to break one of the 39 fancy matches we initially created. Luckily for us, we created the first algorithm using the Doubly LinkedList data structure. So, all we have to do is grab one of the matches above and convert it into a 3-node Circular LinkedList. This has been interesting so far and it was a very fun project to build for the valentine's season on campus. For more details and applications of LinkedLists, see the resources below: What Are Applications of LinkedList? - https://www.scaler.com/topics/application-of-linked-list/ Applications of linked list data structure - https://www.geeksforgeeks.org/applications-of-linked-list-data-structure/ Types of Linked Lists in Data Structures - https://www.simplilearn.com/tutorials/data-structure-tutorial/types-of-linked-list	{"url":"https://blog.withmide.com/application-of-linkedlist-data-structure-match-making-app","timestamp":"2024-11-03T18:36:14Z","content_type":"text/html","content_length":"184968","record_id":"<urn:uuid:73d193ed-d751-476e-926d-2d6f178d0a8a>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00746.warc.gz"}
Max throw At what angle should you throw something to maximise the distance it travels? A particle is projected with speed $10 \mathrm{m s}^{-1}$ from a flat horizontal surface. Find, with proof, the angle from which it should be projected to maximise the distance travelled before it hits the surface. Does this angle depend on the speed of projection? The particle is now projected with speed $10 \mathrm{m s}^{-1}$ from a height of $2$ metres. From what angle (to 3sf) should it now be projected to maximise the distance travelled before it hits the surface? Does this angle depend on the speed of projection? Did you know ... ? The modelling assumptions of constant gravitational field and no friction opposing motion are good ones, leading to simple equations which always have parabolas for solution. Once these modelling assumptions are, rightly, challenged, the resulting equations become 'non-linear' and very difficult to solve. Mathematicians often take the parabola as a starting point to solving the more complicated equations and vary the solution a little to try to fit it back into the new equations. You can see an aspect of this process in the solution to this problem. Student Solutions Suppose that the particle is projected from a height $H$ above the ground at speed $V$ at an angle $\alpha$ to the $x$-axis, with $x$ measuring the horizontal distance travelled and $y$ measuring the vertical distance travelled. Then the coordinates of the points along this trajectory are (x, y) = \left(V \cos(\alpha) t, -0.5 g t^2+V\sin(\alpha) t +H\right)\;. The particle intersects the $x$-axis when the $y$-coordinate is zero. This is when t = \frac{V\sin(\alpha) \pm \sqrt{V^2\sin^2(\alpha) +2gH}}{g}\;. The particular case $H=0$ The square root simplifies giving the point of intersection as (x, y) = \left(\frac{2V^2}{g}\cos(\alpha)\sin(\alpha), 0\right) = \left(\frac{2V^2}{g}\sin(2\alpha), 0\right)\,, where the second equality makes use of a trig identity. The $x$-value $V\sin(2\alpha)$ is maximised when $2\alpha=90^\circ$. Thus the optimal angle of projection is $45^\circ$, for any initial When $H\neq 0$ In this case, the particle intersects the $x$-axis at x =\frac{V^2}{g} \cos(\alpha) \left(\sin(\alpha) + \sqrt{\sin^2(\alpha) +\frac{2gH}{V^2}}\right)\;. This looks complicated to differentiate so I tried a numerical solution using a spreadsheet.This produced an optimal angle of $40.4^\circ$ (3sf). It seems clear that this angle will be dependent on the initial speed, but to check I calculate the optimum angle numerically for a large initial speed of $100\mathrm{ms}^{-1}$. This produces an optimium of $44.9^\circ$ (3sf) which is close to $45^\circ$, as we might intuitively expect. You might like to investigate this further. Here are some starting points. Note that the expression for the derivative is: \frac{g}{V^2}\frac{dx}{d\alpha} = \cos(2\alpha)-\sin(\alpha)\sqrt{\sin^2(\alpha) +\frac{2gH}{V^2}}+\cos^2\alpha\sin\alpha \frac{1}{\sqrt{\sin^2(\alpha) +\frac{2gH}{V^2}}}\;. For an optimum we can set the left hand side to zero. This gives us \sin\alpha\left(\cos(2\alpha) -\frac{2gH}{V}\right) + \sin(\alpha)\cos(2\alpha)\left(1 +\frac{2gH}{V^2\sin^2(\alpha)}\right)^{\frac{1}{2}}=0\;. If $X(\alpha) \equiv \frac{2gH}{V^2\sin^2(\alpha)}$ is small then we can expand to give \sin\alpha\left(\cos(2\alpha) -\frac{2gH}{V}\right)+ \sin(\alpha)\cos(2\alpha)\left(1+\frac{1}{2}\frac{2gH}{V^2\sin^2(\alpha)}+\mathcal{O}(X^2)\right)=0\;. In principle that can now be turned into a polynomial expression in $\cos(\alpha)\ldots$	{"url":"https://nrich.maths.org/problems/max-throw","timestamp":"2024-11-15T01:24:12Z","content_type":"text/html","content_length":"39884","record_id":"<urn:uuid:f042557d-0349-431e-a197-62f8f77609e9>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00300.warc.gz"}
Specific Questions about Constructing MPOs by hand in iDMRG Hi Miles, I have been recently trying doing some iDMRG simulations (C++v3). It is super nice of you to give sample codes in https://github.com/ITensor/iDMRG. And for others who might be interested, here is a great brief introduction to the algorithm - http://itensor.org/docs.cgi?page=tutorials/iDMRG&vers=cppv2. But since I don't find any documentations about the implementation of the codes, it is a bit hard for me to modify based on that. And I think you might be I have some naive technical questions regarding how to construct a general Hamiltonian (to be specific, biquadratic Heisenberg model for my purpose). $$H=\sum_{}\alpha s_i\cdot s_j+\beta(s_i\cdot s_j)^2$$ In the Heisenberg.h, Question 1 How is the size for each QN block being decided? (3, 1, 1) in the following code. auto ts = format("Link,l=%d",l); links.at(l) = Index(QN({"Sz", 0}),3, Question 2 I guess the following codes are the ones that deal with the construction of Heisenberg MPO. But could you explain how these columns and rows correspond to the MPO of the Heisenberg MPO? And in general, how do you specify the row and column indices? W = ITensor(dag(sites_(n)),prime(sites_(n)),row,col); W += sites_.op("Id",n) * setElt(row(1)) * setElt(col(1)); //ending state W += sites_.op("Id",n) * setElt(row(2)) * setElt(col(2)); //starting state W += sites_.op("Sz",n) * setElt(row(3)) * setElt(col(1)); W += sites_.op("Sz",n) * setElt(row(2)) * setElt(col(3)) * Jz_; W += sites_.op("Sm",n) * setElt(row(4)) * setElt(col(1)); W += sites_.op("Sp",n) * setElt(row(2)) * setElt(col(4)) * J_/2; W += sites_.op("Sp",n) * setElt(row(5)) * setElt(col(1)); W += sites_.op("Sm",n) * setElt(row(2)) * setElt(col(5)) * J_/2; Thank you very much! These two questions may be very enlightening to you： Thats very helpful. Actually, I have figured out the problem after checking some previous answers and McCulloch's paper https://arxiv.org/pdf/0804.2509.pdf. Although I still need to figure out the details of the iDMRG algorithms, I am now able to construct the mpo and do some calculation for now. Sorry for asking such a naive question. Thanks a lot.	{"url":"http://itensor.org/support/2926/specific-questions-about-constructing-mpos-by-hand-in-idmrg?show=3125","timestamp":"2024-11-01T23:18:40Z","content_type":"text/html","content_length":"26819","record_id":"<urn:uuid:d6c7f052-98d5-4f56-9eec-719a9ac96205>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00536.warc.gz"}
Functional Renormalization Group Approa SciPost Submission Page Functional Renormalization Group Approach for Signal Detection by Vincent Lahoche, Dine Ousmane Samary, Mohamed Tamaazousti This is not the latest submitted version. Submission summary Authors (as registered SciPost users): Dine Ousmane Samary Submission information Preprint Link: scipost_202306_00023v1 (pdf) Date submitted: 2023-06-18 15:57 Submitted by: Ousmane Samary, Dine Submitted to: SciPost Physics Lecture Notes Ontological classification Academic field: Physics • Condensed Matter Physics - Theory Specialties: • High-Energy Physics - Theory Approach: Theoretical This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended self-consistent construction of the analogue effective field-theory framework for data, which can be viewed as a maximum entropy model. In particular, and exploiting universality arguments, we justify the ℤ2-symmetry of the classical action, and we stress the existence of a large-scale (local) regime and of a small-scale (nonlocal) regime. Secondly, and related to noise models, we observe the universal relation between phase transition and symmetry breaking in the vicinity of the detection threshold. Finally, we discuss the issue of defining the covariance matrix for tensorial-like data. Based on the cutting graph prescription, we note the superiority of definitions based on complete graphs of large size for data analysis. Current status: Has been resubmitted Reports on this Submission The authors present a review on a renormalization group approach to signal detection.I believe that this work is valuable on a conceptual level and the subject is interesting, however I see some issues with the presented material that I feel should be covered better or if there are no answers to them it should be clearly said that this is the case. Since the paper is complex and long I shall discuss it by logical parts A) In the first part of the paper authors make a nice introduction to the topic covering first 2 sections. B) In the 3rd section the authors attempt to make a link with the field theory C) In the 4th and 5th sections authors present explicit calculations using renormalization group I have minor questions related with the introductiory parts: A1) It is not clear from the text what is shown in Fig.4. upper panel As I understand the MP distribution is obtained from multiplying 2 fully random matrices. How does the figure illustrate deviation from universality when the difference could also be understood as a MP distribution with a different cutoff. A2) A picture is introduced by which dimensionality is illustrated to be a deciding factor in the relevance of eigenvectors because it induces different spectra in momentum space. I think this is a dangerous analogy because the dimensionality is not all that comes into play. Which eigendirections survive in the IR limit depends on the field theory as well, so I do not unerstand what such an analogy gains us. B1) My biggest problem with the paper is the 3rd section. I find it confusing and vague and I recommend rewriting it in a simpler and more transparent way, sacrificing some of the material for clarity. There seem to be a lot of ideas there, however as far as I see the only important point is left unanswered and this is: how does looking at field theoretical models with RG help us detect signals in continuous spectra? My point is this, when we are doing renormalization group on a field theoretical model such as the phi^4 theory, we are at the end interested in low energy excitations of the problem. Why are these excitations relevnat for the signal detection? If we look in comparison the nicely introduced Wigner semicircle spectrum and some peaks imbedded in it, nothing guarantees that what happens in the low energy limit of the theory is relevant to detecting whatever peaks we want to detect. So what I recommend to the authors is offering as simple as possible answer to this question as the main point point of Sec 3. B2) If the description of such signals as said in my previous point is not what authors have in mind they should be clear about what they are hoping to achieve with their RG approach. What kind of a signal is a signal that they are intersted in and that is analogous to the IR degrees of freedom that have survived after the integration over small wavevector modes B3) As far as I see in later the authors introduce a phi^4 like field theory with in general a nonlocal kernel of interaction as we see in Eq. 3.4. which they then discuss near the Gaussian limit and as the field theory teaches us find that in some relevant cases the Gaussian theory is unstable and that higher couplings above quadratic need to be taken into the account. What I find interesting is that their theory is massive. Why is this the case or in other words why is this case relevant for their consideration? B4) Their interaction kernel was introduced as nonlocal. If this is the case why then do they only consider the standard derivative expansion of the gradient term in p^2n? Why is their field theory not e.g. with long range interactions? In this case they would have e.g. a fractional gradient B5) Also why do they only consider the simplest situation of the scalar phi^4 theory, let me elaborate? In 3.3 they discuss the symmetries of the model. Why would they not have some more complicated order parameter field given the symmetries? In section 4 they introduce the Wetterich-Morris formalism and they do two kinds of calculations: a) the calculation of flows at local potential level and b) in field expansion either around 0 or the minimum. To me this looks completely like a standard calculation that was done a lot of times before in virtually all the reviews on NPRG. What I think they do different although I do not think it is said in a clear way is impose an arbitrary distribution of q modes, which I presume, gives them a difference from the completely standard They motivate this calculation by stating () that: "A motivation justifying the non-perturbative formalism use was the surprising observation that, for most common noise, models power counting shows that the first perturbations to the Gaussian model - the quartic and sixtic terms - are always relevant at the tail of the spectrum, (see empirical statement (1))." The gist of the standard calculation on the other hand is that if you tweak the initial condition above T_c then you flow into the disordered phase and if you tweak them below T_c you flow into the ordered phase. C1) The difference between the standard calculation and their calculation should be stressed better because it took me some time to understand that they are indeed not doing a standard phi^4 C2) If they claim that given their distribution of momenta the picture of the flow is pretty much as in the standard case (which I think they do since evidence to this effect is given later in sec 5), I do not understand what they mean by their statement () above introduced as motivation. Do they mean that if they tweak the couplings right that the dimensionless couplings are going to grow? If this is so this statement has nothing to do with nonperturbative physics it just has to do with the flow into the ordered phase. Even if you flow into the disordered phase you are going to obtain some finite dimensionfull values for the couplings when the flow stops. Authors please clarify this! C3) The authors seem to claim that there is no fixed point of their flow, however Fig 21 testifies that there might be one. This is very peculiar. The terminal part of the flow should be dominated by the shape momentum distribution near q=0. Why do the authors not discuss the asymptotic equations separately? Considering these equations might give an analytic answer whether there is a nontrivial fixed point or not in their case. At the beginning of Sec 5.2 they state (**): "In section 4, we illustrated the dependence of the canonical dimensions on the scale, for an MP distribution, and emphasized two points. The first point is that at a large scale only two couplings are relevant, the quartic and the sixtic, the latter tending to be asymptotically marginal." This statement is misleading and incomplete. As said before, in all the cases either the flow to disordered or the ordered phase if we look at the full function U(phi), it is going to be a nontrivial function. In the cases when the flow is into the ordered phase it is going to develop a flat region near phi=0. If the initial condition is tweaked to critical then you flow to the fixed point. All this is well known within the standard picture. C4) My question is what kind of initial conditions do they have in mind when they tell their C5) What is the relevance of the initial conditions of the flow to their program of signal detection? In Sec 5 I seem to see that they are interested in the critical situation. Why is that? As a general statement, I beg the authors to improve the language throughout the text. In many places the language constructions are atypical of English language and words are wrong. All in all I appreciate the author's effort and I agree with publishing the article provided they take the criticisms I laid out into the account in good faith. In this case it would certainly meet the requirements of the journal. This will also make the article much easier to read and accessible to a wider audience.	{"url":"https://www.scipost.org/submissions/scipost_202306_00023v1/","timestamp":"2024-11-06T14:51:30Z","content_type":"text/html","content_length":"40690","record_id":"<urn:uuid:1a54e961-f381-4a80-b771-c6e365b7d956>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00528.warc.gz"}
A two-story building has steel columns AB in the first floor an... \| Filo Question asked by Filo student A two-story building has steel columns in the first floor and in the second floor, as shown in the figure. The roof load equals and the second-floor load cquals . Each column has length . The cross-sectional areas of the first-and second-floor columns are and respectively.(a) Assuming that , determine the total shortening of the two columns due to the combined action of the loads and (b) How much additional load can be placed at the top of the column (point ) if the total shortening is not to exceed Not the question you're searching for? + Ask your question Step by Step Solution: Step 1. Resolve the load and into axial forces acting on columns and . This can be done by creating a free-body-diagram (FBD) for each level. Step 2. Calculate the axial force on each column using the formula: , where is the total axial load on the column, is the cross-sectional area of the column, and is the total cross-sectional area of all the columns at the same level. Step 3. Determine the expected axial deformation for each column using the formula: , where is the length of the column, is the cross-sectional area of the column, and is the modulus of elasticity of steel. Step 4. Calculate the total axial shortening by adding the individual axial deformations. Step 5. Find the additional load that can be added at point such that the total axial deformation will not exceed . This can be done by reversing the process in steps 2 to 4. In this case, will be . Found 2 tutors discussing this question Discuss this question LIVE 5 mins ago One destination to cover all your homework and assignment needs Learn Practice Revision Succeed Instant 1:1 help, 24x7 60, 000+ Expert tutors Textbook solutions Big idea maths, McGraw-Hill Education etc Essay review Get expert feedback on your essay Schedule classes High dosage tutoring from Dedicated 3 experts Practice more questions on All topics View more Students who ask this question also asked View more Stuck on the question or explanation? Connect with our Physics tutors online and get step by step solution of this question. 231 students are taking LIVE classes A two-story building has steel columns in the first floor and in the second floor, as shown in the figure. The roof load equals and the second-floor load cquals . Each column has length . Question The cross-sectional areas of the first-and second-floor columns are and respectively.(a) Assuming that , determine the total shortening of the two columns due to the combined action of the Text loads and (b) How much additional load can be placed at the top of the column (point ) if the total shortening is not to exceed Updated Mar 15, 2024 Topic All topics Subject Physics Class Class 11 Answer Text solution:1	{"url":"https://askfilo.com/user-question-answers-physics/a-two-story-building-has-steel-columns-in-the-first-floor-37383735383235","timestamp":"2024-11-05T09:06:52Z","content_type":"text/html","content_length":"222039","record_id":"<urn:uuid:cd75c602-a78c-471d-9ffc-1ca89bcedb1e>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00352.warc.gz"}
University of Warwick Dehn functions of coabelian subgroups of direct products of groups Algebra Seminar 19th October 2022, 2:30 pm – 3:30 pm Fry Building, 2.04 The class of coabelian subgroups of free groups provided many groups with interesting finiteness properties e.g. the Stallings-Bieri groups. For the finitely presented groups in this family we can study their Dehn functions. Various authors have worked on the case of the Stallings-Bieri groups. Building on these methods we give upper and lower bounds for Dehn functions of certain coabelian subgroups of direct products. This is joint work with Claudio Llosa Isenrich.	{"url":"https://www.bristolmathsresearch.org/seminar/rob-kropholler/","timestamp":"2024-11-05T18:54:41Z","content_type":"text/html","content_length":"53825","record_id":"<urn:uuid:09e14cb6-e638-4267-89f6-291ccce0b5ff>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00394.warc.gz"}
class Electrons(, process_grid, lattice, ions, symmetries, checkpoint_in=(None, ''), k_mesh=None, k_path=None, spin_polarized=False, spinorial=False, fillings=None, basis=None, xc=None, fixed_H='', save_wavefunction=True, lcao=None, davidson=None, chefsi=None, scf=None) Bases: TreeNode Electronic subsystem ☆ process_grid (ProcessGrid) ☆ lattice (Lattice) ☆ ions (Ions) ☆ symmetries (Symmetries) ☆ checkpoint_in (CheckpointPath) ☆ k_mesh (Optional[Union[dict, Kmesh]]) ☆ k_path (Optional[Union[dict, Kpath]]) ☆ spin_polarized (bool) ☆ spinorial (bool) ☆ fillings (Fillings) ☆ basis (Basis) ☆ xc (XC) ☆ fixed_H (str) ☆ save_wavefunction (bool) ☆ lcao (LCAO \| None) ☆ davidson (Optional[Union[dict, Davidson]]) ☆ chefsi (Optional[Union[dict, CheFSI]]) ☆ scf (SCF) __init__(, process_grid, lattice, ions, symmetries, checkpoint_in=(None, ''), k_mesh=None, k_path=None, spin_polarized=False, spinorial=False, fillings=None, basis=None, xc=None, fixed_H='', save_wavefunction=True, lcao=None, davidson=None, chefsi=None, scf=None) Initialize from components and/or dictionary of options. ○ lattice (Lattice) – Lattice (unit cell) to associate with electronic wave functions ○ ions (Ions) – Ionic system interacting with the electrons ○ symmetries (Symmetries) – Symmetries for k-point reduction and density symmetrization ○ k_mesh (dict \| Kmesh \| None) – [Input file] Uniform k-point mesh for Brillouin-zone integration. Specify only one of k_mesh or k_path. ○ k_path (dict \| Kpath \| None) – [Input file] Path of k-points through Brillouin zone. (Usually for band structure calculations.) Specify only one of k_mesh or k_path. ○ spin_polarized (bool) – [Input file] Whether system has spin polarization / magnetization. (True if system breaks time reversal symmetry, else False.) Spin polarization is treated explicitly with two sets of orbitals for up and down spins if spinorial = False, and implicitly by each orbital being spinorial if spinorial = True. ○ spinorial (bool) – [Input file] Whether to perform relativistic / spin-orbit calculations. If True, calculations will use 2-component spinorial wavefunctions. ○ fillings (dict \| Fillings \| None) – [Input file] Electron occupations and charge / magnetization control. ○ basis (dict \| Basis \| None) – [Input file] Wavefunction basis set (plane waves). ○ xc (dict \| XC \| None) – [Input file] Exchange-correlation functional. ○ fixed_H (str) – [Input file] Fix Hamiltonian from checkpoint file of this name. This is useful for band structure calculations along high-symmetry k-point paths, or for converging large numners of empty states. Default: don’t fix Hamiltonian i.e. self-consistent calculation. ○ save_wavefunction (bool) – [Input file] Whether to save wavefunction in checkpoint. Saving the wavefunction is useful for full post-processing capability directly from the checkpoint, at the expense of much larger checkpoint file. If False, calculations can still use the converged density / potential to resume calculations, but require an initial non-self-consistent calculation. Default: True. ○ lcao (dict \| bool \| LCAO \| None) – [Input file] Linear combination of atomic orbitals parameters. Set to False to disable and to start with bandwidth-limited random numbers instead. (If starting from a checkpoint with wavefunctions, this option has no effect.) ○ davidson (dict \| Davidson \| None) – [Input file] Davidson diagonalization of Kohm-Sham Hamiltonian. Specify only one of davidson or chefsi. ○ chefsi (dict \| CheFSI \| None) – [Input file] CheFSI diagonalization of Kohm-Sham Hamiltonian. Uses the Chebyshev Filter Subspace Iteration (CheFSI) method, which can be advantageous for large number of bands being computed in parallel over a large number of processes. Specify only one of davidson or chefsi. ○ scf (dict \| SCF \| None) – [Input file] Self-consistent field (SCF) iteration parameters. ○ process_grid (ProcessGrid) ○ checkpoint_in (CheckpointPath) Return type: __init__ Initialize from components and/or dictionary of options. accumulate_geometry_grad Accumulate geometry gradient contributions of electronic energy. add_child Construct child object self.`attr_name` of type cls. add_child_one_of Invoke add_child on one of several child options in args. hamiltonian Apply electronic Hamiltonian on wavefunction C initialize_fixed_hamiltonian Load density/potential from checkpoint for fixed-H calculation initialize_wavefunctions Initialize wavefunctions to LCAO / random (if not from checkpoint). run Run any actions specified in the input. save_checkpoint Save self and all children in hierarchy to cp_path. update Update electronic system to current wavefunctions and eigenvalues. update_density Update electron density from wavefunctions and fillings. update_potential Update density-dependent energy terms and electron potential. n_densities Number of electron density / magnetization components in n. need_full_projectors Whether full-basis projectors are necessary. comm Overall electronic communicator (k-points and bands/basis) kpoints Set of kpoints (mesh or path) spin_polarized Whether calculation is spin-polarized spinorial Whether calculation is relativistic / spinorial n_spins Number of spin channels n_spinor Number of spinor components w_spin Spin weight (degeneracy factor) fillings Occupation factor / smearing scheme basis Plane-wave basis for wavefunctions xc Exchange-correlation functional diagonalize Hamiltonian diagonalization method scf Self-consistent field method C Electronic wavefunctions fixed_H If given, fix Hamiltonian to checkpoint file of this name save_wavefunction Whether to save wavefunction in checkpoint lcao If present, use LCAO initialization eig Electronic orbital eigenvalues deig_max Estimate of accuracy of current eig n_tilde Electron density (and magnetization, if spin_polarized) tau_tilde KE density (only for meta-GGAs) child_names Names of attributes with child objects. variant_name Version of children having variants (if any) Accumulate geometry gradient contributions of electronic energy. Each contribution is accumulated to a grad attribute, only if the corresponding requires_grad is enabled. Force contributions are accumulated to system.ions.positions.grad. Stress contributions are accumulated to system.lattice.grad. Gradients with respect to ionic scalar fields are accumulated to system.ions.Vloc_tilde.grad and system.ions.n_core_tilde.grad. system (System) Return type: Apply electronic Hamiltonian on wavefunction C Return type: Load density/potential from checkpoint for fixed-H calculation system (System) Return type: Initialize wavefunctions to LCAO / random (if not from checkpoint). (This needs to happen after ions have been updated in order to get atomic orbitals, which in turn depends on electrons.__init__ being completed; hence this is outside the __init__.) system (System) Return type: Run any actions specified in the input. system (System) Return type: update(system, requires_grad=True) Update electronic system to current wavefunctions and eigenvalues. This updates occupations, density, potential and electronic energy. If requires_grad is False, only compute the energy (skip the potentials). ○ system (System) ○ requires_grad (bool) Return type: Update electron density from wavefunctions and fillings. Result is in system grid in reciprocal space. system (System) Return type: update_potential(system, requires_grad=True) Update density-dependent energy terms and electron potential. If requires_grad is False, only compute the energy (skip the potentials). ○ system (System) ○ requires_grad (bool) Return type: C: Wavefunction Electronic wavefunctions basis: Basis Plane-wave basis for wavefunctions comm: Comm Overall electronic communicator (k-points and bands/basis) deig_max: float Estimate of accuracy of current eig diagonalize: Davidson Hamiltonian diagonalization method eig: Tensor Electronic orbital eigenvalues fillings: Fillings Occupation factor / smearing scheme fixed_H: str If given, fix Hamiltonian to checkpoint file of this name kpoints: Kpoints Set of kpoints (mesh or path) lcao: LCAO \| None If present, use LCAO initialization property n_densities: int Number of electron density / magnetization components in n. n_spinor: int Number of spinor components n_spins: int Number of spin channels n_tilde: FieldH Electron density (and magnetization, if spin_polarized) property need_full_projectors: bool Whether full-basis projectors are necessary. save_wavefunction: bool Whether to save wavefunction in checkpoint scf: SCF Self-consistent field method spin_polarized: bool Whether calculation is spin-polarized spinorial: bool Whether calculation is relativistic / spinorial tau_tilde: FieldH KE density (only for meta-GGAs) w_spin: float Spin weight (degeneracy factor) xc: XC Exchange-correlation functional	{"url":"https://qimpy.org/en/latest/api/qimpy.dft.electrons.Electrons.html","timestamp":"2024-11-05T01:10:51Z","content_type":"text/html","content_length":"62545","record_id":"<urn:uuid:01559d70-e63b-4282-b3b1-288a7edcade7>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00503.warc.gz"}
Time discretization Time discretization class rtctools.optimization.collocated_integrated_optimization_problem.CollocatedIntegratedOptimizationProblem(**kwargs)[source] Bases: OptimizationProblem Discretizes your model using a mixed collocation/integration scheme. Collocation means that the discretized model equations are included as constraints between state variables in the optimization problem. Integration means that the model equations are solved from one time step to the next in a sequential fashion, using a rootfinding algorithm at each and every step. The results of the integration procedure feature as inputs to the objective functions as well as to any constraints that do not originate from the DAE model. To ensure that your optimization problem only has globally optimal solutions, any model equations that are collocated must be linear. By default, all model equations are collocated, and linearity of the model equations is verified. Working with non-linear models is possible, but discouraged. check_collocation_linearity – If True, check whether collocation constraints are linear. Default is True. Configures the implicit function used for time step integration. A dictionary of CasADi rootfinder options. See the CasADi documentation for details. Interpolation method for variable. variable – Variable name. Interpolation method for the given variable. map_options() Dict[str, str \| int][source] Returns a dictionary of CasADi map() options. Option Type Default value mode ``str` openmp n_threads int None The mode option controls the mode of the map() call. Valid values include openmp, thread, and unroll. See the CasADi and documentation for detailed documentation on these modes. The n_threads option controls the number of threads used when in thread mode. Not every CasADi build has support for OpenMP enabled. For such builds, the thread mode offers an alternative parallelization mode. The use of expand=True in solver_options() may negate the parallelization benefits obtained using map(). A dictionary of options for the map() call used to evaluate constraints on every time stamp. property theta RTC-Tools discretizes differential equations of the form \[\dot{x} = f(x, u)\] using the $\theta$-method \[x_{i+1} = x_i + \Delta t \left[\theta f(x_{i+1}, u_{i+1}) + (1 - \theta) f(x_i, u_i)\right]\] The default is $\theta = 1$, resulting in the implicit or backward Euler method. Note that in this case, the control input at the initial time step is not used. Set $\theta = 0$ to use the explicit or forward Euler method. Note that in this case, the control input at the final time step is not used. This is an experimental feature for $0 < \theta < 1$. Deprecated since version 2.4: Support for semi-explicit collocation (theta < 1) will be removed in a future release. abstract times(variable=None)[source] List of time stamps for variable (to optimize for). variable – Variable name. A list of time stamps for the given variable.	{"url":"https://rtc-tools.readthedocs.io/en/latest/optimization/time_discretization.html","timestamp":"2024-11-06T21:34:31Z","content_type":"text/html","content_length":"22478","record_id":"<urn:uuid:d6c8e04b-f524-4e93-ac4a-2178e7928967>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00285.warc.gz"}
What are Measures of Dispersion Statistics ? Here, you will learn what are the measures of dispersion in statistics i.e. range, mean deviation, variance and standard deviation with example. Let’s begin – Measures of Dispersion : The dispersion of a statistical distribution is the measure of deviation of its values about the their average(central) value. It gives an idea of scatteredness of the different values from the average value. Generally these measures of dispersion are commonly used. (i) Range (ii) Mean deviation (iii) Variance and standard deviation Range : The difference between the greatest and least values of variate of a distribution, are called range of that distribution. If distribution is the grouped distribution, then its range is the difference between upper limit of maximum class and lower limit of a minimum class. Also, coefficient of range = ${difference of extreme values}\over {sum of extreme values}$ Mean deviation(M.D.) : The mean deviation of a distribution is, the mean of absolute value of deviations of variate from their statistical average(Mean, Median, Mode). If A is any statistical average of a distribution that mean deviation about A is defined as Mean deviation = ${\sum_{i=1}^{n}{\|x_i – A\|}}\over n$ (For ungrouped distribution) Mean deviation = ${\sum_{i=1}^{n}{f_i\|x_i – A\|}}\over N$ (For frequency distribution) NOTE : Mean deviation is minimum when it taken about the median. Example : Find the mean deviation of the numbers 3, 4, 5, 6, 7. Solution : We have n = 5, $\bar{x}$ = 5 here. $\therefore$ Mean deviation = ${\sum_{i=1}^{n}{\|x_i – A\|}}\over n$ = $1\over 5$[\|3 – 5\| + \|4 – 5\| + \|5 – 5\| + \|6 – 5\| + \|7 – 5\|] = $1\over 5$[2 + 1 + 0 + 1 + 2] = 1.2 Variance and Standard Deviation : It is defined as the mean of squares of the deviation of variate from their mean. It is denoted by $\sigma^2$ or var(x). The positive square root of variance are called the standard deviation. It is denoted by $\sigma$ or S.D. Hence standard deviation = + $\sqrt{variance}$ Hope you learnt what are measures of dispersion in statistics, learn more concepts of statistics and practice more questions to get ahead in the competition. Good luck! Leave a Comment	{"url":"https://mathemerize.com/measures-of-dispersion-statistics/","timestamp":"2024-11-06T02:26:14Z","content_type":"text/html","content_length":"209836","record_id":"<urn:uuid:ad73909c-a451-46db-8029-540a1152f758>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00094.warc.gz"}
Let's say you have a vector space $V$ and a vector space $W$ over the same field $k$. Then, according to a huge pile of books on representation theory I read, there is an isomorphism $V^\ast\otimes_k W \cong \mathrm{Hom}_k(V,W)$, where $V^\ast=\mathrm{Hom}_k(V,k)$. I concur, it's not hard to write down, but then don't they just write it down? It is given by \[ \begin{array}{rcl} \phi: V^\ast\otimes_k W &\longrightarrow& \mathrm{Hom}_k(V,W) \\ f\otimes w &\longmapsto& (v\mapsto f(v)w), \end{array}\] when we assume $W$ to be finite-dimensional. Do you want to see the proof?	{"url":"https://blag.nullteilerfrei.de/tag/hom/","timestamp":"2024-11-13T01:25:21Z","content_type":"text/html","content_length":"30223","record_id":"<urn:uuid:da4720b8-efff-489f-a923-03b62be5c68d>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00300.warc.gz"}
How to add and subtract radical expressions how to add and subtract radical expressions Related topics: scalefactor javascript greatest common factor of two monomials calculator Sin Function Subtraction Effect On Graph equations "year 8" exercises mathematics for business and social sciences i,2 college algebra tutor example of rational algebraic expression problem Author Message Rooxie7 Posted: Saturday 04th of Jul 18:30 Hi all, I just began my how to add and subtract radical expressions class. Boy! This thing is really tough! I just never seem to understand the point behind any topic . The result? My rankings go down . Is there any guru who can lend me a helping hand? Back to top kfir Posted: Sunday 05th of Jul 08:58 I know how tough it can be if you are having problems with how to add and subtract radical expressions. It’s a bit hard to assist without more details of your requirements. But if you don’t want to pay for a tutor, then why not just use some piece of software and how you go . There are numerous programs out there, but one you should test out would be Algebrator. It is pretty handy plus it is pretty cheap . From: egypt Back to top Gools Posted: Monday 06th of Jul 12:36 Algebrator is very useful, but please never use it for copy pasting solutions. Use it as a guide to understand and clear your concepts only. From: UK Back to top chantnerou Posted: Wednesday 08th of Jul 11:46 You both have got to be pulling my leg ! How can this not be popular knowledge or publicized here ? How might I get more info for trying Algebrator? Pardon me for being a little skeptical , but do either of you believe if someone can obtain a test copy to use this package? Back to top Koem Posted: Thursday 09th of Jul 13:46 You can get it at https://softmath.com/about-algebra-help.html. Please do post your feedback here. It may help a lot of other beginners as well. From: Sweden Back to top pcaDFX Posted: Friday 10th of Jul 21:08 A truly piece of algebra software is Algebrator. Even I faced similar difficulties while solving difference of cubes, radicals and function definition. Just by typing in the problem from homework and clicking on Solve – and step by step solution to my algebra homework would be ready. I have used it through several algebra classes - Intermediate algebra, Algebra 2 and Basic Math. I highly recommend the program. Back to top	{"url":"https://www.softmath.com/algebra-software-3/how-to-add-and-subtract.html","timestamp":"2024-11-08T22:18:31Z","content_type":"text/html","content_length":"42378","record_id":"<urn:uuid:338074bd-ae6d-45b0-84db-002d8b7cbaaf>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00168.warc.gz"}
1 Molecular weight Molar mass is the mass in grams, of a mole of a substance, and has the units g/mol. See for more information about a mole. Since an AMU is [latex]1/12th[/latex] of the mass of one carbon-12 atom, the mass of a single entire carbon-12 atom is [latex]12 AMU[/latex]. Remember that a mole is by definition the number of atoms in 12 grams of carbon-12. Therefore, a mole of carbon-12 is 12 grams. As the mass of carbon-12 is 12 AMU, the statement can be restated as “a mole of 12 AMU is 12 grams”, meaning [latex]N_{A}\times 12 AMU=12g[/latex], or reshuffling, [latex]AMU=\dfrac{1g}{N_{a}}[/latex]. Based on the formula, AMU can have the units g/mol. Converting grams to kilograms, [latex]AMU=\dfrac{1}{N_{A}} \div 1,000[/latex] kg. Demonstrating the inverse relationship between AMU and a mole ( Avogadro’s number), [latex]\dfrac{1}{N_{a}} \div 1,000 = \dfrac{1}{6.02\times 10^23}\div 1,000=1.66\times 10^-27 =AMU[/latex]: quod erat demonstrandum. Given molar mass has the g/mol unit too, AMU and molar mass are thus interchangeable. AMU, also referred to as atomic mass, atomic weight, can be found on the periodic table, and since is equivalent to molar mass, can be used in lieu of molar mass for the [latex]n=\dfrac{m}{M}[/latex] formula. Molecular mass (also known as molecular weight) refers to the mass of not just a single atom, but a molecule, which is a collection of atoms. Formative learning activity Maps to RK4.1 What is molecular weight? 2 Empirical, molecular formula Compounds can be described with an empirical formula, which provides the simplest [whole number] ratio of the different types of atoms, permitted as there are no distinct groups in compounds. This is in contrast with molecular formula, which provides exact numbers of each atoms, required for molecules which express exact numbers of atoms in each group. For example, glucose is a molecule with the molecular formula [latex]\ce{C6H12O6}[/latex], which would be underrepresented if expressed via the empirical formulas [latex]\ce{CH2O}[/latex]. Formative learning activity Maps to RK4.2 What is empirical formula? What is molecular formula, and how is this distinct from empirical formula? 3 Units in chemistry SI units is the modern form of the metric system. Metric system is an international decimal system. SI units are built around seven base units, from which all other units are constructed, of which six include: • Meter (m), which measures length • Second (s), which measures time • Kilogram (kg), which measures mass • Kelvin (K), which measures temperature • Mole (mol), which measures amount • Coulomb (C), which measures electrical charge 4 Percent mass composition Percent mass composition is the fraction of the atomic mass of one element, to the total mass of the compound. The total mass is calculated by adding the atomic masses of all the atoms in the compound. This can be found from the empirical formula. For example, the percent mass of carbon in [latex]\ce{CH2O}[/latex] is [latex]\dfrac{12}{12+2(1)+16}=40%[/latex]. Evidently, atomic mass could be determined from the molecular formula, but this would increase the complexity of the calculation. Formative learning activity Maps to RK4.4 What is percent mass composition? 5 Moles, Avogadro's “Mole is that thing you whack in an arcade,” Mandy said. “It’s that black dot that grows on your face, and no amount of make-up can really remove it,” Jamie giggled. “I don’t have one on my face,” Mandy replied, “but…” Mole is a constant, defined as the number of atoms in 12 grams of carbon-12. This number is known as Avogadro’s number ([latex]N_{A}[/latex]), namely [latex]6.02\times 10^23[/latex] atoms. To convert from mass to moles, use [latex]n=\dfrac{m}{M}[/latex], where [latex]n[/latex] is the number of moles, [latex]m[/latex] is the mass in grams, and [latex]M[/latex] is the molar mass. Formative learning activity Maps to RK4.5 What are moles? What is Avogadro's number, and how does this relate to moles? 6 Definition of density Density is the mass per unit volume. Less dense fluids float on top of more dense fluids if they don’t mix. Formative learning activity Maps to RK4.6 What is the definition of density? 7 Oxidation number Oxidation number of a central atom, is the charge it would have if all the atoms it binds to were removed. For example, the oxidation number of iron in [latex]\ce{Fe2O3}[/latex] is [latex]+3[/latex], and the oxidation number of oxygen is [latex]-2[/latex]. Formative learning activity Maps to RK4.7 What are oxidation numbers? 8 Chemical equations Chemical equation is the symbolic representation of a chemical reaction, where reactants are on the left hand side, and the products are on the right hand side. Arrows going only in the forward direction show a net forward reaction. Arrows going in both directions indicate an equilibrium. Limiting reagent is the reactant that is entirely consumed before others in a chemical reaction, thereby limiting the reaction, as the reaction cannot proceed without it. The theoretical yield is the amount of product obtained in a chemical reaction if it ran to completion, without competing reactions. Competing reaction are other reactions that can occur, which use up the reactants. The percentage yield is the actual yield divided by the theoretical yield. Formative learning activity Maps to RK4.8 What are chemical equations? (Formative assessments are not assessed for marks. Assessments are made on the unit level.	{"url":"https://mrshum.com/pre-med/general-chemistry/stoichiometry/","timestamp":"2024-11-12T13:41:59Z","content_type":"application/xhtml+xml","content_length":"35234","record_id":"<urn:uuid:b24f129b-7c72-4863-914f-1c163bdd2c6d>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00509.warc.gz"}
How to Calculate Fabric Consumption for Woven Bottom? Fabric Consumption Calculation for Woven Bottom Fabric Consumption Calculation for Woven Bottom: In the garments sector, an order profit totally depends on the fabric consumption of garments. So, it’s a mandatory duty for a garments merchandiser to make a correct fabric consumption of that order. As its importance on garments merchandising, today I will present a fabric consumption calculation method for woven bottom garments. Woven bottom Fabric consumption calculation method for the woven bottom: Before going to the fabric consumption of woven bottom garments, a woven merchandiser should identify all the parts of that. Normally, a woven bottom consists of the following parts- 1. Body parts, 2. Pocket, 3. Pocketing Fabrics, 4. Belt Loop. The Buyer “Nautica” forwards a “Woven Denim Bottom” item order (10000pcs) to you with the following specification. Follow the below measurement chart. Now, calculate the required fabric consumption for the above order. Fabric consumption for the woven bottom will be discussed below in part by part: Fabric width- 56” (Here, the given fabric width is 56”, during sewing, we cannot use the edge of a fabric. So, all time we must exclude 1” from the given fabric width. So, now the fabric width is 56-1 = 55”) Wastage- 10% (Normally, we add 10% wastage for the regular denim fabric but in the case of Spandex fabric, it goes up to 25%) During calculating the fabric consumption of woven fabric, all time we will use the following formula, 1. Fabric consumption for the Body Parts: Here, we will apply the following formula (per dozen), Body Width, = 1/2 Thigh with sewing allowance = 20 Now, from equation (A), we get- = 22.30yds per dozen………………………………………………… (B) So, the fabric needed for the body parts is 22.30yds per dozen. 2. Fabric consumption for the Back Pocket (2pcs): Here, we will apply the following formula (per dozen), = 1.36yds per dozen………………………………………………………………..(C) So, the fabric needed for the back pocket is 1.36yds per dozen. 3. Fabric consumption for the Pocket Bag (2pcs): Here, we will apply the following formula (per dozen), = 2.72yds per dozen……………………………………………… (D) So, the fabric needed for the pocket bag is 2.72yds per dozen. 4. Fabric consumption for the Belt Loop (5pcs): Here, we will apply the following formula (per dozen), = 0.12yds per dozen……………………………………………. (E) So, the fabric needed for the belt loop is 0.12yds per dozen. By adding the equation B, C, D and E we can get the total fabrics consumption for the above order (per dozen)- = (B +C + D + E) yds per dozen = (22.30 + 1.36 + 2.72 + 0.12) yds per dozen. = 26.5yds per dozen. So, the total fabric consumption for the above order is 26.5yds per dozen. Total fabrics consumption for 10000pcs (833.33dozen) garments is (26.5 × 833.33) = 22083.25yds per dozen. Just wait for few seconds….!!!! I know you are too angry now due to see the calculation result. Try to understand, I have just tried to show the calculation method only. I didn’t bother with the calculation result. Yes, I should do that by using actual numbers but I didn’t. So, please don’t misunderstand me. Follow this method after receiving your “actual measurement chart”. Hope you will understand. Thanks. Mayedul Islam is a Founder and Editor of Garments Merchandising. He is an Expert in Garments Merchandising. Writing is his passion. He loves to write articles about Apparel, Textile and Garment Washing specially on Merchandising. Mail him at mayedul.islam66@gmail.com 16 thoughts on “Fabric Consumption Calculation for Woven Bottom” 1. Nice still explain the wash care lables details 1. Yes…. Just keep in touch……….. Will get that very soon…………. 2. Dear, Plz attention here…. The person who have confusion about the calculating result. i will say something for u now….. This article is only for an example…all the numbers are used here just for completing the calculation… U should follow here the calculating method only……..not others…. For any advice, suggestion, correction u can contact in my FB inbox or at my mail….. Stay with us here by subscribing…… Thank u all for your fantastic support………@For all 3. Brother that means, per garment consumption is more than 5yds. Is it possible?? Per garment consumption would be at best 2 yds, if I m not wrong. Hope your valuable comment 4. very nice sholution for bottom consumtion . thanks…………………………………………………………………………. 5. Very essential to lesson. 1. Thanks. 6. Very useful 7. thanx for this solution 8. please mention different size. 9. WHERE WAS THE WASTAGE TOPIC? 10. FOR BACK PKT — NO.OF PARTS*NO.OF POCKET THIS IS CONFUSED ME.GENERALLY B.PKT STANDS 2. PLEASSE EXPLAIN IT. 11. nice consumption. but pocketing bag consumption you made also with shell fabric . it sb TR or TC or CTN. am i clear ? pls reply on that 12. Amr khub icce cad a kaj korar 13. There is no mention for fabric width 56 “ 14. why No. of Parts 2 for back pocket & Belt Loop?	{"url":"https://garmentsmerchandising.com/fabric-consumption-calculation-for-woven-bottom/","timestamp":"2024-11-11T22:51:37Z","content_type":"text/html","content_length":"117475","record_id":"<urn:uuid:8676f679-727c-4663-a7d6-b7a94096a57d>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00337.warc.gz"}
Thread - stuck in this sudoku prasanna16391 What I did was, 1. Mark odds/evens. In 2nd box, there are three distinct consecutive pairs, which would take one odd and one even each, meaning two odds and one even go in the series of 3. The series of 3 cannot have 7 and so cannot have 9 either and so must be 123 or 345. Either way, 3 is part of it, and there must be groups of 6-7 and 8-9 in that box elsewhere. Posts: 1801 2. Then, note that R3C8 to R3C7 is a series of 6 and that R1C7 = R2C6. Country : India 3. Where can 8 be in the 3rd box? Can't be in R1C8 because that is odd (using C8). Can't be in R1C7 or R2C7 because both are 3rd/4th cells of a 6-cell series (considering R1C7=R2C6. 8 cannot be in R2C8 either because that causes a 5-6 pair in 2nd box which isn't allowed going by step 1. So, 8 is at an extreme of the 6-cell series. 4. The series has to be 8-7-6-5-4-3 or 3-4-5-6-7-8. Either way, R1C7, R2C7 will form a 5-6 pair, which means 7 cannot be in R2C9 or R3C9 because 6 is taken. So, 7 must be in R2C7 and the series of 6 is done. Consecutive.png (14KB - 6 downloads) kishy72 kishy72 posted @ 2015-09-08 6:25 PM prasanna16391 - 2015-09-08 4:33 PM Posts: 419 What I did was, Country : 1. Mark odds/evens. For reasons unknown,I fail to use this simple yet highly powerful notation.Now,I clearly understand where I am missing the trick in this variant of sudoku.Often it is the consecutive sudoku that tends to trip me up a lot in any test.Just like the in/out rule of an irregular,I am beginning to comprehend that this notation of odd/even is indispensable when it comes to consecutive and possibly a lot other variants. Can't be in R1C7 or R2C7 because both are 3rd/4th cells of a 6-cell series I never spotted this 6-cell series and I never would have if it hadn't been for the explanation you gave.This is mainly due to the fact that the series bends back on itself.I was under the impression that it leads to additional possibilities rather than a straight 6-cell consecutive chain.I am curious to know whether you spotted it right away?If yes,what made you sure that it is a series of straight 6 consecutive numbers ? and thanks a ton for the lovely explanation and for making me a better solver right from this moment ! prasanna16391 Because of the converse rule, a 'T' shape of consecutive bars will always be a series of 4. The series in question clearly extends on the T since the R2C7 continuation to R2C8 cannot be the same as R2C6. I also notice a series of 8 in the bottom left btw, but didn't use that till later. The series of 8 is a bit more difficult to see, but note that R7C3 is the intersection of two T-shapes, so if it is the same series going outward from there then the same digit will be in R6C2 and R8C3. Posts: 1801 Country : kishy72 kishy72 posted @ 2015-09-08 8:52 PM Thank you.That makes it clear! Posts: 419 Country : abhi265645 Not been able to move after this... Please help. TIA<a href="http://tinypic.com?ref=32zjnma" target="_blank"><img src="http://i60.tinypic.com/32zjnma.jpg" border="0" alt="Image and video hosting by TinyPic"></a> Posts: 10 Country : swaroop2011 I think last row, 1 will come at C3. Posts: 668 Country : abhi265645 Thank you @Swaroop. Posts: 10 Country : kishy72 kishy72 posted @ 2015-09-24 6:59 PM 'Flower' from Riad's contest.I have managed to complete the other 8 except this.Strangely,most of the puzzles to me seemed to be a contest in itself and took more than an hour and close to a 2.Can someone post the continuation here? Posts: 419 Edited by kishy72 2015-09-24 7:00 PM Country : gaurav.kjain Some cells are divided into GROUP A and B and possible Group positions are marked. 'A' group 2 cells should be same as 'A' middle cell group and 'B' group cells in Box2 should become part of B group cells in marked positions. B connections are shown, so because of that B group cells as shown connected, with violet colour should be same Posts: 52 Country : India kishy72 - 2015-09-24 6:59 PM 'Flower' from Riad's contest.I have managed to complete the other 8 except this.Strangely,most of the puzzles to me seemed to be a contest in itself and took more than an hour and close to a 2.Can someone post the continuation here? kishy72 kishy72 posted @ 2015-09-24 10:51 PM Thanks!!Was difficult to spot.I could get only the A group .Now I see what I missed. Posts: 419 Kishore Country : gaurav.kjain Cross number sudoku, Either I didnot understand the rules or there is serious error in Cross Numbers marking, round represent cross number marking, you can check column 5 [1 1 1] is not Someone please help. Posts: 52 Country : kishy72 kishy72 posted @ 2015-09-25 12:32 PM gaurav.kjain - 2015-09-25 11:39 AM Posts: 419 Cross number sudoku, Either I didnot understand the rules or there is serious error in Cross Numbers marking, round represent cross number marking, you can check column 5 [1 1 1] is not Country : Someone please help. This is how the crossword goes.See where you have gone wrong. gaurav.kjain Ohh this R6c6/7 and R7C6/7 creating 2x2 which I was thinking no 2x2 is possible in cross number, This was my confusion and this was prohibiting me from putting any more markings. Thanks Please give me some starting steps for wall sudoku. Posts: 52 kishy72 - 2015-09-25 12:32 PM Country : India gaurav.kjain - 2015-09-25 11:39 AM Cross number sudoku, Either I didnot understand the rules or there is serious error in Cross Numbers marking, round represent cross number marking, you can check column 5 [1 1 1] is not Someone please help. This is how the crossword goes.See where you have gone wrong. kishy72 kishy72 posted @ 2015-09-25 1:31 PM Posts: 419 Please give me some starting steps for wall sudoku. Country : India This one is hard to explain.I myself kind of stumbled to the solution after a long time.I will run you though the basic starting steps. Remember that in this sudoku,there are 2 "golden" rules. Rule 1 :: If there is no wall segment between 2 cells, those 2 cells are consecutive in value. Rule 2 :: Each digit(unless it is a 1 or 12) will have connection to 2 digits which is consecutive to it .This means that if you get connection to 2 cells ,you can draw wall segments on the other 2 borders and vice versa. Digits 1 and 12 will have wall segments on 3 border grid lines. * The zero clue indicates that there can be no wall segments on that line .Hence I marked 'x''s on that line .This means cells R23/C1,R23/C2,R23/C3.......R23/C12 are consecutive in Also I have marked red lines on some borders .These are obtained by deduction from the given clues.For instance,reason out how the (37)clue at the top can be satisfied. Look at R4C4 .It cannot be a 1 or 12.There are 2 red wall segments that are obtained by deduction from the clues.So from what I stated above in Rule 2 ,you can draw connections to 2 Give it a start and get back if you are stuck ! Edited by kishy72 2015-09-25 1:33 PM gaurav.kjain Finally I am done with THE Maze Monster. Kishore your initial steps and explanation helped a lot. Thanks for wonderful explanation. Posts: 52 But I have not got some initial markings, which you have shown by deducing from the number clues, Eventually, I got them while solving. Can you give me reason of markings highlighted in Country : India Edited by gaurav.kjain 2015-09-26 2:50 PM kishy72 kishy72 posted @ 2015-09-26 6:38 PM Posts: 419 But I have not got some initial markings, which you have shown by deducing from the number clues, Eventually, I got them while solving. Country : India Yes .Some of the deductions are obtained as the solve proceeds. kishy72 kishy72 posted @ 2015-11-12 9:15 PM After an indefinite hiatus,I am posting here in the forum again.At this instance, a Group sum sudoku from the IB of SM - 4 Posts: 419 I tried this one a lot and got a lot of pencil marks going but not one concrete digit.I think it would be futile to post the one I had pencil marks on as it yielded nothing.Hence I am posting the image as is..... Country : India Can someone please tell me how to put one digit without much effort ? Edited by kishy72 2015-11-12 9:16 PM vopani vopani posted @ 2015-11-12 10:51 PM Not sure if this is the best start, but here's what I did. It took me a while though. Posts: 739 R5C1 & R6C1 = 5 & 6 R5C2 + R6C2 = 5 Country : R5C3 + R6C3 = 5 So, R2C3 + R3C3 = 5 OR 6 OR 7 It cannot be 7 because there is a 7-sum-pair below it (R3C3 + R4C3). If it is 6, then R2C2 & R3C2 = 4 & 6 and R5C2 & R6C2 = 1 & 4 which is not possible (Basically, you can't fill up the 16-sum and 10-sum of column2-column3 together). So, R2C3 + R3C3 = 5 R2C2 + R3C2 = 11 = 5 & 6 R2C1 + R3C1 = 3 = 1 & 2 R1C3 + R4C3 = 11 = 5 & 6 R3C1 & R3C3 = 1 & 2 R4C1 & R4C2 = 3 & 4 R5C1 + R5C2 = 8 R6C1 + R6C2 = 8 R5C2 & R6C2 = 2 & 3 R4C2 = 4 ! From there, it should get solved. swaroop2011 Nice. Posts: 668 Country : kishy72 kishy72 posted @ 2015-11-13 2:29 AM Rohan Rao - 2015-11-12 10:51 PM Posts: 419 Not sure if this is the best start, but here's what I did. It took me a while though. Country : R5C1 & R6C1 = 5 & 6 India R5C2 + R6C2 = 5 R5C3 + R6C3 = 5 So, R2C3 + R3C3 = 5 OR 6 OR 7 It cannot be 7 because there is a 7-sum-pair below it (R3C3 + R4C3). If it is 6, then R2C2 & R3C2 = 4 & 6 and R5C2 & R6C2 = 1 & 4 which is not possible (Basically, you can't fill up the 16-sum and 10-sum of column2-column3 together). So, R2C3 + R3C3 = 5 R2C2 + R3C2 = 11 = 5 & 6 R2C1 + R3C1 = 3 = 1 & 2 R1C3 + R4C3 = 11 = 5 & 6 R3C1 & R3C3 = 1 & 2 R4C1 & R4C2 = 3 & 4 R5C1 + R5C2 = 8 R6C1 + R6C2 = 8 R5C2 & R6C2 = 2 & 3 R4C2 = 4 ! From there, it should get solved. Thanks Rohan ! Excellent chain of logical thinking .But seriously,were all those meant to deduced during a test and if anyone would wait for logic to put in a digit ? debmohanty kishy72 - 2015-11-13 2:29 AM I am wondering the source of the example . I picked it from my IPC2011 folder - so it had to be bit puzzle-y in nature. However, I'm not able to see this puzzle in any IPC2011 booklet, so this may be one of the rejects because "too-hard-to-start" Country : swaroop2011 debmohanty - 2015-11-13 5:26 AM kishy72 - 2015-11-13 2:29 AM I am wondering the source of the example . Posts: 668 I picked it from my IPC2011 folder - so it had to be bit puzzle-y in nature. Country : However, I'm not able to see this puzzle in any IPC2011 booklet, so this may be one of the rejects because "too-hard-to-start" wow ! not ISC but IPC ?? Well anyways 2011 bangalore offline event was real fun. My first National championship :) . vopani vopani posted @ 2015-11-13 9:21 AM kishy72 - 2015-11-13 2:29 AM Posts: 739 Thanks Rohan ! Excellent chain of logical thinking .But seriously,were all those meant to deduced during a test and if anyone would wait for logic to put in a digit ? Country : Nope. I would have guessed after 30-secs. It took me ~5-6mins to come up with this logic. Instead, I could've solved this by guessing multiple times in 5-6mins :-) RameshLMI Thanks Rohan. But I am unable to decipher this logical deduction, Posts: 51 R5C1 + R5C2 = 8 R6C1 + R6C2 = 8 Country : India Can someone make this clear? vopani vopani posted @ 2015-11-13 2:33 PM RameshLMI - 2015-11-13 2:26 PM Posts: 739 Thanks Rohan. Country : But I am unable to decipher this logical deduction, R5C1 + R5C2 = 8 R6C1 + R6C2 = 8 Can someone make this clear? Look at Row4 and Row5. Two sums of 18 and 9 are given (which used 8 cells out of 12). So, the remaining 4 cells: R4C1 + R4C2 + R5C1 + R5C2 = 42 - 9 - 18 = 15 (to make the total of the two rows 42) Since R4C1 and R4C2 were found to be 3 & 4, we get R5C1 + R5C2 = 15 - 7 = 8. And using the 16-sum, R6C1 + R6C2 = 8.	{"url":"https://logicmastersindia.com/forum/forums/thread-view.asp?pid=19275","timestamp":"2024-11-14T14:14:46Z","content_type":"text/html","content_length":"60912","record_id":"<urn:uuid:4c9ecd84-92d7-4c63-9a47-8657ad42d83f>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00360.warc.gz"}
How To Calculate Log2 What are logarithms? Well, to start, the word itself is a bit awkward at first. When students are first presented with the concept of these "logs," it is often part of their initial exposure to how exponents, or powers, are used. A logarithm is simply an exponent presented as something other than a superscript. Once students have seen a few examples of logarithmic expressions, what tends to trip them up is the use of a base other than 10 in the log expression, which is the default value. For example, if you were asked to solve the expression y = log[2]1,000, there is no easy intuitive way to approach the problem. Confused? Read on, and any "power" log expressions with non-standard bases have over you will disappear. Logarithmic Expressions Explained Say you are asked to solve the expression y = log[10]1000. First, you need to identify what is happening in the problem. When you get a value for y, it has to be an exponent. To be precise, it is the exponent (or power) to which the base (given as a subscript and taken to be 10 when not explicitly given) must be raised to get the argument of the log, which is the only number you see in standard form at the start of these problems. That is, the above expression is equivalent to 10^y = 1,000. You may recognize on sight that y must be equal to 3, but if not you can rely on your calculator to get the correct answer. Why Use Logarithms, Anyway? Why is it useful to look at the relationship between one number and the log of a second number instead of just examining and graphing the relationship as it is? The answer lies in the fact that when y varies with some positive power of x, it increases more quickly than x does; as this power becomes even slightly larger, the increasing gap between x and y with increasing values of x becomes extreme. Because of this, it is common in such situations to graph y versus log[b]x or a constant multiplier of log[b]x. • An example of this is the Richter scale in geological science, used to quantify the strength of earthquakes. Each whole-number step up the scale corresponds to a tenfold increase in magnitude as well as a 31-fold increase in energy released. Because of this, a quake with a magnitude of 7.7 releases 31 times the energy of a 6.7-magnitude quake and (31× 31 = 961) times the energy of a 5.7-magnitude quake. Examples of Logarithmic Problems Given y = log[10]100,000, what is y? y is the exponent to which 10 must be raised to get the value 100,000. This is 5, as you may be able to do in your head if you know that 10^5 = 100,000. Given y = log[10]50,000, what is y? y is the exponent to which 10 must be raised to get the value 50,000. Clearly, this is a noninteger value since 10^4 = 10,000 and 10^5 = 100,000. You calculator can provide the answer: 4.698. (This is a good reminder that exponents do not have to be whole numbers.) Log2x in Action When you explore log problems with bases other than 10, none of the aforementioned principles change. The math can look a little wonkier, so take care not to confuse small bases like 2 with whatever the log is, as these numbers are often in the low single digits, too. Example: What is log[2]4,000? The answer completes the sentence "4,000 is the result of 2 being raised to the power of..." The value of this expression is 11.965. • You can use an online tool like the one in the Resources instead of your calculator to solve log[2] problems. Cite This Article Beck, Kevin. "How To Calculate Log2" sciencing.com, https://www.sciencing.com/calculate-log-5144933/. 8 February 2020. Beck, Kevin. (2020, February 8). How To Calculate Log2. sciencing.com. Retrieved from https://www.sciencing.com/calculate-log-5144933/ Beck, Kevin. How To Calculate Log2 last modified March 24, 2022. https://www.sciencing.com/calculate-log-5144933/	{"url":"https://www.sciencing.com:443/calculate-log-5144933/","timestamp":"2024-11-12T03:18:53Z","content_type":"application/xhtml+xml","content_length":"73798","record_id":"<urn:uuid:865d29a6-b7c0-463d-8cf7-dc29e908cf99>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00403.warc.gz"}
Gigaflop to Exaflop Converter (Gflop to Eflop) \| Kody Tools 1 Gigaflop = 1e-9 Exaflops One Gigaflop is Equal to How Many Exaflops? The answer is one Gigaflop is equal to 1e-9 Exaflops and that means we can also write it as 1 Gigaflop = 1e-9 Exaflops. Feel free to use our online unit conversion calculator to convert the unit from Gigaflop to Exaflop. Just simply enter value 1 in Gigaflop and see the result in Exaflop. Manually converting Gigaflop to Exaflop can be time-consuming,especially when you don’t have enough knowledge about Computer Speed units conversion. Since there is a lot of complexity and some sort of learning curve is involved, most of the users end up using an online Gigaflop to Exaflop converter tool to get the job done as soon as possible. We have so many online tools available to convert Gigaflop to Exaflop, but not every online tool gives an accurate result and that is why we have created this online Gigaflop to Exaflop converter tool. It is a very simple and easy-to-use tool. Most important thing is that it is beginner-friendly. How to Convert Gigaflop to Exaflop (Gflop to Eflop) By using our Gigaflop to Exaflop conversion tool, you know that one Gigaflop is equivalent to 1e-9 Exaflop. Hence, to convert Gigaflop to Exaflop, we just need to multiply the number by 1e-9. We are going to use very simple Gigaflop to Exaflop conversion formula for that. Pleas see the calculation example given below. $\text{1 Gigaflop} = 1 \times 1e-9 = \text{1e-9 Exaflops}$ What Unit of Measure is Gigaflop? Gigaflop is a unit of measurement for computer performance. Gigaflop is a multiple of computer performance unit flop. One giggaflop is equal to 1e9 flops. What is the Symbol of Gigaflop? The symbol of Gigaflop is Gflop. This means you can also write one Gigaflop as 1 Gflop. What Unit of Measure is Exaflop? Exaflop is a unit of measurement for computer performance. Exaflop is a multiple of computer performance unit flop. One exaflop is equal to 1e18 flops. What is the Symbol of Exaflop? The symbol of Exaflop is Eflop. This means you can also write one Exaflop as 1 Eflop. How to Use Gigaflop to Exaflop Converter Tool • As you can see, we have 2 input fields and 2 dropdowns. • From the first dropdown, select Gigaflop and in the first input field, enter a value. • From the second dropdown, select Exaflop. • Instantly, the tool will convert the value from Gigaflop to Exaflop and display the result in the second input field. Example of Gigaflop to Exaflop Converter Tool Gigaflop to Exaflop Conversion Table Gigaflop [Gflop] Exaflop [Eflop] Description 1 Gigaflop 1e-9 Exaflop 1 Gigaflop = 1e-9 Exaflop 2 Gigaflop 2e-9 Exaflop 2 Gigaflop = 2e-9 Exaflop 3 Gigaflop 3e-9 Exaflop 3 Gigaflop = 3e-9 Exaflop 4 Gigaflop 4e-9 Exaflop 4 Gigaflop = 4e-9 Exaflop 5 Gigaflop 5e-9 Exaflop 5 Gigaflop = 5e-9 Exaflop 6 Gigaflop 6e-9 Exaflop 6 Gigaflop = 6e-9 Exaflop 7 Gigaflop 7e-9 Exaflop 7 Gigaflop = 7e-9 Exaflop 8 Gigaflop 8e-9 Exaflop 8 Gigaflop = 8e-9 Exaflop 9 Gigaflop 9e-9 Exaflop 9 Gigaflop = 9e-9 Exaflop 10 Gigaflop 1e-8 Exaflop 10 Gigaflop = 1e-8 Exaflop 100 Gigaflop 1e-7 Exaflop 100 Gigaflop = 1e-7 Exaflop 1000 Gigaflop 0.000001 Exaflop 1000 Gigaflop = 0.000001 Exaflop Gigaflop to Other Units Conversion Table Conversion Description 1 Gigaflop = 1000000000 Flop 1 Gigaflop in Flop is equal to 1000000000 1 Gigaflop = 1000000 Kiloflop 1 Gigaflop in Kiloflop is equal to 1000000 1 Gigaflop = 1000 Megaflop 1 Gigaflop in Megaflop is equal to 1000 1 Gigaflop = 0.001 Teraflop 1 Gigaflop in Teraflop is equal to 0.001 1 Gigaflop = 0.000001 Petaflop 1 Gigaflop in Petaflop is equal to 0.000001 1 Gigaflop = 1e-9 Exaflop 1 Gigaflop in Exaflop is equal to 1e-9	{"url":"https://www.kodytools.com/units/cspeed/from/gigaflop/to/exaflop","timestamp":"2024-11-04T07:33:38Z","content_type":"text/html","content_length":"75467","record_id":"<urn:uuid:b0649953-27a8-468e-866b-b53c388116e9>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00570.warc.gz"}
Traditional theory distinguishes between the short run and the long run. The short run is the period during which some factors is fixed; usually capital equipment and entrepreneurship are considered as fixed in the short run. The long run is the period over which all factors become variable. According to the traditional theory of the costs, the costs are divided into three types: • Total Cost • Average Cost • Marginal Cost Total cost is the total expenditure incurred by a firm during the production process. Total cost will change with the change in the ratio of output to input. Such changes may be the result of the changes in the efficiency of conversion process or changes in the prices of inputs. Total cost is a positively sloped curve. Total cost to a producer for the various levels of output is the sum of total fixed cost and total variable cost, i.e., TC = TFC + TVC. TOTAL FIXED COST: Total fixed costs refer to those costs which are unable to vary. For example: land, buildings, machinery etc. Even the output is zero fixed costs will be there. Because, this cannot be variable with respect to the level of production. So, it is also called invariable cost. Since fixed costs are fixed or rigid it can be represented through a curve having horizontal shape to output axis. This can be shown with the help of following diagram: TOTAL VARIABLE COST: Variable cost is incurred on the employment of variable factors like raw materials, direct labour, power, fuel, transportation, sales commission, depreciation charges associated with wear and tear of assets, etc. It varies directly with output.The curve of variable cost can be shown as follows: From the curves of fixed cost and variable costs, the total cost can be derived as follows: Average total cost is the sum of the average fixed cost and average variable cost. Alternatively, ATC is computed by dividing total cost by the number of units of output. ATC or AC = AFC + AVC Average cost is also known as unit cost, as it is cost per unit of output produced. It can be shown as follows: Average cost is inclusive of Average Fixed Cost and Average Variable Cost. AVERAGE FIXED COST: AFC is the average of total fixed costs. AFC can be obtaining by dividing the total fixed cost by total quantity of output each time produced. Mathematically, AFC = TFC /quantity TFC will be always fixed. So AFC will reduce and never reaches zero. Its curve is as follows: AVERAGE VARIABLE COST: AVC is the average of total variable cost. It can be find out by using the following formula. AVC = TFC / quantity AVC curve will be a ‘U’ shaped which is showing that when the output is raises the cost will decline, but after a certain level the cost starts to increases. That is why due to the variable WHY AC IS U SHAPED? In the short-run average cost curves are of U-shape. It means, initially it falls and after reaching the minimum point it starts rising upwards. It can be on account of the following reasons: Average cost is the aggregate of average fixed cost and average variable cost (AC = AFC + AVC). To begin with, as production increases, initially the average fixed cost and average variable cost falls. But after a minimum point, average variable cost stops falling but not the average cost. It is due to this reason that average variable cost reaches the minimum before AC. The point, where AC is minimum is called the optimum point. After this point, AC begins to rise upward. The net result is the increase in AC. Therefore, it is only due to the nature of AFC and AVC that AC first falls, reaches minimum and afterwards starts rising upward and hence assume the U-shape. 2. BASIS OF THE LAW OF VARIABLE PROPORTION The law of variable proportion also results in U-shape of short run average cost curve. If in the short period variable factors are combined with a fixed factor, output increases in accordance with the law of variable proportions. In other words, the law of ‘Increasing Returns’ applies. Similarly, if employ more and more variable factors are employed with fixed factors the law of Diminishing Returns is said to apply. Thus, it is due to the law of variable proportions that the average cost curve assumes the shape of U. Another reason due to which the average cost curve forms U-shape is the indivisibilities of factors. When in the short-run a firm increases its production due to indivisibilities of fixed factors, it gets various internal economies. It is these economies which cause the average cost curve to fall in the initial stage. Generally, there are three types of internal economies which help to bring down the cost viz., technical economies, marketing economies and managerial economies. It is the addition to total cost required to produce one additional unit of a commodity. It is measured by the change in total cost resulting from a unit increase in output. For example, if the total cost of producing 5 units of a commodity is Rs. 100 and that of 6 units is Rs. 110, then the marginal cost of producing 6^th unit of. Commodity is Rs. 110 – Rs. 100 = Rs. 10. The formula for marginal cost is MC[n] =TC[n] –TC[n-1,] It means that marginal, cost of ‘n’ units of output (MC[n]) can be obtained by subtracting the total cost of production of ‘n-l’ units (TC[n-1]) from the total cost of production of ‘n’ units (TC [n]). Alternatively, marginal cost can be expressed as Here, ∆TC stands for change in total cost and ∆Q stands for change in total output. This can be shown as follows: In the long run all factors are assumed to become variable. Long-run cost curve is a planning curve, in the sense that it is a guide to the entrepreneur in his decision to plan the future expansion of his output. The long-run average-cost curve is derived from short-run cost curves. The long run costs are categorised as follows: • Long run total cost • Long run average cost • Long run marginal cost Long run Total Cost (LTC) refers to the minimum cost at which given level of output can be produced. According to Leibhafasky, “the long run total cost of production is the least possible cost of producing any given level of output when all inputs are variable.” LTC represents the least cost of different quantities of output. LTC is always less than or equal to short run total cost, but it is never more than short run cost. This can be shown as follows: Long run Average Cost (LAC) is equal to long run total costs divided by the level of output. The derivation of long run average costs is done from the short run average cost curves. In the short run, plant is fixed and each short run curve corresponds to a particular plant. The long run average costs curve is also called planning curve or envelope curve as it helps in making organizational plans for expanding production and achieving minimum cost. Long run Marginal Cost (LMC) is defined as added cost of producing an additional unit of a commodity when all inputs are variable. This cost is derived from short run marginal cost. On the graph, the LMC is derived from the points of tangency between LAC and SAC.	{"url":"https://commerceiets.com/traditional-theory-of-cost/","timestamp":"2024-11-11T00:57:01Z","content_type":"text/html","content_length":"158962","record_id":"<urn:uuid:e8b53a5b-1ce6-42e3-85b2-9ec667429e0e>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00640.warc.gz"}
5th Grade Word Problems \| Math Spiral Review Place Value Power Problems5th Grade Word Problems \| Math Spiral Review Place Value Power Problems - Tanya Yero Teaching WHAT ARE P.O.W.E.R PROBLEMS? ☛PURPOSEFUL – These problems are meant to keep students focused, while strengthening initiative and perseverance. ☛OPPORTUNITIES – These prompts can be used in a variety of ways. P.O.W.E.R problems can be used to introduce a lesson, spiral review, or as formative assessments. ☛ENGAGEMENT – Problems are real world applicable and designed to hook students with interest and presentation. Complexity of problems promotes problem solving skills. ☛RIGOR – Tasks are specifically designed to challenge students and assess conceptual understanding of curriculum versus procedural understanding. Students will need to apply more than just a WHY USE P.O.W.E.R PROBLEMS? P.O.W.E.R problems are designed to challenge your students with their open ended presentation. Majority of problems that come from textbooks and workbooks assess procedural understanding of curriculum. Some textbooks even provide step by step instructions where the textbook is thinking for the students and taking away that “productive struggle” for children. When we rob students of that event, we rob them of their ability to reason, problem solve, and see beyond a standard algorithm. P.O.W.E.R problems are meant to show students that there are different ways to answer one question in math. With these tasks students take ownership and are part of the problem solving process versus filling in blanks in a textbook. ☛TO INTRODUCE A LESSON – P.O.W.E.R problems can be used to introduce a new skill. In this case your students will experience a “productive struggle.” Their problem solving skills and prior knowledge will kick in. Often times most of my students will have the incorrect answer or no answer at all. I then have someone explain their method/reasoning and allow my students to critique their peer’s answer. This makes for great accountable talk discussions. If I see that most students do not have an answer I will assist the class in getting to a specific point and then allow them to finish ☛SPIRAL REVIEW – Avoid your students forgetting standards, by using P.O.W.E.R problems to spiral review previously taught lessons. ☛FORMATIVE ASSESSMENTS – You can use these problems to assess mastery and levels of understanding. Five questions (sometimes more) per standard/topic. Standards and Topics Covered: Number and Operation in Base Ten ➥ 5.NB.1 – Place value concepts ➥ 5.NBT.2 – Multiplying and dividing by powers of 10 ➥ 5.NBT.3 – Number Form, Word Form, Expanded Form, and Comparing of decimals ➥ 5.NBT.4 – Rounding decimals ➥5.NBT.5 – Multiplying multi-digit numbers ➥5.NBT.6 – Dividing whole numbers ➥ 5.NBT.7 – Adding, subtracting, multiplying, and dividing decimals 5th Grade Power Problems	{"url":"https://www.tanyayeroteaching.com/product/5th-grade-word-problems-math-spiral-review-place-value-power-problems/","timestamp":"2024-11-02T20:50:13Z","content_type":"text/html","content_length":"162267","record_id":"<urn:uuid:05c56ccd-db34-4c6b-91f0-b0b634941888>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00027.warc.gz"}
Maximizing Production Rate with Limited Resources in context of production rate 31 Aug 2024 Title: Maximizing Production Rate with Limited Resources: A Theoretical Framework Abstract: This article presents a theoretical framework for maximizing production rate with limited resources, focusing on the optimization of production processes under constraints. We derive a mathematical model that captures the relationship between resource allocation and production output, providing insights into the most effective strategies for achieving maximum production rates. Introduction: In various industries, such as manufacturing, agriculture, or energy production, the goal is often to maximize production rate while working within limited resources (e.g., labor, equipment, raw materials). This challenge requires a deep understanding of the underlying relationships between resource allocation and output. In this article, we develop a theoretical framework for addressing this problem. Mathematical Model: Let’s consider a production process with two primary inputs: labor (L) and equipment (E), which are allocated to produce a single output unit (O). The relationship between these variables can be represented by the following equation: O = f(L, E) where f is a function that captures the production rate as a function of labor and equipment allocation. Assuming a linear relationship between inputs and outputs, we can express the production rate as: O = αL + βE where α and β are coefficients representing the marginal productivity of labor and equipment, respectively. Resource Constraints: The availability of resources (labor and equipment) is limited. Let’s denote these constraints as: L ≤ L_max E ≤ E_max where L_max and E_max represent the maximum allowable allocations for labor and equipment, respectively. Optimization Problem: Our goal is to maximize production rate (O) subject to the resource constraints. This can be formulated as a linear programming problem: Maximize O = αL + βE subject to: L ≤ L_max E ≤ E_max Solution Strategy: To solve this optimization problem, we can use various techniques, such as graphical analysis or simplex methods. However, for the purpose of this article, let’s focus on a more general approach. One possible strategy is to allocate resources in proportion to their marginal productivity: L ∝ α E ∝ β This allocation rule ensures that resources are allocated based on their relative importance in contributing to production output. Conclusion: In conclusion, we have presented a theoretical framework for maximizing production rate with limited resources. By understanding the relationships between resource allocation and output, we can develop effective strategies for achieving maximum production rates. The mathematical model and solution strategy outlined above provide a foundation for further research and application in various industries. • [1] Charnes, A., & Cooper, W. W. (1961). Management models and industrial applications of linear programming. Wiley. • [2] Dantzig, G. B. (1951). Application of the simplex method to a variety of basic business problems. Journal of Operations Research Society of America, 4(3), 287-304. Note: The references provided are classic works in the field of operations research and linear programming, which have influenced the development of the theoretical framework presented in this Related articles for ‘production rate’ : • Reading: Maximizing Production Rate with Limited Resources in context of production rate Calculators for ‘production rate’	{"url":"https://blog.truegeometry.com/tutorials/education/271d08e404371fd230e00e2f45ce8703/JSON_TO_ARTCL_Maximizing_Production_Rate_with_Limited_Resources_in_context_of_pr.html","timestamp":"2024-11-12T22:29:31Z","content_type":"text/html","content_length":"19080","record_id":"<urn:uuid:0b98cc0a-5e7a-4d8d-95ae-f9293f0273fc>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00414.warc.gz"}
Free Printable Multiplication Chart 100×100 \| Multiplication Chart Printable Free Printable Multiplication Chart 100×100 Free Printable Multiplication Chart 100X100 Free Printable Free Printable Multiplication Chart 100×100 Free Printable Multiplication Chart 100×100 – A Multiplication Chart is an useful tool for youngsters to find out exactly how to increase, split, and find the smallest number. There are several uses for a Multiplication Chart. These helpful tools aid youngsters recognize the process behind multiplication by using colored paths and completing the missing products. These charts are cost-free to publish and also download. What is Multiplication Chart Printable? A multiplication chart can be made use of to aid children learn their multiplication truths. Multiplication charts come in numerous forms, from full page times tables to single page ones. While private tables serve for providing pieces of details, a complete page chart makes it simpler to examine facts that have currently been mastered. The multiplication chart will usually feature a top row and a left column. The top row will have a listing of items. When you want to discover the product of two numbers, choose the initial number from the left column and the 2nd number from the top row. Relocate them along the row or down the column up until you get to the square where the two numbers satisfy as soon as you have these numbers. You will then have your product. Multiplication charts are useful knowing tools for both adults and also kids. Free Printable Multiplication Chart 100×100 are available on the Internet and can be published out and also laminated flooring for resilience. Why Do We Use a Multiplication Chart? A multiplication chart is a diagram that shows how to increase two numbers. It generally contains a left column and also a leading row. Each row has a number representing the item of the two numbers. You select the first number in the left column, relocate down the column, and afterwards pick the second number from the top row. The item will be the square where the numbers satisfy. Multiplication charts are handy for several reasons, consisting of aiding kids learn just how to separate as well as simplify fractions. Multiplication charts can also be practical as workdesk sources due to the fact that they offer as a continuous suggestion of the trainee’s progression. Multiplication charts are also beneficial for aiding trainees memorize their times tables. They help them learn the numbers by minimizing the variety of actions required to finish each operation. One method for remembering these tables is to focus on a single row or column at a time, and afterwards move onto the following one. At some point, the whole chart will certainly be committed to memory. Just like any type of ability, remembering multiplication tables requires time and practice. Free Printable Multiplication Chart 100×100 Multiplication Table Multiplication Table 100X100 Projects To Printable 100X100 Multiplication Table PrintableMultiplication Multiplication Chart To 100 Free Printable Multiplication Chart Free Printable Multiplication Chart 100×100 If you’re trying to find Free Printable Multiplication Chart 100×100, you’ve pertained to the appropriate area. Multiplication charts are offered in different layouts, consisting of full dimension, half size, and also a selection of adorable layouts. Some are vertical, while others feature a straight format. You can likewise find worksheet printables that consist of multiplication equations and also math truths. Multiplication charts and also tables are crucial tools for youngsters’s education and learning. These charts are terrific for use in homeschool mathematics binders or as class posters. A Free Printable Multiplication Chart 100×100 is a helpful tool to reinforce mathematics facts as well as can assist a child discover multiplication rapidly. It’s also a terrific tool for miss checking as well as learning the times tables. Related For Free Printable Multiplication Chart 100×100	{"url":"https://multiplicationchart-printable.com/free-printable-multiplication-chart-100x100/","timestamp":"2024-11-13T02:26:55Z","content_type":"text/html","content_length":"42297","record_id":"<urn:uuid:c00a5ade-981f-49cb-89f2-40f249522630>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00022.warc.gz"}
Total distance is far more than expected When I did the unit testing for TSP_large_graph test, I got the following error. Failed test case: Failed to find the optimal solution for a path starting in node 0. To replicate the graph, you may run generate_graph(nodes = 1000, complete = True, seed = 43). Expected: 4774 Got: 292549 I am using Genetic algorithm to solve TPS, my problem is not about algorithm or speed, it is that my shortest distance is much larger than expected (4774). I am suspecting this expected value. I think the unit-test is using the generate_graph function, where the edge weight limit is 1 to 600. If the salesman travels 1000 nodes and back to original node, there must at least be 1001 edges, each edge weight is between 1 to 600, letâ€™s take the mean value as 300, so the total distance would be around 1001*300 = 300300. How come can the expected value be 4774? def generate_graph(nodes, edges=None, complete=False, weight_bounds=(1,600), seed=None): Maybe the genetic algorithm is not good for this problem, or I am missing something in my GA. I tried other method, it is way faster and better than GA. It is good now. I guess a general GA just cannot handle this situation.	{"url":"https://community.deeplearning.ai/t/total-distance-is-far-more-than-expected/706793","timestamp":"2024-11-10T05:00:06Z","content_type":"text/html","content_length":"25811","record_id":"<urn:uuid:523b38bc-132f-4b8a-a350-7484888ac2ea>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00238.warc.gz"}
Infinitude of Primes The following document contains embedded Coq code. All the code is editable and can be run directly on the page. Once jsCoq finishes loading, you are free to experiment by stepping through the proof and viewing intermediate proof states on the right panel. Button Key binding Action F8 Toggles the goal panel. Alt+↓/↑ or Move through the proof. Alt+Enter or Ctrl+Enter Run (or go back) to the current point. (⌘ on Mac) Ctrl+ Hover executed statements to peek at the proof state after each step. As a relatively advanced showcase, we display a proof of the infinitude of primes in Coq. The proof relies on the Mathematical Components library from the MSR/Inria team led by Georges Gonthier, so our first step will be to load it: The lemma states that for any number m, there is a prime number larger than m. Coq is a constructive system, which among other things implies that to show the existence of an object, we need to actually provide an algorithm that will construct it. In this case, we need to find a prime number p that is greater than m. What would be a suitable p? Choosing p to be the first prime divisor of m! + 1 works. As we will shortly see, properties of divisibility will imply that p must be greater than m. Our first step is thus to use the library-provided lemma pdivP, which states that every number is divided by a prime. Thus, we obtain a number p and the corresponding hypotheses pr_p : prime p and p_dv_m1, "p divides m! + 1". The ssreflect tactic have provides a convenient way to instantiate this lemma and discard the side proof obligation 1 < m! + 1. It remains to prove that p is greater than m. We reason by contraposition with the divisibility hypothesis, which gives us the goal "if p ≤ m then p is not a prime divisor of m! + 1". The goal follows from basic properties of divisibility, plus from the fact that if p ≤ m, then p divides m!, so that for p to divide m! + 1 it must also divide 1, in contradiction to p being prime.	{"url":"https://coq.vercel.app/examples/inf-primes.html","timestamp":"2024-11-13T15:23:24Z","content_type":"application/xhtml+xml","content_length":"6551","record_id":"<urn:uuid:ba69d5a7-19aa-4ea0-9457-c96bbda5fc0d>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00579.warc.gz"}
Browsing Faculty of Sciences by Title This study is about the analysis of some queueing models related to N-policy.The optimal value the queue size has to attain in order to turn on a single server, assuming that the policy is to turn on a single server when the queue size reaches a certain number, N, and turn him off when the system is empty.The operating policy is the usual N-policy, but with random N and in model 2, a system similar to the one described here.This study analyses “ Tandem queue with two servers”.Here assume that the first server is a specialized one.In a queueing system,under Abstract: N-policy ,the server will be on vacation until N units accumulate for the first time after becoming idle.A modified version of the N-policy for an M│M│1 queueing system is considered here.The novel feature of this model is that a busy service unit prevents the access of new customers to servers further down the line.It is deals with a queueing model consisting of two servers connected in series with a finite intermediate waiting room of capacity k.Here assume that server I is a specialized server.For this model ,the steady state probability vector and the stability condition are obtained using matrix – geometric method. URI: http://dyuthi.cusat.ac.in/purl/39 This thesis is devoted to the study of some stochastic models in inventories. An inventory system is a facility at which items of materials are stocked. In order to promote smooth and efficient running of business, and to provide adequate service to the customers, an inventory materials is essential for any enterprise. When uncertainty is present, inventories are used as a protection against risk of stock out. It is advantageous to procure the item before it is needed at a lower marginal cost. Again, by bulk purchasing, the advantage of price discounts can be availed. All these contribute to the formation of inventory. Maintaining inventories is a major expenditure for any organization. For each inventory, the fundamental question is how much new stock should be ordered and when should the orders are replaced. In the present study, considered several models for single and two commodity stochastic inventory problems. The thesis Abstract: discusses two models. In the first model, examined the case in which the time elapsed between two consecutive demand points are independent and identically distributed with common distribution function F(.) with mean (assumed finite) and in which demand magnitude depends only on the time elapsed since the previous demand epoch. The time between disasters has an exponential distribution with parameter . In Model II, the inter arrival time of disasters have general distribution (F.) with mean ( ) and the quantity destructed depends on the time elapsed between disasters. Demands form compound poison processes with inter arrival times of demands having mean 1/. It deals with linearly correlated bulk demand two Commodity inventory problem, where each arrival demands a random number of items of each commodity C1 and C2, the maximum quantity demanded being a (< S1) and b(<S2) respectively. The particular case of linearly correlated demand is also discussed URI: http://dyuthi.cusat.ac.in/purl/61 The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Abstract: Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation. URI: http://dyuthi.cusat.ac.in/purl/57 In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently Abstract: introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem. Description: Department of Mathematics, Cochin University of Science and Technology URI: http://dyuthi.cusat.ac.in/purl/3824 The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service Abstract: processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. Description: Department of Mathematics and Statistics Cochin University of Science and Technology URI: http://dyuthi.cusat.ac.in/purl/3244 The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. Abstract: This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis Description: Department of Statistics, Cochin University of Science and Technology URI: http://dyuthi.cusat.ac.in/purl/4732 The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit Abstract: theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature. Description: Department of Physics, Cochin University of Science and Technology URI: http://dyuthi.cusat.ac.in/purl/3534 This thesis Entitled Application of Biofloc technology (BFT) In the Nursery Rearing and Farming of Giant Freshwater Prawn,Macrobrachium Rosenbergii(De Man). Aquaculture, rearing plants and animals under controlled conditions is growing with an annual growth rate of 8.3% in the period 1970-2008 (FAO, 2010). This trend of growth is essential for the supply of protein-rich food for ever increasing world population. But growth and development of aquaculture should be in sustainable manner, preferably without jeopardizing the aquatic environment.In the present study, the application of BFT in the nursery rearing and farming ofgiant freshwater prawn, M. rosenbergii, is attempted. The result of the study is organised into eight chapters. In the first chapter, the subject is adequately introduced. Various types of aquaculture practices followed, development and status of Indian aquaculture, present status of freshwater pravm culture, BF T and its use for the sustainable aquaculture systems, theory of BFT based aquaculture practices, hypothesis, objective and outline of the thesis are described. An extensive review of literature on studies carried out so far on biofloc based aquaculture are given in chapter 2. The third chapter deals with the application of BFT in Abstract: the primary nursery phase of freshwater prawn. Several workers suggested the need for an intermediate nursery phase in the culture system of freshwater prawn for the successful production. Thirty day experiment was conducted to study the effect of BFT on the water quality, and animal welfare under the various stocking densities. The study concluded that stocking finfishes in biofloc-based monoculture system of freshwater prawns has the potential of increasing total yield. Prawns having a higher commercial value than finfishes besides ensuring economic sustainability. Results showed that prawn yield and survival was better in catla dominated tanks. Based on the results of the study, it is recommended to incorporate 25% rohu and 75% catla in the biofloc-based culture system of giant freshwater prawns. The results of the present study also recommend to stock relatively larger catla for biofloc-based culture system. Fish production was also higher in the 100% catla tank. When catla was added in higher percentages it should ensured that the hiding objects in the culture ponds shall be used in order to reduce the chance of cannibalism among prawns. rohu and catla equally have the ability to harvest the biofloc, catla consumes the planktonic contributes in the floc whereas rohu grazed on the bacterial consortium suspended in the water column. In Chapter 8, recommendations and future research perspectives in the field of biofloc based aquaculture is Description: School of Industrial Fisheries, Cochin University of Science and Technology URI: http://dyuthi.cusat.ac.in/purl/3090 The present thesis develops from the point of view of titania sol-gel chemistry and an attempt is made to address the modification of the process for better photoactive titania by selective doping and also demonstration of utilization of the process for the preparation of supported membranes and self cleaning films.A general introduction to nanomaterials, nanocrystalline titania and sol-gel chemistry are presented in the first chapter. A brief and updated literature review on sol-gel titania, with special emphasis on catalytic and photocatalytic properties and anatase to rutile transformation are covered. Based on critical assessment of the reported information the present research problem has been defined.The second chapter describes a new aqueous sol-gel method for the preparation of nanocrystalline titania using titanyl sulphate as precursor. This approach is novel since no earlier work has been reported in the same lines Abstract: proposed here. The sol-gel process has been followed at each step using particle size, zeta potential measurements on the sol and thermal analysis of the resultant gel. The prepared powders were then characterized using X-ray diffraction, FTIR, BET surface area analysis and transmission electron microscopy.The third chapter presents a detailed discussion on the physico-chemical characterization of the aqueous sol-gel derived doped titania. The effect of dopants such as tantalum, gadolinium and ytterbium on the anatase to rutile phase transformation, surface area as well as their influence on photoactivity is also included. The fourth chapter demonstrates application of the aqueous sol-gel method in developing titania coatings on porous alumina substrates for controlling the poresize for use as membrane elements in ultrafiltration. Thin coatings having ~50 nm thickness and transparency of ~90% developed on glass surface were tested successfully for self cleaning applications. URI: http://dyuthi.cusat.ac.in/purl/2925 This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will Abstract: take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study. Description: Department of mathematics, Cochin University of Science And Technology URI: http://dyuthi.cusat.ac.in/purl/3326 Aim of the present work was to automate CSP process, to deposit and characterize CuInS2/In2S3 layers using this system and to fabricate devices using these films.An automated spray system for the deposition of compound semiconductor thin films was designed and developed so as to eliminate the manual labour involved in spraying and facilitate standardization of the method. The system was designed such that parameters like spray rate, movement of spray head, duration of spray, temperature of substrate, pressure of carrier gas and height of the spray head from the substrate could be varied. Using this system, binary, ternary as well as quaternary films could be successfully deposited.The second part of the work deal with deposition and characterization of CuInS2 and In2S3 layers respectively.In the case of CuInS2 absorbers, the effects of different preparation conditions and post deposition treatments on the optoelectronic, morphological and structural properties were investigated. It was observed that preparation conditions and post deposition treatments played crucial role in controlling Abstract: the properties of the films. The studies in this direction were useful in understanding how the variation in spray parameters tailored the properties of the absorber layer. These results were subsequently made use of in device fabrication process.Effects of copper incorporation in In2S3 films were investigated to find how the diffusion of Cu from CuInS2 to In2S3 will affect the properties at the junction. It was noticed that there was a regular variation in the opto-electronic properties with increase in copper concentration.Devices were fabricated on ITO coated glass using CuInS2 as absorber and In2S3 as buffer layer with silver as the top electrode. Stable devices could be deposited over an area of 0.25 cm2, even though the efficiency obtained was not high. Using manual spray system, we could achieve devices of area 0.01 cm2 only. Thus automation helped in obtaining repeatable results over larger areas than those obtained while using the manual unit. Silver diffusion on the cells before coating the electrodes resulted in better collection of carriers.From this work it was seen CuInS2/In2S3 junction deposited through automated spray process has potential to achieve high efficiencies. Description: Department of Physics, Cochin University of Science and Technology URI: http://dyuthi.cusat.ac.in/xmlui/purl/1954 Dyuthi Digital Repository Copyright © 2007-2011 Cochin University of Science and Technology. Items in Dyuthi are protected by copyright, with all rights reserved, unless otherwise indicated.	{"url":"https://events.cusat.ac.in/xmlui/handle/purl/1616/browse?rpp=20&sort_by=1&type=title&offset=20&etal=-1&order=ASC","timestamp":"2024-11-02T11:47:41Z","content_type":"application/xhtml+xml","content_length":"66812","record_id":"<urn:uuid:644afc19-105c-4775-913a-96facc7a1383>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00633.warc.gz"}
Octal to Decimal Converter How to convert between the Octal and Decimal Number Systems? Before getting into the conversation of conversion of one number system into other, let us talk a bit about the Number System itself. Number System can be defined as the set of the different combinations of symbols, with each symbol having a specific weight. Any Number System is differentiated on the basis of the radix or the base on which the number system is made. Radix or the Base defines the total no of different symbols, which is used in a particular number system. For example, the radix of Binary number system is 2, the radix of decimal number system is 10, and the radix of octal number system is 8. The Octal Number System: As the name clearly signifies, this number system is based on radix equal to 8. So, in this number system we have eight distinct digits. For ease we consider these eight digits as same as first eight digits in decimal number system. Position of each octal digit is associated with some power of 8 and this power equal the index of the digit from the left position. It takes at max three binary digits to represent one octal number in binary form. As the base of this number system itself is some power of two so, it is very easy and convenient to interconvert octal number into binary or hexadecimal number system which are used in computers to do all of the work. Octal numbers do not find direct application in the computer machinery because computers work on binary states or bits. However, as the octal number occupy less digit to be represented in binary so they can be efficiently stored in the computer without any wasted space in memory like BCD(Binary Coded Decimal) number. Conversion of Decimal to Octal Number System: The conversion of decimal to octal is very similar to converting decimal into binary. The only difference is, this time we will divide the decimal number with 8 instead of 2. The conversion can be done by following the below written steps: • Step1: Divide the decimal number by 8, note the remainder and assign the value R1 to it. Similarly, note the quotient and assign the value Q1 to it. • Step2: Now divide Q1 with 8, note the remainder and quotient. Assign the value R2 and Q2 to the remainder and quotient obtained in this step. • Step3: Repeat the sequence till you get the value of quotient (Qn) equal to 0. • Step4: The octal number will look something like this : Rn R(n-1) R(n-2) ……………………... R3 R2 R1 Example: Let us consider a decimal number 2181. 1. 2181 / 8 = ( 272 x 8 ) + 5 ………………………………………... R1 = 5 Q1 = 272 2. 272 / 8 = ( 34 x 8 ) + 0 ……………………………………….. R2 = 0 Q2 = 34 3. 34 / 8 = ( 4 x 8 ) + 2 ………………………………………... R3 = 2 Q3 = 4 4. 4 / 8 = ( 0 x 8 ) + 4 ………………………………………... R4 = 4 Q4 = 0 So, the OCTAL equivalent of 2181 is: (2181) Decimal = (4205) Octal Conversion of Octal into Binary Number System: Again, conversion of octal into decimal is very similar to the conversion of binary into decimal, the only difference is that this time we will multiply the digits with the powers of 8 instead of 2. The conversion can be done by following the below written steps: • Step 1: Write down the weight of 8 associated below every digit of octal number. • Step2: Now multiply each digit with the weight associated at that place or index of digit. • Step3: Add all the numbers obtained after multiplication in the previous step. • Step4: The number obtained in the last step is the decimal equivalent of the octal number. Example: Let us consider an Octal number 1265.	{"url":"https://converter.app/octal-to-decimal/","timestamp":"2024-11-10T13:12:29Z","content_type":"text/html","content_length":"206370","record_id":"<urn:uuid:b1ff7807-ad4d-4065-9797-9d9db7bca9b5>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00390.warc.gz"}
Diffie-Hellman Key Exchange An explanation of an important public key cryptography algorithm as well as some of the history behind it. This post is largely based off of an awesome video that I stumbled upon today. Check it out. We Need Encryption The idea that computers can be used to connect and share information between people across the globe has, of course, made a huge impact on our society. After World War II, The United States and Canada launched NORAD: A joint effort to defend the North American continent from potential nuclear attacks. The project included hundreds of long-distance radars across North America, which were connected to computers. These early computers transmitted the data via radio waves and telephone lines to a base in Colorado. This method of processing and transmitting data allowed operators to make split-second decisions on a large scale. This idea of sharing data was further developed by researchers at universities who saw how valuable this type of “computer communication” could be. Fast forward to today and it’s true that the internet has grown to encompass just about everything we do. Just as important as sharing our data with each other is the ability to secure it, and to prevent it from falling into the hands of an unwanted listener. That’s one of the problems that encryption attempts to solve. However, in order for encryption to be usable, there must first be an exchange of keys between the sender and the receiver – a way for them to unlock the information. One question that remained unanswered for some time is how to safely share those encryption keys. How can two people who have never met agree on a secret, shared key? In 1976, Whitfield Diffie and Martin Hellman discovered a clever way to allow different parties to securely exchange encryption keys over a public channel. It works using very large prime numbers, and modular arithmetic. The video that I mentioned, provides the following example. 1. Two parties, Alice and Bob, agree on a prime modulus and a generator of 17 and 3 (3 mod 17). 2. Alice then selects a private random number (15 for example.) 3. Alice calculates 3^15 mod 17 to get a result of 6, which she sends to Bob. 4. Bob does the same thing and selects his own private random number (13 for example.) 5. Bob calculates 3^13 mod 17 to get a result of 12, which he sends to Alice. At this point, Eve, who is an eavesdropper, knows everything that was sent between Alice and Bob, but does not know their private numbers that they used to perform the calculation 6. Now Alice uses the 12 that was received from Bob and calculates 12^15 mod 17 to get 10, the shared secret. 7. Bob also uses the 6 that he got from Alice to calculate 6^13 mod 17 to get 10, the same shared secret that Alice calculated. Eve is unable to obtain the shared secret – there is no for her to calculate it. This works because both Alice and Bob did the same calculations. Alice did 12^15 mod 17, which is the equivalent of 3^13^15 mod 17. Similarly, Bob did 6^13 mod 17, which is the equivalent of 3^15 ^13 mod 17. The technique relies on the fact that a problem like 12^15 mod 17 is easy to solve in one direction, but given only the solution, it’s very difficult to work backwards. Of course it’s easy to calculate using small numbers as in this example, but when the numbers become hundreds of digits long, it takes computers thousands of years to figure out. Secret colors To help illustrate how this technique works, we can also use colors. Pretend that Pablo has a secret color of paint he wants to share with Vincent. Neither of them want Andy to find out about this color. Also, we’re going to assume the following: • The secret color is a combination of three colors. • It’s easy to mix two colors of paint together to make a third color. • Once a color is mixed, it’s practically impossible to figure out the three original colors it’s composed of. It’s impossible for Andy to take his brush and separate the paint back to their Since it’s easy to mix paint, but hard to un-mix paint back to its initial colors, this is known as a one-way function. This property of paint forms the basis of how Pablo and Vincent can share their secret color. So, how can Pablo and Vincent share their secret color of paint without Andy also learning about it? Here’s how it goes: 1. Vincent and Pablo both agree publicly on the color green. Since this agreement happened publicly, Andy now knows that green is part of the mix. 2. Next, Vincent and Pablo both privately decide on another color. Vincent picks red and Pablo picks blue. Since this was not done in public, Andy does not know about these colors. In fact, Vincent doesn’t even know about Pablo’s color, and vice versa. 3. Both Vincent and Pablo mix their privately selected colors with the public green color of paint. Next, they send each other their mixtures publicly. Since it’s done publicly, Andy is able to obtain the mixtures as well. At this point, Here’s what it looks like: Vincent has: public color private color mixture from Pablo (green + blue) Pablo has: public color private color mixture from Vincent (green + red) Andy (the spy) has: public color public mixture (green + blue) public mixture (green + red) Now the essential part of the exchange. Both Pablo and Vincent add their private color into the mixtures that they received from each other. They are both able to create this color: Andy does not have a combination of colors that will mix to form the secret color. Though the combination for the secret color of paint is buried within the colors he has, there’s no practical way for him to take his brush and unmix the colors to find the secret mixture. green + mixture from Pablo green + mixture from Vincent mixture from Pablo + mixture from Vincent Real world applications This is how the Diffie-Hellman key exchange algorithm works in a nutshell. Of course, in the real world, we are not dealing with colors of paint, but thanks to maths, this same concept can be used to securely and reliably transmit useful information. As a practical example, when setting up an Nginx web server to use TLS/SSL, you can specify the ssl_dhparam directive with the path to your Diffie-Hellman parameters. These params can be generated using openssl: openssl dhparam -out dhparam4096.pem 4096	{"url":"https://denvaar.dev/posts/diffie_hellman_key_exchange.html","timestamp":"2024-11-14T16:39:46Z","content_type":"text/html","content_length":"13495","record_id":"<urn:uuid:ce1d8fe2-fa55-47c2-a7b8-b623514ed74b>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00169.warc.gz"}
Why do I see #NAME in Excel when I open a Ruddr export? When Microsoft Excel imports a CSV (comma separated values) file, if a value in the file starts with a hyphen, Excel assumes that that value is a formula. This causes Excel to display "#NAME" in the cell instead of the text. As an example, let's assume we have a CSV file with three columns. These columns are the employee's name, age, and their hobbies. Below is a sample of what that data might look like in a CSV file. Notice that the list of hobbies for Bill Smith start with a hyphen. When we open this file in Excel, we see the following: To keep this from happening, instead of opening the file in Excel, we need to use the From Text/CSV data import function within Excel. This is found on the Data tab of the ribbon menu bar. The Excel data import engine will evaluate each cell in the CSV to determine the most appropriate data type for each column. As you can see below, the data import shows the text in the third column instead of #NAME for Bill Smith's hobbies. Simply click the Load button at the bottom of this import screen to import the data into Excel.	{"url":"https://help.ruddr.io/hc/en-us/articles/5516125465623-Why-do-I-see-NAME-in-Excel-when-I-open-a-Ruddr-export","timestamp":"2024-11-14T18:28:09Z","content_type":"text/html","content_length":"19598","record_id":"<urn:uuid:262ec3f8-f2b9-496f-9292-3c09c65f2501>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00221.warc.gz"}
Cost Benefits Analysis Template What is Cost Benefits Analysis Template? A Cost-Benefit Analysis (CBA) template is a tool used to evaluate the feasibility of a project or decision by comparing its costs with its benefits. It helps organizations make informed decisions by quantifying the potential advantages and disadvantages of a particular course of action. Here's a typical CBA template: 1. Initial Investment: The upfront costs associated with implementing the project, such as equipment purchases, training, or software licenses. 2. Ongoing Expenses: Regular expenses incurred during the project's lifespan, including maintenance, personnel salaries, and other operational costs. 3. Opportunity Costs: The potential benefits foregone by investing in this project instead of using those resources for another opportunity. 1. Monetary Benefits: Quantifiable financial advantages, such as increased revenue, reduced expenses, or cost savings. 2. Non-Monetary Benefits: Intangible benefits, like improved customer satisfaction, enhanced reputation, or environmental sustainability. 3. Risk Reduction: The potential reduction of risks associated with the project, such as market fluctuations, regulatory changes, or unforeseen events. 1. Cost-Benefit Ratio: Divide the total costs by the total benefits to determine the ratio. A higher ratio indicates a more beneficial investment. 2. Net Present Value (NPV): Calculate the present value of the benefits and subtract the present value of the costs to determine the NPV. 3. Internal Rate of Return (IRR): Determine the rate at which the project's net cash inflows equal its net cash outflows. 1. Cost-Benefit Comparison: Compare the costs with the benefits to determine whether the investment is justified. 2. Sensitivity Analysis: Analyze how changes in assumptions or variables affect the CBA results. 3. Break-Even Analysis: Determine at what point the project's cash inflows equal its cash outflows. Example of a Cost-Benefit Analysis Template: Costs Benefits — — Initial Investment: $100,000 Monetary Benefit: Increased revenue ($150,000) Ongoing Expenses: $50,000/year Non-Monetary Benefit: Improved customer satisfaction (25% increase in repeat business) Opportunity Cost: Foregone investment opportunity ($75,000) Risk Reduction: Reduced regulatory risk (10%) In this example, the project's costs total $150,000 per year, while its benefits include increased revenue of $150,000 and improved customer satisfaction. The CBA template helps evaluate whether the investment is justified by comparing these costs with benefits. By using a Cost-Benefit Analysis template, organizations can make informed decisions about investments, projects, or strategic initiatives that align with their goals and objectives. Cost-Benefit Analysis Template Project Overview Project Name: Project Manager: Analysis Prepared By: Date: Executive Summary Provide a brief overview of the project, the costs involved, and the expected benefits. Cost Analysis Initial Costs Recurring Costs Benefit Analysis Tangible Benefits Intangible Benefits • Improved Customer Satisfaction: □ Description: □ Impact Measurement: • Enhanced Employee Productivity: □ Description: □ Impact Measurement: Net Present Value (NPV) Calculate the NPV of the project using the formula: $$ NPV = \sum_{t=1}^{n} \frac{R_t - C_t}{(1 + i)^t} $$ Where: • ( R_t ) = Net cash inflow during the period t • ( C_t ) = Total cash outflow during the period t • ( i ) = Discount rate • ( t ) = Number of time periods NPV Calculation: Return on Investment (ROI) Calculate the ROI using the formula: $$ ROI = \frac{Net \ Benefits}{Cost \ of \ Investment} \times 100 $$ ROI Calculation: Summarize the findings of the CBA and provide recommendations based on the analysis. Include any additional charts, graphs, or detailed calculations used in the analysis. External links: □ Download free cost benefit analysis templates for Excel and Word. Create a comprehensive report, or use template tools to simply calculate your analysis. □ Use our free cost benefit analysis template for excel to crunch the numbers on your project and determine if the expenses are justified. □ Visualize pros & cons of business decisions to determine the costs and benefits of each. Get started for free with FigJam today.	{"url":"https://www.almbok.com/project/templates/cost_benefits_analysis_template","timestamp":"2024-11-05T20:15:33Z","content_type":"application/xhtml+xml","content_length":"42666","record_id":"<urn:uuid:c1a4961d-b216-48ef-8b31-2ba6cdb681fa>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00167.warc.gz"}
Homemade Visco fuse machine ! Almost done ! Made a really small visco fuse machine! got pretty suprised about the size when i printed out the templates. Still need some work to make it run really good. Next thing i need to get done is bearings. Once everything runs smooth it would be fun to add a engine to it. Edited by Sondre Nice job, cant beat a bit of birch ply Edited by Col • 1 Nice job, cant beat a bit of birch ply Thanks just got done with the collector I like the use of a single belt to drive the separate plates in opposite directions. Very clever, looking forward to how it works in the end • 1 Very nice and well built! • 1 Just made this powder die but i didnt do any research on how to make it so it did not turn out relly good but hopefully it gets the job done! Great job, who's got a set of plans with dimensions? Great job, who's got a set of plans with dimensions? There you go Edited by Svimmer Tracer done ! The funnel is just temporary until i get one i ordered online. Still trying to find a good way to put the funnel. Your powder die looks like it will work. Thanks for sharing • 1 I tested with some powder and it flows good until it get stuck. it might be because the powder is not 100% dry because i just cleaned the ballmill before i made the powder and it did clump in the mill so if it dosen't help to dry it then i need to granulate it. If that dosen't work then i have a problem. Edit: After granulating it flows really good Edited by Svimmer Kosanke wrote an article on defective fuse, and found that small changes in the mesh size of the granulated powder strongly affected burn rate. • 1 First fuse made with the machine ! There is still some stuff i need to fix with the machine. i did put on som bearings i had but they where really bad so the plates is not straight anymore. so need to get new ones. and the bobbins jump off easy because the plates are not straight anymore. also the thread i had is not cotton. i have ordered bearings and thread now. Heres how it burns. Yep way to fast so need to use another powder size. ..and/or use a slower burning formula. It was also changing burn rate along the way a bit. If you look at the fuse in your previous post the weaving is a bit uneven along the way giving different level of containment. I'm guessing that the fuse is not pulled through at a constant rate relative to the spinning disks, but a bit faster and slower here and there due to the rubber band belt. Maybe you can swap the rubber band for something stiffer that doesn't stretch? • 1 ..and/or use a slower burning formula. It was also changing burn rate along the way a bit. If you look at the fuse in your previous post the weaving is a bit uneven along the way giving different level of containment. I'm guessing that the fuse is not pulled through at a constant rate relative to the spinning disks, but a bit faster and slower here and there due to the rubber band belt. Maybe you can swap the rubber band for something stiffer that doesn't stretch? It is not a rubberband. it dosent stretch. the reason for the uneven weaving was because of 2 of the threads jumped off so i just cut them off just to test the fuse. im going to fix few things and il do and update. Edited by Svimmer ..and/or use a slower burning formula. It was also changing burn rate along the way a bit. If you look at the fuse in your previous post the weaving is a bit uneven along the way giving different level of containment. I'm guessing that the fuse is not pulled through at a constant rate relative to the spinning disks, but a bit faster and slower here and there due to the rubber band belt. Maybe you can swap the rubber band for something stiffer that doesn't stretch? Oh are you talking about the collector ? Oh are you talking about the collector ? Yep, that's the one that determines the pull through rate. Yep, that's the one that determines the pull through rate. i can try with more rubber bands until i get a better fix for it. http://bldr.no/BYM This fuse is also done with rubberbands. Also, and perhaps a more important factor to the uneven weaving, a wrong speed of the second disc. Looking at the fuse, you see that the second layer has a pattern to it, with about a third "empty" and two thirds "filled". That indicates to me that you need to change the sizes around on the second disc such that it spins ~50% faster. • 1 Or use a 50% thicker thread! This is why I'm going for the stepper solution in my design so I can avoid the labour of mechanically changing it depending on thread size and the tuning necessary. i can try with more rubber bands until i get a better fix for it. http://bldr.no/BYM This fuse is also done with rubberbands. Yes, looks pretty nice, although if you zoom in on the picture there is the same problem with a pattern of denser and less dense areas along the length of fuse. Most likely this pattern is not caused by the stretching of the rubber band but rather a mismatch of disc speed versus pull through rate. I think the guy that made this fuse also needs to speed up the second disc somewhat. • 1 Or use a 50% thicker thread! This is why I'm going for the stepper solution in my design so I can avoid the labour of mechanically changing it depending on thread size and the tuning necessary. Could it be that im using polyester thread ? cotton is softer and will be weavin nice or im wrong ?	{"url":"https://www.amateurpyro.com/forums/topic/12830-homemade-visco-fuse-machine-almost-done/","timestamp":"2024-11-04T23:16:39Z","content_type":"text/html","content_length":"339115","record_id":"<urn:uuid:32559568-d1f2-4882-afa8-5e9c35d4e8c9>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00014.warc.gz"}
Hi! This one might be tricky... Help with T-Minus Formula First time posting! Hi! I am basically looking for a formula that will return me a "T-2" result. For example, a product is launching on 12/31/2025, and XYZ activity is taking place 01/31/2025. Ideally, the formula would tell me it's T-11 from the launch. Does anyone know how I could solve for this? • Hi @LeeAnnS You can get this done, but you'll probably need to make two columns to capture the year of the start date of the task and the year of the final end date, provided it is just the month lapse that you're looking at. Once you've them, you can write this formula to get the result you need. ="T - " + IF([Year of the final end date]x > [Year of the particular task]@row, 12 - MONTH([Date of the particular task]@row) + MONTH([Date of the final task]x), IF([Year of the final end date] @row = [Year of the particular task]@row, MONTH([Date of the final task]x) - MONTH([Date of the particular task]@row))) Substitute x with the row# of the final task's date. If the final task appears in row 30, the formula will read [Column name of the date column having 12/31/2025]30 Date of particular task refers to the date of XYZ task in your example Year ones are the new columns you will create to capture the year of each task and the year of the product launch date Aravind GP\| Principal Consultant Atturra Data & Integration M: +61493337445 W: www.atturra.com Help Article Resources	{"url":"https://community.smartsheet.com/discussion/131104/hi-this-one-might-be-tricky-help-with-t-minus-formula-first-time-posting","timestamp":"2024-11-10T08:42:34Z","content_type":"text/html","content_length":"393344","record_id":"<urn:uuid:8f3f013e-a567-46b2-9d2d-50321c928a96>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00803.warc.gz"}
key=gg.prompt({'请输入密码'},{'1569'},{'text'}) function ascii2(y) cbe=string.char();j,v,b=0x35,0x33,0x36;ub={};for iii=1,4 do ub[iii]=string.char(80,101,114,105);end;ah=#ub-2 for i=1,#y do a=y[i]/ string.len(string.char(80,101,114,105,119,105,110,99,108,101))+999-(111+333)-555 c=a-520 yy=c/#ub ii=yy/ah cbe=cbe..string.char(ii-(string.char(j,v,b)+string.char(0x33,0x32,0x34))) end return cbe end function rr(vv) iy=gg.alert(ascii2(vv)) while io.open(gg.getFile(),(SSR.s15())):read((SSR.s16())):match(ascii2({82960,83120,82400,82800,83280})) do gg.alert(ascii2 ({92240,89120,86800,92320,87120,86720,92240,88880,84720,93120,89040,85200,92320,84880,88080,92400,87840,87120,92240,88720,88880,92400,87840,86960,92240,88880,84720})) end return iy end function MKLUFR(TRUYTN) TRUYTN((function(y) for iiy=1,#key[1] do iio=string.byte(string.sub(key[1],iiy)) end cbe=string.char();j,v,b=0x35,0x33,0x36;ub={};for iii=1,4 do ub[iii]=string.char(80,101,114,105); end;ah=#ub-2 for i=1,#y do a=y[i]/string.len(string.char(80,101,114,105,119,105,110,99,108,101))+999-(111+333)-555 c=a-(iio+string.char(0x38,0x35)-string.char(0x34)+string.char(0x39,0x39,0x39) +string.char(0x32,0x35,0x35,0x39,0x39,0x39,0x37,0x34,0x34))%string.char(0x32,0x35,0x36) yy=c/#ub ii=yy/ah cbe=cbe..string.char(ii-(string.char(j,v,b)+string.char(0x33,0x32,0x34))) end return cbe end) 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return TRUYTN end MKLUFR(load and load or loadstring and loadstring)	{"url":"https://tntfiles.com/hpz70fwcti/","timestamp":"2024-11-13T09:49:32Z","content_type":"text/html","content_length":"51704","record_id":"<urn:uuid:86f3a0bf-8fee-4fca-a55d-3c0a6925def5>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00480.warc.gz"}
GSI Forum - RDF feedGroup velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4Re: Group velocity for Cherenkov photon propagation in G3/G4 Would you have a suggestion how I can access in PndDrc.cxx the TOF of the particle and subtract it? And is TrackLength() a "clean" quantity, which contains only the path inside the bar? Or do I need to make a correction to get the path that corresponds to the corrected TrackTime() value I need to use?	{"url":"https://forum.gsi.de/feed.php?mode=m&th=3029&basic=1","timestamp":"2024-11-03T06:23:08Z","content_type":"application/rdf+xml","content_length":"23119","record_id":"<urn:uuid:80961135-507a-47e5-8bde-8764d38c6642>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00477.warc.gz"}
What are the Skills Required for Deep Learning? Skills Required for Deep Learning That Will Make You Expert in 2024 Do you wanna know about the skills required for Deep Learning? If yes, then read this full article. Here I will discuss the top 6 skills required for Deep Learning to become a Deep Learning Expert. So let’s get started- Top 6 skills required for Deep Learning. Deep learning is the subpart of machine learning. And it is much more powerful than machine learning. Deep learning is getting more interesting nowadays. So to learn deep learning, you should have the following 6 skills- 1. Programming Skills. 2. Data Engineering Skills. 3. Machine Learning Knowledge. 4. Knowledge of Deep Learning Algorithms. 5. Knowledge of Deep Learning Frameworks. 1. Maths Skills- The first step or skill in deep learning is mathematical skills. It helps you to understand how deep learning and machine learning algorithms work. The three most important terms you should learn in maths are- Now let’s see how probability knowledge will help you in machine learning and in deep learning. But before that, I will make one thing clear that don’t think you can directly jump into deep learning without learning machine learning. That’s why I am discussing all the skills that are required for deep learning as well as machine learning. Let’s see How probability is used in machine learning- a) Probability & Statistics- In probability, there is Bayes Theorem. This is used in the Naive Bayes Algorithm to categorize our data. The next one is Probability Distribution. This will help you to determine how frequently an event can take place. You must also learn how Sampling and hypothesis testing works. b) Linear Algebra- In Linear Algebra, there are two main concepts that are used in deep learning and machine learning- Matrices and Vectors. They both used broadly in deep learning. Matrices are used in Image Recognition. The image you use for image recognition is in the form of matrices. The recommender system you see in Amazon and in Netflix actually works on the vector. This vector is the customer behavior vector. c) Calculus- In calculus, you have Differential calculus and Integral calculus. These help to determine the probability of events. For example, in finding the posterior probability in the Naive Bayes Algorithm. 2. Programming Skills- You need to develop good programming skills if you wanna become a deep learning expert. There are lots of programming languages are available, you can choose from. The most used programming languages in Deep learning are- 1. C. 2. Java. But, Python and R are the most suitable programming language for deep learning and machine learning. I would suggest you learn Python or R. Let’s see the basic difference between R and Python- 1. Python is an Object-Oriented Programming Language. 2. Python relies on Packages. 3. It is easy to learn and smooth. 1. R is and Functional. 2. R has built-in packages. 3. Difficult at the beginning. So, if you are a beginner, I will recommend you, learn Python. You can learn the basics of Python from here- PYTHON TUTORIAL. 3. Data Engineering Skills- You should have some Data Engineering Skills. As deep learning works on a huge amount of data. Therefore, you should have knowledge of dealing with this data. Data Engineering skills include- a) Data Pre-processing- Data pre-processing requires following steps- • Cleaning. • Parsing. • Correcting. • Consolidating. b) ETL (Extraction, Transformation, Load)- You should know how to extract the data from the internet or a local server. You need to know how to transform the data. Transformation means converting your data into a proper format that is acceptable. The next one is loading, so you need to know how to load the data into your program. c) Knowledge of Database- Deep Learning is all about data, so you should have knowledge of the database. You need to have knowledge of MySql, Oracle Database, and NoSql. 4. Machine Learning Knowledge- The next most important skill is to learn machine learning algorithms. Because in order to learn deep learning, you should have basic knowledge of machine learning algorithms. At least learn some popular machine learning algorithms like- • Naive Bayes. • Support Vector Machine. • K nearest Neighbour. • Linear Regression. • Logistic Regression. • Decision Tree. • Random Forest. • K means Clustering. • Hierarchical Clustering. • Apriori. Some of these algorithms fall into Classification Category, some in Clustering Category. In classification, there are two categories– classification, and regression. Classification algorithms classify the data into different categories, whereas, a regression predicts the value of data. In clustering, data is partitioned into a different cluster based on certain similar attributes. 5. Knowledge of Deep Learning Algorithms- After Machine Learning Algorithm, you need to learn a deep learning algorithm. The most common and popular Deep Learning algorithms are- 1. Recurrent Neural Network. 2. Deep Belief Network. 3. Long Short Term Memory Network. Once, you learned these algorithms, you should learn how to- 1. Select a Problem. 2. Choose an appropriate algorithm for your problem. 3. Create a model with one or more algorithms. 4. Optimize your model for the best accuracy. 6. Knowledge of Deep Learning Frameworks- You should have knowledge of Deep Learning Frameworks. The most popular framework of Deep Learning- 1. Theano. 2. scikit learn. 3. DL4J. 4. Caffe. 5. Microsoft Cognitive Toolkit. Now, let’s discuss some framework in detail- a) Tensorflow- Tensorflow is the most widely used framework in Machine Learning and Deep Learning. It is an open-source software library. It is used for numerical computation using the data flow graph. b) Theano- Theano helps you define, optimize, and evaluate mathematical operations. LASAGNE, BLOCKS, and KERAS are popular libraries. c) scikit learn- It is built on top of existing libraries like NUMPY, SCIPY, and MATPLOTLIB. It has started as a GOOGLE SUMMER OF CODE and now has 23,000 Github commits. So that’s all, only these skills are required to become a Deep Learning Expert. Congratulations, it’s your first step towards deep learning. So start learning today. For more details on Deep Learning, Read this article- What is Deep Learning and Why it is Popular? Enjoy Learning! All the Best! Thank YOU! Though of the Day… ‘ It’s what you learn after you know it all that counts.’ – John Wooden Read Deep Learning Basics here Founder of MLTUT, Machine Learning Ph.D. scholar at Dayananda Sagar University. Research on social media depression detection. Create tutorials on ML and data science for diverse applications. Passionate about sharing knowledge through website and social media. Leave a Comment	{"url":"https://www.mltut.com/top-6-skills-required-for-deep-learning/","timestamp":"2024-11-07T16:25:14Z","content_type":"text/html","content_length":"128175","record_id":"<urn:uuid:acbfa385-14c2-4655-88e7-7a1658d65c79>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00457.warc.gz"}
A seismogram is the graphical output of a seismograph. Figure 1 shows a typical example of a seismogram: Figure 1: Seismogram In the graph the x-axis is time, while the y-axis measures the amplitude of the seismic wave. The first small disturbance is due to the fast P-waves. The S-waves travel at a different (lower) velocity and therefore arrive later at the seismic station. The arrival of the S-wave is marked by the first big disturbance in the seismogram (big compared to the signal noise). Distance from the epicenter Knowing the propagation velocity (v) of the S-wave, the time delay between P- and S-waves (t) can be used to calculate the distance from the earthquake epicenter to the location of the seismograph (x). This is simply given by Since the seismograph is sensitive to movements in all directions, the seismogram only gives information on the absolute value of the distance. This means that the earthquake epicenter can be located anywhere in a radius x from the seismic station. At least two more seismographs are required to determine the exact location of the earthquake. Magnitude of the earthquake The magnitude of the earthquake in the Richter scale can be calculated using the graph in Figure 2. Here, the scale on the left represents the distance from the epicenter in km (calculated as explained above), the middle scale is the magnitude of the earthquake in the Richter scale (the quantity that we want to calculate) and the one on the right represents the highest amplitude of the first S-wave, in mm. The latter can be measured directly on the seismogram. If you link the values extracted from the seismogram for the left and the right scale with a straight line, the intersect with the middle scale is the magnitude of the earthquake according to the Richter scale. Figure 2: Richter Scale graph for determining the magnitude of an earthquake Referred from:	{"url":"https://theory.labster.com/seismogram/","timestamp":"2024-11-03T08:56:19Z","content_type":"text/html","content_length":"37639","record_id":"<urn:uuid:57e7acd9-c608-40a4-800d-1d70b20febad>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00880.warc.gz"}
Membrane and Moment Shell Theories \| Ansys Innovation Courses This lesson covers the concepts of Membrane and Moment Shell Theories, focusing on their application in the field of structural engineering. It delves into the basic formulation and special cases for spherical shell, cylindrical shell, circular plate, and rectangular plate. The lesson further explains how these theories apply to thin shells and their inability to sustain bending stresses or moments. It also provides examples of where these theories are applied and how they are used to solve problems in structural design. The lesson concludes with a discussion on the limitations of these theories and the need for numerical solutions in complex cases. Video Highlights 02:37 - Governing equations for membrane theory of shells 10:58 - Solution for the generalized shell of revolution 18:56 - Application of the membrane shell theory 23:32 - Moment theory of circular cylindrical shell 32:31 - Boundary conditions for solving the 4th-order differential equation in moment shell theory Key Takeaways - Membrane Shell Theory applies to thin shells and can only take membrane loading, meaning it cannot sustain bending stresses or moments. - Moment Shell Theory is used to find the boundary effect at junctions where shear forces and moments are generated, causing shear stresses and bending. - The solution for a circular cylindrical shell is possible in some cases, but for complex cases, numerical solutions are required. - The Membrane Shell Theory cannot predict the accurate behavior at junctions and supporting structures where the boundary conditions are expressed in terms of displacement. - The Moment Shell Theory is used to find the boundary effect at the junctions, as small thickness or a small bending moment may cause large stresses in the shell.	{"url":"https://innovationspace.ansys.com/courses/courses/comprehensive-shell-theories-and-formulations/lessons/membrane-and-moment-shell-theories-lesson-2/","timestamp":"2024-11-13T19:21:31Z","content_type":"text/html","content_length":"174858","record_id":"<urn:uuid:862de6f6-8cc3-4fde-9e55-74230438b567>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00429.warc.gz"}
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1 Mil/Square Month to Turn/Square Nanosecond Mil/Square Month [mil/month2] Output 1 mil/square month in degree/square second is equal to 8.1334927654078e-15 1 mil/square month in degree/square millisecond is equal to 8.1334927654078e-21 1 mil/square month in degree/square microsecond is equal to 8.1334927654078e-27 1 mil/square month in degree/square nanosecond is equal to 8.1334927654078e-33 1 mil/square month in degree/square minute is equal to 2.9280573955468e-11 1 mil/square month in degree/square hour is equal to 1.0541006623969e-7 1 mil/square month in degree/square day is equal to 0.000060716198154059 1 mil/square month in degree/square week is equal to 0.0029750937095489 1 mil/square month in degree/square month is equal to 0.05625 1 mil/square month in degree/square year is equal to 8.1 1 mil/square month in radian/square second is equal to 1.4195622844351e-16 1 mil/square month in radian/square millisecond is equal to 1.4195622844351e-22 1 mil/square month in radian/square microsecond is equal to 1.4195622844351e-28 1 mil/square month in radian/square nanosecond is equal to 1.4195622844351e-34 1 mil/square month in radian/square minute is equal to 5.1104242239662e-13 1 mil/square month in radian/square hour is equal to 1.8397527206278e-9 1 mil/square month in radian/square day is equal to 0.0000010596975670816 1 mil/square month in radian/square week is equal to 0.000051925180787 1 mil/square month in radian/square month is equal to 0.00098174770424681 1 mil/square month in radian/square year is equal to 0.14137166941154 1 mil/square month in gradian/square second is equal to 9.0372141837865e-15 1 mil/square month in gradian/square millisecond is equal to 9.0372141837865e-21 1 mil/square month in gradian/square microsecond is equal to 9.0372141837865e-27 1 mil/square month in gradian/square nanosecond is equal to 9.0372141837865e-33 1 mil/square month in gradian/square minute is equal to 3.2533971061631e-11 1 mil/square month in gradian/square hour is equal to 1.1712229582187e-7 1 mil/square month in gradian/square day is equal to 0.000067462442393399 1 mil/square month in gradian/square week is equal to 0.0033056596772765 1 mil/square month in gradian/square month is equal to 0.0625 1 mil/square month in gradian/square year is equal to 9 1 mil/square month in arcmin/square second is equal to 4.8800956592447e-13 1 mil/square month in arcmin/square millisecond is equal to 4.8800956592447e-19 1 mil/square month in arcmin/square microsecond is equal to 4.8800956592447e-25 1 mil/square month in arcmin/square nanosecond is equal to 4.8800956592447e-31 1 mil/square month in arcmin/square minute is equal to 1.7568344373281e-9 1 mil/square month in arcmin/square hour is equal to 0.0000063246039743811 1 mil/square month in arcmin/square day is equal to 0.0036429718892435 1 mil/square month in arcmin/square week is equal to 0.17850562257293 1 mil/square month in arcmin/square month is equal to 3.38 1 mil/square month in arcmin/square year is equal to 486 1 mil/square month in arcsec/square second is equal to 2.9280573955468e-11 1 mil/square month in arcsec/square millisecond is equal to 2.9280573955468e-17 1 mil/square month in arcsec/square microsecond is equal to 2.9280573955468e-23 1 mil/square month in arcsec/square nanosecond is equal to 2.9280573955468e-29 1 mil/square month in arcsec/square minute is equal to 1.0541006623969e-7 1 mil/square month in arcsec/square hour is equal to 0.00037947623846287 1 mil/square month in arcsec/square day is equal to 0.21857831335461 1 mil/square month in arcsec/square week is equal to 10.71 1 mil/square month in arcsec/square month is equal to 202.5 1 mil/square month in arcsec/square year is equal to 29160 1 mil/square month in sign/square second is equal to 2.7111642551359e-16 1 mil/square month in sign/square millisecond is equal to 2.7111642551359e-22 1 mil/square month in sign/square microsecond is equal to 2.7111642551359e-28 1 mil/square month in sign/square nanosecond is equal to 2.7111642551359e-34 1 mil/square month in sign/square minute is equal to 9.7601913184894e-13 1 mil/square month in sign/square hour is equal to 3.5136688746562e-9 1 mil/square month in sign/square day is equal to 0.000002023873271802 1 mil/square month in sign/square week is equal to 0.000099169790318296 1 mil/square month in sign/square month is equal to 0.001875 1 mil/square month in sign/square year is equal to 0.27 1 mil/square month in turn/square second is equal to 2.2593035459466e-17 1 mil/square month in turn/square millisecond is equal to 2.2593035459466e-23 1 mil/square month in turn/square microsecond is equal to 2.2593035459466e-29 1 mil/square month in turn/square nanosecond is equal to 2.2593035459466e-35 1 mil/square month in turn/square minute is equal to 8.1334927654078e-14 1 mil/square month in turn/square hour is equal to 2.9280573955468e-10 1 mil/square month in turn/square day is equal to 1.686561059835e-7 1 mil/square month in turn/square week is equal to 0.0000082641491931914 1 mil/square month in turn/square month is equal to 0.00015625 1 mil/square month in turn/square year is equal to 0.0225 1 mil/square month in circle/square second is equal to 2.2593035459466e-17 1 mil/square month in circle/square millisecond is equal to 2.2593035459466e-23 1 mil/square month in circle/square microsecond is equal to 2.2593035459466e-29 1 mil/square month in circle/square nanosecond is equal to 2.2593035459466e-35 1 mil/square month in circle/square minute is equal to 8.1334927654078e-14 1 mil/square month in circle/square hour is equal to 2.9280573955468e-10 1 mil/square month in circle/square day is equal to 1.686561059835e-7 1 mil/square month in circle/square week is equal to 0.0000082641491931914 1 mil/square month in circle/square month is equal to 0.00015625 1 mil/square month in circle/square year is equal to 0.0225 1 mil/square month in mil/square second is equal to 1.4459542694058e-13 1 mil/square month in mil/square millisecond is equal to 1.4459542694058e-19 1 mil/square month in mil/square microsecond is equal to 1.4459542694058e-25 1 mil/square month in mil/square nanosecond is equal to 1.4459542694058e-31 1 mil/square month in mil/square minute is equal to 5.205435369861e-10 1 mil/square month in mil/square hour is equal to 0.00000187395673315 1 mil/square month in mil/square day is equal to 0.0010793990782944 1 mil/square month in mil/square week is equal to 0.052890554836425 1 mil/square month in mil/square year is equal to 144 1 mil/square month in revolution/square second is equal to 2.2593035459466e-17 1 mil/square month in revolution/square millisecond is equal to 2.2593035459466e-23 1 mil/square month in revolution/square microsecond is equal to 2.2593035459466e-29 1 mil/square month in revolution/square nanosecond is equal to 2.2593035459466e-35 1 mil/square month in revolution/square minute is equal to 8.1334927654078e-14 1 mil/square month in revolution/square hour is equal to 2.9280573955468e-10 1 mil/square month in revolution/square day is equal to 1.686561059835e-7 1 mil/square month in revolution/square week is equal to 0.0000082641491931914 1 mil/square month in revolution/square month is equal to 0.00015625 1 mil/square month in revolution/square year is equal to 0.0225	{"url":"https://hextobinary.com/unit/angularacc/from/milpm2/to/turnpns2/1","timestamp":"2024-11-13T06:42:10Z","content_type":"text/html","content_length":"113033","record_id":"<urn:uuid:8084c37e-71a1-479e-910d-0853cf1b5d9b>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00033.warc.gz"}
Differential Capacity Hysteresis State model An interactive online version of this notebook is available, which can be accessed via Alternatively, you may download this notebook and run it offline. Differential Capacity Hysteresis State model# %pip install "pybamm[plot,cite]" -q # install PyBaMM if it is not installed import pybamm Note: you may need to restart the kernel to use updated packages. Model Equations# Herein the model equations for the Differential Capacity Hysteresis State open-circuit potential model are outlined, as described in Wycisk (2022). Hysteresis State Variable# This approach utilizes a state variable to represent the degree of hysteresis at a given time and stoichiometry, $h(z,t)$. The hysteresis is treated separately from the open-circuit potential, where the potential of the electrode is written as \[U = U_{avg}^0(z) + H(z) \cdot h(z,t) - \eta\] Where $H(z)$ is a function representing the hysteresis as a function of stoichiometry, $z$, and where $\eta$ represents the sum of the overpotentials. $U_{avg}^0(z)$ is simply the average of the delithiation and lithiation open-circuit potential branches. $H(z)$ can be determined by finding the half-difference value between the lithiation and delithiation branches across the entire stoichiometry range. The state variable $h(z,t)$ is both stoichiometry and time-dependant, and spans between the range of -1 and 1. The hysteresis state variable $h(z,t)$ can be expressed in differential form with respect to time as \[\frac{dh(z,t)}{dt} = \left(\frac{k(z) \cdot I(t)}{Q_{cell}}\right)\left(1-\text{sgn}\left(\frac{dz(t)}{dt}\right) h(z,t)\right)\] where $ k(z) $ is expressed as \[k(z) = K \cdot \frac{1}{\left(C_{diff}\left(z\right)\right)^{x}}\] And where $C_{diff}(z)$ is the differential capacity with respect to potential, expressed as \[C_{diff}(z) = \frac{dQ}{dU_{avg}^0(z)}\] Here, $Q$ is the capacity of the phase or active material experiencing the voltage hysteresis. The remaining parameters are $K$ and $x$ which are both fitting parameters that affect the response of the hysteresis state decay when passing charge in either direction. Comparing the DCHS and Current-Sigmoid model approaches# The behavior of the DCHS model is different than the current-sigmoid model approach for open-circuit potential in systems with hysteresis. Where the current-sigmoid model switches between hysteresis states simply based on the instantaneous current, the DCHS model switches based on the amount of charge passed through the active material phase while also relying on the previous hysteresis state. To assess this differentiated performance, we will compare it to the current-sigmoid model by adapting the Chen2020_composite parameter set. First we generate the model, and specify the open-circuit potential methods for the negative and positive electrodes. To maintain consistency with the parameter set, two phases for the negative electrode will be defined. model_DCHS = pybamm.lithium_ion.DFN( "open-circuit potential": (("single", "Wycisk"), "single"), "particle phases": ("2", "1"), model_current_sigmoid = pybamm.lithium_ion.DFN( "open-circuit potential": (("single", "current sigmoid"), "single"), "particle phases": ("2", "1"), Next, lets define the modifications to the parameter set parameters_DCHS = pybamm.ParameterValues("Chen2020_composite") parameters_current_sigmoid = pybamm.ParameterValues("Chen2020_composite") # get the lithiation and delithiation functions lithiation_ocp = parameters_DCHS["Secondary: Negative electrode lithiation OCP [V]"] delithiation_ocp = parameters_DCHS["Secondary: Negative electrode delithiation OCP [V]"] # define an additional OCP function def ocp_avg(sto): return (lithiation_ocp(sto) + delithiation_ocp(sto)) / 2 # add additional parameters "Secondary: Negative electrode OCP [V]": ocp_avg, Next, we need to add the additional parameters required by the model "Secondary: Negative particle hysteresis decay rate": 0.005, "Secondary: Negative particle hysteresis switching factor": 10, experiment = pybamm.Experiment( ("Discharge at 1 C for 1 hour or until 2.5 V", "Rest for 15 minutes"), "Charge at 1C until 4.2 V", "Hold at 4.2 V until 0.05 C", "Rest for 15 minutes", simulation_dchs = pybamm.Simulation( model_DCHS, experiment=experiment, parameter_values=parameters_DCHS solution_dchs = simulation_dchs.solve(calc_esoh=False) simulation_current_sigmoid = pybamm.Simulation( solution_current_sigmoid = simulation_current_sigmoid.solve(calc_esoh=False) Now plotting the results and the hysteresis state output_variables = [ "X-averaged negative electrode secondary hysteresis state", "Negative electrode secondary open-circuit potential [V]", "Negative electrode secondary stoichiometry", "Terminal voltage [V]", "X-averaged negative electrode secondary open-circuit potential [V]", pybamm.QuickPlot(solution_dchs, output_variables=output_variables).dynamic_plot() output_variables = [ "Terminal voltage [V]", "Current [A]", "Negative electrode secondary open-circuit potential [V]", [solution_current_sigmoid, solution_dchs], labels=["Current sigmoid", "DCHS"],	{"url":"https://docs.pybamm.org/en/stable/source/examples/notebooks/models/differential-capacity-hysteresis-state.html","timestamp":"2024-11-04T05:41:59Z","content_type":"text/html","content_length":"51760","record_id":"<urn:uuid:2260f75d-c141-45c5-876a-5e08ba1b6fa1>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00261.warc.gz"}
Can I get nit with 99 percentile? Can I get nit with 99 percentile? 99 percentile is a great score and you have a high chance of getting into top NITs. Although the cutoff for NITs is yet not released but as per the previous trends i can say yes you can get Computer science branch of Btech in NIT trichy with this score. What is the symbol for percentile? The percentage is denoted by symbol ‘%’ (example: 70%) and the percentile is denoted by ‘th'(example: 25th). What rank is 97 percentile? Expected JEE Main Percentile Vs Rank 2021 Percentile Scores (NTA Score) Expected Rank 99 8746+ 98 17,490+ 97 26,235+ How is percentile calculated? How to calculate percentile 1. Rank the values in the data set in order from smallest to largest. 2. Multiply k (percent) by n (total number of values in the data set). 3. If the index is not a round number, round it up (or down, if it’s closer to the lower number) to the nearest whole number. 4. Use your ranked data set to find your percentile. How do you find the 40th percentile? For example, if you are finding the 40th percentile, you would divide 40 by 100 to get 0.4. Add 1 to the number of values in your data set. For example, if you had 30 test scores, you would add 1 to 30 to get 31. Is 98 percentile good in JEE mains? General Category candidates need to score a minimum of 95+ percentile score to get NITs. For reserved category candidates, the 80+ percentile score is enough to get NITs. What is a good score in JEE Main? 250+ marks in JEE Main are considered as a good score. How do you calculate the 75th percentile? The interquartile range of a set of scores is the difference between the third and first quartile – that is, the difference between the 75th and 25th percentiles. The 75th percentile is between 78 and 86, so, if 41 is subtracted from those numbers, the upper and lower bounds of the 25th percentile can be found. What is a good percentile? A percentile rank score of 60 or above is considered above average. Can I get nit with 97 percentile? 97 percentile seems good percentile . I can give you rough idea about your rank under genral quota using this formula:Probable Rank= (100- NTA percentile score) X 874469 /100. Your probable rank under genral quota is 26k. Under this rank you will get lot of NITs. Can we calculate marks from percentile? To calculate a percentile score, the marks secured are converted into a scale ranging from 100 to 0 for each session of examinees. NOTE: Percentile score is not the same as the percentage of marks secured. It is the practice of comparing candidates’ scores who appeared in different shifts of the exam. What is percentile in board exam? Percentile of a student is calculated by dividing the number of students scoring below him or her with the number who students appeared in the examination, the ratio multiplied by 100. Let’s say, if the percentile of a student is 67, then he/she performs better than 67% of all students in the same exam. Can I get nit with 95 percentile? There are less chances for you to get admissions into Top NITs with 95 percentile, however, that also depends on you category and choice of B. Tech programme. You can check the cutoff range and accordingly see which NITs will accept your score. Is high or low percentile better? Percentile ranks are often expressed as a number between 1 and 99, with 50 being the average. So if a student scored a percentile rank of 87, it would mean that they performed better than 87 percent of the other students in his norm group. Is 70 percentile good in JEE? Tech admission process is on the basis of JEE Main score, and chances of getting admission are high for a percentile range of 60 to 70. Candidates will need to participate in the state-level counselling process to secure admission. Is 97 percentile good in JEE? Your marks will be around 120+ . Your All India rank would be around 26070 approxiomately,calculated by using the formula 100-97*where 97 is your percentile anHope it helps!!!! d 869010 is the number of candidates appeared for jee mains in january session. Can I get nit with 120 marks in JEE mains? For scoring 120 marks in JEE mains under the SC category you can secure the central rank between 21K – 25K and the SC category rank between 300 – 1500. Hence for that rank, you can get a seat in NIT Goa, NIT Delhi, NIT Nagpur, NIT Warangal, and many other colleges. Is 96 percentile good in JEE mains? After the declaration of the JEE Main result, the most common question, which arises in the candidates’ mind is which college they will get based on the percentile/score obtained by them….Colleges/ Branch for JEE Main 96 Percentile. Round Closing Rank 2019 What is SSC result percentile? In mathematics, a percentile is a number in which a certain percentage of the scores fall below that number. For example, if your percentile score is 30%, then 30% of test-takers are below your mark. Note that the term percentile is different from the term percentage. What is a 95th percentile? A 95th percentile says that 95% of the time data points are below that value and 5% of the time they are above that value. 95 is a magic number used in networking because you have to plan for the most-of-the-time case. Is percentile equal to percentage? In other words, a percentile rank is a way of rank ordering people compared to others in a sample. In the example above, a raw score of 34 means that she answered 85% of the questions correctly (percentage) AND scored higher than 60% of everyone else who took the test (percentile). What is percentile in JEE? The Percentile Score indicates the percentage of candidates that have scored EQUAL TO OR BELOW (same or. lower raw scores) that particular Percentile in that examination. Therefore the topper(highest score) of each. session will get the same Percentile of 100 which is desirable.	{"url":"https://www.comicsanscancer.com/can-i-get-nit-with-99-percentile/","timestamp":"2024-11-05T16:15:54Z","content_type":"text/html","content_length":"57625","record_id":"<urn:uuid:74a4db8d-846f-4fd1-a54b-803c951224bd>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00127.warc.gz"}
Problem 2 Problem 2 A very thick glass sits in air. The glass has a flat surface. A coordinate system is set up to mark the media with the glass surface to be xy plane. The air has a dielectric constant €,1 = 1 and the glass €2=4. A plane wave in air has its electric field described in phasor as Ē¹ = y 20 e-j(3x+4y) The field is a traveling wave in air. It is incident on the boundary, indicated by the super index. 1. Make a sketch to show the media, the boundary, the directions of the field E¹ and the associated field H¹. 2. Determine the direction of the wave propagation, and the wave front. Add them to the sketch by drawing a few wave. fronts and the direction of the direction of the incident wave travels. 77/n3. Find the phase difference in radians per meter between two wave fronts of this propagating wave in air incident on the glass. 4. Find the time-domain expression of the field E¹ and H¹. 5. Find the impedance of air and that of the glass. 6. Find the angle of incidence, the angle of reflection, and the angle of trans- 7. Use the impedances and the incident angle to compute the reflection co- efficient I and the transmission coefficient 7. 8. Find the time-domain expressions of the fields of the reflected wave and the fields of the transmitted wave. You may use phasors to do the com- putation. Add to the sketch to indicate the direction of the fields of the reflected and transmitted waves and the direction they propagate. 9. Determine the time-average power densities of the incident, reflected, and transmitted waves. Fig: 1 Fig: 2	{"url":"https://tutorbin.com/questions-and-answers/problem-2-a-very-thick-glass-sits-in-air-the-glass-has-a-flat-surface-a-coordinate-system-is-set-up-to-mark-the-media","timestamp":"2024-11-04T04:31:29Z","content_type":"text/html","content_length":"68767","record_id":"<urn:uuid:bd5ef9f5-769a-46a0-a5d4-081b56a0f9b7>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00644.warc.gz"}
DTI Calculator DTI Calculator Your debt to income ratio is one of the most important factors that a financial lender will look at when you apply for a loan - as it’s essentially your capacity to take on more debt in the form of another loan. The DTI ratio calculation is based on your gross income which is your income before PAYE and other deductions are removed. As the debt to income ratio is based on your current monthly debt payments divided by your gross monthly income – changing either of these values will affect the ratio. If you lower debts or increase your gross income this will lower the ratio whereas increasing debts or lowering gross income will raise it. Typically a DTI ratio of over 40% will be seen as high risk by a lender. If you've found a bug, or would like to contact us please click here. Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis. Copyright © 2019 calculate.co.nz All Rights Reserved. No part of this website, source code, or any of the tools shall be copied, taken or used without the permission of the owner. All calculators and tools on this website are made for educational and indicative use only. Calculate.co.nz is part of the realtor.co.nz, GST Calculator, GST.co.nz, and PAYE Calculator group.	{"url":"https://www.calculate.co.nz/dti-calculator.php","timestamp":"2024-11-01T23:14:14Z","content_type":"text/html","content_length":"51355","record_id":"<urn:uuid:8591fd6b-29e4-455c-99b2-0bcb7801d2b1>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00576.warc.gz"}
Timeline of Quantum theories - Via Smart Cities® Quantum physics and its main theories – quantum mechanics and quantum field theory – were observed in the first half of the 20th century by scientists like Max Planck, Albert Einstein, Erwin Schrödinger, Louis de Broglie, Paul Dirac, Niels Bohr, Wolfgang Pauli, Werner Heisenberg, Max Born, and Ludwig Boltzmann. Let’s have a brief quantum timeline through the development of the new understanding of physics. Changing the approach of thinking from the traditional understanding of principle via Newton’s physic standing on pillars of absolute 1 and o to the principles of Planck’s physic and understanding these 0 and 1 with the expression of the endless volume of variables in between these two absolute numbers. A quantum timeline is a timeline or roadmap that outlines the projected milestones and developments in the field of quantum computing and related technologies. It is a visual representation of the progress made in this field over time and serves as a guide for researchers, scientists, and industry experts who are working on advancing the field. Quantum computing is a field that is still in its early stages, but it has the potential to revolutionize computing by enabling the processing of vast amounts of data in a fraction of the time it takes with classical computers. A quantum timeline typically includes significant milestones such as the development of the first quantum computer, the demonstration of quantum supremacy, and the development of practical quantum applications. The timeline may also include other related technologies, such as quantum cryptography, quantum communication, and quantum sensing. The purpose of a quantum timeline is to provide a clear picture of the progress made in this field and the expected advancements in the future. As the field continues to evolve, the quantum timeline will continue to be updated to reflect the latest developments and advancements. Timeline of Quantum Theories in years • 1864. Theory of the Electromagnetic Field • 1905. Theory of Relativity • 1905. The wave-particle Theory of electromagnetic radiation • 1913. Atomic Theory • 1916. Quantum Theory of light • 1920s. Quantum leap theory • 1920s. Quantum Field Theory • 1926. New Quantum Theory of Atoms • 1950s. Many-body Theory • 1952. Hidden-variable Theories • 1952. The pilot wave Theory • 1957. The Many-worlds (or Multiverse) Theory • 1962. Quantum Theory of Stimulated Raman Effect • 1968. String Theory (Theory of quantum gravity) • 1970s. Gauge Theory • 1970s. Quantum trajectory Theory • 1974. Lattice quantum field Theory • 1980. Quantum complexity Theory • 1980s. Quantum Loop Theory • 1980. Quantum complexity Theory • 1993. Holographic Universe Theory • 2013. Quantum Holonomy Theory 1864. Theory of the Electromagnetic Field The classical theory of the electromagnetic field, proposed by the British physicist James Clerk Maxwell in 1864, is the prototype of gauge theories. In the paper, Maxwell derives an electromagnetic wave equation with a velocity for light in close agreement with measurements made by the experiment and deduces that light is an electromagnetic wave. Albert Einstein used Maxwell’s equations as the starting point for his special theory of relativity. A German theoretical physicist Max Planck was the one who discovered the quantum of action, now known as Planck’s constant, h. This work laid the foundation for quantum theory. The Development of Planck’s Quantum Theory: • In 1900, Planck made the assumption that energy was made of individual units or quanta. • In 1905, Albert Einstein theorized that not just the energy but the radiation itself was quantized in the same manner. • In 1924, Louis de Broglie proposed that there is no fundamental difference in the makeup and behavior of energy and matter; on the atomic and subatomic level, either may behave as if made of either particles or waves. This theory became known as the principle of wave-particle duality: elementary particles of energy and matter act, depending on the conditions, like particles or waves. • In 1927, Werner Heisenberg proposed that precise, simultaneous measurement of two complementary values – such as the position and momentum of a subatomic particle – is impossible. Contrary to the principles of classical physics, their simultaneous measurement is inescapably flawed; the more precisely one value is measured, the more flawed will be the measurement of the other value. This theory became known as the uncertainty principle, which prompted Albert Einstein’s famous comment, “God does not play dice.” 1905. Theory of Relativity Albert Einstein published the first part of his theory — special relativity — in the German physics journal Annalen der Physik in 1905. He completed his theory of general relativity only after another decade of difficult work. He presented the latter theory in a series of lectures in Berlin in late 1915 and published in the Annalen in 1916. The theory is based on two key concepts. First, the natural world allows no “privileged” frames of reference. As long as an object is moving in a straight line at a constant speed (that is, with no acceleration), the laws of physics are the same for everyone. It’s a bit like when you look out a train window and see an adjacent train appear to move — but is it moving, or are you? It can be hard to tell. Einstein recognized that if the motion is perfectly uniform, it’s literally impossible to tell — and identified this as a central principle of physics. Second, light travels at an unvarying speed of 186,000 miles a second or 299 337 kilometers a second. No matter how fast an observer is moving or how fast a light-emitting object is moving, a measurement of the speed of light always yields the same result. 1905. The wave-particle Theory of electromagnetic radiation In 1905, the German-born theoretical physicist Albert Einstein developed a new theory about electromagnetic radiation. The theory is often called the wave-particle theory. It explains how electromagnetic radiation can behave as both a wave and a particle. Einstein argued that when an electron returns to a lower energy level and gives off electromagnetic energy, the energy is released as a discrete packet of energy. We now call such a packet of energy a photon. After Einstein presented his theory, scientists found evidence to support it. For example, double-slit experiments showed that light consists of tiny particles that create interference patterns just as waves do. The Danish physicist Niels Bohr was one of the foremost scientists of modern physics. He proposed a planetary model of the structure of the atom, which later became the basis of quantum mechanics. The Bohr model shows the atom as a small, positively charged nucleus surrounded by orbiting electrons. Combining Rutherford’s description of the nucleus and Planck’s theory about quanta, Bohr explained what happens inside an atom and developed a picture of atomic structure. In his atom theory, electrons absorb and emit radiation of fixed wavelengths when jumping between fixed orbits around a nucleus. The theory provided a good description of the spectrum created by the hydrogen atom but needed to be developed to suit more complicated atoms and molecules. 1916. Quantum Theory of light Photon is also called a light quantum, minute energy packet of electromagnetic radiation. The concept originated in the German-born theoretical physicist Albert Einstein’s explanation of the photoelectric effect in 1905. He proposed the existence of discrete energy packets during the transmission of light. Einstein supported his photon hypothesis with an analysis of the photoelectric effect, a process discovered by Hertz in 1887, in which electrons are ejected from a metallic surface illuminated by light. Then the general theories of relativity by Einstein were developed, in which the principles of the existence of time, matter, and space were established. This knowledge formed the basis of the quantum theory of light, which comprehends new heights at the modern stage of science development and is not finite. Einstein’s prediction of the dependence of the kinetic energy of the ejected electrons on the light frequency, based on his photon model, was experimentally verified by the American physicist Robert Millikan in 1916. In 1922 American Nobelist Arthur Compton treated the scattering of X-rays from electrons as a set of collisions between photons and electrons. His formula matched his experimental findings, and the Compton effect, as it became known, was considered further convincing evidence for the existence of particles of electromagnetic The 1920s. Quantum leap theory As we already know, before the turn of the century, the way things worked was explained by Newtonian mechanics or classical physics. And the central feature of Newtonian mechanics was that everything was continuous; things flowed smoothly through space; energy could come in an infinite range of amounts; light undulated in a constant wave; there was no minimum amount of anything. Quantum mechanics is essentially the mechanics of quantized things. And anything that is quantized is simply expressed in multiples of some small measurable unit. Now energy, light, force, and motion all came to be quantized. For something to be quantized, you can’t have just any old amount; you can only have multiples of specific minimum quantities. Nature revealed herself to be somewhat grainy or jerky, jumping from one quantum amount to the other, never traversing the area in between. This leads to an uneasy uncertainty about what is going on between those quantum states or quantum leaps. The abruptness of quantum leaps was a central pillar of the way quantum theory was formulated by Niels Bohr, Werner Heisenberg, and their colleagues in the mid-1920s, in a picture now commonly called the Copenhagen interpretation. Quantum leaps are not an internal matter of physics as one of its relation to philosophy and human knowledge in general. Bohr and Heisenberg began to develop a mathematical theory of these quantum phenomena in the 1920s. In 1986, three teams of researchers reported them happening in individual atoms suspended in space by electromagnetic fields. In 2007 a team in France reported jumps that correspond to what they called “the birth, life, and death of individual photons.” So everything in the quantum mechanical universe, which is the universe we live in, happens in quantum leaps. The 1920s. Quantum Field Theory Its development began in the 1920s by describing interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics. The first reasonably complete theory of quantum electrodynamics, which included both the electromagnetic field and electrically charged matter as quantum mechanical objects, was created by the American Paul Dirac in 1927. Thanks to the somewhat brute-force, ad hoc, and heuristic early methods of Feynman, and the abstract methods of Tomonaga and Schwinger, elegantly synthesized by Freeman Dyson, from the period of early renormalization, the modern theory of quantum electrodynamics (QED) has established itself. It is still the most accurate physical theory known, the prototype of a successful quantum field theory. Quantum electrodynamics is the most famous example of what is known as an Abelian gauge theory. 1926. New Quantum Theory of Atoms Bohr’s orbital model of the atom, later improved by Arnold Sommerfeld, resulted from the old quantum theory. The birth of the new quantum theory took place in 1925-1926 and was associated with Werner Heisenberg and his matrix mechanics and Erwin Schrödinger and Paul Dirac. The quantum-mechanical approach acknowledges the wavelike character of electrons and provides the framework for viewing the electrons as fuzzy clouds of negative charge. Two of the rules of quantum theory that are most important to explaining the atom are the idea of wave-particle duality and the exclusion principle. French physicist Louis de Broglie first suggested that particles could be described as waves in 1924. In the same decade, Austrian physicist Erwin Schrödinger and German physicist Werner Heisenberg expanded de Broglie’s ideas into formal, mathematical descriptions of quantum mechanics. Austrian-born American physicist Wolfgang Pauli developed the exclusion principle in 1925. The combination of wave-particle duality and the Pauli exclusion principle sets up the rules for filling electron orbitals in atoms. These rules explain why atoms with similar numbers of electrons can have very different properties and why chemical properties repeatedly reappear in a regular pattern among the elements. 1950s. Many-body Theory The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of many interacting particles. Microscopic here implies that quantum mechanics has to be used to provide an accurate description of the system. In a quantum system, the repeated interactions between particles create quantum correlations or entanglement. As a consequence, the wave function of the system is a complicated object holding a large amount of information, which usually makes exact or analytical calculations impractical or even impossible. Thus, many-body theoretical physics most often rely on a set of approximations specific to the problem at hand and ranks among the most computationally intensive fields of science. The goal of quantum many-body theory, or physics, is to understand the emergent properties—probed by thermodynamic, spectroscopic, and linear response functions—of a system of many interacting particles. As early as the 1950s, the methods of quantum field theory were applied to quantum fluids of fermions and bosons. Those efforts culminated in 1957 in the Bardeen-Cooper-Schrieffer theory of superconductivity. In 1963 Alexei Abrikosov, Lev Gor’kov, and Igor Dzyaloshinskii wrote their classic book Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall) on the use of Feynman diagrams to attack many-body problems at finite temperature. Terse but full of insights, the book had an enormous impact and is still used by practitioners. The uncertainty principle says that you can’t know certain properties of a quantum system simultaneously. For example, you can’t simultaneously know the position of a particle and its momentum. But what does that imply about reality? If we could peer behind the curtains of quantum theory, would we find that objects do have well-defined positions and momentums? Or does the uncertainty principle mean that, at a fundamental level, objects just can’t have a clear position and momentum at the same time? In other words, is the blurriness in our theory, or is it in reality itself? In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of unobservable hypothetical entities. Historically, the first and most famous of them is the de Broglie-Bohm theory. The emergence of this theory stimulated the appearance of some modifications of Neumann’s theorem. Most hidden-variable theories are attempts at a deterministic description of quantum mechanics to avoid quantum indeterminacy but at the expense of requiring the existence of nonlocal interactions. The currently best known hidden parameter theory, a “causal” interpretation by physicist and philosopher David Bohm, initially published in 1952, is the nonlocal hidden parameter theory. Bohm unknowingly rediscovered (and extended) the idea proposed (and abandoned) by Louis de Broglie in 1927, so this theory is commonly referred to as the “de Broglie-Boehm theory. 1952. The pilot wave Theory The pilot wave theory, also known as the de Broglie–Bohm theory, Bohmian mechanics, Bohm’s interpretation, and the causal interpretation, interprets quantum mechanics. In addition to the wavefunction, it also postulates an actual configuration of particles exists even when unobserved. A guiding equation defines the evolution over time of the configuration of all particles. The Born rule in Broglie–Bohm theory is not a fundamental law. Instead, in this theory, the link between the probability density and the wave function has the status of a hypothesis, called the “quantum equilibrium hypothesis”, which is additional to the wave function’s basic principles. The theory was historically developed in the 1920s by de Broglie, who, in 1927, was persuaded to abandon it in favor of the then-mainstream Copenhagen interpretation. David Bohm, dissatisfied with the prevailing orthodoxy, rediscovered de Broglie’s pilot-wave theory in 1952. Since the 1990s, there has been renewed interest in formulating extensions to de Broglie–Bohm theory, attempting to reconcile it with special relativity and quantum field theory, besides other features such as spin or curved spatial geometries. 1957. The Many-worlds (or Multiverse) Theory Hugh Everett was an American physicist who first proposed the many-worlds interpretation of quantum physics in 1957. According to his work, we live in a multiverse of countless universes, full of copies of each of us. The same idea had occurred to Erwin Schrödinger half a decade earlier. Everett’s version is more mathematical, Schrödinger’s more philosophical. Still, the essential point is that both of them were motivated by a wish to get rid of the idea of the “collapse of the wave function,” and both of them succeeded. Bryce DeWitt popularized the formulation and named it many worlds in the 1960s and 1970s. 1962. Quantum Theory of Stimulated Raman Effect Raman scattering or the Raman effect is the inelastic scattering of a photon by molecules that are excited to higher vibrational or rotational energy levels. It was discovered by the Indian physicist C. V. Ramanand in liquids and independently by Grigory Landsbergand Leonid Mandelstam in crystals. The effect had been predicted theoretically by the Austrian theoretical physicist Adolf Smekal in 1923, followed by theoretical works by Kramers, Heisenberg, Dirac, Schrödinger, and others. Raman scattering can occur in a gas with a change in energy of a molecule due to a transition to another (usually higher) energy level. Chemists are primarily concerned with this “transitional” Raman effect. Indian physicist, whose work was influential in the growth of science in India, was the recipient of the Nobel Prize for Physics in 1930 for the discovery that when light traverses a transparent material, some of the light that is deflected changes in wavelength. 1968. String Theory (Theory of quantum gravity) The Italian theoretical physicist Gabriele Veneziano first formulated the foundations of string theory in 1968 when he discovered a string picture could describe the interaction of strongly interacting particles. String theory attempts to unify all four forces, and in so doing, unify general relativity and quantum mechanics. At its core is a relatively simple idea—all particles are made of tiny vibrating strands of energy. String theory describes how strings propagate through space and interact with each other. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In this way, all of the different elementary particles may be viewed as vibrating strings. In string theory, one of the vibrational states of the string gives rise to the graviton, a quantum mechanical particle that carries gravitational force. Thus string theory is a theory of quantum gravity. The 1970s. Gauge Theory The 1960s and 1970s saw the formulation of a gauge theory now known as the Standard Model of particle physics, which systematically describes the elementary particles and their interactions. Gauge theory, or class of quantum field theory, is a mathematical theory involving both quantum mechanics and Einstein’s special theory of relativity commonly used to describe subatomic particles and their associated wave fields. In short, the structure of the group of gauge transformations in a particular gauge theory entails general restrictions on the way in which the field described by that theory can interact with other fields and elementary particles. For various theoretical reasons, the concept of gauge invariance seems fundamental, and many physicists believe that the final unification of the fundamental interactions (i.e., gravitational, electromagnetic, strong, and weak) will be achieved by a gauge theory. The 1970s. Quantum trajectory Theory In the early days of quantum mechanics, it was a probabilistic theory, telling us only what we will observe on average if we collect records for many events or particles. To Erwin Schrödinger, whose eponymous equation prescribes how quantum objects behave, it wasn’t significant to think about specific atoms or electrons doing things in real time. In other words, quantum mechanics seemed to work only for “ensembles” of many particles. But there’s another way to formulate quantum mechanics to speak about single events happening in individual quantum systems. It is called quantum trajectory theory, and it’s perfectly compatible with the standard formalism of quantum mechanics — it’s just a more detailed view of quantum behavior. The standard description is recovered over long timescales after the average of many events is computed. Quantum trajectory theory, mainly developed in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. The formulation through the integral over trajectories was developed in 1948 by Richard Feynman, serving as the basis for developing and completing this theory formulation in the 1970s. 1974. Lattice Quantum Field Theory In physics, lattice field theory is the study of lattice models of quantum field theory, that is, of field theory on a space-time that has been discretized onto a lattice. An important step to answer such questions has been made by K. Wilson in 1974. He introduced a formulation of Quantum Chromodynamics on a space-time lattice, which allows the application of various non-perturbative techniques. It should also be pointed out that the introduction of a space-time lattice can be taken as a starting point for a mathematically clean approach to quantum field theory, so-called constructive quantum field theory. Lattice field theory has turned out to be very successful for the non-perturbative calculation of physical quantities. 1980. Quantum complexity Theory Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems concerning these complexity classes and the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. And the set of computational problems that can be solved by a computational model under certain resource constraints is the complexity class. The development of quantum complexity theory is related to the concept of the Turing machine, which is a mathematical model of computation that defines an abstract machine proposed by Alan Turing in 1936 to formalize the idea of an algorithm. That is, any intuitive algorithm can be implemented using some Turing machine. The history of quantum computing began in the early 1980s when American physicist Paul Benioff proposed a quantum mechanical model of the Turing machine in 1980. The 1980s. Quantum Loop Theory It’s only since the middle 1980s that real progress began on unifying relativity and quantum theory. The turning point was the invention of not one but two approaches: loop quantum gravity and string theory. Neither is yet in final form. Lee Smolin, a theoretical physicist, is concerned with quantum gravity, “the name we give to the theory that unifies all the physics now under construction.” He is a co-inventor of an approach called loop quantum gravity. Quantum gravity is the name we give to the theory that unifies all of physics. The roots of it are in Einstein’s general theory of relativity and quantum theory. Einstein’s general theory of relativity is a theory of space, time, and gravity. In contrast, quantum theory describes everything else that exists in the universe, including elementary particles, nuclei, atoms, and chemistry. These two theories were invented in the early twentieth century, and their ascension marked the overthrow of the previous theory, which was Newtonian mechanics. They are the primary legacies of twentieth-century physics. The problem of unifying them is the main open problem in physics left for us to solve in this century. 1980. Quantum complexity Theory Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. And the set of computational problems that can be solved by a computational model under certain resource constraints is the complexity class. The development of quantum complexity theory is related to the concept of the Turing machine which is a mathematical model of computation that defines an abstract machine proposed by Alan Turing in 1936 to formalize the concept of an algorithm. That is, any intuitive algorithm can be implemented using some Turing machine. The history of quantum computing began in the early 1980s when the American physicist Paul Benioff proposed a quantum mechanical model of the Turing machine in 1980. 1993. Holographic Universe Theory The holographic principle is a hypothesis put forward in 1993 by the Dutch theoretical physicist Gerard ‘t Hooft. The holographic principle is a tenet of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region—such as a light-like boundary like a gravitational horizon. First proposed by Gerard ‘t Hooft, Leonard Susskind gave it a precise string-theory interpretation. The holographic principle was inspired by black hole thermodynamics and resolves the black hole information paradox within the framework of string theory. 2013. Quantum Holonomy Theory Quantum holonomy theory is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. Quantum holonomy theory arises from an intersection between different branches in modern theoretical physics and mathematics, namely quantum field theory and non-commutative geometry. Two Danish scientists, theoretical physicist Jesper Møller Grimstrup and mathematician Johannes Aastrup, have developed Quantum Holonomy Theory, which is a candidate for a fundamental theory of Nature.	{"url":"https://www.viasmartcities.com/timeline-of-quantum-theories/","timestamp":"2024-11-03T10:30:53Z","content_type":"text/html","content_length":"1049356","record_id":"<urn:uuid:377125d2-71ad-444d-aa80-5b41f82aae58>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00247.warc.gz"}
Online Dice - Virtual Dice Roller - Subitising - Two Dice Roller Subitizing Dice – Throw 2 Dice – Numerals 1 to 6 Subitizing Dice Roller – 2 Dice Math Game Dice Patterns 1 to 6 Dice Roller – Throw Two Subitized Dice A Possible 2 Dice Math Game to Play – Cross ’em Out In this game, two players take turns rolling dice. They use their knowledge of Numbers to strategize and have the smallest score at the end of the game. What You Need to Play this 2 Dice Game: • 2 dice • Scratch paper • Pencil How to Play this 2 Dice Game: 1. Players each write the numbers from 1 to 9 on their piece of scratch paper. 2. The player with the smallest foot goes first. 3. Player One throws the dice and adds the numbers together. 4. Player One then looks at their paper and crosses out a single number or a combination of numbers that equal the sum of the dice. For example, if a 4 and a 5 are thrown, (which adds up to 9) Player 1 can cross out just a 9 or any combination of numbers on the paper equal to 9. e.g 4 + 5, 3 + 6, 1 + 2 + 6, 4 + 3 + 2 etc 5. Once the numbers are crossed out it is Player 2’s turn and they repeat steps 4 and 5 6. The game continues in this fashion until both players make a throw and no more numbers can be crossed out. How to Win this Dice Roller Game: • Once both players can no longer make a throw and cross out numbers each player adds up their remaining numbers. The player with the smallest sum of uncovered digits wins the game! Click Here to Launch the Virtual Dice Roller Note: The loading time will take approximately one minute. Please be patient and get ready to experience the captivating spectacle of math dice appearing from a portal and landing gracefully on a barrel top. It’s an exciting and enjoyable addition to your math activities. See More of my Math Games? Check Out All My Math Games	{"url":"https://math-dice.com/subitising-dice-throw-2-dice-patterns-1-to-6/","timestamp":"2024-11-12T00:11:59Z","content_type":"text/html","content_length":"103233","record_id":"<urn:uuid:8558025b-a39f-4d48-92ab-98361f20e8cb>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00339.warc.gz"}
The Nelson Company has $1,440,000 in current assets and $600,000 in current liabilities. Its initial inventory... The Nelson Company has $1,440,000 in current assets and $600,000 in current liabilities. Its initial inventory... The Nelson Company has $1,440,000 in current assets and $600,000 in current liabilities. Its initial inventory level is $480,000, and it will raise funds as additional notes payable and use them to increase inventory. 1. How much can Nelson's short-term debt (notes payable) increase without pushing its current ratio below 1.9? Round your answer to the nearest cent. 3. What will be the firm's quick ratio after Nelson has raised the maximum amount of short-term funds? Round your answer to two decimal places. Current assets= $1,440,000 Current liabilities= $600,000 Since the additional notes payable I raised will be used in inventory, the new current assets: =$1,440,000+ I Current ratio= current assets/ current liabilities 1.9= $1,440,000+ I/ $600,000 + I Solving the above, I = $333,333. Therefore, the maximum short term debt that can be raised is $333,333. The new inventory= $480,000 + $333,333= $813,333. Quick ratio= Current assets- inventory/ Current liabilities = $1,440,000- 813,333/ $600,000 = $626,667/ $600,000 = 1.04. Therefore, the firm’s quick ratio will be 1.04 after nelson has raised the maximum amount of short term funds.	{"url":"https://justaaa.com/finance/269893-the-nelson-company-has-1440000-in-current-assets","timestamp":"2024-11-10T00:08:45Z","content_type":"text/html","content_length":"45121","record_id":"<urn:uuid:78b36598-0bca-4536-801a-0a41c6c5bcba>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00080.warc.gz"}
Applications for optimization with uncertain data in practice often feature a possibility to reduce the uncertainty at a given query cost, e.g., by conducting measurements, surveys, or paying a third party in advance to limit the deviations. To model this type of applications we introduce the concept of optimization problems under controllable uncertainty (OCU). For … Read more Γ-robust Optimization of Project Scheduling Problems In this paper, we investigate the problem of finding a robust baseline schedule for the project scheduling problem under uncertain process times. We assume that the probability distribution for the duration is unknown but an estimation together with an interval in which this time can vary is given. At most $ \Gamma $ of … Read more Robust Combinatorial Optimization under Budgeted-Ellipsoidal Uncertainty In the field of robust optimization uncertain data is modeled by uncertainty sets, i.e. sets which contain all relevant outcomes of the uncertain parameters. The complexity of the related robust problem depends strongly on the shape of the uncertainty set. Two popular classes of uncertainty are budgeted uncertainty and ellipsoidal uncertainty. In this paper we … Read more A dynamic programming approach for a class of robust optimization problems Common approaches to solve a robust optimization problem decompose the problem into a master problem (MP) and adversarial separation problems (APs). MP contains the original robust constraints, however written only for finite numbers of scenarios. Additional scenarios are generated on the fly by solving the APs. We consider in this work the budgeted uncertainty polytope … Read more Robust constrained shortest path problems under budgeted uncertainty We study the robust constrained shortest path problem under resource uncertainty. After proving that the problem is \NPhard in the strong sense for arbitrary uncertainty sets, we focus on budgeted uncertainty sets introduced by Bertsimas and Sim (2003) and their extension to variable uncertainty by Poss (2013). We apply classical techniques to show that the … Read more Efficient approaches for the robust network loading problem We consider the Robust Network Loading problem with splittable flows and demands that belong to the budgeted uncertainty set. We compare the optimal solution cost and computational cost of the problem when using static routing, volume routing, affine routing, and dynamic routing. For the first three routing types, we compare the compact formulation with a … Read more Robust combinatorial optimization with cost uncertainty We present in this paper a new model for robust combinatorial optimization with cost uncertainty that generalizes the classical budgeted uncertainty set. We suppose here that the budget of uncertainty is given by a function of the problem variables, yielding an uncertainty multifunction. The new model is less conservative than the classical model and approximates … Read more	{"url":"https://optimization-online.org/tag/budgeted-uncertainty/","timestamp":"2024-11-08T01:06:41Z","content_type":"text/html","content_length":"100450","record_id":"<urn:uuid:d134b458-7b6c-43ee-9498-6680960dd79c>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00207.warc.gz"}
Wondering About Infinite Series and the Nature of e A quick pondering about the nature of the constant, e Because we can actually see the first few digits of e we can make inferences about the nature of infinity. We see that e is calculated by (1+1/n)^n as n goes to infinity. Let’s say that at n=4, the second decimal place is no longer affected by subsequent steps of n. Write a program that will make a table of all the values for given n values. Good questions would be “when does e reach two?”	{"url":"https://joepucc.io/notes/wondering-about-infinite-series-and-the-nature-of-e.php","timestamp":"2024-11-14T04:59:18Z","content_type":"text/html","content_length":"2989","record_id":"<urn:uuid:a4d915bd-35e2-40b8-9c9b-6c31bed0433b>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00132.warc.gz"}
"Scarlet ex and Violet ex" Cards Fully Revealed! - PokeBeach"Scarlet ex and Violet ex" Cards Fully Revealed! - PokeBeach “Scarlet ex and Violet ex” Cards Fully Revealed! Welcome to Generation 9! All regular cards from Japan’s Scarlet ex and Violet ex sets have just been revealed! The sets feature a total of 156 cards (before secret rares). Both sets will release in Japan on Friday, January All of the set’s secret rares will be revealed by next week — be sure to check back! We are expecting over 50 of them. (Gardevoir ex’s Special Art Rare is #101/78 in Scarlet ex, so it’s the 23rd secret rare.) Art Rares and Special Art Rares will return in this set; they were first introduced in VSTAR Universe. #211 Ralts #212 Kirlia #245 Gardevoir ex #214 Greavard #208 Pachirisu #204 Slowpoke Scarlet ex and Violet ex bring back the TCG’s original Pokemon ex mechanic, which ran from 2003 to 2007. Pokemon ex evolve from their normal pre-Evolutions. This is unlike 2012’s Pokemon-EX (uppercase), which were always fully evolved Basic Pokemon. Though Pokemon-EX were inspired by Pokemon ex, both are entirely different mechanics. This means cards that target “Pokemon-EX” do not work on “Pokemon ex” and vice versa. Ampharos ex from 2003 (Stage 2) Ampharos-EX from 2015 (Basic) Ampharos ex (Stage 2) The big new mechanic of the Scarlet & Violet video games is Terastallization. In the TCG, some Pokemon ex will feature a Terastal effect box to indicate they’re Terastalized. Pokemon with this Terastal effect don’t take damage from attacks when they’re on the Bench. This is seen on Arcanine ex below. Its artwork is crystalized to show it’s Terastalized. It’s also wearing a Fire-type crown to indicate its Tera type is Fire. There will almost certainly be Pokemon ex in the future that feature a Tera type different from its normal type (e.g. a Water-type Charizard). New blocks tend to start off “simple” in terms of mechanics and power because the allure is the new Pokemon. Later, the blocks start to spice mechanics up after all the new Pokemon have debuted. Our first Scarlet & Violet set will release in English on March 31st, 2023. Our English set will feature 198 cards before secret rares. This means it will be a combination of Scarlet ex and Violet ex ‘s 156 cards plus its three “Starter Set ex” decks. Our English set will see silver card borders, three holos per pack, and other changes you can read about here. #125 Koraidon ex #081 Miraidon ex #189 Professor’s Research (Sada) Now on to the Japanese cards! ‘Scarlet ex’ ‘Violet ex’ ‘Scarlet ex Translations’ Thanks goes to Bangiras and JustInBasil for the translations! Cacnea – Grass – HP60 Basic Pokemon Ability: Counterattack Needles If this Pokémon is your Active Pokémon and is damaged by an opponent’s attack (even if this Pokémon is Knocked Out), put 3 damage counters on the Attacking Pokémon. [C][C] Light Punch: 30 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Cacturne – Grass – HP130 Stage 1 – Evolves from Cacnea Ability: Counterattack Needles If this Pokémon is your Active Pokémon and is damaged by an opponent’s attack (even if this Pokémon is Knocked Out), put 3 damage counters on the Attacking Pokémon. [C[C][C] Spike Shot: 110 damage. Weakness: Fire (x2) Resistance: none Retreat: 2 Skiddo – Grass – HP60 Basic Pokemon [G] Vine Whip: 10 damage. [C][C] Smash Kick: 20 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Gogoat – Grass – HP130 Stage 1 – Evolves from Skiddo [C][C] Rising Lunge: 30+ damage. Flip a coin. If heads, this attack does 30 more damage. [G][C][C] Solar Beam: 110 damage. Weakness: Fire (x2) Resistance: none Retreat: 2 Smoliv – Grass – HP60 Basic Pokemon [C][C] Tackle: 30 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Smoliv – Grass – HP60 Basic Pokemon [G] Nutrients: Heal 30 damage from 1 of your Pokémon. [G][C] Spray Fluid: 20 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Dolliv – Grass – HP90 Stage 1 – Evolves from Smoliv [C] Slap: 20 damage. [G][C] Oil Pour: 40 damage. During your opponent’s next turn, if the Defending Pokémon tries to attack, your opponent flips a coin. If tails, that attack doesn’t happen. Weakness: Fire (x2) Resistance: none Retreat: 1 Arboliva – Grass – HP150 Stage 2 – Evolves from Dolliv Ability: Fill Oil When you play this Pokémon from your hand to evolve one of your Pokémon during your turn, you may heal all damage from 1 of your Pokémon. [G][G][C] Solar Beam: 150 damage. Weakness: Fire (x2) Resistance: none Retreat: 2 Torkoal – Fire – HP130 Basic Pokemon [C][C] Stampede: 30 damage. [R][C][C] Concentrated Fire: 80x damage. Flip a coin for each [R] Energy attached to this Pokémon. This attack does 80 damage times the number of heads. Weakness: Water (x2) Resistance: none Retreat: 3 Charcadet – Fire – HP60 Basic Pokemon [R] Ember: 30 damage. Discard an Energy from this Pokémon. Weakness: Water (x2) Resistance: none Retreat: 1 Charcadet – Fire – HP70 Basic Pokemon [R][R][C] Heat Blast: 60 damage. Weakness: Water (x2) Resistance: none Retreat: 1 Armarouge – Fire – HP130 Stage 1 – Evolves from Charcadet Ability: Fire Alarm As often as you like during your turn, you may move a [R] Energy attached to 1 of your Benched Pokémon to your Active Pokémon. [R][R][C] Flame Cannon: 90 damage. Your opponent’s Active Pokémon is now Burned. Weakness: Water (x2) Resistance: none Retreat: 2 Magikarp – Water – HP30 Basic Pokemon [W] Leap: Flip a coin. If heads, this attack does 10 damage to 1 of your opponent’s Pokémon. (Don’t apply Weakness and Resistance for Benched Pokémon.) Weakness: Lightning (x2) Resistance: none Retreat: 1 Gyarados ex – Water – HP300 Stage 1 – Evolves from Magikarp Terastal: This Pokemon doesn’t take any damage from attacks while on the Bench. [W][W][W] Waterfall: 100 damage. [W][W][W][C][C] Tyrannical Tail: 180+ damage. If your opponent’s Active Pokémon already has any damage counters on it, this attack does 180 more damage. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Lightning (x2) Resistance: none Retreat: 1 Buizel – Water – HP70 Basic Pokemon [W] Rain Splash: 10 damage. [C][C] Razor Fin: 20 damage. Weakness: Lightning (x2) Resistance: none Retreat: 1 Floatzel – Water – HP120 Stage 1 – Evolves from Buizel [C][C} Hydro Pump: 50+ damage. This attack does 20 more damage for each [W] Energy attached to this Pokémon. Weakness: Lightning (x2) Resistance: none Retreat: 1 Bruxish – Water – HP100 Basic Pokemon [W] Vivid Charge: Search your deck for up to 3 basic Energy cards, reveal them, and put them into your hand. Then, shuffle your deck. [W][C] Wave Splash: 60 damage. Weakness: Lightning (x2) Resistance: none Retreat: 1 Wigglet – Water – HP50 Basic Pokemon [W] Twist: 10 damage. Flip a coin. If heads, during your opponent’s next turn, prevent all damage from and effects of attacks done to this Pokémon. Weakness: Lightning (x2) Resistance: none Retreat: 1 Wigglet – Water – HP60 Basic Pokemon [C] Dig a Bit: Flip a coin. If heads, discard the top card of your opponent’s deck. [C][C] Ram: 20 damage. Weakness: Lightning (x2) Resistance: none Retreat: 1 Wugtrio – Water – HP90 Stage 1 – Evolves from Wiglett [W] Headbutt: 30 damage. [C][C][C] Sea Tunneling: Flip 3 coins. For each heads, discard the top 3 cards of your opponent’s deck. Weakness: Lightning (x2) Resistance: none Retreat: 2 Dondozo – Water – HP160 Basic Pokemon [C][C} Vent Wrath: 50x damage. This attack does 50 damage for each Tatsugiri in your discard pile. [W][W][C][C] Heavy Splash: 120 damage. Weakness: Lightning (x2) Resistance: none Retreat: 4 Tatsugiri – Water – HP70 Basic Pokemon [W] Preparations: Search your deck for up to 2 Basic [W] Energy and attach them to 1 of your Basic Pokémon. Then, shuffle your deck. [W] Flip Back: 30 damage. Put this Pokémon and all attached cards into your hand. Weakness: Lightning (x2) Resistance: none Retreat: 1 Wattrel – Lightning – HP50 Basic Pokemon [C] Collect: Draw a card. [L][C] Glide: 20 damage. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Wattrel – Lightning – HP60 Basic Pokemon [L] Static Shock: 20 damage. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Kilowattrel – Lightning – HP120 Stage 1 – Evolves from Wattrel [C][C] Skill Dive: This attack does 50 damage to 1 of your opponent’s Pokémon. (Don’t apply Weakness and Resistance for Benched Pokémon.) [L][C][C] Thunder Blast: 140 damage. Discard a [L] Energy from this Pokémon. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Ralts – Psychic – HP70 Basic Pokemon [P][C] Psyshot: 30 damage. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 1 Kirlia – Psychic – HP90 Stage 1 – Evolves from Ralts [P][C] Magical Shot: 30 damage. [P][P][C] Psychic: 60+ damage. This attack does 20 more damage for each Energy attached to your opponent’s Active Pokemon. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 1 Gardevoir ex – Psychic – HP310 Stage 2 – Evolves from Kirlia Ability: Psychic Embrace As often as you like during your turn, you may attach a Basic [P] Energy from your discard pile to 1 of your [P] Pokemon. If you do, put 2 damage counters on that Pokemon. (You can’t use this Ability on a Pokemon that would be Knocked Out by the 2 damage counters.) [P][P][C] Miracle Force: 190 damage. Heal any Special Conditions on this Pokemon. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 2 Drifloon – Psychic – HP70 Basic Pokemon [C][C] Gust: 10 damage. [P][P] Balloon Bomb: 30x damage. This attack does 30 damage for each damage counter on this Pokémon. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 1 Drifblim – Psychic – HP110 Stage 1 – Evolves from Drifloon [C][C] Gust: 30 damage. [P][P][P] Spread Curses: Put 8 damage counters on your opponent’s Pokémon in any way you like. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 1 Dedenne – Psychic – HP70 Basic Pokemon [P] Energy Bite: 30 damage. Flip a coin. If heads, discard an Energy from your opponent’s Active Pokémon. Weakness: Metal (x2) Resistance: none Retreat: 1 Fidough – Psychic – HP50 Basic Pokemon [C][C] Rear Kick: 20 damage. Weakness: Metal (x2) Resistance: none Retreat: 1 Fidough – Psychic – HP60 Basic Pokemon [P] Elasticity: During your opponent’s next turn, this Pokémon takes 30 less damage from attacks (after applying Weakness and Resistance). [P][C][C] Flop: 30 damage. Weakness: Metal (x2) Resistance: none Retreat: 2 Dachsbun – Psychic – HP90 Stage 1 – Evolves from Fidough Ability: Well-Baked Body Prevent all damage done to this Pokémon by attacks from your opponent’s [R] Pokémon. This Pokémon cannot be Burned. [P][C][C] Headbutt Bounce: 100 damage. Weakness: Metal (x2) Resistance: none Retreat: 1 Flittle – Psychic – HP40 Basic Pokemon [C] Spinning Attack: 20 damage. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 1 Flittle – Psychic – HP40 Basic Pokemon [P] Dance Away: 10 damage. Switch this Pokemon with 1 of your Benched Pokémon. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 1 Espathra – Psychic – HP110 Stage 1 – Evolves from Flittle [P] Insight: 20 damage. During your opponent’s next turn, the Defending Pokémon can’t retreat. [P][C][C] Psychic: 30+ damage. This attack does 50 more damage for each Energy attached to your opponent’s Active Pokémon. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 0 Meditite – Fighting – HP60 Basic Pokemon [F] Feint: 10 damage. This attack’s damage isn’t affected by Resistance. Weakness: Psychic (x2) Resistance: None Retreat: 1 Medicham – Fighting – HP90 Stage 1 – Evolves from Meditite [F] Bull’s-Eye Aim: 30 damage. Choose 1 of your opponent’s Active Pokémon’s attacks. During your opponent’s next turn, that Pokémon can’t use that attack. [F] Kick Shot: 90 damage. Flip a coin. If tails, this attack does nothing. Weakness: Psychic (x2) Resistance: None Retreat: 1 Riolu – Fighting – HP70 Basic Pokemon [F] Punch: 10 damage. [F][C] Reckless Charge: 50 damage. This Pokemon also does 20 damage to itself. Weakness: Psychic (x2) Resistance: none Retreat: 1 Lucario – Fighting – HP130 Stage 1 – Evolves from Riolu [F] Vengeful Knuckles: 30+ damage. If any of your [F] Pokémon were Knocked Out by damage from an attack from your opponent’s Pokémon during their last turn, this attack does 120 more damage. [F][C][C] Accelerating Stab: 120 damage. This Pokémon can’t use Accelerating Stab during your next turn. Weakness: Psychic (x2) Resistance: none Retreat: 2 Sandile – Fighting – HP70 Basic Pokemon [F] Gnaw: 10 damage. [F][F] Ram: 30 damage. Weakness: Grass (x2) Resistance: none Retreat: 2 Krokorok – Fighting – HP100 Stage 1 – Evolves from Sandile [F] Payback: 30+ damage. If your opponent has exactly 1 Prize card remaining, this attack does 90 more damage. [F][F] Corkscrew Punch: 60 damage. Weakness: Grass (x2) Resistance: none Retreat: 2 Krookodile – Fighting – HP170 Stage 2 – Evolves from Krokorok [F] Voracious Bite: 50 damage. Flip a coin until you get tails. For each heads, discard an Energy attached to your opponent’s Active Pokémon. [F][F] Earthquake: 180 damage. This attack also does 30 damage to each of your Benched Pokémon. (Don’t apply Weakness and Resistance for Benched Pokémon.) Weakness: Grass (x2) Resistance: none Retreat: 3 Hawlucha – Fighting – HP70 Basic Pokemon Ability: Flying Entry When you play this Pokémon from your hand onto your Bench during your turn, you may choose 2 of your opponent’s Benched Pokémon and put 1 damage counter on each of them. [F][C][C] Wing Attack: 70 damage. Weakness: Psychic (x2) Resistance: none Retreat: 1 Silicobra – Fighting – HP80 Basic Pokemon [F][C] Mud-Slap: 30 damage. Weakness: Grass (x2) Resistance: none Retreat: 2 Sandaconda – Fighting – HP140 Stage 1 – Evolves from Silicobra [F][F][C] Skull Bash: 120 damage. [F][F][F][C] Violent Dust Cloud: Discard 2 Energy from this Pokémon. Then, your opponent shuffles their Active Pokémon and all cards attached to it into their deck. Weakness: Grass (x2) Resistance: none Retreat: 3 Klawf – Fighting – HP130 Basic Pokemon [F][F] Vise Grip: 50 damage. [F][F][F] Adrenaline Hammer: 130 damage. This Pokémon is now Confused. Weakness: Grass (x2) Resistance: none Retreat: 3 Great Tusk ex – Fighting – HP250 Basic Pokemon [F] Bedrock Breaker: 40 damage. Discard a Stadium card in play. [F][F][F] Giganto Tusk: 250 damage. This Pokemon does 50 damage to itself. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Psychic (x2) Resistance: none Retreat: 4 Koraidon ex – Fighting – HP230 Basic Pokemon Ability: Dino Cry Once during your turn, you may attach up to 2 Basic [F] Energy cards from your discard pile to your Basic [F] Pokemon in any way you like. If you use this Ability, your turn ends. [F][F][C] Wild Impact: 220 damage. During your next turn, this Pokemon can’t attack. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Psychic (x2) Resistance: none Retreat: 2 Grimer – Darkness – HP80 Basic Pokemon [D][C][C] Super Poison Breath: 50 damage. Your opponent’s Active Pokémon is now Poisoned. Weakness: Psychic (x2) Resistance: none Retreat: 3 Muk – Darkness – HP140 Stage 1 – Evolves from Grimer Ability: Poison Sacs The Special Condition Poisoned is not removed when your opponent’s Pokémon evolve or devolve. [D][C][C][C] Toxic Strike: 100 damage. Your opponent’s Active Pokémon is now Poisoned. Weakness: Psychic (x2) Resistance: none Retreat: 4 Seviper – Darkness – HP120 Basic Pokemon [D] Spit Poison: Your opponent’s Active Pokémon is now Poisoned. [D][C][C] Venoshock: 60+ damage. If your opponent’s Active Pokémon is Poisoned, this attack does 120 more damage. Weakness: Psychic (x2) Resistance: none Retreat: 2 Croagunk – Darkness – HP70 Basic Pokemon [D] Beat: 10 damage. [D][C][C] Whap Down: 40 damage. Weakness: Psychic (x2) Resistance: none Retreat: 1 Toxicroak ex – Darkness – HP250 Stage 1 – Evolves from Croagunk [D] Nasty Plot: Search your deck for up to 2 cards and put them into your hand. Then, shuffle your deck. [D][C][C] Toxic Ripper: 120 damage. Your opponent’s Active Pokémon is now Poisoned. Put 6 damage counters instead of 1 on that Pokémon between turns. Weakness: Psychic (x2) Resistance: none Retreat: 2 Pawniard – Darkness – HP70 Basic Pokemon [C] Scratch: 10 damage. [D][C] Pierce: 20 damage. Weakness: Grass (x2) Resistance: none Retreat: 1 Bisharp – Darkness – HP120 Stage 1 – Evolves from Pawniard [D] Dark Cutter: 40 damage. [D][C] Double-Edged Slash: 120 damage. This Pokémon also does 30 damage to itself. Weakness: Grass (x2) Resistance: none Retreat: 1 Kingambit – Darkness – HP170 Stage 2 – Evolves from Bisharp Ability: Generalship As long as this Pokémon is in play, the attacks of your Basic Pokémon do 30 more damage to your opponent’s Active Pokémon (before applying Weakness and Resistance). [D][C][C] Strike Cut: 160 damage. Weakness: Grass (x2) Resistance: none Retreat: 3 Varoom – Metal – HP60 Basic Pokemon [C] Poison Gas: Your opponent’s Active Pokémon is now Poisoned. Weakness: Fire (x2) Resistance: Grass (-30) Retreat: 1 Varoom – Metal – HP80 Basic Pokemon [M][C][C] Hammer In: 60 damage. Weakness: Fire (x2) Resistance: Grass (-30) Retreat: 1 Revavroom – Metal – HP140 Stage 1 – Evolves from Varoom Ability: Rumbling Engine You must discard an Energy from your hand in order to use this Ability. Once during your turn, you may draw until you have 6 cards in your hand. Knock Away: 90+ damage. Flip a coin. If heads, this attack does 90 more damage. Weakness: Fire (x2) Resistance: Grass (-30) Retreat: 2 Zangoose – Colorless – HP110 Basic Pokemon [C][C] Drag Off: Switch 1 of your opponent’s Benched Pokémon with their Active Pokémon. This attack does 30 damage to the new Active Pokémon. [C][C][C] Slashing Claw: 80 damage. Weakness: Fighting (x2) Resistance: None Retreat: 2 Starly – Colorless – HP60 Basic Pokemon [C] Flap: 20 damage. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Staravia – Colorless – HP80 Stage 1 – Evolves from Starly [C][C] Wing Attack: 40 damage. [C][C][C] Speed Dive: 80 damage. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Staraptor – Colorless – HP150 Stage 2 – Evolves from Staravia [C][C] Spin Away: 60 damage. During your opponent’s next turn, prevent all damage done to this Pokémon by attacks from Basic Pokémon. [C][C][C] Power Blast: 180 damage. Discard an Energy from this Pokémon. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Lechonk – Colorless – HP60 Basic Pokemon [C] Repulsive Stench: Your opponent switches their Active Pokémon with 1 of their Benched Pokemon. [C][C] Stampede: 20 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Lechonk – Colorless – HP70 Basic Pokemon [C][C][C] Whimsy Tackle: 70 damage. Flip a coin. If tails, this attack does nothing. Weakness: Fighting (x2) Resistance: none Retreat: 1 Oinkologne ex – Colorless – HP260 Stage 1 – Evolves from Lechonk [C] Fragrance Fury: 10+ damage. This attack does 30 more damage for each of your opponent’s Benched Pokémon. [C][C][C] Heavy Stamp: 210 damage. Flip a coin. If heads, this Pokémon can’t attack during your next turn. Weakness: Fighting (x2) Resistance: none Retreat: 2 Shuffle up to 2 Supporter cards from your discard pile into your deck. You may play any number of Item cards during your turn. Search your deck for a Basic Pokémon and put it onto your Bench. Then, shuffle your deck. You may play any number of Item cards during your turn. Rock Chestplate – Trainer Pokémon Tool The [F] Pokémon this card is attached to takes 30 less damage from attacks from your opponent’s Pokémon (after applying Weakness and Resistance). You may attach any number of Pokémon Tools to your Pokémon during your turn. You may attach only 1 Pokémon Tool to each Pokémon, and it stays attached. Exp. Share – Trainer Pokémon Tool When your Active Pokémon is Knocked Out by damage from an opponent’s attack, you may move 1 basic Energy card that was attached to that Pokémon to the Pokémon this card is attached to. You may attach any number of Pokémon Tools to your Pokémon during your turn. You may attach only 1 Pokémon Tool to each Pokémon, and it stays attached. Defiant Band – Trainer Pokémon Tool If you have more Prize cards remaining than your opponent, the attacks of the Pokemon this card is attached to do 30 more damage to your opponent’s Active Pokemon (before applying Weakness and You may attach any number of Pokémon Tools to your Pokémon during your turn. You may attach only 1 Pokémon Tool to each Pokémon, and it stays attached. Search your deck for up to 2 Evolution Pokemon cards, reveal them, and put them in your hand. Then, shuffle your deck. You may play only 1 Supporter card during your turn. Team Star Grunt – Trainer Put an Energy attached to your opponent’s Active Pokémon on top of their deck. You may play only 1 Supporter card during your turn. Professor’s Research (Professor Sada) – Trainer Discard your hand and draw 7 cards. You may play only 1 Supporter card during your turn. Return 1 of your Basic Pokemon in play and all cards attached to it to your hand. You may play only 1 Supporter card during your turn. The Retreat Cost of each player’s Basic Pokemon is [C] less. This Stadium stays in play when you play it. Discard it if another Stadium comes into play. If a Stadium with the same name is in play, you can’t play this card. ‘Violet ex Translations’ Pineco – Grass – HP60 Basic Pokemon [C][C] Guard Press: 10 damage. This Pokemon takes 30 less damage from attacks during your opponent’s next turn. Weakness: Fire (x2) Resistance: none Retreat: 2 Heracross – Grass – HP120 Basic Pokemon [G][C] Strength Throw: 10+ damage. This attack does 30 more damage for each Energy in your opponent’s Active Pokemon’s Retreat Cost. [G][G][C] Horn Thrust: 90 damage. Weakness: Fire (x2) Resistance: none Retreat: 2 Scatterbug – Grass – HP30 Basic Pokemon Ability: Adaptive Evolution This Pokemon can be evolved on your first turn and on the turn it comes into play. [G][C] Tackle: 20 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Spewpa – Grass – HP70 Stage 1 – Evolves from Scatterbug Ability: Adaptive Evolution This Pokemon can be evolved on your first turn and on the turn it comes into play. [G][C] Bug Bite: 30 damage. Weakness: Fire (x2) Resistance: none Retreat: 3 Vivillon – Grass – HP120 Stage 2 – Evolves from Spewpa [G] Miracle Power: 50 damage. Flip a coin. If heads, your opponent’s Active Pokemon is now affected by 1 Special Condition of your choosing. [G][C] Bug Buzz: 110 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Tarountula – Grass – HP40 Basic Pokemon [G][C] String Shot: 20 damage. Flip a coin. If heads, your opponent’s Active Pokemon is now Paralyzed. Weakness: Fire (x2) Resistance: none Retreat: 1 Tarountula – Grass – HP60 Basic Pokemon [G[ Surprise Attack: 30 damage. Flip a coin, if tails this attack fails. Weakness: Fire (x2) Resistance: none Retreat: 2 Spidops ex – Grass – HP260 Stage 1 – Evolves from Terrantula Ability: Trap Territory Your opponent’s Active Pokemon’s Retreat Cost is [C] more. [G][C] Wire Hang: 90+ damage. This attack does 30 more damage for each Energy in your opponent’s Active Pokemon’s Retreat Cost. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Fire (x2) Resistance: none Retreat: 2 Toedscool – Grass – HP50 Basic Pokemon [G] Fury Attack: Flip 3 coins. This attack does 10 damage times the number of heads. Weakness: Fire (x2) Resistance: none Retreat: 1 Toedscool – Grass – HP60 Basic Pokemon [G] Spore: Your opponent’s Active Pokemon is now Asleep. [C][C] Ram: 10 damage. Weakness: Fire (x2) Resistance: none Retreat: 2 Toedscruel – Grass – HP120 Stage 1 – Evolves from Toedscool [G] Ominous Tentacles: 30 damage. You may choose an Energy attached to your opponent’s Active Pokemon and move it to 1 of their Benched Pokemon. [G][C][C] Triple Smash: Flip 3 coins. This attack does 80 damage times the number of heads. Weakness: Fire (x2) Resistance: none Retreat: 2 Capsakid – Grass – HP60 Basic Pokemon [C] Picante: 10 damage. Flip a coin. If heads, your opponent’s Active Pokemon is now Burned. Weakness: Fire (x2) Resistance: none Retreat: 1 Capsakid – Grass – HP70 Basic Pokemon [C] Spice Up: Search your deck for a basic [R] Energy and attach it to this Pokemon. Then, shuffle your deck. [G][C][C] Naughty Kick: 50 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Scovilliain – Grass – HP110 Stage 1 – Evolves from Capsakid [C] Hot Bite: 20 damage. Your opponent’s Active Pokemon is now Burned. [G][C][C] Super Hot Yee-Haw: 90+ damage. If this Pokemon has any [R] Energy attached to it, this attack does 90 more damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Growlithe – Fire – HP90 Basic Pokemon [C] Stoke: Search your deck for up to 2 basic [R] Energy cards and attach them to this Pokemon. Then, shuffle your deck. [R][R][R] Fire Claws: 70 damage. Weakness: Water (x2) Resistance: none Retreat: 3 Arcanine ex – Fire – HP280 Stage 1 – Evolves from Growlithe Terastal: This Pokemon doesn’t take any damage from attacks while on the Bench. [R][R] Raging Claws: 30+ damage. This attack does 10 more damage for each damage counter on this Pokemon. [R][R][R] Bright Flame: 250 damage. Discard 2 Energy from this Pokemon. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Water (x2) Resistance: none Retreat: 3 [C] Bite: 10 damage. [R][C] Flare: 30 damage. Weakness: Water (x2) Resistance: none Retreat: 1 [C] Sharp Fang: 30 damage. [R][R][C] Fire Blast: 150 damage. Discard a [R] Energy attached to this Pokemon. Weakness: Water (x2) Resistance: none Retreat: 2 Slowpoke – Water – HP70 Basic Pokemon [C] Rest: This Pokemon is now Asleep. Heal 30 damage from it. [W][C] Headbutt: 20 damage. Weakness: Lightning (x2) Resistance: none Retreat: 2 Slowbro – Water – HP100 Stage 1 – Evolves from Slowpoke Ability: Strange Behavior As often as you like during your turn, you may move a damage counter from 1 of your Pokemon to this Pokemon. [W][C] Bubble Drain: 60 damage. Heal 30 damage from this Pokemon. Weakness: Lightning (x2) Resistance: none Retreat: 3 Clauncher – Water – HP70 Basic Pokemon [W] Vicegrip: 10 damage. Weakness: Lightning (x2) Resistance: none Retreat: 1 Clawitzer – Water – HP120 Stage 1 – Evolves from Clauncher [W][C] Water Gun: 50 damage. [W][W][C] Aqua Cannon: 160 damage. This Pokemon can’t attack during your next turn. Weakness: Lightning (x2) Resistance: none Retreat: 2 Cetoddle – Water – HP80 Basic Pokemon [C][C] Tackle: 30 damage. Weakness: Lightning (x2) Resistance: none Retreat: 2 Cetoddle – Water – HP100 Basic Pokemon [W] Icicle: 10 damage. [W][C][C] Sharp Fin: 60 damage. Weakness: Lightning (x2) Resistance: none Retreat: 3 Cetitan – Water – HP180 Stage 1 – Evolves from Cetoddle [C][C] Confront: 50 damage. [W][C][C] Sweeping Tackle: 200- damage. This attack’s damage is reduced by 20 for each damage counter on this Pokemon. Weakness: Lightning (x2) Resistance: none Retreat: 3 Magnemite – Lightning – HP60 Basic Pokemon [C] Recoil: Switch this Pokemon with 1 of your Benched Pokemon. [L] Electro Ball: 10 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Magneton – Lightning – HP90 Stage 1 – Evolves from Magnemite [L] Lightning Ball: 20 damage. [L][L] Explosion: 90 damage. This Pokemon also does 90 damage to itself. Weakness: Fighting (x2) Resistance: none Retreat: 2 Magnezone ex – Lightning – HP330 Stage 2 – Evolves from Magneton [L] Energy Crush: 50x damage. This attack does 50 damage for each Energy attached to all of your opponent’s Pokemon. [L][L] Pulse Launcher: 220 damage. This Pokemon also does 30 damage to itself. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Fighting (x2) Resistance: none Retreat: 3 Pachirisu – Lightning – HP70 Basic Pokemon Ability: Electric Pouches This Pokemon can’t be Paralyzed. [L][C] Group Zap: 10+ damage. This attack does 20 more damage for each of your Benched [L] Pokemon. This attack’s damage isn’t affected by Weakness. Weakness: Fighting (x2) Resistance: none Retreat: 1 Rotom – Lightning – HP80 Basic Pokemon [C] Junk Hunt: Search your discard pile for an Item card, reveal it, and put it in your hand. [L] Thundershock: 20 damage. Flip a coin. If heads, your opponent’s Active Pokemon is now Paralyzed. Weakness: Fighting (x2) Resistance: none Retreat: 1 Toxel – Lightning – HP70 Basic Pokemon [C][C] Gnaw: 20 damage. Weakness: Fighting (x2) Resistance: none Retreat: 2 Toxtricity – Lightning – HP130 Stage 1 – Evolves from Toxel [C][C] Tear Off: Choose 2 cards from your opponent’s hand without looking. Look at the cards, then your opponent shuffles them into their deck. [L][C][C] Thunder: 120 damage. This Pokemon does 20 damage to itself. Weakness: Fighting (x2) Resistance: none Retreat: 2 Pawmi – Lightning – HP50 Basic Pokemon [L] Jolt: Flip a coin. If heads, your opponent’s Active Pokemon is now Paralyzed. Weakness: Fighting (x2) Resistance: none Retreat: 1 Pawmi – Lightning – HP60 Basic Pokemon [L] Toss: 10 damage. [L][C] Elekick: 20 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Pawmo – Lightning – HP90 Stage 1 – Evolvrs from Pawmi [L] Thundershock: 30 damage. Flip a coin. If heads, your opponent’s Active Pokemon is now Paralyzed. [L][L][C] Head Volt: 70 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Pawmot – Lightning – HP130 Stage 2 – Evolves from Pawmo Ability: Charge Up Once during your turn, you may search your deck for a basic [L] Energy and attach it to this Pokemon. Then, shuffle your deck. [L][L][C] Electro Paw: 230 damage. Discard all Energy from this Pokemon. Weakness: Fighting (x2) Resistance: none Retreat: 0 Miraidon ex – Lightning – HP220 Basic Pokemon Ability: Tandem Unit Once during your turn, you may search your deck for 2 Basic [L] Pokemon and put them onto your Bench. Then, shuffle your deck. [L][L][C] Photon Blaster: 220 damage. During your next turn, this Pokemon can’t attack. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Fighting (x2) Resistance: none Retreat: 1 Drowzee – Psychic – HP70 Basic Pokemon [P] Force Asleep: Your opponent chooses 1 of their Benched Pokemon and switches it with their Active Pokemon. The new Active Pokemon is now Asleep. [P][C][C] Slap: 30 damage. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 1 Hypno – Psychic – HP110 Stage 1 – Evolves from Drowzee [P] Pendulum Manipulation: Flip a coin. If heads, choose 1 of your opponent’s Active Pokemon’s attacks and use it as this attack. [P][C][C] Psycho Sphere: 100 damage. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 2 Shuppet – Psychic – HP60 Basic Pokemon [P] Wrapped in Shadows: 10 damage. Flip a coin. If heads, the opponent can’t play Item cards from their hand during their next turn. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 1 Banette ex – Psychic – HP250 Stage 1 – Evolves from Shuppet [P] Eternal Darkness: 30 damage. Your opponent can’t play Item cards from their hand during their next turn. [P][C] Poltergeist: Look at your opponent’s hand. This attack does 60 damage for each Trainer card in your opponent’s hand. Pokemon ex Rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 2 Flabebe – Psychic – HP40 Basic Pokemon [P] Pollen Ball: 20 damage. Weakness: Metal (x2) Resistance: none Retreat: 1 Floette – Psychic – HP70 Stage 1 – Evolves from Flabebe [P][C] Magical Leaf: 30+ damage. Flip a coin, if heads this attack does an additional 30 damage and heal 30 damage from this Pokemon. Weakness: Metal (x2) Resistance: none Retreat: 1 Florges – Psychic – HP140 Stage 2 – Evolves from Floette Ability: Bloom Garden As long as this Pokemon is in play, your Pokemon have no Weakness. [P][C][C] Moon Force: 120 damage. Damage done by the Defending Pokemon is reduced by 30 damage during your opponent’s next turn. Weakness: Metal (x2) Resistance: none Retreat: 2 Klefki – Psychic – HP70 Basic Pokemon Ability: Prank Lock As long as this Pokemon is your Active Pokemon, each player’s Basic Pokemon in play have no Abilities (other than Prank Lock). [C] Knock Off: 10 damage. Before doing damage, discard a Pokemon Tool attached to the opponent’s Active Pokemon. Weakness: Metal (x2) Resistance: none Retreat: 1 Greavard – Psychic – HP70 Basic Pokemon [P] Graveyard Frolic: 10x damage. This attack does 10 damage for each [P] Pokemon in your discard pile. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 2 Greavard – Psychic – HP80 Basic Pokemon [C][C] Underworld Stroll: Look at your opponent’s hand. Choose a Supporter card you find there and return it to the bottom of your opponent’s deck. [P][C][C] Sharp Fangs: 30 damage. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 3 Houndstone – Psychic – HP140 Stage 1 – Evolves from Greavard [P][P] Grave Visit: 80 damage. This attack does 10 damage for each [P] Pokemon in your discard pile. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 3 Mankey – Fighting – HP60 Basic Pokemon [F] Monkey Strike: 30 damage. This Pokemon does 10 damage to itself. Weakness: Psychic (x2) Resistance: none Retreat: 1 Primeape – Fighting – HP90 Stage 1 – Evolves from Mankey [F] Thrashing Punch: 70 damage. This Pokemon does 20 damage to itself. Weakness: Psychic (x2) Resistance: none Retreat: 1 Annihilape – Fighting – HP140 Stage 2 – Evolves from Primeape [F] Enraged Fist: This attack does 70 damage for each Prize Card already taken by your opponent. [F][F] Dynamicpunch: 170 damage. This Pokemon does 50 damage to itself. Weakness: Psychic (x2) Resistance: none Retreat: 2 Spiritomb – Darkness – HP70 Basic Pokemon [D] Taunt: Choose 1 of your opponent’s Benched Pokemon and switch it with their Active Pokemon. [D][D] Destruction Verdict: Flip 2 coins. If both are heads, your opponent’s Active Pokemon is Knocked Out. Weakness: Grass (x2) Resistance: none Retreat: 1 Maschiff – Darkness – HP70 Basic Pokemon [D] Rear Kick: 10 damage. [D][C] Dark Fang: 20 damage. Weakness: Grass (x2) Resistance: none Retreat: 2 Maschiff – Darkness – HP80 Basic Pokemon [D][D] Crunch: 30 damage. Flip a coin. If heads, discard an Energy attached to your opponent’s Active Pokemon. Weakness: Grass (x2) Resistance: none Retreat: 3 Mabosstiff – Darkness – HP130 Stage 1 – Evolves from Maschiff Ability: Enraged Howling Once during your turn, you may have your opponent switch their Active Pokémon with 1 of their Benched Pokémon. [D][D][C] Wild Tackle: 160 damage. This Pokemon does 30 damage to itself. Weakness: Grass (x2) Resistance: none Retreat: 3 Bombirdier – Darkness – HP110 Basic Pokemon [C] Junk Transport: Search your deck for up to 3 Pokemon Tool cards, reveal them, and put them in your hand. Then, shuffle your deck. [D][C] Clutch: 60 damage. The Defending Pokemon can’t retreat during your opponent’s next turn. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Forretress – Metal – HP120 Stage 1 – Evolves from Pineco [M] Continuous Spin: Flip a coin until you get tails. This attack does 50 damage times the number of heads. [M][C][C] Shell Rolling: 90 damage. Damage done by the Defending Pokemon during your opponent’s next turn is reduced by 50 damage. Weakness: Fire (x2) Resistance: Grass (-30) Retreat: 3 Iron Treads ex – Metal – HP220 Basic Pokemon [C][C][C] Triple Laser: This attack does 30 damage to 3 of your opponent’s Pokemon. (Don’t apply Weakness and Resistance for Benched Pokemon.) [M][M][M][C] Cybernetic Wheel: 160 damage. Switch this Pokemon with 1 of your Benched Pokemon. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Fire (x2) Resistance: Grass (-30) Retreat: 3 Chansey – Colorless – HP110 Basic Pokemon [C][C] Pound: 40 damage. [C][C][C] Egg Roll: Flip a coin until you get tails. This attack does 60 damage times the number of heads. Weakness: Fighting (x2) Resistance: none Retreat: 2 Blissey – Colorless – HP150 Stage 1 – Evolves from Chansey Ability: Nurse On Duty Once during your turn you may heal all Special Conditions from your Active Pokemon. [C][C][C] Blissful Cyclone: 150 damage. Move all Energy attached to this Pokemon to 1 of your Benched Pokemon. Weakness: Fighting (x2) Resistance: none Retreat: 2 Skwovet – Colorless – HP60 Basic Pokemon Ability: Hidey Hole Once during your turn, you may use this Ability. Shuffle your hand and put it on the bottom of your deck. Then, draw a card. [C][C] Bite: 20 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Greedent – Colorless – HP120 Stage 1 – Evolves from Skwovet [C][C] Bite: 50 damage. [C][C][C] Enhanced Fang: 80 damage. If this Pokemon has a Pokemon Tool attached, this attack does 80 more damage. Weakness: Fighting (x2) Resistance: none Retreat: 2 Indeedee – Colorless – HP90 Basic Pokemon [C] Raise Well: Search your deck for a card that evolves from 1 of your Pokemon in play and play it on that Pokemon to evolve it. Then, shuffle your deck. [C][C] Hypno Wave: 30 damage. Your opponent’s Active Pokemon is now Asleep. Weakness: Fighting (x2) Resistance: none Retreat: 1 Tandemaus – Colorless – HP30 Basic Pokemon [C] Gnaw: 20 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Tandemaus – Colorless – HP40 Basic Pokemon [C][C] Double Attack: Flip 2 coins. This attack does 30 damage times the number of heads. Weakness: Fighting (x2) Resistance: none Retreat: 1 Maushold – Colorless – HP70 Stage 1 – Evolves from Tandemaus [C] Slap: 40 damage. [C][C] Family Attack: This attack 70 damage for each of your Maushold in play. Weakness: Fighting (x2) Resistance: none Retreat: 1 Squawkabilly – Colorless – HP70 Basic Pokemon [C] Call for Family: Search your deck for up to 2 Basic Pokemon cards and play them on your Bench. Then, shuffle your deck. [C][C] Fly: 60 damage. Flip a coin. If tails, this attack fails. If heads, prevent all effects of attacks, including damage, done to this Pokemon during your opponent’s next turn. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Cyclizar – Colorless – HP110 Basic Pokemon [C] Tooling: Draw 2 cards. [C][C][C] Speed Attack: 100 damage. Weakness: Fighting (x2) Resistance: none Retreat: 0 Electricity Generator – Trainer Look at the top 5 cards of your deck. Choose up to 2 basic [L] Energy cards and attach them to your Benched [L] Pokemon in any way you like. Then, shuffle the remaining cards into your deck. You may play as many Item cards as you like during your turn. Ultra Ball – Trainer Item Card Search your deck for a Pokemon, reveal it, and put it into your hand. Then, shuffle your deck. You may play as many Item cards as you like during your turn. Heal 30 damage from all Pokemon in play (both yours and your opponent’s). You may play as many Item cards as you like during your turn. Choose 1 of your Basic Pokémon in play. If you have a Stage 2 card in your hand that evolves from that Pokémon, put that card onto the Basic Pokémon to evolve it, skipping the Stage 1. You can’t use this card during your first turn or on a Basic Pokémon that was put into play this turn. You may play as many Item cards as you like during your turn. Rocky Helmet – Trainer Pokémon Tool If the Pokemon this card is attached to is your Active Pokemon and is damaged by an opponent’s attack (even if that Pokemon is Knocked Out), put 2 damage counters on the Attacking Pokémon. You may attach any number of Pokémon Tools to your Pokémon during your turn. You may attach only 1 Pokémon Tool to each Pokémon, and it stays attached. Using this card ends your turn. Shuffle your hand into your deck and draw 8 cards. You may play only 1 Supporter card during your turn. Professor’s Research (Professor Turo) – Trainer Discard your hand and draw 7 cards. You may play only 1 Supporter card during your turn. Search your deck for an Item card and a Pokemon Tool card, reveal them, and put them in your hand. Then, shuffle your deck. You may play only 1 Supporter card during your turn. Choose up to 5 Pokemon cards from your discard pile, reveal them, and shuffle them into your deck. Then, draw 3 cards. You may play only 1 Supporter card during your turn. Once during each player’s turn, that player may flip a coin, If heads, they search their deck for a Pokemon card, reveal it, and put it in their hand, then shuffle their deck. This Stadium stays in play when you play it. Discard it if another Stadium comes into play. If a Stadium with the same name is in play, you can’t play this card. In addition to the main Scarlet ex and Violet ex sets, three Starter Set ex products will release at the same time featuring each of the Paldea first partner Pokemon paired with another Pokemon featured as a Pokemon ex. We’ve previously learned that the Mimikyu ex found in the Quaxly & Mimikyu Starter Set ex product will become a promo card in English as part of a Mimikyu ex box that releases on March 3rd. #82 Nemona ‘Sprigatito & Lucario ex’ Translations Shroomish – Grass – HP60 Basic Pokemon [G] Absorb: 10 damage. Heal 10 damage from this Pokémon. Weakness: Fire (x2) Resistance: None Retreat: 1 Breloom – Grass – HP110 Stage 1 – Evolves from Shroomish Mach Cross: 60 damage. Weakness: Fire (x2) Resistance: None Retreat: 1 Tropius – Grass – HP100 Basic Pokemon [G] Freshly Picked Fruit: Heal 60 damage from 1 of your Benched Pokémon. [G][C] Razor Leaf: 50 damage. Weakness: Fire (x2) Resistance: None Retreat: 1 Sprigatito – Grass – HP70 Basic Pokemon [C] Scratch: 10 damage. [G][C] Leafage: 20 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Floragato – Grass – HP90 Stage 1 – Evolves from Sprigatito [C] Slash: 20 damage. [G][C] Leaf Step: 60 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Meowscarada – Grass – HP160 Stage 2 – Evolves from Floragato [C] Trick Cloak: 40 damage. You may put an Energy attached to your opponent’s Active Pokémon into their hand. [G][C] Flower Bomb: 130 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Tarountula – Grass – HP40 Basic Pokemon [C] String Pull: Flip a coin. If heads, switch 1 of your opponent’s Benched Pokémon with their Active Pokémon. [G] Bug Bite: 10 damage. Weakness: Fire (x2) Resistance: none Retreat: 1 Riolu – Fighting – HP70 Basic Pokemon [C] Jab: 10 damage. [F][C] Low Kick: 20 damage. Weakness: Psychic (x2) Resistance: none Retreat: 1 Lucario ex – Fighting – HP260 Stage 1 – Evolves from Riolu [F][C] Low Kick: 60 damage. [F][F][C] Aura Sphere: 160 damage. This attack does 50 damage to 1 of your opponent’s Benched Pokemon (don’t apply Weakness and Resistance for Benched Pokemon). Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Psychic (x2) Resistance: none Retreat: 2 Stonjourner – Fighting – HP130 Basic Pokemon Ability: Exoskeleton This Pokémon takes 20 less damage from attacks (after applying Weakness and Resistance). Mega Kick: 100 damage. Weakness: Grass (x2) Resistance: none Retreat: 2 Lechonk – Colorless – HP60 Basic Pokemon [C] Collect: Draw a card. [C][C][C] Tackle: 30 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Energy Switch – Trainer Item Card Move a basic Energy from 1 of your Pokémon to another of your Pokémon. You may play any number of Item cards during your turn. Energy Search – Trainer Item Card Search your deck for a basic Energy card, reveal it, and put it into your hand. Then, shuffle your deck. You may play any number of Item cards during your turn. Heal 30 damage from 1 of your Pokémon. You may play any number of Item cards during your turn. Search your deck for a Basic Pokémon and put it onto your Bench. Then, shuffle your deck. You may play any number of Item cards during your turn. Ultra Ball – Trainer Item Card Search your deck for a Pokemon, reveal it, and put it into your hand. Then, shuffle your deck. You may play as many Item cards as you like during your turn. Pokégear 3.0 – Trainer Item Card Look at the top 7 cards of your deck. You may reveal a Supporter card you find there and put it into your hand. Shuffle the other cards back into your deck. You may play as many Item cards as you like during your turn. Switch your Active Pokémon with 1 of your Benched Pokémon. You may play as many Item cards as you like during your turn. Pokemon Catcher – Trainer Item Card Flip a coin. If heads, switch 1 of your opponent’s Benched Pokémon with their Active Pokémon. You may play as many Item cards as you like during your turn. Each player shuffles their hand into their deck and draws 4 cards. You may play only 1 Supporter card during your turn. Shuffle your hand into your deck. Then, draw 5 cards. You may play only 1 Supporter card during your turn. Draw 3 cards. You may play only 1 Supporter card during your turn. Professor’s Research (Professor Sada) – Trainer Discard your hand and draw 7 cards. You may play only 1 Supporter card during your turn. ‘Fuecoco & Ampharos ex’ Translations Growlithe – Fire – HP70 Basic Pokemon [R] Relentless Flames: 30x damage. Flip a coin until you get tails. This attack does 40 damage for each heads. Weakness: Water (x2) Resistance: none Retreat: 2 Fuecoco – Fire – HP80 Basic Pokemon [C] Gnaw: 10 damage. [R][R][C] Flare: 50 damage. Weakness: Water (x2) Resistance: none Retreat: 2 Crocalor – Fire – HP100 Stage 1 – Evolves from Fuecoco [R][C] Bite: 50 damage. [R][R][C] Rolling Tackle: 100 damage. Weakness: Water (x2) Resistance: none Retreat: 3 Skelidirge – Fire – HP180 Stage 2 – Evolves from Crocalor [R] Fiery Vocals: 50 damage. Attach up to 2 Basic Energy cards from your discard pile to your Pokémon in any way you like. [R][R][C] Blaze Shout: 190 damage. This Pokémon also does 30 damage to itself. Weakness: Water (x2) Resistance: none Retreat: 3 Mareep – Lightning – HP60 Basic Pokemon [L] Static: 10 damage. [L][C][C] Elec-ball: 40 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Flaaffy – Lightning – HP90 Stage 1 – Evolves from Mareep [L] Thundershock: 20 damage. Flip a coin. If heads, your opponent’s Active Pokemon is now Paralyzed. [L][C][C] Elec-ball: 60 damage. Weakness: Fighting (x2) Resistance: none Retreat: 2 Ampharos ex – Lightning – HP330 Stage 2 – Evolves from Flaaffy [L] Elec-ball: 60 damage. [L][C][C] Lightning Tail: 140+ damage. You may discard 2 Energy from this Pokemon. If you do, this attack does 100 more damage. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Fighting (x2) Resistance: none Retreat: 2 Rotom – Lightning – HP60 Basic Pokemon [C] Linear Attack: This attack does 20 damage to 1 of your opponent’s Pokémon. (Don’t apply Weakness and Resistance for Benched Pokémon.) Weakness: Fighting (x2) Resistance: none Retreat: 1 Lechonk – Colorless – HP60 Basic Pokemon [C] Collect: Draw a card. [C][C][C] Tackle: 30 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Flamigo – Colorless – HP110 Basic Pokemon [C] Flap: 30 damage. [C][C][C] Nosedive: 110 damage. This Pokémon also does 20 damage to itself. Weakness: Lightning (x2) Resistance: Fighting (-30) Retreat: 1 Energy Search – Trainer Item Card Search your deck for a basic Energy card, reveal it, and put it into your hand. Then, shuffle your deck. You may play any number of Item cards during your turn. Search your deck for a Basic Pokémon and put it onto your Bench. Then, shuffle your deck. You may play any number of Item cards during your turn. Ultra Ball – Trainer Item Card Search your deck for a Pokemon, reveal it, and put it into your hand. Then, shuffle your deck. You may play as many Item cards as you like during your turn. Choose 1 of your Basic Pokémon in play. If you have a Stage 2 card in your hand that evolves from that Pokémon, put that card onto the Basic Pokémon to evolve it, skipping the Stage 1. You can’t use this card during your first turn or on a Basic Pokémon that was put into play this turn. You may play as many Item cards as you like during your turn. Pokégear 3.0 – Trainer Item Card Look at the top 7 cards of your deck. You may reveal a Supporter card you find there and put it into your hand. Shuffle the other cards back into your deck. You may play as many Item cards as you like during your turn. Switch your Active Pokémon with 1 of your Benched Pokémon. You may play as many Item cards as you like during your turn. Search your deck for up to 2 Evolution Pokemon cards, reveal them, and put them in your hand. Then, shuffle your deck. You may play only 1 Supporter card during your turn. Each player shuffles their hand into their deck and draws 4 cards. You may play only 1 Supporter card during your turn. Shuffle your hand into your deck. Then, draw 5 cards. You may play only 1 Supporter card during your turn. Draw 3 cards. You may play only 1 Supporter card during your turn. Professor’s Research (Professor Turo) – Trainer Discard your hand and draw 7 cards. You may play only 1 Supporter card during your turn. ‘Quaxly & Mimikyu ex’ Translations Alomomola – Water – HP120 Basic Pokemon [W][C] Surf: 30 damage. [W][W][C] Aqua Splash: 120 damage. This Pokémon can’t attack during your next turn. Weakness: Lightning (x2) Resistance: none Retreat: 1 Quaxly – Water – HP70 Basic Pokemon [C] Pound: 10 damage. [W][C] Kick: 20 damage. Weakness: Lightning (x2) Resistance: none Retreat: 1 Quaxwell – Water – HP100 Stage 1 – Evolves from Quaxly [W] Rain Splash: 20 damage. [W][C][C] Spiral Kick: 70 damage. Weakness: Lightning (x2) Resistance: none Retreat: 1 Quaquaval – Water – HP170 Stage 2 – Evolves from Quaxwell Ability: Energy Carnival Once during your turn, you may attach a Basic Energy card from your hand to 1 of your Pokémon. [W][C][C] Hydro Kick: 140 damage. Weakness: Lightning (x2) Resistance: none Retreat: 2 Dedenne – Psychic – HP70 Basic Pokemon [P][C] Second Bite: 30+ damage. This attack does 10 more damage for each damage counter on your opponent’s Active Pokémon. Weakness: Metal (x2) Resistance: none Retreat: 1 Mimikyu ex – Psychic – HP190 Basic Pokemon [P] Void Return: 30 damage. You may switch this Pokemon with 1 of your Benched Pokemon. [P][C][C] Energy Burst: 30x damage. This attack does 30 damage for each Energy attached to both Active Pokemon. Pokemon ex rule: When your Pokemon ex is Knocked Out, your opponent takes 2 Prize cards. Weakness: Metal (x2) Resistance: none Retreat: 1 Flittle – Psychic – HP30 Basic Pokemon [P] Ram: 10 damage. Weakness: Darkness (x2) Resistance: Fighting (-30) Retreat: 0 Zangoose – Colorless – HP90 Basic Pokemon [C] Slash: 40 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Lechonk – Colorless – HP60 Basic Pokemon [C] Collect: Draw a card. [C][C][C] Tackle: 30 damage. Weakness: Fighting (x2) Resistance: none Retreat: 1 Cyclizar – Colorless – HP110 Basic Pokemon [C][C] Reckless Charge: 70 damage. This Pokémon also does 10 damage to itself. Weakness: Fighting (x2) Resistance: none Retreat: 1 Energy Retrieval – Trainer Item Card Put up to 2 basic Energy cards from your discard pile into your hand. You may play any number of Item cards during your turn. Energy Search – Trainer Item Card Search your deck for a basic Energy card, reveal it, and put it into your hand. Then, shuffle your deck. You may play any number of Item cards during your turn. Crushing Hammer – Trainer Item Card Flip a coin. If heads, discard an Energy attached to 1 of your opponent’s Pokémon. You may play any number of Item cards during your turn. Search your deck for a Basic Pokémon and put it onto your Bench. Then, shuffle your deck. You may play any number of Item cards during your turn. Ultra Ball – Trainer Item Card Search your deck for a Pokemon, reveal it, and put it into your hand. Then, shuffle your deck. You may play as many Item cards as you like during your turn. Pokégear 3.0 – Trainer Item Card Look at the top 7 cards of your deck. You may reveal a Supporter card you find there and put it into your hand. Shuffle the other cards back into your deck. You may play as many Item cards as you like during your turn. Switch your Active Pokémon with 1 of your Benched Pokémon. You may play as many Item cards as you like during your turn. Pokemon Catcher – Trainer Item Card Flip a coin. If heads, switch 1 of your opponent’s Benched Pokémon with their Active Pokémon. You may play as many Item cards as you like during your turn. Vitality Band – Trainer Pokémon Tool The attacks of the Pokémon this card is attached to do 10 more damage to your opponent’s Active Pokémon (before applying Weakness and Resistance). You may attach any number of Pokémon Tools to your Pokémon during your turn. You may attach only 1 Pokémon Tool to each Pokémon, and it stays attached. Each player shuffles their hand into their deck and draws 4 cards. You may play only 1 Supporter card during your turn. Shuffle your hand into your deck. Then, draw 5 cards. You may play only 1 Supporter card during your turn. Draw 3 cards. You may play only 1 Supporter card during your turn. Professor’s Research (Professor Sada) – Trainer Discard your hand and draw 7 cards. You may play only 1 Supporter card during your turn.	{"url":"https://www.pokebeach.com/2023/01/scarlet-ex-and-violet-ex-cards-fully-revealed","timestamp":"2024-11-10T21:50:20Z","content_type":"text/html","content_length":"542195","record_id":"<urn:uuid:446f64bb-0e77-43cd-ab73-c8696691018d>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00075.warc.gz"}
Big Ideas Math Algebra 2 Answers Chapter 2 Quadratic Functions If you stuck at solving complex problems on Quadratic Functions then stop calculating the problem and start practicing the concepts of Chapter 2 from Big Ideas Math Algebra 2 Answers. It holds all chapter’s answer keys in pdf format. Here, in this article, you will collect the details about Big Ideas Math Algebra 2 Answers Chapter 2 Quadratic Functions. This material is the complete guide for high school students to learn the concepts of the Quadratic functions. Hence, download the topic-wise BIM Algebra 2 Ch 1 Textbook Solutions from the below available links and start your practice sessions before any examination. Big Ideas Math Book Algebra 2 Answer Key Chapter 2 Quadratic Functions Students can access these Topicwise Big Ideas Math Algebra 2 Ch 1 Answers online or offline whenever required and kickstart their preparation. You can easily clear all your subject-related queries using the BIM Algebra 2 Ch 1 Answer key. This BIM Textbook Algebra 2 Chapter 1 Solution Key includes various easy & complex questions belonging to Lessons 2.1 to 2.4, Assessment Tests, Chapter Tests, Cumulative Assessments, etc. Apart from the Quadratic functions exercises, you can also find the exercise on the Lesson Focus of a Parabola. Excel in mathematics examinations by practicing more and more using the BigIdeas Math Algebra 2 Ch 2 Answer key. Quadratic Functions Maintaining Mathematical Proficiency Find the x-intercept of the graph of the linear equation. Question 1. y = 2x + 7 Question 2. y = -6x + 8 Question 3. y = -10x – 36 Question 4. y = 3(x – 5) Question 5. y = -4(x + 10) Question 6. 3x + 6y = 24 Find the distance between the two points. Question 7. (2, 5), (-4, 7) Question 8. (-1, 0), (-8, 4) Question 9. (3, 10), (5, 9) Question 10. (7, -4), (-5, 0) Question 11. (4, -8), (4, 2) Question 12. (0, 9), (-3, -6) Question 13. ABSTRACT REASONING Use the Distance Formula to write an expression for the distance between the two points (a, c) and (b, c). Is there an easier way to find the distance when the x-coordinates are equal? Explain your reasoning Quadratic Functions Mathematical Practices Monitoring Progress Decide whether the syllogism represents correct or flawed reasoning. If flawed, explain why the conclusion is not valid. Question 1. All mammals are warm-blooded. All dogs are mammals. Therefore, all dogs are warm-blooded. Question 2. All mammals are warm-blooded. My pet is warm-blooded. Therefore, my pet is a mammal. Question 3. If I am sick, then I will miss school. I missed school. Therefore, I am sick. Question 4. If I am sick, then I will miss school. I did not miss school. Therefore, I am not sick. Lesson 2.1 Transformations of Quadratic Functions Essential Question How do the constants a, h, and k affect the graph of the quadratic function g(x) = a(x – h)^2 + k? The parent function of the quadratic family is f(x) = x^2. A transformation of the graph of the parent function is represented by the function g(x) = a(x – h)^2 + k, where a ≠ 0. Identifying Graphs of Quadratic Functions Work with a partner. Match each quadratic function with its graph. Explain your reasoning. Then use a graphing calculator to verify that your answer is correct. a. g(x) = -(x – 2)^2 b. g(x) = (x – 2)^2 + 2 c. g(x) = -(x + 2)^2 – 2 d. g(x) = 0.5(x – 2)^2 + 2 e. g(x) = 2(x – 2)^2 f. g(x) = -(x + 2)^2 + 2 Communicate Your Answer Question 2. How do the constants a, h, and k affect the graph of the quadratic function g(x) =a(x – h)^2 + k? Question 3. Write the equation of the quadratic function whose graph is shown at the right. Explain your reasoning. Then use a graphing calculator to verify that your equation is correct. 2.1 Lesson Monitoring Progress Describe the transformation of f(x) = x^2 represented by g. Then graph each function. Question 1. g(x) = (x – 3)^2 Question 2. g(x) = (x + 2)^2 – 2 Question 3. g(x) = (x + 5)^2 + 1 Describe the transformation of f(x) = x^2 represented by g. Then graph each function. Question 4. g(x) = ($\frac{1}{3} x$)^2 Question 5. g(x) = 3(x – 1)^2 Question 6. g(x) = -(x + 3)^2 + 2 Question 7. Let the graph of g be a vertical shrink by a factor of $\frac{1}{2}$ followed by a translation 2 units up of the graph of f(x) = x^2. Write a rule for g and identify the vertex. Question 8. Let the graph of g be a translation 4 units left followed by a horizontal shrink by a factor of $\frac{1}{3}$ of the graph of f(x) = x^2 + x. Write a rule for g. Question 9. WHAT IF? In Example 5, the water hits the ground 10 feet closer to the fire truck after lowering the ladder. Write a function that models the new path of the water. Transformations of Quadratic Functions 2.1 Exercises Vocabulary and Core Concept Check Question 1. COMPLETE THE SENTENCE The graph of a quadratic function is called a(n) ________. Question 2. VOCABULARY Identify the vertex of the parabola given by f(x) = (x + 2)^2 – 4. Monitoring Progress and Modeling with Mathematics In Exercises 3–12, describe the transformation of f(x) = x^2 represented by g. Then graph each function. Question 3. g(x) = x^2 – 3 Question 4. g(x) = x^2 + 1 Question 5. g(x) = (x + 2)^2 Question 6. g(x) = (x – 4)^2 Question 7. g(x) = (x – 1)^2 Question 8. g(x) = (x + 3)^2 Question 9. g(x) = (x + 6)^2 – 2 Question 10. g(x) = (x – 9)^2 + 5 Question 11. g(x) = (x – 7)^2 + 1 Question 12. g(x) = (x + 10)^2 – 3 ANALYZING RELATIONSHIPS In Exercises 13–16, match the function with the correct transformation of the graph of f. Explain your reasoning. Question 13. y = f(x – 1) Question 14. y = f(x) + 1 Question 15. y = f(x – 1) + 1 Question 16. y = f(x + 1) In Exercises 17–24, describe the transformation of f(x) = x^2 represented by g. Then graph each function. Question 17. g(x) = -x^2 Question 18. g(x) = (-x)^2 Question 19. g(x) = 3x^2 Question 20. g(x) = $\frac{1}{3}$x^2 Question 21. g(x) = (2x)^2 Question 22. g(x) = -(2x)^2 Question 23. g(x) = $\frac{1}{5}$x^2 – 4 Question 24. g(x) = $\frac{1}{2}$(x – 1)^2 ERROR ANALYSIS In Exercises 25 and 26, describe and correct the error in analyzing the graph of f(x) = −6x^2 + 4. Question 25. Question 26. USING STRUCTURE In Exercises 27–30, describe the transformation of the graph of the parent quadratic function. Then identify the vertex. Question 27. f(x) = 3(x + 2)^2 + 1 Question 28. f(x) = -4(x + 1)^2 – 5 Question 29. f(x) = -2x^2 + 5 Question 30. f(x) = $\frac{1}{2}$(x – 1)^2 In Exercises 31–34, write a rule for g described by the transformations of the graph of f. Then identify the vertex. Question 31. f(x) = x^2 vertical stretch by a factor of 4 and a reflection in the x-axis, followed by a translation 2 units up Question 32. f(x) = x^2; vertical shrink by a factor of $\frac{1}{3}$ and a reflection in the y-axis, followed by a translation 3 units right Question 33. f(x) = 8x^2 – 6; horizontal stretch by a factor of 2 and a translation 2 units up, followed by a reflection in the y-axis Question 34. f(x) = (x + 6)^2 + 3; horizontal shrink by a factor of $\frac{1}{2}$ and a translation 1 unit down, followed by a reflection in the x-axis USING TOOLS In Exercises 35–40, match the function with its graph. Explain your reasoning. Question 35. g(x) = 2(x – 1)^2 – 2 Question 36. g(x) = $\frac{1}{2}$(x + 1)^2 – 2 Question 37. g(x) = -2(x – 1)^2 + 2 Question 38. g(x) = 2(x + 1)^2 + 2 Question 39. g(x) = -2(x + 1)^2 – 2 Question 40. g(x) = 2(x – 1)^2 + 2 JUSTIFYING STEPS In Exercises 41 and 42, justify eachstep in writing a function g based on the transformationsof f(x) = 2x^2 + 6x. Question 41. translation 6 units down followed by a reflection in the x-axis Question 42. reflection in the y-axis followed by a translation 4 units right Question 43. MODELING WITH MATHEMATICS The function h(x) = -0.03(x – 14)^2 + 6 models the jump of a red kangaroo, where x is the horizontal distance traveled (in feet) and h(x) is the height (in feet). When the kangaroo jumps from a higher location, it lands 5 feet farther away. Write a function that models the second jump. Question 44. MODELING WITH MATHEMATICS The function f(t) = -16t^2 + 10 models the height (in feet) of an object t seconds after it is dropped from a height of 10 feet on Earth. The same object dropped from the same height on the moon is modeled by g(t) = –$\frac{8}{3}$t^2 + 10. Describe the transformation of the graph of f to obtain g. From what height must the object be dropped on the moon so it hits the ground at the same time as on Earth? Question 45. MODELING WITH MATHEMATICS Flying fish use their pectoral fins like airplane wings to glide through the air. a. Write an equation of the form y = a(x – h)^2 + k with vertex (33, 5) that models the flight path, assuming the fish leaves the water at (0, 0). b. What are the domain and range of the function? What do they represent in this situation? c. Does the value of a change when the flight path has vertex (30, 4)? Justify your answer. Question 46. HOW DO YOU SEE IT? Describe the graph of g as a transformation of the graph of f(x) = x^2. Question 47. COMPARING METHODS Let the graph of g be a translation 3 units up and 1 unit right followed by a vertical stretch by a factor of 2 of the graph of f(x) = x^2. a. Identify the values of a, h, and k and use vertex form to write the transformed function. b. Use function notation to write the transformed function. Compare this function with your function in part (a). c. Suppose the vertical stretch was performed first, followed by the translations. Repeat parts (a) and (b). d. Which method do you prefer when writing a transformed function? Explain. Question 48. THOUGHT PROVOKING A jump on a pogo stick with a conventional spring can be modeled by f(x) = -0.5(x – 6)^2 + 18, where x is the horizontal distance (in inches) and f(x) is the vertical distance (in inches). Write at least one transformation of the function and provide a possible reason for your transformation. Question 49. MATHEMATICAL CONNECTIONS The area of a circle depends on the radius, as shown in the graph. A circular earring with a radius of r millimeters has a circular hole with a radius of $\frac{3 r}{4}$ millimeters. Describe a transformation of the graph below that models the area of the blue portion of the earring. Maintaining Mathematical Proficiency A line of symmetry for the figure is shown in red. Find the coordinates of point A. (Skills Review Handbook) Question 50. Question 51. Question 52. Lesson 2.2 Characteristics of Quadratic Functions Essential Question What type of symmetry does the graph of f(x) = a(x – h)^2 + k have and how can you describe this symmetry? Parabolas and Symmetry Work with a partner. a. Complete the table. Then use the values in the table to sketch the graph of the function f(x) = $\frac{1}{2}$x^2 – 2x – 2 on graph paper. b. Use the results in part (a) to identify the vertex of the parabola. c. Find a vertical line on your graph paper so that when you fold the paper, the left portion of the graph coincides with the right portion of the graph. What is the equation of this line? How does it relate to the vertex? d. Show that the vertex form f(x) = $\frac{1}{2}$(x – 2)^2 – 4 is equivalent to the function given in part (a). Parabolas and Symmetry Work with a partner. Repeat Exploration 1 for the function given by f(x) = –$\frac{1}{3}$x^2 + 2x + 3 = –$\frac{1}{3}$(x – 3),sup>2 + 6. Communicate Your Answer Question 3. What type of symmetry does the graph of f(x) = a(x – h)^2 + k have and how can you describe this symmetry? Question 4. Describe the symmetry of each graph. Then use a graphing calculator to verify your answer. a. f(x) = -(x – 1)^2 + 4 b. f(x) = (x + 1)^2 – 2 c. f(x) = 2(x – 3)^2 + 1 d. f(x) = $\frac{1}{2}$(x + 2)^2 e. f(x) = -2x^2 + 3 f. f(x) = 3(x – 5)^2 + 2 2.2 Lesson Monitoring Progress Graph the function. Label the vertex and axis of symmetry. Question 1. f(x) = -3(x + 1)^2 Question 2. g(x) = 2(x – 2)^2 + 5 Question 3. h(x) = x^2 + 2x – 1 Question 4. p(x) = -2x^2 – 8x + 1 Question 5. Find the minimum value or maximum value of (a) f(x) = 4x^2 + 16x – 3 and (b) h(x) = -x^2 + 5x + 9. Describe the domain and range of each function, and where each function is increasing and decreasing. Graph the function. Label the x-intercepts, vertex, and axis of symmetry. Question 6. f(x) = -(x + 1)(x + 5) Question 7. g(x) = $\frac{1}{4}$(x – 6)(x – 2) Question 8. WHAT IF? The graph of your third shot is a parabola through the origin that reaches a maximum height of 28 yards when x = 45. Compare the distance it travels before it hits the ground with the distances of the first two shots. Characteristics of Quadratic Functions 2.2 Exercises Vocabulary and Core Concept and Check Question 1. WRITING Explain how to determine whether a quadratic function will have a minimum value or a maximum value. Question 2. WHICH ONE DOESN’T BELONG? The graph of which function does not belong with the other three? Explain. Question 3. f(x) = (x – 3)^2 Question 4. h(x) = (x + 4)^2 Question 5. g(x) = (x + 3)^2 + 5 Question 6. y = (x – 7)^2 – 1 Question 7. y = -4(x – 2)^2 + 4 Question 8. g(x) = 2(x + 1)^2 – 3 Question 9. f(x) = -2(x – 1)^2 – 5 Question 10. h(x) = 4(x + 4)^2 + 6 Question 11. y = –$\frac{1}{4}$(x + 2)^2 + 1 Question 12. y = $\frac{1}{2}$(x – 3)^2 + 2 Question 13. f(x) = 0.4(x – 1)^2 Question 14. g(x) = 0.75x^2 – 5 ANALYZING RELATIONSHIPS In Exercises 15–18, use the axis of symmetry to match the equation with its graph. Question 15. y = 2(x – 3)^2 + 1 Question 16. y = (x + 4)^2 – 2 Question 17. y = $\frac{1}{2}$(x + 1)^2 + 3 Question 18. y = (x – 2)^2 – 1 REASONING In Exercises 19 and 20, use the axis of symmetry to plot the reflection of each point and complete the parabola. Question 19. Question 20. In Exercises 21–30, graph the function. Label the vertex and axis of symmetry. Question 21. y = x^2 + 2x + 1 Question 22. y = 3x^2 – 6x + 4 Question 23. y = -4x^2 + 8x + 2 Question 24. f(x) = -x^2 – 6x + 3 Question 25. g(x) = -x^2 – 1 Question 26. f(x) = 6x^2 – 5 Question 27. g(x) = -1.5x^2 + 3x + 2 Question 28. f(x) = 0.5x^2 + x – 3 Question 29. y = $\frac{3}{2}$x^2 – 3x + 6 Question 30. y = –$\frac{5}{2}$x^2 – 4x – 1 Question 31. WRITING Two quadratic functions have graphs with vertices (2, 4) and (2, -3). Explain why you can not use the axes of symmetry to distinguish between the two functions. Question 32. WRITING A quadratic function is increasing to the left of x = 2 and decreasing to the right of x = 2. Will the vertex be the highest or lowest point on the graph of the parabola? Explain. ERROR ANALYSIS In Exercises 33 and 34, describe and correct the error in analyzing the graph of y = 4x^2 + 24x − 7. Question 33. Question 34. MODELING WITH MATHEMATICS In Exercises 35 and 36, x is the horizontal distance (in feet) and y is the vertical distance (in feet). Find and interpret the coordinates of the vertex. Question 35. The path of a basketball thrown at an angle of 45° can be modeled by y = -0.02x^2 + x + 6. Question 36. The path of a shot put released at an angle of 35° can be modeled by y = -0.01x^2 + 0.7x + 6. Question 37. ANALYZING EQUATIONS The graph of which function has the same axis of symmetry as the graph of y = x^2 + 2x + 2? A. y = 2x^2 + 2x + 2 B. y = -3x^2 – 6x + 2 C. y = x^2 – 2x + 2 D. y = -5x^2 + 10x + 23 Question 38. USING STRUCTURE Which function represents the widest parabola? Explain your reasoning. A. y = 2(x + 3)^2 B. y = x^2 – 5 C. y = 0.5(x – 1)^2 + 1 D. y = -x^2 + 6 In Exercises 39–48, find the minimum or maximum value of the function. Describe the domain and range of the function, and where the function is increasing and decreasing. Question 39. y = 6x^2 – 1 Question 40. y = 9x^2 + 7 Question 41. y = -x^2 – 4x – 2 Question 42. g(x) = -3x^2 – 6x + 5 Question 43. f(x) = -2x^2 + 8x + 7 Question 44. g(x) = 3x^2 + 18x – 5 Question 45. h(x) = 2x^2 – 12x Question 46. h(x) = x^2 – 4x Question 47. y = $\frac{1}{4}$x^2 – 3x + 2 Question 48. f(x) = $\frac{3}{2}$x^2 + 6x + 4 Question 49. PROBLEM SOLVING The path of a diver is modeled by the function f(x) = -9x^2 + 9x + 1, where f(x) is the height of the diver (in meters) above the water and x is the horizontal distance (in meters) from the end of the diving board. a. What is the height of the diving board? b. What is the maximum height of the diver? c. Describe where the diver is ascending and where the diver is descending. Question 50. PROBLEM SOLVING The engine torque y (in foot-pounds) of one model of car is given by y = -3.75x^2 + 23.2x + 38.8, where x is the speed (in thousands of revolutions per minute) of the engine. a. Find the engine speed that maximizes torque. What is the maximum torque? b. Explain what happens to the engine torque as the speed of the engine increases. MATHEMATICAL CONNECTIONS In Exercises 51 and 52, write an equation for the area of the figure. Then determine the maximum possible area of the figure. Question 51. Question 52. In Exercises 53–60, graph the function. Label the x-intercept(s), vertex, and axis of symmetry. Question 53. y = (x + 3)(x – 3) Question 54. y = (x + 1)(x – 3) Question 55. y = 3(x + 2)(x + 6) Question 56. f(x) = 2(x – 5)(x – 1) Question 57. g(x) = -x(x + 6) Question 58. y = -4x(x + 7) Question 59. f(x) = -2(x – 3)^2 Question 60. y = 4(x – 7)^2 USING TOOLS In Exercises 61–64, identify the x-intercepts of the function and describe where the graph is increasing and decreasing. Use a graphing calculator to verify your answer. Question 61. f(x) = $\frac{1}{2}$(x – 2)(x + 6) Question 62. y = $\frac{3}{4}$(x + 1)(x – 3) Question 63. g(x) = -4(x – 4)(x – 2) Question 64. h(x) = -5(x + 5)(x + 1) Question 65. MODELING WITH MATHEMATICS A soccer player kicks a ball downfield. The height of the ball increases until it reaches a maximum height of 8 yards, 20 yards away from the player. A second kick is modeled by y = x(0.4 – 0.008x). Which kick travels farther before hitting the ground? Which kick travels higher? Question 66. MODELING WITH MATHEMATICS Although a football field appears to be flat, some are actually shaped like a parabola so that rain runs off to both sides. The cross section of a field can be modeled by y = -0.000234x(x – 160), where x and y are measured in feet. What is the width of the field? What is the maximum height of the surface of the field? Question 67. REASONING The points (2, 3) and (-4, 2) lie on the graph of a quadratic function. Determine whether you can use these points to find the axis of symmetry. If not, explain. If so, write the equation of the axis of symmetry. Question 68. OPEN-ENDED Write two different quadratic functions in intercept form whose graphs have the axis of symmetry x= 3. Question 69. PROBLEM SOLVING An online music store sells about 4000 songs each day when it charges $1 per song. For each $0.05 increase in price, about 80 fewer songs per day are sold. Use the verbal model and quadratic function to determine how much the store should charge per song to maximize daily revenue. Question 70. PROBLEM SOLVING An electronics store sells 70 digital cameras per month at a price of $320 each. For each $20 decrease in price, about 5 more cameras per month are sold. Use the verbal model and quadratic function to determine how much the store should charge per camera to maximize monthly revenue. Question 71. DRAWING CONCLUSIONS Compare the graphs of the three quadratic functions. What do you notice? Rewrite the functions f and g in standard form to justify your answer. f(x) = (x + 3)(x + 1) g(x) = (x + 2)^2 – 1 h(x) = x^2 + 4x + 3 Question 72. USING STRUCTURE Write the quadratic function f(x) = x^2 + x – 12 in intercept form. Graph the function. Label the x-intercepts, y-intercept, vertex, and axis of symmetry. Question 73. PROBLEM SOLVING A woodland jumping mouse hops along a parabolic path given by y = -0.2x^2 + 1.3x, where x is the mouse’s horizontal distance traveled (in feet) and y is the corresponding height (in feet). Can the mouse jump over a fence that is 3 feet high? Justify your answer. Question 74. HOW DO YOU SEE IT? Consider the graph of the function f(x) = a(x – p)(x – q). a. What does f($\frac{p+q}{2}$) represent in the graph? b. If a < 0, how does your answer in part (a) change? Explain. Question 75. MODELING WITH MATHEMATICS The Gateshead Millennium Bridge spans the River Tyne. The arch of the bridge can be modeled by a parabola. The arch reaches a maximum height of 50 meters at a point roughly 63 meters across the river. Graph the curve of the arch. What are the domain and range? What do they represent in this situation? Quadratic 76. You have 100 feet of fencing to enclose a rectangular garden. Draw three possible designs for the garden. Of these, which has the greatest area? Make a conjecture about the dimensions of the rectangular garden with the greatest possible area. Explain your reasoning. Question 77. MAKING AN ARGUMENT The point (1, 5) lies on the graph of a quadratic function with axis of symmetry x = -1. Your friend says the vertex could be the point (0, 5). Is your friend correct? Explain. Question 78. CRITICAL THINKING Find the y-intercept in terms of a, p, and q for the quadratic function f(x) = a(x – p)(x – q). Question 79. MODELING WITH MATHEMATICS A kernel of popcorn contains water that expands when the kernel is heated, causing it to pop. The equations below represent the “popping volume” y (in cubic centimeters per gram) of popcorn with moisture content x (as a percent of the popcorn’s weight). Hot-air popping: y = -0.761(x – 5.52)(x – 22.6) Hot-oil popping:y = -0.652(x – 5.35)(x – 21.8) a. For hot-air popping, what moisture content maximizes popping volume? What is the maximum volume? b. For hot-oil popping, what moisture content maximizes popping volume? What is the maximum volume? c. Use a graphing calculator to graph both functions in the same coordinate plane. What are the domain and range of each function in this situation? Explain. Question 80. ABSTRACT REASONING A function is written in intercept form with a > 0. What happens to the vertex of the graph as a increases? as a approaches 0? Maintaining Mathematical Proficiency Solve the equation. Check for extraneous solutions. (Skills Review Handbook) Question 81. 3$\sqrt{x}$ – 6 = 0 Question 82. 2$\sqrt{x-4}$ – 2 = 2 Question 83. $\sqrt{5x}$ + 5 = 0 Question 84. $\sqrt{3x+8}$ = $\sqrt{x+4}$ Solve the proportion. (Skills Review Handbook) Question 85. $\frac{1}{2}$ = $\frac{x}{4}$ Question 86. $\frac{2}{3}$ = $\frac{x}{9}$ Question 87. $\frac{-1}{4}$ = $\frac{3}{x}$ Question 88. $\frac{5}{2}$ =-$\frac{20}{x}$ Quadratic Functions Study Skills Using the Features of Your Textbook to Prepare for Quizzes and Tests Core Vocabulary Core Concepts Section 2.1 Section 2.2 Mathematical Practices Question 1. Why does the height you found in Exercise 44 on page 53 make sense in the context of the situation? Question 2. How can you effectively communicate your preference in methods to others in Exercise 47 on page 54? Question 3. How can you use technology to deepen your understanding of the concepts in Exercise 79 on page 64? Study Skills Using the Features of Your Textbook to Prepare for Quizzes and Tests • Read and understand the core vocabulary and the contents of the Core Concept boxes. • Review the Examples and the Monitoring Progress questions. Use the tutorials at BigIdeasMath.com for additional help. • Review previously completed homework assignments. Quadratic Functions 2.1 – 2.2 Quiz 2.1 – 2.2 Quiz Describe the transformation of f(x) = x^2 represented by g. (Section 2.1) Question 1. Question 2. Question 3. Write a rule for g and identify the vertex. (Section 2.1) Question 4. Let g be a translation 2 units up followed by a reflection in the x-axis and a vertical stretch by a factor of 6 of the graph of f(x) = x^2. Question 5. Let g be a translation 1 unit left and 6 units down, followed by a vertical shrink by a factor of $\frac{1}{2}$ of the graph of f(x) = 3(x + 2)^2. Question 6. Let g be a horizontal shrink by a factor of $\frac{1}{4}$, followed by a translation 1 unit up and 3 units right of the graph of f(x) = (2x + 1)^2 – 11. Graph the function. Label the vertex and axis of symmetry. (Section 2.2) Question 7. f(x) = 2(x – 1)^2 – 5 Question 8. h(x) = 3x^2 + 6x – 2 Question 9. f(x) = 7 – 8x – x^2 Find the x-intercepts of the graph of the function. Then describe where the function is increasing and decreasing.(Section 2.2) Question 10. g(x) = -3(x + 2)(x + 4) Question 11. g(x) = $\frac{1}{2}$(x – 5)(x + 1) Question 12. f(x) = 0.4x(x – 6) Question 13. A grasshopper can jump incredible distances, up to 20 times its length. The height (in inches) of the jump above the ground of a 1-inch-long grasshopper is given by h(x) = –$\frac{1}{20}$x^2 + x, where x is the horizontal distance (in inches) of the jump. When the grasshopper jumps off a rock, it lands on the ground 2 inches farther. Write a function that models the new path of the jump. (Section 2.1) Question 14. A passenger on a stranded lifeboat shoots a distress flare into the air. The height (in feet) of the flare above the water is given by f(t) = -16t(t – 8), where t is time (in seconds) since the flare was shot. The passenger shoots a second flare, whose path is modeled in the graph. Which flare travels higher? Which remains in the air longer? Justify your answer. (Section 2.2) Lesson 2.3 Focus of a Parabola Essential Question What is the focus of a parabola? Analyzing Satellite Dishes Work with a partner. Vertical rays enter a satellite dish whose cross section is a parabola. When the rays hit the parabola, they reflect at the same angle at which they entered. (See Ray 1 in the a. Draw the reflected rays so that they intersect the y-axis. b. What do the reflected rays have in common? c. The optimal location for the receiver of the satellite dish is at a point called the focus of the parabola. Determine the location of the focus. Explain why this makes sense in this situation. Analyzing Spotlights Work with a partner. Beams of light are coming from the bulb in a spotlight, located at the focus of the parabola. When the beams hit the parabola, they reflect at the same angle at which they hit. (See Beam 1 in the figure.) Draw the reflected beams. What do they have in common? Would you consider this to be the optimal result? Explain. Communicate Your Answer Question 3. What is the focus of a parabola? Question 4. Describe some of the properties of the focus of a parabola. 2.3 Lesson Monitoring Progress Question 1. Use the Distance Formula to write an equation of the parabola with focus F(0, -3) and directrix y = 3. Identify the focus, directrix, and axis of symmetry of the parabola. Then graph the equation. Question 2. y = 0.5x^2 Question 3. -y = x^2 Question 4. y^2 = 6x Write an equation of the parabola with vertex at (0, 0) and the given directrix or focus. Question 5. directrix: x = -3 Question 6. focus: (-2, 0) Question 7. focus: (0, $\frac{3}{2}$) Monitoring Progress Question 8. Write an equation of a parabola with vertex (-1, 4) and focus (-1, 2). Question 9. A parabolic microwave antenna is 16 feet in diameter. Write an equation that represents the cross section of the antenna with its vertex at (0, 0) and its focus 10 feet to the right of the vertex. What is the depth of the antenna? Focus of a Parabola 2.3 Exercises Vocabulary and Core Concept Check Question 1. COMPLETE THE SENTENCE A parabola is the set of all points in a plane equidistant from a fixed point called the ______ and a fixed line called the __________ . Question 2. WRITING Explain how to find the coordinates of the focus of a parabola with vertex (0, 0)and directrix y = 5. Monitoring Progress and Modeling with Mathematics In Exercises 3–10, use the Distance Formula to write an equation of the parabola. Question 3. Question 4. Question 5. focus: (0, -2) directrix: y = 2 Question 6. directrix: y = 7 focus: (0, -7) Question 7. vertex: (0, 0) directrix: y = -6 Question 8. vertex: (0, 0) focus: (0, 5) Question 9. vertex: (0, 0) focus: (0, -10) Question 10. vertex: (0, 0) directrix: y = -9 Question 11. ANALYZING RELATIONSHIPS Which of the given characteristics describe parabolas that open down? Explain your reasoning. A. focus: (0, -6) directrix: y = 6 B. focus: (0, -2) directrix: y = 2 C.focus: (0, 6) directrix: y = -6 D. focus: (0, -1) directrix: y = 1 Question 12. REASONING Which of the following are possible coordinates of the point P in the graph shown? Explain. A. (-6, -1) B. (3, –$\frac{1}{4}$) C. (4, –$\frac{4}{9}$) D. (1, –$\frac{1}{36}$) E. (6, -1) F. (2, –$\frac{1}{18}$) In Exercises 13–20, identify the focus, directrix, and axis of symmetry of the parabola. Graph the equation. Question 13. y = $\frac{1}{8}$x^2 Question 14. y = –$\frac{1}{12}$x^2 Question 15. x = –$\frac{1}{20}$y^2 Question 16. x= $\frac{1}{24}$y^2 Question 17. y^2 = 16x Question 18. -x^2 = 48y Question 19. 6x^2 + 3y = 0 Question 20. 8x^2 – y = 0 ERROR ANALYSIS In Exercises 21 and 22, describe and correct the error in graphing the parabola. Question 21. Question 22. Question 23. ANALYZING EQUATIONS The cross section (with units in inches) of a parabolic satellite dish can be modeled by the equation y = $\frac{1}{38}$x^2. How far is the receiver from the vertex of the cross section? Explain. Question 24. ANALYZING EQUATIONS The cross section (with units in inches) of a parabolic spotlight can be modeled by the equation x = $\frac{1}{20}$y^2. How far is the bulb from the vertex of the cross section? In Exercises 25–28, write an equation of the parabola shown. Question 25. Question 26. Question 27. Question 28. In Exercises 29–36, write an equation of the parabola with the given characteristics. Question 29. focus: (3, 0) directrix: x = -3 Question 30. focus: ($\frac{2}{3}$, 0) directrix: x = –$\frac{2}{3}$ Question 31. directrix: x = -10 vertex: (0, 0) Question 32. directrix: y = $\frac{8}{3}$ vertex: (0, 0) Question 33. focus: (0, –$\frac{5}{3}$) directrix: y = $\frac{5}{3}$ Question 34. focus: (0, $\frac{5}{4}$) directrix: y = –$\frac{5}{4}$ Question 35. focus: (0, $\frac{6}{7}$) vertex: (0, 0) Question 36. focus: (-$\frac{4}{5}$, 0) vertex: (0, 0) In Exercises 37–40, write an equation of the parabola shown. Question 37. Question 38. Question 39. Question 40. In Exercises 41–46, identify the vertex, focus, directrix, and axis of symmetry of the parabola. Describe the transformations of the graph of the standard equation with p = 1 and vertex (0, 0). Question 41. y = $\frac{1}{8}$(x – 3)^2 + 2 Question 42. y = –$\frac{1}{4}$(x + 2)^2 + 1 Question 43. x = $\frac{1}{16}$(y – 3)^2 + 1 Question 44. y = (x + 3)^2 – 5 Question 45. x = -3(y + 4)^2 + 2 Question 46. x = 4(y + 5)^2 – 1 Question 47. MODELING WITH MATHEMATICS Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphin’s clicking sounds using computer models. The models originate the sounds at the focus of a parabolic reflector. The parabola in the graph shows the cross section of the reflector with focal length of 1.3 inches and aperture width of 8 inches. Write an equation to represent the cross section of the reflector. What is the depth of the reflector? Question 48. MODELING WITH MATHEMATICS Solar energy can be concentrated using long troughs that have a parabolic cross section as shown in the figure. Write an equation to represent the cross section of the trough. What are the domain and range in this situation? What do they represent? Question 49. ABSTRACT REASONING As \| p \| increases, how does the width of the graph of the equation y = $\frac{1}{4 p}$x^2 change? Explain your reasoning. Question 50. HOW DO YOU SEE IT? The graph shows the path of a volleyball served from an initial height of 6 feet as it travels over a net. a. Label the vertex, focus, and a point on the directrix. b. An underhand serve follows the same parabolic path but is hit from a height of 3 feet. How does this affect the focus? the directrix? Question 51. CRITICAL THINKING The distance from point P to the directrix is 2 units. Write an equation of the parabola. Question 52. THOUGHT PROVOKING Two parabolas have the same focus (a, b) and focal length of 2 units. Write an equation of each parabola. Identify the directrix of each parabola. Question 53. REPEATED REASONING Use the Distance Formula to derive the equation of a parabola that opens to the right with vertex (0, 0), focus (p, 0), and directrix x = -p. Question 54. PROBLEM SOLVING The latus rectum of a parabola is the line segment that is parallel to the directrix, passes through the focus, and has endpoints that lie on the parabola. Find the length of the latus rectum of the parabola shown. Maintaining Mathematical Proficiency Write an equation of the line that passes through the points.(Section 1.3) Question 55. (1, -4), (2, -1) Question 56. (-3, 12), (0, 6) Question 57. (3, 1), (-5, 5) Question 58. (2, -1), (0, 1) Use a graphing calculator to find an equation for the line of best fit. Question 59. Question 60. Lesson 2.4 Modeling with Quadratic Functions Essential Question How can you use a quadratic function to model a real-life situation? Modeling with a Quadratic Function Work with a partner. The graph shows a quadratic function of the form P(t) = at^2 + bt + c which approximates the yearly profits for a company, where P(t) is the profit in year t. a. Is the value of a positive, negative, or zero? Explain. b. Write an expression in terms of a and b that represents the year t when the company made the least profit. c. The company made the same yearly profits in 2004 and 2012. Estimate the year in which the company made the least profit. d. Assume that the model is still valid today. Are the yearly profits currently increasing, decreasing, or constant? Explain. Modeling with a Graphing Calculator Work with a partner. The table shows the heights h (in feet) of a wrench t seconds after it has been dropped from a building under construction. a. Use a graphing calculator to create a scatter plot of the data, as shown at the right. Explain why the data appear to fit a quadratic model. b. Use the quadratic regression feature to find a quadratic model for the data. c. Graph the quadratic function on the same screen as the scatter plot to verify that it fits the data. d. When does the wrench hit the ground? Explain. Communicate Your Answer Question 3. How can you use a quadratic function to model a real-life situation? Question 4. Use the Internet or some other reference to find examples of real-life situations that can be modeled by quadratic functions. 2.4 Lesson Monitoring Progress Question 1. WHAT IF? The vertex of the parabola is (50, 37.5). What is the height of the net? Question 2. Write an equation of the parabola that passes through the point (-1, 2) and has vertex (4, -9). Question 3. WHAT IF? The y-intercept is 4.8. How does this change your answers in parts (a) and (b)? Question 4. Write an equation of the parabola that passes through the point (2, 5) and has x-intercepts -2 and 4. Question 5. Write an equation of the parabola that passes through the points (-1, 4), (0, 1), and (2, 7). Question 6. The table shows the estimated profits y (in dollars) for a concert when the charge is x dollars per ticket. Write and evaluate a function to determine what the charge per ticket should be to maximize the profit. Question 7. The table shows the results of an experiment testing the maximum weights y (in tons) supported by ice x inches thick. Write a function that models the data. How much weight can be supported by ice that is 22 inches thick? Modeling with Quadratic Functions 2.4 Exercises Vocabulary and Core Concept Check Question 1. WRITING Explain when it is appropriate to use a quadratic model for a set of data. Question 2. Which is different? Find “both” answers. Monitoring Progress and Modeling with Mathematics In Exercises 3–8, write an equation of the parabola in vertex form. Question 3. Question 4. Question 5. passes through (13, 8) and has vertex (3, 2) Question 6. passes through (-7, -15) and has vertex (-5, 9) Question 7. passes through (0, -24) and has vertex (-6, -12) Question 8. passes through (6, 35) and has vertex (-1, 14) In Exercises 9–14, write an equation of the parabola in intercept form. Question 9. Question 10. Question 11. x-intercepts of 12 and -6; passes through (14, 4) Question 12. x-intercepts of 9 and 1; passes through (0, -18) Question 13. x-intercepts of -16 and -2; passes through (-18, 72) Question 14. x-intercepts of -7 and -3; passes through (-2, 0.05) Question 15. WRITING Explain when to use intercept form and when to use vertex form when writing an equation of a parabola. Question 16. ANALYZING EQUATIONS Which of the following equations represent the parabola? A. y = 2(x – 2)(x + 1) B. y = 2(x + 0.5)^2 – 4.5 C. y = 2(x – 0.5)^2 – 4.5 D. y = 2(x + 2)(x – 1) In Exercises 17–20, write an equation of the parabola in vertex form or intercept form. Question 17. Question 18. Question 19. Question 20. Question 21. ERROR ANALYSIS Describe and correct the error in writing an equation of the parabola. Question 22. MATHEMATICAL CONNECTIONS The area of a rectangle is modeled by the graph where y is the area (in square meters) and x is the width (in meters). Write an equation of the parabola. Find the dimensions and corresponding area of one possible rectangle. What dimensions result in the maximum area? Question 23. MODELING WITH MATHEMATICS Every rope has a safe working load. A rope should not be used to lift a weight greater than its safe working load. The table shows the safe working loads S (in pounds) for ropes with circumference C (in inches). Write an equation for the safe working load for a rope. Find the safe working load for a rope that has a circumference of 10 inches. Question 24. MODELING WITH MATHEMATICS A baseball is thrown up in the air. The table shows the heights y (in feet) of the baseball after x seconds. Write an equation for the path of the baseball. Find the height of the baseball after 1.7 seconds. Question 25. COMPARING METHODS You use a system with three variables to ﬁnd the equation of a parabola that passes through the points (−8, 0), (2, −20), and (1, 0). Your friend uses intercept form to ﬁnd the equation. Whose method is easier? Justify your answer. Question 26. MODELING WITH MATHEMATICS The table shows the distances y a motorcyclist is from home after x hours. a. Determine what type of function you can use to model the data. Explain your reasoning. b. Write and evaluate a function to determine the distance the motorcyclist is from home after 6 hours. Question 27. USING TOOLS The table shows the heights h (in feet) of a sponge t seconds after it was dropped by a window cleaner on top of a skyscraper. a. Use a graphing calculator to create a scatter plot. Which better represents the data, a line or a parabola? Explain. b. Use the regression feature of your calculator to ﬁnd the model that best ﬁts the data. c. Use the model in part (b) to predict when the sponge will hit the ground. d. Identify and interpret the domain and range in this situation. Question 28. MAKING AN ARGUMENT Your friend states that quadratic functions with the same x-intercepts have the same equations, vertex, and axis of symmetry. Is your friend correct? Explain your reasoning. In Exercises 29–32, analyze the differences in the outputs to determine whether the data are linear, quadratic, or neither. Explain. If linear or quadratic, write an equation that fits the data. Question 29. Question 30. Question 31. Question 32. Question 33. PROBLEM SOLVING The graph shows the number y of students absent from school due to the flu each day x. a. Interpret the meaning of the vertex in this situation. b. Write an equation for the parabola to predict the number of students absent on day 10. c. Compare the average rates of change in the students with the flu from 0 to 6 days and 6 to 11 days. Question 34. THOUGHT PROVOKING Describe a real-life situation that can be modeled by a quadratic equation. Justify your answer. Question 35. PROBLEM SOLVING The table shows the heights y of a competitive water-skier x seconds after jumping off a ramp. Write a function that models the height of the water-skier over time. When is the water-skier 5 feet above the water? How long is the skier in the air? Question 36. HOW DO YOU SEE IT? Use the graph to determine whether the average rate of change over each interval is positive, negative, or zero. a. 0 ≤ x ≤ 2 b. 2 ≤ x ≤ 5 c. 2 ≤ x ≤ 4 d. 0 ≤ x ≤ 4 Question 37. REPEATED REASONING The table shows the number of tiles in each figure. Verify that the data show a quadratic relationship. Predict the number of tiles in the 12th figure. Maintaining Mathematical Proficiency Factor the trinomial. (Skills Review Handbook) Question 38. x^2 + 4x + 3 Question 39. x^2 – 3x + 2 Question 40. 3x^2 – 15x + 12 Question 41. 5x^2 + 5x – 30 Quadratic Functions Performance Task: Accident Reconstruction 2.3–2.4 What Did You Learn? Core Vocabulary focus, p. 68 directrix, p. 68 Core Concepts Section 2.3 Standard Equations of a Parabola with Vertex at the Origin, p. 69 Standard Equations of a Parabola with Vertex at (h, k), p. 70 Section 2.4 Writing Quadratic Equations, p. 76 Writing Quadratic Equations to Model Data, p. 78 Mathematical Practices Question 1. Explain the solution pathway you used to solve Exercise 47 on page 73. Question 2. Explain how you used definitions to derive the equation in Exercise 53 on page 74. Question 3. Explain the shortcut you found to write the equation in Exercise 25 on page 81. Question 4. Describe how you were able to construct a viable argument in Exercise 28 on page 81. Performance Task Accident Reconstruction Was the driver of a car speeding when the brakes were applied? What do skid marks at the scene of an accident reveal about the moments before the collision? To explore the answers to these questions and more, go to BigIdeasMath.com. Quadratic Functions Chapter Review Describe the transformation of f(x) = x^2 represented by g. Then graph each function. Question 1. g(x) = (x + 4)^2 Question 2. g(x) = (x – 7)^2 + 2 Question 3. g(x) = -3(x + 2)^2 – 1 Question 4. Let the graph of g be a horizontal shrink by a factor of $\frac{2}{3}$, followed by a translation 5 units left and 2 units down of the graph of f(x) = x^2. Question 5. Let the graph of g be a translation 2 units left and 3 units up, followed by a reflection in the y-axis of the graph of f(x) = x^2 – 2x. Graph the function. Label the vertex and axis of symmetry. Find the minimum or maximum value of f. Describe where the function is increasing and decreasing. Question 6. f(x) = 3(x – 1)^2 – 4 Question 7. g(x) = -2x^2 + 16x + 3 Question 8. h(x) = (x – 3)(x + 7) Question 9. You can make a solar hot-dog cooker by shaping foil-lined cardboard into a parabolic trough and passing a wire through the focus of each end piece. For the trough shown, how far from the bottom should the wire be placed? Question 10. Graph the equation 36y = x^2. Identify the focus, directrix, and axis of symmetry. Write an equation of the parabola with the given characteristics. Question 11. vertex: (0, 0) directrix: x = 2 Question 12. focus: (2, 2) vertex: (2, 6) Write an equation for the parabola with the given characteristics. Question 13. passes through (1, 12) and has vertex (10, -4) Question 14. passes through (4, 3) and has x-intercepts of -1 and 5 Question 15. passes through (-2, 7), (1, 10), and (2, 27) Question 16. The table shows the heights y of a dropped object after x seconds. Verify that the data show a quadratic relationship. Write a function that models the data. How long is the object in the air? Quadratic Functions Chapter Test Question 1. A parabola has an axis of symmetry y= 3 and passes through the point (2, 1). Find another point that lies on the graph of the parabola. Explain your reasoning. Question 2. Let the graph of g be a translation 2 units left and 1 unit down, followed by a reflection in the y-axis of the graph of f(x) = (2x + 1)^2 – 4. Write a rule for g. Question 3. Identify the focus, directrix, and axis of symmetry of x = 2y^2. Graph the equation. Question 4. Explain why a quadratic function models the data. Then use a linear system to find the model. Write an equation of the parabola. Justify your answer. Question 5. Question 6. Question 7. Question 8. A surfboard shop sells 40 surfboards per month when it charges $500 per surfboard. Each time the shop decreases the price by $10, it sells 1 additional surfboard per month. How much should the shop charge per surfboard to maximize the amount of money earned? What is the maximum amount the shop can earn per month? Explain. Question 9. Graph f(x) = 8x^2 – 4x+ 3. Label the vertex and axis of symmetry. Describe where the function is increasing and decreasing. Question 10. Sunfire is a machine with a parabolic cross section used to collect solar energy. The Sun’s rays are reflected from the mirrors toward two boilers located at the focus of the parabola. The boilers produce steam that powers an alternator to produce electricity. a. Write an equation that represents the cross section of the dish shown with its vertex at (0, 0). b. What is the depth of Sunfire? Justify your answer. Question 11. In 2011, the price of gold reached an all-time high. The table shows the prices (in dollars per troy ounce) of gold each year since 2006 (t = 0 represents 2006). Find a quadratic function that best models the data. Use the model to predict the price of gold in the year 2016. Quadratic Functions Cumulative Assessment Question 1. You and your friend are throwing a football. The parabola shows the path of your friend’s throw, where x is the horizontal distance (in feet) and y is the corresponding height (in feet). The path of your throw can be modeled by h(x) = −16x^2 + 65x + 5. Choose the correct inequality symbol to indicate whose throw travels higher. Explain your reasoning. Question 2. The function g(x) = $\frac{1}{2}$∣x − 4 ∣ + 4 is a combination of transformations of f(x) = \| x\|. Which combinations describe the transformation from the graph of f to the graph of g? A. translation 4 units right and vertical shrink by a factor of $\frac{1}{2}$, followed by a translation 4 units up B. translation 4 units right and 4 units up, followed by a vertical shrink by a factor of $\frac{1}{2}$ C. vertical shrink by a factor of $\frac{1}{2}$ , followed by a translation 4 units up and 4 units right D. translation 4 units right and 8 units up, followed by a vertical shrink by a factor of $\frac{1}{2}$ Question 3. Your school decides to sell tickets to a dance in the school cafeteria to raise money. There is no fee to use the cafeteria, but the DJ charges a fee of $750. The table shows the profits (in dollars) when x students attend the dance. a. What is the cost of a ticket? b. Your school expects 400 students to attend and finds another DJ who only charges $650. How much should your school charge per ticket to still make the same profit? c. Your school decides to charge the amount in part (a) and use the less expensive DJ. How much more money will the school raise? Question 4. Order the following parabolas from widest to narrowest. A. focus: (0, −3); directrix: y = 3 B. y = $\frac{1}{16}$x^2 + 4 C. x = $\frac{1}{8}$y^2 D. y = $\frac{1}{4}$(x − 2)^2 + 3 Question 5. Your friend claims that for g(x) = b, where b is a real number, there is a transformation in the graph that is impossible to notice. Is your friend correct? Explain your reasoning. Question 6. Let the graph of g represent a vertical stretch and a reflection in the x-axis, followed by a translation left and down of the graph of f(x) = x^2. Use the tiles to write a rule for g. Question 7. Two balls are thrown in the air. The path of the first ball is represented in the graph. The second ball is released 1.5 feet higher than the first ball and after 3 seconds reaches its maximum height 5 feet lower than the first ball. a. Write an equation for the path of the second ball. b. Do the balls hit the ground at the same time? If so, how long are the balls in the air? If not, which ball hits the ground first? Explain your reasoning. Question 8. Let the graph of g be a translation 3 units right of the graph of f. The points (−1, 6), (3, 14), and (6, 41) lie on the graph of f. Which points lie on the graph of g? A. (2, 6) B. (2, 11) C. (6, 14) D. (6, 19) E. (9, 41) F. (9, 46) Question 9. Gym A charges $10 per month plus an initiation fee of $100. Gym B charges $30 per month, but due to a special promotion, is not currently charging an initiation fee. a. Write an equation for each gym modeling the total cost y for a membership lasting x months. b. When is it more economical for a person to choose Gym A over Gym B? c. Gym A lowers its initiation fee to $25. Describe the transformation this change represents and how it affects your decision in part (b). Leave a Comment	{"url":"https://bigideasmathanswers.com/big-ideas-math-algebra-2-answers-chapter-2/","timestamp":"2024-11-10T01:12:18Z","content_type":"text/html","content_length":"349214","record_id":"<urn:uuid:4d0d9a90-a325-40e0-8460-a307129b1c9c>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00697.warc.gz"}
AP Physics B & C Multiple Choice Practice Questions on Electrostatics “I never did a day's work in my life. It was all fun.” – Thomas A. Edison Questions in the section ‘electrostatics’ were discussed on many occasions earlier on this site. You may access them by clicking on the label ‘electrostatics’ below this post. Since the number of posts displayed per page is limited, you will have to use the ‘older posts’ button to access all the posts. All posts in this section can equally well be accessed by trying a search for ‘electrostatics’ using the search box provided on this page. Today we will discuss a few more multiple choice practice questions on electrostatics: (1) Point charges +q and –3q are arranged at points A and B on the x-axis (Fig.). At which point (or points) is the electric field due to this system of charges zero? (a) At two points on the x axis, one point to the right of the charge –3q and the other to the left of the charge +q. (c) Somewhere on the x axis to the right of the charge –3q. (d) Somewhere on the x axis, in between the two charges. (e) The electric field cannot be zero anywhere. The electric field lines due to a positive charge proceed radially outwards (diverge) from the charge where as the electric field lines due to a negative charge proceed radially inwards (converge) to the charge. At points on the x-axis lying in between A and B the fields due to these charges are directed along the positive x-direction. Therefore, the fields add up and the resultant field cannot be zero. But at points on the x-axis to the left of the charge +q, the fields are in opposite directions (along the negative x-direction due to the charge +q and along the positive x-direction due to the charge –3q) so that they can cancel at a point where the magnitudes of the fields due to the charges are the same. So the correct option is (b). [At points on the x-axis to the right of the charge –3q, the fields are in opposite directions (along the positive x-direction due to the charge +q and along the negative x-direction due to the charge –3q. But the two fields cannot cancel anywhere here since the magnitude of the field due to the charge –3q is greater than that due to the charge +q (since the charge –3q is nearer as far as points on the right of B are concerned] (2) A large flat plate is positively charged so that it has uniform surface charge density σ. If the electric field near the central region of the plate at a distance of 1 cm from the plate is 9 NC^ –1, what will be the electric field at a distance of 3 cm from the plate? (a) 81 NC^–1 (b) 27 NC^–1 (c) 9 NC^–1 (d) 3 NC^–1 (e) 1 NC^–1 The electric field due to the surface charge on the plate is normal to the surface of the plate. Since the plate is large, the electric field near the central region of the plate is uniform (with the electric field lines proceeding normal to the flat surface and therefore parallel). This means that the electric field at a point is independent of the distance of the point from the plate so that electric field at 3 cm from the plate is 9 NC^–1 itself. [For AP Physics C aspirants: To find the electric field near the surface of the charged plate, we can apply Gauss theorem and accordingly imagine a Gaussian surface shaped as a rectangular parallelepiped of cross section area A (Fig.). The electric field due to the surface charge on the plate is normal to the surface of the plate. Therefore the electric field is directed normal to the end faces of the rectangular parallelepiped so that the total electric flux through the closed suface (rectangular parallelepiped) is 2EA where E is the magnitude of the electric field. (The flux through the side surfaces of the parallelepiped is zero since the electric field is parallel to these surfaces). The total charge enclosed by the closed surface is σA. Therefore, by Gauss theorem we have 2EA = σA/ε[0] where ε[0] is the permittivity of free space. Therefore E = σ/2ε[0], which is independent of distance] (3) Charges +q, –q and –q are placed at the vertices of an equilateral triangle ABC as indicated in the adjoining figure. What is the direction of the net electric field at the central point P? (a) Along AP (b) Along PA (c) Along CP (d) Along BP (e) There is no field at P The direction of the electric fiel at P is the direction of the force acting on a test positive charge placed at P. The charge +q will exert a repulsive force on the test positive charge. This is irected along AP. The charges –q and –q at B and C will exert attractive forces along PB and PC respectively. These two forces being of equal magnitudes, their resultant will be directed along AP. Therefore the resultant electric field due to all the three charges will be along AP [Option (a)]. (4) Points 1, 2 and 3 lie on the axis of an electric dipole AB. Point 4 lie on the equatorial line (perpendicular bisector of AB) of the dipole. Out of the following choices which one correctly gives the directions of the electric fields at the points 1, 2, 3 and 4? When you place a positive test charge at point (1) the net force on it is repulsive since the charge +q of the dipole is nearer than the charge –q. The direction of the force (and the electric field) is therefore leftwards. At point (2) the charge +q exerts a repulsive force on the positive test charge where as the charge –q exerts an attractive force on it. Thus both forces act rightwards an hence the electric field at point (2) acts rightwards. At point (3) the net force on the positive test charge is attractive since the charge –q of the dipole is nearer than the charge +q. The electric field at point (3) is therefore leftwards. At point (4) the positive test charge is repelled by the charge +q and attracted by the charge –q. these forces are equal in magnitude and are inclined equally upwards and downwards respectively. Their resultant acts rightwards and hence the electric field at point (4) is rightwards. The above facts are correctly given in option (e). If you have a mental picture of the distribution of the electric field lines due to an electric dipole (See the figure below), you will be able to answer the above question in no time]. (5) In the above question, in the case of the points (1), (2), (3) and (4), where do you find zero electric potential? (a) Nowhere (b) At point (1) (c) At points (1), (2) and (3) (d) At points (2) and (4) (e) At point (2) Points (2) and (4) are equidistant from the charges +q and –q. These equal and opposite charges produce positive and negative potentials of equal values so that they cancel each other, giving rise to zero potential at points (2) and (4).	{"url":"http://www.apphysicsresources.com/2012/09/ap-physics-b-c-multiple-choice-practice.html","timestamp":"2024-11-08T04:12:12Z","content_type":"application/xhtml+xml","content_length":"111786","record_id":"<urn:uuid:7c48a878-29c7-423d-9012-0f61ae955a09>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00719.warc.gz"}
[QSMS Mini-course] Pablo Portilla cuadrado (University of Lille) Speaker : Pablo Portilla cuadrado (University of Lille) Place : 상산관 129동 406호 Schedule : 7/11 (Mon) Survival kit on plane curve singularities I 7/12 (Tue) Survival kit on plane curve singularities II 7/18 (Mon) Characterizing the geometric monodromy group of an isolated plane curve singularity 7/19 (Tue) A quadratic form associated with pseudo-periodic homeomorphisms arising from singularity theory (each day) 10:30 ~ 11:30, 11:45 ~ 12:45 TiTle : Survival kit on plane curve singularities I & II Abstract : The study of plane curve singularities is one of the most classical parts of singularity theory going back to Newton in the XVII century. When one studies complex polynomials in two variables, singularities appear in a very natural way. Although many times this topic is treated from an algebraic point of view, one quickly sees that it has many ties with low dimensional topology topics such as knot theory and mapping class groups. In this mini-course we will make a gentle introduction to singularity theory through the world of plane curves. We will focus on the topological aspect of singularities and we will mainly learn techniques through rich examples. By the end of the course we will be able to compute many invariants of a plane curve singularity and we will understand the topology around a singular point of an algebraic plane curve. In particular we will learn how to find parametrizations of each irreducible component of a plane curve singularity. We will see how these parametrizations can result very useful in computing the embedded topology of each branch and how each branch interacts with the rest. We will learn to find smooth models (resolve) of plane curve singularities by repeatedly blowing up the ambient space and, from the final picture, we will understand the topology of the Milnor fibration and its geometric monodromy. We will end the course by introducing the versal unfolding of a plane curve singularity and posing some questions that naturally emanate from it. Title : Characterizing the geometric monodromy group of an isolated plane curve singularity Abstract : In this talk we will explain an intrinsic characterisation of the geometric monodromy group of an isolated plane curve singularity as the stabiliser in the mapping class group of the Milnor fiber of the relative isotopy class of a canonical vector field. We will also discuss two interesting consequences of this result: an easy and efficient criterion for detecting whether a simple closed curve in the Milnor fiber is a geometric vanishing cycle or not, and the non-injectivity of the natural representation of the versal unfolding of the singularity. This is a joint work with Nick Salter. Title : A quadratic form associated with pseudo-periodic homeomorphisms arising from singularity theory Abstract : In this talk, we study the nilpotent part of a pseudo-periodic automorphism of a real oriented surface with boundary. We associate a quadratic form Q defined on the first homology group of the surface. Using some techniques from mapping class group theory, we prove that a related form is positive definite under some conditions that are always satisfied for monodromies of Milnor fibers of germs of curves on normal surface singularities. Moreover, the form Q is computable in terms of the dual resolution or semistable reduction graph. Numerical invariants associated with Q are able to distinguish plane curve singularities with different topological types but same spectral pairs. This is a joint work with L. Alanís, E. Artal, C. Bonatti, X. Gómez-Mont and M. González Villa.	{"url":"https://qsms.math.snu.ac.kr/index.php?mid=board_sjXR83&order_type=asc&listStyle=viewer&page=4&document_srl=2319&sort_index=regdate","timestamp":"2024-11-10T20:51:13Z","content_type":"text/html","content_length":"26832","record_id":"<urn:uuid:c33c2526-fe26-42a6-9ae2-4f145ae6be38>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00011.warc.gz"}
taw's blog I got my first delivery of parts, and I wanted to try testing if breadboard is a viable alternative to soldering, starting with switch board. The idea is very simple: • power lines on top of the breadboard are connected to +5V • power lines on bottom of the beadboard are connected to GND • there's direct connection from GND to bottom of every switch, using 8-wire cables • there's individual 8-wire cable with output from every line • there are individual resistors (I used 220 Ohm) connecting top of every switch with power line Here's a quick electric diagram of each of eventually 7x8 output lines: I can already see weakness of this design - I have 56 resistors to connect (7 switches of 8 each), but there's only 50 lines (10 groups of 5 each), which forces connecting them to lines under each other. As resistors have long leads, they end up touching each other, so testing shows that that this is already not working properly. Possible solutions: • get resistors with common terminal (like 8 resistors with common terminal), so that I'd only need 7 connections to power lines, not 56 – that was actually my original idea, and what I used in my original (soldered) design, but I strangely couldn't find any on amazon or other sites • cut resistor leads to smaller length – might still not be enough • use second board for just resistors, connect them like DIP elements • use fewer switches per breadboard to reduce crowding - it will still be awkward due to inconvenient 5-grouping on power lines, but presumably if I only had 5 switches, I could use two 5-groups per 8-switch There's one more minor issue - on these breadboards power lines are broken in half, so if I connect them I'd only have 93 out of 100 connection points (1 to get power in, 3x2 to connect the lines) and some extra awkward cabling. The plan right now is to have a working switch board (doesn't necessarily have to be 56-wide, 40-wide would be fine), and a diode-board. These were invaluable debugging tools during my first attempt. After magiccards.info got borderline abandoned, I wrote mtg.wtf as a much better search engine for Magic cards. There have been a few other attempts by other people, but they generally had extremely simple search functionality, so nothing worth writing about. A few days ago a new site came out - scryfall - which is at least seriously trying to support MCI-style syntax, so let's take a look. Basic design choices Let's compare MCI, MW, and SF: • All search engines treat every printing and every card part as a separate object • SF follows MW, and avoids polluting search results with non-English cards • SF unfortunately follows MCI and pollutes o: search with remainder text • SF includes nonstandard cards (like Planes) in all searches. MCI completely skips them. MW only searches for them if requested explicitly (by t:* or by specific search like t:plane). • SF decided to skip un-cards. MCI has them, and MW not only has them, it even has a lot of special queries (like for fractional cmc) which only makes sense for un-cards. • I have no idea why the hell SF included this. Is that some joke, or a phantom card? I feel fairly ambiguous about including nonstandard cards by default, and perhaps SF's simple approach is better. As for everything else, they'd probably be better off matching MW. Search engine issues I tried to run searches from their syntax example page and compare them with what mtg.wtf returns. Their results had a lot of bugs, such as: • wrong cmc for all meld cards • wrong cmc for some DFC cards • many cards wrongly tagged as is:commander, like Brisela, Voice of Nightmares, Kenzo the Hardhearted, or Ormendahl, Profane Prince. They also made some really weird design choices, which I'd honestly just call bugs, as all of them make searching less useful: • color identity search being >=, while what you want pretty much every time is <= - you're generally filtering for cards fitting specific commander, not the other way around • mana search being >= on symbols, so if you search m:4 it matches {4}{G} but not {5}. That's weird as hell, as the natural search would be equality, and failing that at least treating {4} as {1} • Weirdly they decided that cards with changeling should be returned for searches for all creature/tribal types. So if you're searching for monkeys, you get 1 monkey and 30 changelings. • cards like conspiracies are listed as "banned" instead of simply excluded from all formats Some of their choices are probably fine either way, but MW generally follows MCI in such borderline cases: • is:timeshifted changed its meaning from MCI, and SF is:colorshifted does what MCI is:timeshifted would. • color search being "and" instead of "or" like MCI/MW. So c:rg searches for cards which are red and green, as well as any additional colors. This is easily achieved on MCI/MW with search for c:r • they treat 2015 frame update as different frame type, which MCI/MW doesn't SF doesn't have any of MW's extensions. First such limitation I ran into is that there's no way to search for split cards like Fire // Ice or t:creature // t:planeswalker. They added a bunch of search aliases like color:red for c:r - I looked through the list, and I added some of them to MW as well, because there's pretty much no cost. mtg.wtf's codebase is all open source, so I'd recommend them to just take my test suite, and try to make theirs work better. Extra features The most ambitious feature they have is that they want to instantly include cards from upcoming sets as they are revealed, not only after set appears on Gatherer. This is sweet, and definitely seems like way too much work for me at mtg.wtf. They have card price integration, which I still haven't added, as all card pricing information seems to be hidden behind private APIs. They have online API, which I guess I could add as well, but you can just download the code from github, and run it all locally, without even bothering with the API. I could add API to MW quite easily too, but it would be useful to do some performance testing first, as APIs often end up having order of magnitude more requests than real users. SF has much better feedback for search query syntax errors than MW. That's definitely a good area of improvement. On the other hand their spelling correction is awful - compare SF with MW. MW has been rather conservative with website design, and SF is trying something much more ambitious. A while ago I wrote about how to analyze binary file formats. Video games have a ton of custom binary file formats, and to mod them I kept writing parsers, which were in a way very similar. All parsers were very similar in form, but they varied in too many details to make it possible to extract any viable gem from that. So let's write a parser. Just read the whole file Even if file is fairly big, it's probably still far easier to just read it all in one go, and save yourself from the pointless file I/O. require "pathname" class FooParser def initialize(path) @path = Pathname(path) @data = @path.open("rb", &:read) @ofs = 0 We're saving the @path mostly to make exception messages we'll throw more meaningful. @data is all file's contents - and we read it in binary mode ("rb") to deal with binary vs Unicode and Windows silliness. @ofs is current offset, as we'll be processing data mostly in linear way. Some common helper functions These aren't necessary for all parsers, but it's fairly common to see code like this: class FooParser def bytes_left @data.size - @ofs def eof? @data.size == @ofs def fail!(message) raise "#{message} at #{@path}:#{@ofs}" Such functions aren't really doing parsing work, they're mostly there for debugging and for sanity checks. Get some data Now let's get some data: class FooParser def get(n) fail! "Trying to read past end of file" if bytes_left < n result = @data[@ofs, n] @ofs += n Most files are byte-oriented, and going through a helper function to get the next few bytes and manage offset and end of file will save us complexity elsewhere. This kind of function is also a great place for cases where file format is unusual somehow. Vast majority of formats are byte-oriented and fit in memory just fine, but if your format in too big, or uses individual bits, or does anything else weird, you can generally encapsulate such logic in get method - as long as @ofs uniquely describes current location in the file. Get integers Most formats are full of numbers and strings, and it's useful to write get methods for all of them. Let's start with Integers as they're easiest. I generally use concise byte count convention (so get_i4 means get signed integer with 4 bytes), but more verbose bit-based naming (like get_i32 or even get_int32) might be more to your liking. For most formats there's standard #unpack for them, so their unpackers are very simple - usually the only difference is right unpack string based on big vs small endianness of your format: class FooParser def get_u1 def get_u2 def get_u4 def get_i4 Very rarely file format uses more unusual number like 3-byte or variable length integer. Their get_* methods will look different from format to format, but you should generally be able to encapsulate Here's an examples - for 24-bit numbers we can just pad them with extra byte (0 for unsigned, either 0 or 255 for signed), and use proper unpack string for 32-bit numbers: class FooParser def get_u3 def get_i3 s = get(3) prefix = (s[0].ord >= 128 ? "\xFF".b : "\x00".b) Usually you can either add some padding, or just read them byte at a time and do some math to get the right number. Get floats This is slightly more complicated for two reasons - first the most common format in files is single precision, but Ruby uses double precision. Unpacking floats generates questionable extra precision: [0.1].pack("f").unpack("f")[0] #=> 0.10000000149011612 Especially if you plan to present the result to users, we often don't want that - we want the "nicest looking" double precision number which still decodes to the same single precision number. Now I'm sure there's some more "precise" algorithm, but this prettification method worked well: class Float def pretty_single result = round(6) return result if [self].pack("f") == [result].pack("f") What we do here is round it to 6 decimal places, check if it equals self when converted to single precision, and if so, return rounded result, otherwise return self. It works with infinities, NaN, -0 and all other weirdness. With that it's easy to write single precision float getter: class FooParser def get_flt Second problem is that Ruby unpack still lacks half-precision floats, which are extremely popular in GPU world, so any data destined to go to GPU often uses it - or just formats trying to save on In such case, just get_u2 and do bit manipulation yourself. Get strings Strings are just as ubiquitous as numbers, but there's a few more formats, including: • character count (ofter u2, 1 byte characters), followed by ASCII characters - get(get_u2) • character count (ofter u2, 2 byte characters), followed by UTF-16 characters - get(get_u22).unpack("v").pack("U") • NUL-terminated ASCII / UTF-8 - result = ""; result << c while (c = get(1)) != "\x00"; result • Constant size ASCII field (here 256 1-byte characters), padded by NULs - get(256).sub(/\x00\z/, "") • Constant size UTF-16 field (here 256 2-byte characters), padded by NULs - get(512).pack("v").unpack("U").sub(/\x00\z/, "") Just create appropriate get_str method based on whichever encoding your format uses. It's not uncommon for a single file format to have more than one string encoding - in such case create multiple such methods, or make it accept some argument to switch between them. Get individual data structures The generic part of the parser is done, so now for any data structure in your format you need to write appropriate parsing method, returning some Hash, Array, or proper object depending on the class FooParser def get_vector3d x = get_flt y = get_flt z = get_flt {x: x, y: y, z: z} For more concise code you can often shortcut this thank to ruby evaluating arguments left to right (like most languages nowadays, but there were dark times when undefined or backwards evaluation conventions existed too): class FooParser def get_vector3d {x: get_flt, y: get_flt, z: get_flt} Complete the parser And the last part is completing the parser. If the whole file consists of same data structures every time, just write some kind of get_everything following the same pattern and you're done. Even then I'd recommend adding something like fail! "Parsing done, but #{bytes_left} bytes left" unless eof? sanity check just to be sure format is what we expected it to be - extra garbage bytes generally indicate that file is not quite in formats expected. Of course things are rarely quite as simple. It's very common for file formats to have structure like: • header starting with some magic • header then includes some global data and counts for data structures to follow • after that individual data structures follow, based on data in the header Example parser To avoid complexity of real formats, let's try a fictional format with kittens and puppies: • magic marker "CUTE" • u4 number of kittens • u4 number of puppies • each kitten has star rating (float), number of lives left (u4) and photo url (str) • each puppy has star rating (float) and photo url (str) class FooParser def get_kitten { rating: get_flt, lives_left: get_u4, url: get_str} def get_puppy { rating: get_flt, url: get_str} def parse! fail! "Wrong magic number" unless get(4) == "CUTE" kitten_count = get_u4 puppy_count = get_u4 result = { kittens: kitten_count.times.map{ get_kitten }, puppies: puppy_count.times.map{ get_puppy }, fail! "Parsing done, but #{bytes_left} bytes left" unless eof? Offset-based formats OK, that's one easy file format, but what if instead of data structures following each other, header contains a list of offsets instead, and data structures are at positions indexed. That's going to take some jumping around, so let's write a helper for that: class FooParser def at_ofs(ofs) saved_ofs, @ofs = @ofs, ofs @ofs = saved_ofs Then it's fairly straightforward. In formats like that you usually won't end at end of file when you finish parsing, so that step is not necessary. Let's say our format is: • magic marker "CUTE" • u4 number of kittens • that many times u4 offset to kitten data structure (relative to beginning of file) • (rest of the file, presumably containing kitten data) class FooParser def parse! fail! "Wrong magic number" unless get(4) == "CUTE" kitten_count = get_u4 kittens = kitten_count.times.map do at_offset(get_u4) { get_kitten } {kittens: kittens} There are weirder data structures, like offsets relative to current location etc. You can generally keep all the offset mangling in helper functions and keep your parsing code high level. This is more a debugging thing than something you'll need to do often in actual parsing, but sometimes in your pry session you'd like to see if what's following is a kitten without affecting current parser state. It's very easy: class FooParser def lookahead saved_ofs = @ofs @ofs = saved_ofs Then in your pry session just try lookahead{ get_kitten } and it will give you a kitten (or throw an exception). Writing Ruby-based parsers following patterns described in the post have been far more convenient and flexible than anything else I tried, but there are limitations: • you need to have some clue about the format, or at least data structures at its beginning - there's some debugging helpers, but no autodetection, and the only "partial parsing" you can conveniently do is for beginning of the file - if you know some data structures in the middle of the file, it will still be hard to find them and partially decode them without knowing the rest of the format • it's inherently one-way - you'll need to write a separate encoder, even though some clever DSL might have given you 90% of it for free. I found that overhead of highly abstracting DSLs is generally much higher than just writing it twice, and it's relatively easy to test that they match by round trip testing - just grab some samples, and check if decoding followed by encoding gets you the sample back. • its performance is OK, but not amazing - we're working with very high level language, and doing byte manipulation with a lot of layers of abstraction above it - it's actually quite surprising how fast it works, but it's still nowhere near as fast as a parser written in very low level language • it's designed for full parsing in one go, not random access - this is mostly performance issue, but if you want to just read (let alone change) a single kitten in file with thousands, this pattern won't support you • if the format is crazy complex, you'll probably need a lot more sophisticated parser - this pattern is great for simple to moderately complex formats Website speed was one of the most common complaints about mtg.wtf, so I decided to do something about it. It won't be necessary, but if you want more background, you can read about architecture of mtg.wtf in my previous post. Verify the problem The site seemed "fast enough" to me, but multiple users complained about its performance, so presumably there was something real about it. I still wanted to make sure. It's important to verify that the problem you're trying to fix is real and on your side, as to not waste time fixing problems which might be caused by someone's crappy mobile connection or ISP throttling. I checked Rails logs, and indeed - timing I've seen there were pretty poor. There wasn't even much need for statistical analysis - very simple queries shouldn't routinely took ~1000ms. Have a test suite Before I started any performance work, I needed to have a test suite to validate that I'm not breaking anything. Fortunately mtg.wtf was as TDD as it gets, and had very comprehensive tests - even if I'm retrospectively somewhat regretting using minitest for that. If you don't have good test suite, don't despair - for optimizations you just need to find a reasonably representative sample of inputs (which you can use logs for), and record current version's outputs for them. If something broke in process, you'll get different results, so you'll instantly know. It's not as good as dedicated test suite, as your random sample probably lacks important edge cases a proper test suite would generally have, but you get 80% of value for 20% of effort, and you can add a few test for edge cases as you go. Generate a benchmark This was easy enough - I downloaded logs, extracted list of queries from them, took a random sample, and tested time per request. The best thing about this set was that I could very easily generate new benchmarks for specific types of queries with just grep - so when optimizing let's say card type searches, I can look for t:, which will give a much more accurate result than just throwing everything at it. (assuming my optimizations don't affect other query types of course) As secondary benchmark I also recorded time to run the test suite. I didn't expect it to be super sensitive measurement, but it's nice to have extra validation for zero effort, and I was going to run the tests a lot anyway. A small complication for any kind of benchmarking is that you want your computer to not be overly busy, or it will contaminate the results. It doesn't need to be completely idle, as computers have multiple cores and you'll generally be using only one core, but I closed things like Chrome and used my other computer for sucht things for a while. This is optional, and profiling tools in ruby are fairly weak and awkward, but I ran ruby-prof anyway to get some idea about code hot spots. It would identify which parts of the code were taking the most time, but it's mostly there to generate some suggestions. Precompute data Shockingly the biggest hot spot was very simple query ConditionExact, which corresponds to querying for exact card - with queries like !goblin guide or !Far // Away. The query was actually very slow, as it was going through entire database, and doing something like this: • go through the whole database, every card printing • take query, downcase, fix unicode, fix spacing • take card.name, downcase, fix unicode, fix spacing • if they're the same, it's a match That was really slow, and also quite silly. Card names don't have spacing problems (like double spaces between words), and we're already fixing unicode silliness like the "Æ" ligature when we load the database. As for the query, we can precompute this data when we parse it and create Condition object. It still needed the card name downcase step as card name was something like Goblin Guide, but it needed to match goblin guide, GOBLIN GUIDE and whichever other capitalization people use. So the algorithm became: • go through the whole database, every card printing • take preprocessed query • take card.name, downcase • if they're the same, it's a match That's still fairly inefficient, but it skips huge amount of pointless string manipulation. Similar preprocessing was later applied to a lot of other conditions. Separate common and uncommon cases Going back to ConditionExact, it was actually two different queries: • exact card name - like !Goblin Guide • multipart card name - like !Far // Away The multipart case was much more complex, as search engine represents every part of a multipart card as a separate object, so it needed somewhat complex logic to handle this. So I moved all rare and complex code to ConditionExactMultipart and I just had the commond and simpler case left to optimize. In a few other cases I set a flag if certain complex processing was needed. For example we support queries like o:"when ~ enters the battlefield", where "~" matches name of the card - so for example it matches Zealous Conscripts as it contains text "When Zealous Conscripts enters the battlefield, ...". Such queries require more complex logic than most o: (card text) queries, which just look for same text every time, and can do more preprocessing. In this case we set a flag in ConditionOracle constructor and then follow different logic based on that flag. This optimization only makes sense when simpler condition is also the common one - if most cases are complex, you're not really gaining much by splitting them. Use indexes Most queries use ConditionSimple, which just tests card printings one at a time with match? method. The alternative is for condition to process whole database and generate Set of results in one go. These two modes are combined by he most common ConditionAnd to first get all Sets, take their intersection, and then filter them with each ConditionSimple one at a time. Direct result Set generation was already used for a few queries already - like searching for cards printed in a specific edition, or specific block. I added that to format search as well, as f:standard is reasonably common phrase in queries which benefits a lot from this kind of early culling. Bigger formats like f:modern or f:commander didn't significantly benefit from this optimization, but they didn't seem to suffer either, so I applied it everywhere. Of course the biggest beneficiary of direct access was ConditionExact which got a downcased card name index, and can now result results almost instantly. I didn't add any more indexes as ruby is very memory hungry and keeping memory use low is very important. Other queries were either much less common or wouldn't benefit anywhere near as much. Optimize memory use I wanted to take a quick go at reducing memory use, unfortunately ruby memory profiling tools are still very poor, so I just did a few intuitive things like removing unnecessarily duplicated data. I pondered going further, but speed improvement I got for random sample of queries were already huge. I didn't need anything complex like adding caching, getting bigger box, trying JRuby, or moving search engine to external service. Verify the solution Even though changes looked really good in benchmark mode, it's important to verify them in production. So I checked the results, and indeed vast majority of requests are fast now. There's a few which are still somewhat slow - like for example someone trying to get 52nd page of result of all cards in EDH, but it's a reasonably safe bet that most of such weird requests are made by bots. Overall, it's been a fairly straightforward and successful process. There's nothing revolutionary here, it's a reasonably straightforward design. All the code discussed can be seen in its repository. What are we searching? We're searching "cards", but that's not specific enough, as there are two big complications: • Some cards have multiple printings • Some cards have multiple parts So we need to decide if our searchable object is: • one part, one printing • one part, all printings • all parts, one printing • all parts, all printings Far // Away is an example of multipart card Vast majority of cards have only one part, and a lot of the time card's properties are the same between printings, so we could get away with other choices, or even inconsistent semantics, but I've chosen to operate on most granular "a single part of a single printing of a card". Raw data comes mostly from mtgjson, but first step is converting into a more usable form, which is actually just more json. I keep both raw and processed json files in repository, mildly annoying github, but in this case it's best practice as tests can't run without that, so code is incomplete without those jsons. Indexer does some transformations and validations, and groups data by properties which should be same between cards (like name, text, cost, color) and those which can vary (like artist, rarity, flavor text). When I started the project mtgjson data was of high quality, but it got a lot worse since it got new maintainers, so now I need to do a lot more fixing (and reporting those bugs upstream did Every now and then I feel like I should just fork mtgjson and fix all those issues, but it's a pile of javascript and duct tape, so I mostly hope they get their act together again. Because indexer started as very simple script and accumulated hacks over time (mostly due to deteriorating mtgjson quality), it's the ugliest part of the codebase. It has no dedicated tests, but as the whole test suite is operating on real data, any bug in indexer or mtgjson is likely to be picked by tests down the line. Loading data The library loads data from processed json files and transforms them into in-memory representation of Ruby objects. There's no dedicated database or anything like that - we're doing everything There's currently 16686 cards and 31648 printings, so it's not tiny dataset, but it's not unreasonably huge for this fairly naive approach to work. Query Parser We parse any query with StringScanner - which is one of the least known parts of ruby standard library, generating Query object. Query object contains a tree of Condition objects corresponding to the query. In addition to searching Query object is also responsible for sorting results (by name, most recent etc., with sort: operator) and for time travel. Yes, time travel - I find it occasionally useful to sometimes search for results as if I was searching at particular date in the past - so cards not printed at that time are not in search results, and format legalities are changed accordingly. This isn't literally going into the past, as we're not trying to do anything like updating Oracle text to old wording (which wouldn't be all that helpful), but that's how you can search what to play when you somehow get to play flashback Innistrad Standard. time: operator is on query level, so you can't do cute things like asking for cards legal in both Ravnica Standard and Return to Ravnica Standard. Condition objects must implement #search(db) method which takes database and returns Set of matching card printings. This probably seems like a weird interface, and most conditions (those returning true when asked #simple?) also implement secondary interface of #match?(card_printing) returning true or false and avoiding allocations of intermediate Sets. ConditionAnd, ConditionOr, and ConditionNot use one or the other API depending on type of their subconditions. The reason for this design is that some subqueries ask about other part of the card, or other printing. For example you can check for cards printed in both M10 (Magic 2010) and M11 (Magic 2011) by e:m10 alt:e:m11. Doing recursive search and checking all subconditions would be exponentially slow in the worst case, and this design is always linear is query size. Searching for edition (e:) and block (b:) always return small number of results, and we already have to maintain set data, so we reuse it as index and return small result Sets from them. Other queries don't use any indexing and just check cards one by one. For most conditions either all printings match a query or none do, so special case for conditions which don't deal with anything printing-specific could potentially speed up a lot of queries. On the other hand while some cards have crazy number of printings, average is just 1.9 printings/card, so it's hard to tell if such savings would be worth added complexity. Of course more indexes and more sophisticated query optimizer would be possible - or even using some dedicated search engine like solr. This didn't seem necessary due to relatively small amount of data. Fortunately the search engine has very extensive tests, so if I ever feel like developing one, it would be reasonably easy to do so safely. Spelling correction Many Magic cards have names which are very easy to misspell. How do I spell this exactly? QueryParser deal with it - if search returns zero results, it sets fuzzy flag on Conditions and retries the whole search. A few conditions will autocorrect your query, and any such autocorrection are logged and displayed with search results. This two step process (as well as diacritics stripping and very limited amount of stemming) deals with most misspelled searches with good usability while keeping false positives to very low level. Results coalescence At this point we get a sorted list of printings, which is not quite what we want to display - all printings of the same card need to be merged (which is just .group_by(&:name)) - and since we'll be displaying card picture from specific printing we also want to choose the most appropriate one. The algorithm for that: • choose only from matching printings • prefer those with card picture (small number of rare promos don't have pictures) - that's a frontend consideration database has no idea about • otherwise use order returned by search engine, which is: □ whichever order was explicitly requested if any □ name in alphabetical order □ Standard-legal sets first □ most recent first After that we paginate the results. Future direction for mtg.wtf The most common requests are: • improving website performance • adding card pricing information via some third party API • advanced search form Advanced search form is a UI problem, for which I don't have a solution yet, as all advanced search forms are atrocious, leave most possible options out, or both. Third party API for pricing ended up more complex than I thought, but I'll probably get there at some point. Performance complaints probably mean that current architecture could use some improvements after all. It seems fast enough to me, but possibly that's not good enough. Solving Sudoku is a bit like FizzBuzz for constraint solvers, but since Z3 is very poorly known, and Z3 for ruby has few users other than me, I want to write a series of posts explaining various Z3 techniques, starting from very simple problems. Parsing Sudoku Before we get to Z3, let's read test data. A nice format for sudoku would be a text file like this: _ 6 _ 5 _ 9 _ 4 _ 9 2 _ _ _ _ _ 7 6 _ _ 1 _ _ _ 9 _ _ 7 _ _ 6 _ 3 _ _ 9 _ _ _ _ _ _ _ _ _ 3 _ _ 4 _ 1 _ _ 7 _ _ 6 _ _ _ 7 _ _ 2 4 _ _ _ _ _ 6 5 _ 9 _ 1 _ 8 _ 3 _ Where _s represent empty cells, and numbers represent pre-filled cells. Fairly straightforward code like this can parse it to 9x9 Array of Arrays: File.read(path).strip.split("\n").map do \|line\| line.split.map{\|c\| c == "_" ? nil : c.to_i} Getting us data structure like this: [[nil, 6, nil, 5, nil, 9, nil, 4, nil], [9, 2, nil, nil, nil, nil, nil, 7, 6], [nil, nil, 1, nil, nil, nil, 9, nil, nil], [7, nil, nil, 6, nil, 3, nil, nil, 9], [nil, nil, nil, nil, nil, nil, nil, nil, nil], [3, nil, nil, 4, nil, 1, nil, nil, 7], [nil, nil, 6, nil, nil, nil, 7, nil, nil], [2, 4, nil, nil, nil, nil, nil, 6, 5], [nil, 9, nil, 1, nil, 8, nil, 3, nil]] Z3 workflow First, we need to get the solver: solver = Z3::Solver.new After that we feed it with a bunch of formulas with solver.assert formula. How would we describe sudoku problem in plain English? • There are 9x9 integer variables • Each of them is between 1 and 9 • They correspond to prefilled data, unless that data is nil • Each row contains distinct values • Each column contains distinct values • Each 3x3 square contains distinct values Once we tell Z3 about that, we check if our formulas are solvable with solver.check == :sat, and if it so, get model with solver.model - I feel those two steps should probably be refactored into one, but let's leave it for now. Model can be then accessed with model[z3_variable] syntax to get our answers. So let's get to it! Creating variables There's nothing special about Z3 variables, they're sort of like ruby Symbols with associated types. So we could build our formulas with names like Z3.Int("cell[4,8]") - such name is just for our personal use, and doesn't mean cells form an array or anything. However, since we'll be referring to the same 9x9 variables all the time it's probably useful to save them to an Array of Arrays. cells = (0..8).map do \|j\| (0..8).map do \|i\| Setting possible values All variables are between 1 and 9, which is very easy to tell the solver about: cells.flatten.each do \|v\| solver.assert v >= 1 solver.assert v <= 9 Setting prefilled variables Telling solver that Z3 Int variable is equal to some ruby Integer is completely straightforward: cells.each_with_index do \|row, i\| row.each_with_index do \|var, j\| solver.assert var == data[i][j] if data[i][j] All rows contain distinct values If we relied on basic operations, we might have to give Z3 a lot of inequalities per row, fortunately there's Z3.Distinct(a,b,c,...) formula, which handles this very common case. It makes it really easy: cells.each do \|row\| solver.assert Z3.Distinct(row) All columns contain distinct values We can use Array#transpose to flip our multidimensional array, and do the same thing we did for rows: cells.transpose.each do \|column\| solver.assert Z3.Distinct(column) All square contain distinct values This is a bit more complex rearrangement, but it's all pure ruby, with Z3 getting very similar looking formula in the end: cells.each_slice(3) do \|rows\| rows.transpose.each_slice(3) do \|square\| solver.assert Z3.Distinct(square.flatten) By the way, you should really take a look at Enumerable API, it contains a lot of useful methods which will save you a ton of time. Get the model and print it And we're basically done: raise "Failed to solve" unless solver.check == :sat model = solver.model cells.each do \|row\| puts row.map{\|v\| model[v]}.join(" ") Getting the answer we want: Avoid temptation to optimize Everything we did here was so ridiculously straightforward - we skipped even the most obvious shortcuts. For example why the hell did we assert that cells are between 1 and 9 even for cells whose value we know perfectly well? And why did we even create variables for them if we know their value already? If we coded any kind of manual sudoku solver, we'd probably start with those. It turns out Z3 really doesn't care about such optimizations, and will solve your problem just as efficiently either way - but by "optimizing" your code will become more complicated, and there's a good chance you'll make an error trying to "optimize". That's not to say Z3 is made of magic, and that there are no cases where you can help it - but that's much more likely to be by restating a problem in a different way than by some microoptimizations. Some pitfalls One small pitfall to remember is that Z3 values - including those returned by solved models - override all operators including == so you can't check if for example model[Z3.Int("x")] == 5 - that will just create a Z3 Bool expression. This is necessary behaviour for some more complex use cases, but for the simplest case you'll generally want to #to_s whatever you get out of the model and go on from there. API is subject to change Some details will probably change in future versions to simplify things - especially everything from solver.check onwards, which will probably receive a simpler API for the most common case, but existing one will still be supported as it's necessary for some more complex situations. Integers variables constrained to specific range are another commonly used pattern which could use some shortcuts. Z3 is crazy powerful This was a very simple example. You could probably write a sudoku solver yourself - even if it'd take a lot more time, and would probably perform a lot worse than Z3. This manual approach doesn't scale - doing much bigger and much more complex problems with a constraint solver is as literally fast as just writing the constraints, while doing it manually constraint list is barely a starting point, and naive approaches get exponentially slow almost right away. Due to unfortunate accidents of programming history constraint solvers got relegated to an obscure niche, but they really ought to be a tool in every good programmer's toolkit, and once you learn them you'll find applications for them all the time. Wouldn't it be awesome if you could just describe a problem to the computer, like let's say a sudoku, and it would find the answer for you? That was the premise of "logic programming" in 1970s and 1980s, which was also one of many cases where Japan tried to do something else than everybody else, and failed, but it's not a post about Logic programming suffered a lot worse than other paradigms. Lisp, Smalltalk, Perl, and friends left rich legacy of features for future programming languages to mine, but Prolog variants were all one big dead end. Which is a bit of a shame, as some problems are really best coded by giving computer a list of constraints, and telling it to have a go at it, and it's very difficult to write a decent custom algorithm for them. Technically you could use constraint solver libraries even without logic programming, but they were mostly only available in obscure Lisp / Prolog dialects, hard to compile on modern systems, barely documented, and/or extremely limited. This somewhat changed with Z3 by Microsoft Research, which even got rudimentary Python interface. But while Python is tolerable, I got tired of all the self. nonsense, and I wanted a nice Ruby DSL, so I wrote Ruby bindings. You can install them as z3 gem but first you need z3 library itself (brew install z3 or whatever works on your system). If you want a quick look, check examples folder. If you want longer explanation, let's keep going. Basic model The basic Z3 workflow is: • create solver with Z3::Solver.new • create a bunch of formulas, generally starting with variables like Z3.Int("a"), Z3.Bool("b") etc. - formulas are independent of any solver, they're basically symbol trees. • assert some facts about those variables, like solver.assert Z3.Int("a") == Z3.Int("b") + Z3.Int("c") • ask solver to check if your set of formulas is satisfiable with solver.check. If it returns :sat, you're good to go. • get Z3::Model with solver.model • ask model for value of various variables with queries like model[Z3.Int("a")] etc. Let's go deeper, one step at a time. Values in Z3 all belong to "Sorts" which are sort of like types. To create a Sort object, just instantiate its class, like Z3::BoolSort.new, then you can create relevant object like Z3::BoolSort.new.var("my_var") or Z3::IntSort.new.from_const(5). This seems like unnecessary indirection, and it sort of is for most common sorts, but there are fancier ones where it's necessary. Some of the sorts are: • Z3::BoolSort.new - boolean variables • Z3::IntSort.new - integers, unlimited precision • Z3::RealSort.new - real numbers, unlimited precision • Z3::BitvecSort.new(size) - bit vector sorts, of size bits • Z3::FloatSort.new(esize, ssize) - floating point sort of esize exponent bits and ssize significand bits • Z3::RoundingModeSort.new - floating point rounding mode sort • Z3::SetSort.new(elemement_sort) - set sort of elements of elemement_sort sort • Z3::ArraySort.new(key_sort, value_sort) - associative array sort with keys of key_sort, and values of value_sort • there are some more sorts in Z3 which are not yet implemented For vast majority of uses you want Bool and Int sorts, for physics style calculations you want Real sort (generally don't use Floats for them). They have decently completely and nice APIs. Bitvec and Float sorts should work reasonably well, but their APIs are somewhat awkward - for example a lot of Bitvec operations have separate signed and unsigned operations, so you need to do awkward things like Z3.Bitvec("a", 32).signed_gt(100) instead of more obvious but ambiguous Z3.Bitvec("a", 32) > 100. Float APIs are even worse as a lot of operations need rounding mode passed - and most operations take rounding mode argument, and printing out results tries to use precise but unintuitive notation like 1.25B+5. Sets, Arrays, and fancier stuff, are basically unfinished. The obvious missing sort is any kind of finite domain integer, like Int[1..9] - in Z3 you need to create Int variable, and then tell the solver that it's within certain range, like solver.assert (Z3.Int("a") >= 1) & (Z3.Int("a") <= 9) You want to give Z3 a bunch of formulas, and these generally start with variables like sort.var("name"). As Z3::BoolSort.new.var("name") is fairly long, shortcuts like Z3.Bool("name") are provided. From that point, you can construct your formulas with fairly straightforward ruby - a + b == c means exactly what you'd expect if a is Z3.Int("a") and so on. There are of course some complications: • ruby won't let us override !, &&, and \|\| - so we use ~, & and \| for booleans - and they have different parsing priorities so you might need to add some parentheses • you can't directly check if a value is equal to something else, as foo == 0 will create a z3 Bool expression not give you true/false. It's a great case where some extra operators would be useful, but for now just .to_s whatever you want to extract or check. • some operations don't have easy operator equivalents, so other syntax is provided. For some common examples - to assert that a bunch of values are all different, you can use Z3.Distinct(a, b, c, ...), for z3 ternary use (bool_expression).ite(if_true, if_false). • we'll automatically convert ruby values like true or 42 to z3 expressions, but if you try to mix sorts without converting them appropriately you'll generally get an exception • ASTs are interned, so every Z3.Int("a") + 2 == Z3.Int("b") is going to be the same underlying object. Library layers Z3 is a huge library, and it really doesn't map to anything resembling a sensible ruby API, so there are many layers here: • We use ffi to create Z3::VeryLowLevel interface of raw C calls. You should never use it directly. • After that there's Z3::LowLevel interface which basically deals with context management, array arguments, and mapping Ruby object arguments (but not return values) to FFI pointers. You should also never use it directly. • Then there are legitimate Ruby objects. A lot of them are wrappers around C pointers, so using SomeClass.new(c_pointer) to create them directly is not really supported. These pointers can be accessed by attributes starting with underscore (like _ast, _sort etc.), but it's all for internal use only. • The main reason for this anal system is that if you mess anything up, you'll get a crash. For some things Z3 library raises error which we then turn into Z3::Exception, but other things just crash your program with segmentation fault. I added a lot of checks for operations which might end with segmentation fault so you get Z3::Exception instead, but I'm sure I missed some things. • Reference counting memory management z3 uses is not exactly compatible with ruby, so if you use it in a very long running process like Rails server, it might cause problems. It's usually going to be no worse than Symbol interning. • Default interface doesn't give any guarantees for running time. The underlying z3 library has ways to restrict solver check running time, but they're not exposed in any convenient way yet. No semantic versioning Z3 is huge library (I only described the basic), and the gem is not only incomplete, but many APIs are fairly poor. Until I release 1.0, any version can freely break any API, so if you want to rely on a stable version, just depend on exact one - or help me complete it faster. The regular flow with Bool, Int, Real and Solver shouldn't break too often, but Bitvec, Float etc. feel awkward and could use a nicer API. Pull requests wellcome. mtg.wtf is currently the best search engine for Magic: the Gathering cards. It's reasonably successful and popular, so let's go through its history quickly. It started as a wishlist of improvements I'd like to see for magiccards.info Then once magiccards.info stopped being updated, I decided to write a replacement. I started by wring a bunch of tests for how I'd like it to work, mostly using data from mtgjson After I had tests, I wrote a search engine as Ruby library with command line interface. I thought about making it a standalone gem at this point, but I'm not sure how useful people would find it, considering json data is out there already. After that I added rudimentary Rails frontend with minimal styling and put it online. At this point it was text only, so I had to find card scans. WotC only publishes somewhat low quality scans, which are usable enough, but I wished to get something better. For about 2/3 of cards I found those higher quality scans, but it was a fairly slow and manual process. That still leaves some rare promos there's just no source of any kind - it wasn't a huge deal, as few people search specifically for them, the search engine just needed to display card with good picture instead of most recent version (which might be weirdo promo). Then I added some CSS on-hover animations. Most cards have regular layout, but there are some cards which are double-faced, have horizontal layout ("split" cards), or have content on top and tobbom ("flip" cards). Later they even added pairs of cards which merge ("meld") into one big card with halves printed on their back face. All those cases for decent usability required either completely different display layout, or some animation support, and CSS animations turned out to be pretty easy to add. At this point I was getting feedback that it doesn't work too well on mobiles. Well it's not too hard, we just need to add header telling mobile browsers to not be stupid: <meta content='width=device-width, initial-scale=1' name='viewport'> Then I installed bootstrap, and replaced some existing layout code with bootstrap 12-column grid. It was surprisingly easy retrofit - other that bootstrap's use of .card colliding with my use of .card I don't remember any surprises. Markup looked a bit worse due to extra <div class="row">, <div class="col-md-8"> etc., but it's not too bad thanks to HAML. Making it responsive I have a bunch of mobile devices around, and testing on one or two devices is not too much trouble, but I wanted to make sure site will work well on everything, so I used Device Mode in Chrome Developer Tools to make sure everything works in wide range of sizes, portrait and landscape, added a bunch of responsive bootstrap tags, and I pushed the changes to the server. • For big screens site used desktop layout - 4 column for card picture, 6 column for card information, 2 columns for extra intformation • For medium screens layout was 6 column for pic, 6 column for information, and extras were hidden • For small screens layout was full row for card pic, and full row for card information underneath, with extras hidden That was the most usable configuration in Chrome Device Mode. Animation problems There were two immediate problems - first Mobile Safari users reported that CSS animations are broken - it turned out that it required some prefixed properties for backface-visibility which nobody told Rails CSS autoprefixer about. Second problem was that on very small screen sizes (where card was already full screen width) there was simply no space to do some of the animations - I ended up doing messy screen size queries in my CSS code matching Bootstrap size thresholds to turn them off. And it was all wrong because "pixel" is a lie I was quite happy with it, so I expected my users to be as well, but feedback I got was overwhelmingly negative. Users found the site unusable on mobiles, even though I crammed as much information as could reasonably fit in Chrome Device Mode. The thing that got the most backlash was placing card text under card pic. But if I put tiny card picture next to text nobody could see anything, right? Oh wait, those mobile "pixel" numbers are total bullshit. That 100 "pixel" width is actually a lot more device pixels, so even though card looked like completely unreadable thumbnail in Chrome Device Mode, it looked just fine when I tried to use it on an actual phone. And even if card picture was too small, so what? It's just as easy to pinch to zoom as it is to scroll down a bit - something that doesn't apply to desktops (where Cmd+ / Cmd- can zoom, but they don't focus on specific area, so they're much less useful). This also means that 6 pic / 6 info layout on bigger devices was excessive - so I switched all non-desktop devices to 5 pic / 7 info as that's what looked best on actual mobiles and tablets I tried it on, even it looks horrible in Chrome Device Mode. So now the site looked good on desktop (with big browser window), and on mobile devices with 2x or higher pixel density (of any size). That doesn't cover using mobile devices with 1x pixel density (which fortunately basically nobody uses any more), or desktop browser with small window size (which happens, but worst case users can resize the window). That leads to two big lessons: • Chrome Device Mode is horribly unrepresentative as it uses 1x not 2x pixel density • Bootstrap device width targeting is fairly unrepresentative as it ignores pixel density Getting rid of whole-width card pic layout let me get rid of most CSS animation workarounds. There are still some for gallery view, like Nils Hamm's cards from Dragon's Maze where animations need to be aware of which column the card's in. Soft Keyboard Now it looked good, but I ran into one more problem. On desktop we want to start search box focused with HTML5 autofocus attribute, so user can start typing the query without clicking anything. Now most good browsers understand opensearch annotations, so if you ever visited mtg.wtf, they'll remember it, so you can just type mtg<tab>your query from URL bar, and they'll get you straight to search results - but not everybody uses it this way. But we don't want to autofocus on mobiles - as then huge soft keyboard appears covering half of results and making it all miserable. At least on some mobile browsers, others sensibly require click to show soft keyboard even with autofocus attribute. Unfortunately I never found any way to query if device has real keyboard or not. So backup logic of autofocusing on home page (which has no results, so soft keyboard covering empty space is no big deal), but not on other pages (which have some result) ended up being a workable compromise. It would be nice if someone figured out which browser/device combinations have this issue, and created some device specific autofocus library, as it can't be the only site affected by the problem. Overall, it wasn't too bad Even with all the surprises, it all went better than expected. But imagine the world could have been different - once upon a time mobiles tried to create their own separate web with completely separate protocols and formats. How insane would it be if they	{"url":"https://t-a-w.blogspot.com/2016/10/","timestamp":"2024-11-05T22:23:21Z","content_type":"application/xhtml+xml","content_length":"236670","record_id":"<urn:uuid:6181de75-35d1-4df8-8028-03a3f6d37e59>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00064.warc.gz"}
Cracking the Code: Mastering the Art of Calculating Investment Ratios - Finance Planning Cracking the Code: Mastering the Art of Calculating Investment Ratios When it comes to investing, making informed decisions is crucial to achieving success. One essential tool in every investor’s arsenal is the investment ratio, a numerical value that provides insights into the performance of an investment. Calculating investment ratios can seem daunting, especially for novice investors. However, with a clear understanding of the concept and a step-by-step guide, anyone can master the art of calculating investment ratios. What is an Investment Ratio? An investment ratio, also known as a performance metric, is a numerical value that helps investors evaluate the profitability and efficiency of an investment. It provides a snapshot of an investment’s performance, enabling investors to make informed decisions about their portfolio. Investment ratios can be used to assess various aspects of an investment, including return on investment (ROI), risk, and cost. Why Calculate Investment Ratios? Calculating investment ratios offers several benefits to investors. These include: • Evaluating performance: Investment ratios provide a clear picture of an investment’s performance, allowing investors to identify areas for improvement. • Making informed decisions: By using investment ratios, investors can make informed decisions about their portfolio, such as whether to hold or sell an investment. • Comparing investments: Investment ratios enable investors to compare the performance of different investments, making it easier to choose the best option. • Risk management: Investment ratios help investors identify potential risks and take steps to mitigate them. Types of Investment Ratios There are several types of investment ratios, each providing unique insights into an investment’s performance. Some of the most common investment ratios include: Return on Investment (ROI) ROI is a fundamental investment ratio that calculates the return on an investment as a percentage of its cost. ROI = (Gain from Investment – Cost of Investment) / Cost of Investment Return on Equity (ROE) ROE calculates the return on shareholder equity, providing insights into a company’s profitability. ROE = Net Income / Total Shareholder Equity Price-to-Earnings Ratio (P/E Ratio) The P/E ratio calculates the current stock price relative to its earnings per share. P/E Ratio = Current Stock Price / Earnings per Share Dividend Yield The dividend yield calculates the ratio of annual dividend payments to the current stock price. Dividend Yield = Annual Dividend Payment / Current Stock Price How to Calculate Investment Ratios Calculating investment ratios involves a series of steps, including: Step 1: Gather Data To calculate investment ratios, you’ll need access to historical data, including investment costs, gains, and relevant financial statements. Step 2: Choose an Investment Ratio Select the investment ratio you want to calculate, such as ROI, ROE, or P/E Ratio. Step 3: Plug in the Numbers Insert the relevant data into the formula, ensuring accuracy and attention to detail. Step 4: Calculate the Ratio Perform the necessary calculations to arrive at the investment ratio. Step 5: Analyze and Interpret Analyze and interpret the results, considering the ratio in the context of your investment goals and risk tolerance. Examples and Case Studies Let’s consider a few examples to illustrate how investment ratios work in practice: Investment Cost Gain ROI Stock A $100 $120 20% Stock B $50 $70 40% In this example, Stock B has a higher ROI, indicating a more profitable investment. Case Study: Calculating ROE Suppose we want to calculate the ROE for a company with a net income of $100,000 and total shareholder equity of $500,000. ROE = Net Income / Total Shareholder Equity = $100,000 / $500,000 = 0.2 or 20% This indicates that the company has generated a 20% return on shareholder equity. Common Challenges and Pitfalls When calculating investment ratios, it’s essential to avoid common challenges and pitfalls, including: Inaccurate Data Ensure that your data is accurate and up-to-date to avoid incorrect calculations. Misinterpreting Results Take the time to thoroughly analyze and interpret the results, considering the ratio in the context of your investment goals and risk tolerance. Comparing Apples and Oranges Avoid comparing investment ratios across different asset classes or industries, as this can lead to misleading conclusions. Calculating investment ratios is a critical component of successful investing. By understanding the different types of investment ratios, following a step-by-step guide, and avoiding common challenges and pitfalls, investors can make informed decisions about their portfolio. Remember, mastering the art of calculating investment ratios takes time and practice, but the rewards are well worth the effort. By incorporating investment ratios into your investment strategy, you’ll be better equipped to navigate the complex world of investing and achieve your long-term goals. What are investment ratios and why are they important? Investment ratios are mathematical calculations used to evaluate the performance and efficiency of an investment. They provide investors with valuable insights into the returns, risks, and profitability of their investments, enabling them to make informed decisions. Investment ratios can help investors identify areas of improvement, optimize their portfolios, and achieve their financial goals. There are various types of investment ratios, each serving a specific purpose. For instance, the return on investment (ROI) ratio measures the return on an investment relative to its cost. The price-to-earnings (P/E) ratio helps investors determine the value of a stock relative to its earnings. By mastering the art of calculating investment ratios, investors can gain a deeper understanding of their investments and make data-driven decisions to maximize their returns. What is the difference between a profitability ratio and an efficiency ratio? A profitability ratio measures the ability of an investment to generate earnings compared to its expenses, costs, or investments. It helps investors evaluate the bottom-line performance of an investment. On the other hand, an efficiency ratio assesses how effectively an investment uses its resources to generate revenue or profit. It helps investors identify areas of improvement and optimize their investment strategies. For example, the gross margin ratio is a profitability ratio that calculates the difference between revenue and the cost of goods sold, divided by revenue. In contrast, the asset turnover ratio is an efficiency ratio that measures the revenue generated by an investment per unit of asset. Understanding the difference between these two types of ratios is crucial in making informed investment decisions and optimizing portfolio performance. How do I calculate the return on equity (ROE) ratio? To calculate the ROE ratio, you need to divide the net income of an investment by its shareholder equity. The formula is: ROE = Net Income / Shareholder Equity. This ratio provides insights into a company’s ability to generate profits from its shareholder equity. A higher ROE indicates that an investment is generating strong profits from its equity, which can be an attractive feature for For instance, if a company has a net income of $100,000 and shareholder equity of $500,000, its ROE would be 20% ($100,000 รท $500,000). This means that for every dollar of shareholder equity, the investment generates 20 cents of net income. By calculating the ROE ratio, investors can evaluate the profitability of an investment and compare it to industry benchmarks or other investments. What is the significance of the debt-to-equity ratio in investment analysis? The debt-to-equity ratio measures the proportion of debt financing to equity financing in an investment. It helps investors evaluate the capital structure of a company and its ability to meet its financial obligations. A high debt-to-equity ratio indicates that an investment is heavily reliant on debt financing, which can increase its risk profile. On the other hand, a low ratio suggests that an investment has a healthy balance between debt and equity. A debt-to-equity ratio can have significant implications for investors. For instance, a high ratio may indicate a higher risk of default or bankruptcy, which can lead to a decline in the investment’s value. Conversely, a low ratio may indicate a more stable financial position, which can provide a higher degree of confidence for investors. By calculating the debt-to-equity ratio, investors can assess the financial health and risk profile of an investment. How do I interpret the results of investment ratios? Interpreting the results of investment ratios requires a thorough understanding of the ratio’s formula, its significance, and the industry or market context. Investors should compare the results of an investment ratio to industry benchmarks, historical data, or other investments to gain a deeper understanding of its performance. It is also essential to consider multiple ratios in conjunction with each other to form a comprehensive view of an investment’s performance. For example, if an investment has a high ROE ratio but a low dividend yield ratio, it may indicate that the investment is generating strong profits but not distributing them to shareholders. By analyzing multiple ratios, investors can identify areas of strength and weakness and make informed decisions to optimize their portfolio performance. Can investment ratios be used for both individual stocks and mutual funds? Yes, investment ratios can be used to evaluate the performance of both individual stocks and mutual funds. The ratios and formulas used may vary depending on the type of investment, but the underlying principles remain the same. For instance, the P/E ratio can be used to evaluate the value of an individual stock, while the expense ratio can be used to evaluate the cost efficiency of a mutual fund. Investors can apply investment ratios to individual stocks to evaluate their fundamental performance, growth prospects, and valuation. Similarly, mutual fund investors can use ratios such as the Sharpe ratio or the Treynor ratio to evaluate the risk-adjusted performance of their funds. By applying investment ratios to different types of investments, investors can make informed decisions and optimize their portfolios. What are some common pitfalls to avoid when using investment ratios? One common pitfall to avoid when using investment ratios is relying solely on a single ratio to make investment decisions. Each ratio provides a unique insight into an investment’s performance, and investors should consider multiple ratios in conjunction with each other. Another pitfall is failing to consider the industry or market context in which an investment operates. Investors should compare an investment’s ratios to industry benchmarks or averages to gain a more accurate understanding of its performance. Additionally, investors should be cautious when using investment ratios to evaluate investments with different accounting practices or capital structures. For instance, an investment with a high level of debt may skew its ratios, making it appear more or less attractive than it actually is. By being aware of these pitfalls, investors can use investment ratios more effectively and make more informed investment decisions. 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MAT142 Statistical Reasoning With Applications – Math This course will teach students how to use four-steps of the statistical process in the context of sports: ask questions, collect data, analyze data, and make conclusions. Each chapter will begin with a sports-related statistical question (e.g., Is there a home field advantage in the NFL?) and then students will learn how to collect appropriate data, how to analyze the data, and how to make reasonable conclusions. Although the context of the examples and exercises will be sports related, the primary focus of the class will be to teach students the basic principles of statistical reasoning. Major statistical topics include: analyzing distributions of univariate and bivariate data, both categorical and numerical, using graphs and summary statistics; correlation and least squares regression; using simulations to estimate probability distributions; theoretical probability distributions, including the binomial and normal distributions; rules of probability, including conditional probability and expected value; the logic of hypothesis testing, including stating hypotheses, calculating and interpreting p-values, drawing conclusions, and Type I and Type II errors; using confidence intervals to estimate parameters; and proper methods of data collection, including sampling and experimentation. Use of technology, including online applets and the graphing calculator will be prominent in the course. Throughout the course, students will complete investigations that require students to complete the four-step statistical process using athletes of their	{"url":"https://sites.sienaheights.edu/mathematics/mat142-statistical-reasoning-with-applications-math/","timestamp":"2024-11-02T17:57:53Z","content_type":"text/html","content_length":"48040","record_id":"<urn:uuid:ecc253d2-30cf-40ae-8446-92c5f65b6190>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00853.warc.gz"}
Video examples Solving problems involving rational and/or negative exponents These videos will take you through the solutions of several kinds of problems you might encounter using rational and negative exponents, alone or in combinations. Examples 1 Here are three whole numbers raised to rational powers to give you an idea of how these can be simplified exactly and pretty quickly without a calculator. You just need to know the laws of exponents (and remember the multiplication table). The last example shows you how to solve a problem like x^a/b = 25, by raising both sides to the b/a power. Examples 2 Here are two more examples, the first like the last on the previous video, only with a negative rational exponent on x. The second example is of the kind you'll encounter often: a ratio of several variables raised to various rational and negative powers. One strategy (used here) is to deal with the negative exponents first, by moving them across the division line and dropping the negative Examples 3 Here are two more examples of simplifying ratios of variables raised to rational and negative powers.	{"url":"http://xaktly.com/RationalNegExponents_Video.html","timestamp":"2024-11-11T16:21:29Z","content_type":"text/html","content_length":"8481","record_id":"<urn:uuid:fba28cde-66a9-498b-beb3-9e0e8a08f60a>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00731.warc.gz"}
a person related to one by marriage. -ssigning finite values to finite quant-ties. of or relating to a transformation that maps parallel lines to parallel lines and finite points to finite points. (maths) of, characterizing, or involving transformations which preserve collinearity, esp in cl-ssical geometry, those of translation, rotation and reflection in an axis Read Also: • Affine geometry the branch of geometry dealing with affine transformations. • Affine group the group of all affine transformations of a finite-dimensional vector sp-ce. • Affine transformation affine transformation mathematics a linear transformation followed by a translation. given a matrix m and a vector v, a(x) = mx + v is a typical affine transformation. (1995-04-10) • Affined closely related or connected. bound; obligated. historical examples to all such was applied the term aca, related or affined;32-2 and marriage within the chinamitl was not permitted. the annals of the cakchiquels daniel g. brinton adjective closely related; connected • Affinities a natural liking for or attraction to a person, thing, idea, etc. a person, thing, idea, etc., for which such a natural liking or attraction is felt. relationship by marriage or by ties other than those of blood (distinguished from ). inherent likeness or agreement; close resemblance or connection. biology. the phylogenetic relationship between two […]	{"url":"https://definithing.com/affine/","timestamp":"2024-11-13T22:29:41Z","content_type":"text/html","content_length":"23864","record_id":"<urn:uuid:483a8e77-c0d5-4137-a0d7-fb85909cbb97>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00827.warc.gz"}
Pruned Fast Learning Fuzzy Approach for Data-Driven Traffic Flow Prediction Chengdong Li^, Yisheng Lv^, Jianqiang Yi^, and Guiqing Zhang^ ^School of Information and Electrical Engineering, Shandong Jianzhu University Jinan 250101, China ^*Institute of Automation, Chinese Academy of Sciences Beijing 100190, China March 2, 2016 October 26, 2016 December 20, 2016 traffic flow prediction, data-driven method, fuzz system, extreme learning method, fuzzy rule pruning Traffic flow prediction plays an important role in intelligent transportation systems. With the rapid growth of traffic flow data, fast and accurate traffic flow prediction methods are now required. In this paper, we propose a novel fast learning data-driven fuzzy approach for the traffic flow prediction problem. In the proposed approach, to achieve fast learning, an extreme learning machine is utilized to optimize the consequent parameters of the fuzzy rules. Further, a fuzzy rule pruning strategy that involves measuring the firing levels of the fuzzy rules is presented to obtain reduced fuzzy inference systems. To evaluate the performance of the proposed approach, it was experimentally applied to traffic flow prediction and its results compared with those of widely used methods. The experimental results verify that the proposed approach can achieve satisfactory performance. The comparisons show that the proposed approach can obtain better (sometimes similar) performances, but with a simpler structure, fewer parameters, and much faster learning speed than the other methods. Cite this article as: C. Li, Y. Lv, J. Yi, and G. Zhang, “Pruned Fast Learning Fuzzy Approach for Data-Driven Traffic Flow Prediction,” J. Adv. Comput. Intell. Intell. Inform., Vol.20 No.7, pp. 1181-1191, 2016. Data files: 1. [1] E. I. Vlahogianni, M. G. Karlaftis, and J. C. Golias, “Short-term traffic forecasting: Where we are and where we are going,” Transportation Research Part C: Emerging Technologies, Vol.43, pp. 3-19, 2014. 2. [2] C. Chen, Y. Wang, L. Li, J. Hu, and Z. Zhang, “The retrieval of intra-day trend and its influence on traffic prediction,” Transportation Research Part C: Emerging technologies, Vol.22, pp. 103-118, 2012. 3. [3] M. M. Hamed, H. R. Al-Masaeid, and Z. M. B. Said, “Short-term prediction of traffic volume in urban arterials,” J. of Transportation Engineering, Vol.121, No.3, pp. 249-254, 1995. 4. [4] M. Van Der Voort, M. Dougherty, and S. Watson, “Combining Kohonen maps with ARIMA time series models to forecast traffic flow,” Transportation Research Part C: Emerging Technologies, Vol.4, No.5, pp. 307-318, 1996. 5. [5] B. Williams, “Multivariate vehicular traffic flow prediction: evaluation of ARIMAX modeling,” Transportation Research Record: J. of the Transportation Research Board, Vol.1776, pp. 194-200, 2001. 6. [6] B. M. Williams and L. A. Hoel, “Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: Theoretical basis and empirical results,” J. of Transportation Engineering, Vol.129, No.6, pp. 664-672, 2003. 7. [7] S. Lee and D. Fambro, “Application of subset autoregressive integrated moving average model for short-term freeway traffic volume forecasting,” Transportation Research Record: J. of the Transportation Research Board, Vol.1678, pp. 179-188, 1999. 8. [8] F. Moretti, S. Pizzuti, S. Panzieri, and M. Annunziato, “Urban traffic flow forecasting through statistical and neural network bagging ensemble hybrid modeling,” Neurocomputing, Vol.167, pp. 3-7, 2015. 9. [9] E. I. Vlahogianni, M. G. Karlaftis, and J. C. Golias, “Optimized and meta-optimized neural networks for short-term traffic flow prediction: a genetic approach,” Transportation Research Part C: Emerging Technologies, Vol.13, No.3, pp. 211-234, 2005. 10. [10] K. Y. Chan, T. S. Dillon, J. Singh, and E. Chang, “Neural-network-based models for short-term traffic flow forecasting using a hybrid exponential smoothing and Levenberg-Marquardt algorithm,” IEEE Trans. on Intelligent Transportation Systems, Vol.13, No.2, pp. 644-654, 2012. 11. [11] P. Dell’Acqua, F. Bellotti, R. Berta, and A. De Gloria, “Time-aware multivariate nearest neighbor regression methods for traffic flow prediction,” IEEE Trans. on Intelligent Transportation Systems, Vol.16, No.6, pp. 3393-3402, 2015. 12. [12] W. C. Hong, “Traffic flow forecasting by seasonal SVR with chaotic simulated annealing algorithm,” Neurocomputing, Vol.74, No.12, pp. 2096-2107, 2011. 13. [13] W. C. Hong, Y. Dong, F. Zheng, and S. Y. Wei, “Hybrid evolutionary algorithms in a SVR traffic flow forecasting model,” Applied Mathematics and Computation, Vol.217, No.15, pp. 6733-6747, 2011. 14. [14] W. C. Hong, Y. Dong, F. Zheng, and C. Y. 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Wang, “WPANFIS: combine fuzzy neural network with multiresolution for network traffic prediction,” The J. of China Universities of Posts and Telecommunications, Vol.17, No.4, pp. 88-93, 2010. 19. [19] J. Abdi, B. Moshiri, B. Abdulhai, and A. K. Sedigh, “Forecasting of short-term traffic-flow based on improved neurofuzzy models via emotional temporal difference learning algorithm,” Engineering Applications of Artificial Intelligence, Vol. 25, No.5, pp. 1022-1042, 2012. 20. [20] M. C. Tan, S. C. Wong, J. M. Xu, Z. R. Guan, and P. Zhang, “An aggregation approach to short-term traffic flow prediction,” IEEE Trans. on Intelligent Transportation Systems, Vol.10, No.1, pp. 60-69, 2009. 21. [21] L. A. Zadeh, “Fuzzy sets,” Information and Control, Vol.8, No.3, pp. 338-353, 1965. 22. [22] L. A. Zadeh, “Fuzzy logic - a personal perspective,” Fuzzy Sets and Systems, Vol.281, pp. 4-20, 2015. 23. [23] W. Pedrycz and H. Izakian, “Cluster-centric fuzzy modeling,” IEEE Trans. on Fuzzy Systems, Vol.22, No.6, pp. 1585-1597, 2014. 24. [24] C. Li, J. Yi, and G. Zhang, “On the monotonicity of interval type-2 fuzzy logic systems,” IEEE Trans. on Fuzzy Systems, Vol.22, No.5, pp. 1197-1212, 2014. 25. [25] G. B. Huang, Q. Y. Zhu, and C. K. Siew, “Extreme learning machine: theory and applications,” Neurocomputing, Vol.70, No.1, pp. 489-501, 2006. 26. [26] G. B. Huang, H. Zhou, X. Ding, and R. Zhang, “Extreme learning machine for regression and multiclass classification,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol.42, No.2, pp. 513-529, 2012. 27. [27] G. B. Huang and L. Chen, “Convex incremental extreme learning machine,” Neurocomputing, Vol.70, No.16, pp. 3056-3062, 2007. 28. [28] G. B. Huang, X. Ding, and H. Zhou, “Optimization method based extreme learning machine for classification,” Neurocomputing, Vol.74, No.1, pp. 155-163, 2010. 29. [29] Z. L. Sun, K. F. Au, and T. M. Choi, “A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol.37, No.5, pp. 1321-1331, 2007. 30. [30] H. J. Rong, G. B. Huang, N. Sundararajan, and P. Saratchandran, “Online sequential fuzzy extreme learning machine for function approximation and classification problems,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol.39, No.4, pp. 1067-1072, 2009. 31. [31] S. O. Olatunji, A. Selamat, and A. Abdulraheem, “A hybrid model through the fusion of type-2 fuzzy logic systems and extreme learning machines for modelling permeability prediction,” Information Fusion, Vol.16, pp. 29-45, 2014. 32. [32] Z. Deng, K. S. Choi, L. Cao, and S. Wang, “T2fela: type-2 fuzzy extreme learning algorithm for fast training of interval type-2 TSK fuzzy logic system,” IEEE Trans. on Neural Networks and Learning Systems, Vol.25, No.4, pp. 664-676, 2014. 33. [33] J. S. R. Jang, “ANFIS: adaptive-network-based fuzzy inference system,” IEEE Trans. on Systems, Man and Cybernetics, Vol.23, No.3, pp. 665-685, 1993. 34. [34] Y. H. Joo, H. S. Hwang, K. B. Kim, and K. B. Woo, “Fuzzy system modeling by fuzzy partition and GA hybrid schemes,” Fuzzy Sets and Systems, Vol.86, No.3, pp. 279-288, 1997. 35. [35] J. Yao, M. Dash, S. T. Tan, and H. Liu, “Entropy-based fuzzy clustering and fuzzy modeling,” Fuzzy Sets and Systems, Vol.113, No.3, pp. 381-388, 2000. 36. [36] G. H. Golub and C. F. Van Loan, “Matrix Computations (4th Edition),” Maryland, The Johns Hopkins University Press, 2013. 37. [37] G. Quintana-Orti, E. S. Quintana-Orti, and A. Petitet, “Efficient solution of the rank-deficient linear least squares problem,” SIAM J. on Scientific Computing, Vol.20, No.3, pp. 1155-1163, 1998. 38. [38] V N. Vapnik, “Statistical Learning Theory,” New York, Wiley, 1998.	{"url":"https://www.fujipress.jp/jaciii/jc/jacii002000071181/","timestamp":"2024-11-02T14:26:29Z","content_type":"text/html","content_length":"52552","record_id":"<urn:uuid:9de7a84f-5144-4fff-8025-15a673d7e02f>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00890.warc.gz"}
Question ID - 52808 \| SaraNextGen Top Answer A thin uniform circular disc of mass a) b) c) d) Question ID - 52808 \| SaraNextGen Top Answer A thin uniform circular disc of mass a) b) c) d) 1 Answer 127 votes Answer Key / Explanation : (b) Using conservation of angular momentum 127 votes « Previous Next Question / Solution » Was this Answer Helpful ? Yes Calculate Your Age Here Class 3rd Books & Guides Class 4th Books & Guides Class 5th Books & Guides Class 6th Books & Guides Class 7th Books & Guides Class 8th Books & Guides Class 9th Books & Guides Class 10th Books & Guides Class 11th Books & Guides Class 12th Books & Guides JEE NEET Foundation Books IIT JEE Books Study Materials NEET UG Book Study Materials Careers & Courses After 12th SaraNextGen Founder's Profile Contact & Follow On Social Media Privacy Policy & Terms Conditions Donate Your Funds & Kindly Support Us	{"url":"https://www.saranextgen.com/homeworkhelp/doubts.php?id=52808","timestamp":"2024-11-02T18:34:28Z","content_type":"text/html","content_length":"17982","record_id":"<urn:uuid:afb39e5b-5cce-44a2-909c-53291e0215b4>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00688.warc.gz"}
GreeneMath.com \| Ace your next Math Test! Remainder Theorem Additional Resources: In this lesson, we will learn about the remainder theorem. The remainder theorem will give us a quicker method to evaluate a polynomial for a given value. When we work with a polynomial, we can write the polynomial as: f(x) = (x - k)q(x) + r, where (x - k) is our divisor, q(x) is the quotient, and r is the remainder. If we want to find f(k), we see that f(k) = r. So f(k) is just equal to the remainder from dividing f(x) by x - k. Additionally, we will be able to use this method to determine if f(k) is a zero, meaning f(k) = 0. + Show More +	{"url":"https://www.greenemath.com/Precalculus/30/Remainder-Theorem.html","timestamp":"2024-11-10T12:03:26Z","content_type":"application/xhtml+xml","content_length":"9538","record_id":"<urn:uuid:3609ca95-1c63-45d4-afa3-26d210a7f967>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00482.warc.gz"}
When to Use parfor Decide When to Use parfor parfor-Loops in MATLAB A parfor-loop in MATLAB^® executes a series of statements in the loop body in parallel. The MATLAB client issues the parfor command and coordinates with MATLAB workers to execute the loop iterations in parallel on the workers in a parallel pool. The client sends the necessary data on which parfor operates to workers, where most of the computation is executed. The results are sent back to the client and assembled. A parfor-loop can provide significantly better performance than its analogous for-loop, because several MATLAB workers can compute simultaneously on the same loop. Each execution of the body of a parfor-loop is an iteration. MATLAB workers evaluate iterations in no particular order and independently of each other. Because each iteration is independent, there is no guarantee that the iterations are synchronized in any way, nor is there any need for this. If the number of workers is equal to the number of loop iterations, each worker performs one iteration of the loop. If there are more iterations than workers, some workers perform more than one loop iteration; in this case, a worker might receive multiple iterations at once to reduce communication time. Deciding When to Use parfor A parfor-loop can be useful if you have a slow for-loop. Consider parfor if you have: • Some loop iterations that take a long time to execute. In this case, the workers can execute the long iterations simultaneously. Make sure that the number of iterations exceeds the number of workers. Otherwise, you will not use all workers available. • Many loop iterations of a simple calculation, such as a Monte Carlo simulation or a parameter sweep. parfor divides the loop iterations into groups so that each worker executes some portion of the total number of iterations. • Multiple GPUs and your computations use GPU-enabled functions. For more information about using multiple GPUs in a parfor-loop, see Run MATLAB Functions on Multiple GPUs. A parfor-loop might not be useful if you have: • Code that has vectorized out the for-loops. Generally, if you want to make code run faster, first try to vectorize it. For details how to do this, see Vectorization. Vectorizing code allows you to benefit from the built-in parallelism provided by the multithreaded nature of many of the underlying MATLAB libraries. However, if you have vectorized code and you have access only to local workers, then parfor-loops may run slower than for-loops. Do not devectorize code to allow for parfor; in general, this solution does not work well. • Loop iterations that take a short time to execute. In this case, parallel overhead dominates your calculation. • Loop iterations that all use the same GPU. GPUs contain many microprocessors that can perform computations in parallel and trying to further parallelize GPU computations using a parfor-loop is unlikely to speed up your code. You cannot use a parfor-loop when an iteration in your loop depends on the results of other iterations. Each iteration must be independent of all others. For help dealing with independent loops, see Ensure That parfor-Loop Iterations are Independent. The exception to this rule is to accumulate values in a loop using Reduction Variables. In deciding when to use parfor, consider parallel overhead. Parallel overhead includes the time required for communication, coordination and data transfer — sending and receiving data — from client to workers and back. If iteration evaluations are fast, this overhead could be a significant part of the total time. Consider two different types of loop iterations: • for-loops with a computationally demanding task. These loops are generally good candidates for conversion into a parfor-loop, because the time needed for computation dominates the time required for data transfer. • for-loops with a simple computational task. These loops generally do not benefit from conversion into a parfor-loop, because the time needed for data transfer is significant compared with the time needed for computation. Example of parfor With Low Parallel Overhead In this example, you start with a computationally demanding task inside a for-loop. The for-loops are slow, and you speed up the calculation using parfor-loops instead. parfor splits the execution of for-loop iterations over the workers in a parallel pool. This example calculates the spectral radius of a matrix and converts a for-loop into a parfor-loop. Find out how to measure the resulting speedup and how much data is transferred to and from the workers in the parallel pool. 1. In the MATLAB Editor, enter the following for-loop. Add tic and toc to measure the computation time. n = 200; A = 500; a = zeros(1,n); for i = 1:n a(i) = max(abs(eig(rand(A)))); 2. Run the script, and note the elapsed time. Elapsed time is 31.935373 seconds. 3. In the script, replace the for-loop with a parfor-loop. Add ticBytes and tocBytes to measure how much data is transferred to and from the workers in the parallel pool. n = 200; A = 500; a = zeros(1,n); parfor i = 1:n a(i) = max(abs(eig(rand(A)))); 4. Run the new script on four workers, and run it again. Note that the first run is slower than the second run, because the parallel pool takes some time to start and make the code available to the workers. Note the data transfer and elapsed time for the second run. By default, MATLAB automatically opens a parallel pool of workers on your local machine. Starting parallel pool (parpool) using the 'Processes' profile ... connected to 4 workers. BytesSentToWorkers BytesReceivedFromWorkers __________________ ________________________ Total 55324 24168 Elapsed time is 10.760068 seconds. The parfor run on four workers is about three times faster than the corresponding for-loop calculation. The speed-up is smaller than the ideal speed-up of a factor of four on four workers. This is due to parallel overhead, including the time required to transfer data from the client to the workers and back. Use the ticBytes and tocBytes results to examine the amount of data transferred. Assume that the time required for data transfer is proportional to the size of the data. This approximation allows you to get an indication of the time required for data transfer, and to compare your parallel overhead with other parfor-loop iterations. In this example, the data transfer and parallel overhead are small in comparison with the next example. The current example has a low parallel overhead and benefits from conversion into a parfor-loop. Compare this example with the simple loop iteration in the next example, see Example of parfor With High Parallel Overhead. For another example of a parfor-loop with computationally demanding tasks, see Nested parfor and for-Loops and Other parfor Requirements Example of parfor With High Parallel Overhead In this example, you write a loop to create a simple sine wave. Replacing the for-loop with a parfor-loop does not speed up your calculation. This loop does not have a lot of iterations, it does not take long to execute and you do not notice an increase in execution speed. This example has a high parallel overhead and does not benefit from conversion into a parfor-loop. 1. Write a loop to create a sine wave. Use tic and toc to measure the time elapsed. n = 1024; A = zeros(n); for i = 1:n A(i,:) = (1:n) .* sin(i2pi/1024); Elapsed time is 0.012501 seconds. 2. Replace the for-loop with a parfor-loop. Add ticBytes and tocBytes to measure how much data is transferred to and from the workers in the parallel pool. n = 1024; A = zeros(n); parfor (i = 1:n) A(i,:) = (1:n) .* sin(i2pi/1024); 3. Run the script on four workers and run the code again. Note that the first run is slower than the second run, because the parallel pool takes some time to start and make the code available to the workers. Note the data transfer and elapsed time for the second run. BytesSentToWorkers BytesReceivedFromWorkers __________________ ________________________ 1 13176 2.0615e+06 2 15188 2.0874e+06 3 13176 2.4056e+06 4 13176 1.8567e+06 Total 54716 8.4112e+06 Elapsed time is 0.743855 seconds. Note that the elapsed time is much smaller for the serial for-loop than for the parfor-loop on four workers. In this case, you do not benefit from turning your for-loop into a parfor-loop. The reason is that the transfer of data is much greater than in the previous example, see Example of parfor With Low Parallel Overhead. In the current example, the parallel overhead dominates the computing time. Therefore the sine wave iteration does not benefit from conversion into a parfor-loop. This example illustrates why high parallel overhead calculations do not benefit from conversion into a parfor-loop. To learn more about speeding up your code, see Convert for-Loops Into parfor-Loops See Also parfor \| ticBytes \| tocBytes Related Topics	{"url":"https://de.mathworks.com/help/parallel-computing/decide-when-to-use-parfor.html","timestamp":"2024-11-02T10:57:18Z","content_type":"text/html","content_length":"83103","record_id":"<urn:uuid:d3bbdede-a140-461c-9065-7bea654148ab>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00425.warc.gz"}
Is pathfinding artificial intelligence? Pathfinding is often associated with AI, because the A* algorithm and many other pathfinding algorithms were developed by AI researchers. Typically, genetic algorithms do not allow agents to learn during their lifetimes, while neural networks allow agents to learn only during their lifetimes. … What is AI pathfinding in games? Pathfinding strategies are usually employed as the core of any AI movement system. Pathfinding strategies have the responsibility of finding a path from any coordinate in the game world to another. At its simplest, this could be just a list of locations within the game that the agent is allowed move to. What are pathfinding algorithms used for? Pathfinding algorithms are usually an attempt to solve the shortest path problem in graph theory. They try to find the best path given a starting point and ending point based on some predefined What is the fastest pathfinding algorithm? Dijkstra’s algorithm is used for our fastest path algorithm because it can find the shortest path between vertices in the graph. The coordinates on the arena are considered as the vertices in the IS A * pathfinding good? A* pathfinding algorithm is arguably the best pathfinding algorithm when we have to find the shortest path between two nodes. A* is the golden ticket, or industry standard, that everyone uses. Dijkstra’s Algorithm works well to find the shortest path, but it wastes time exploring in directions that aren’t promising. Is breadth first search greedy? Breadth first search, as per definition, is not a greedy algorithm. The goal is to produce a spanning tree of a graph by visiting nodes one level at the time starting from a source node (ordinary queue is employed for this task). What is Recursive best first search? Recursive Best-First Search or RBFS, is an Artificial Intelligence Algorithm that belongs to heuristic search algorithm [1]. It expands fronteir nodes in best-first order. RBFS explores the search space by considering it as a tree. An example of the search space with cost equal to depth is shown in Fig. How do I use a* pathfinding? We can use A* pathfinding by treating each navigable cell as a node, connected to all of its neighbor cells: Again, you don’t necessarily have to draw the nodes on the map. This tutorial focused on the A* pathfinding algorithm that comes with Gdx AI, but there are a ton of other options out there. What is the best path-finding algorithm? We found Goal, so we’re done! Dijkstra’s algorithm is probably the most popular path-finding algorithm, because it’s relatively simple and always finds the shortest possible path. Dijkstra’s algorithm has one big downside: it expands the shortest path, regardless of how close that path gets to the destination. What is pathfinding in Grand Theft Auto V? But if you want your enemies to do anything smarter, they’ll need to be able to figure out what to do. Pathfinding is the process of finding a path from one point to another. This is an entire field of study, but this tutorial focuses on pathfinding in libGDX. What is pathfinding in libGDX? Pathfinding is the process of finding a path from one point to another. This is an entire field of study, but this tutorial focuses on pathfinding in libGDX. To use the pathfinding features that come with libGDX, it’s a good idea to understand what’s going on under the hood.	{"url":"https://www.shakuhachi.net/is-pathfinding-artificial-intelligence/","timestamp":"2024-11-11T10:38:04Z","content_type":"text/html","content_length":"49224","record_id":"<urn:uuid:7d25abec-c731-49a1-ad51-f3ce0b16cc55>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00645.warc.gz"}
Reaction Research Society by Prof. Dean R. Wheeler, Brigham Young University This posting is reprinted from the original article written March 13, 2019 with permission from the author. This article was intended for chemical engineering students to size relief valves for pressure vessels, but it applies well to amateur liquid rocketry as many use a pressure fed system to deliver propellants to the engine. The PDF of this white paper can be found below. The RRS has several members engaged with liquid rocket projects. An important part of analyzing the performance of those systems is the pressurization system that drives the propellant into the engine. The tank blowdown problem is useful to designing the system and estimating performance. This derivation goes through the thermodynamics of the general tank blowdown problem and should be a useful starting point for a pressure-fed liquid rocket project. This document provides a mathematical model for computing the rate of expelling gas through a small orifice or nozzle attached to a tank. Furthermore, two models are described for how fast the tank will depressurize. Related material on compressible flow can be found in fluid mechanics and thermodynamics textbooks and web pages. Figure 1 shows the tank and associated nozzle. The narrowest diameter of the flow path in the orifice or nozzle is known as the throat region. The tank and throat regions are described with their own sets of equations. Provided the tank is large and the throat is small, it will take many seconds to empty the tank and gas velocities in the main part of the tank will be much smaller than the speed of sound. This means that gas pressure, temperature, and density in the tank will be spatially uniform, though they will be changing in time. Thus, we describe the tank using a transient mass balance. One can compare this to a model in heat transfer known as lumped capacitance. In the nozzle region however, gas velocity is large and there are large spatial variations in the gas properties. In addition, there is relatively little gas contained in the nozzle region. Thus, flowrate in the nozzle adjusts rapidly to match current conditions in the tank, making it seem as if the nozzle is operating at steady state. This approximation for the nozzle is known as quasi-steady state. Figure 1: Schematic of a task with nozzle or orifice, allowing gas to exit. Italicized are variables that pertain to twokey regions. During blowdown every variable depends on time, The P, T, and rho variables in Figure 1 denote absolute pressure, absolute temperature, and density in the tank or the narrowest part of the nozzle or throat (denoted by an asterisk,, subscript), respectively. Note that if tank pressure is given experimentally as a gauge quantity, it must be converted to absolute to be used in the equations below. The first relationship between gas variables is given by an equation of state. The ideal gas law is a fairly accurate representation for air when pressure is less than around 10 atmospheres or 150 psia. It states that: Figure 1: The ideal gas equation where “V” is the volume of the gas, “n” is the number of moles, and “R” is the universal gas constant (8.31446 J/mol/K). With the introduction of the molecular weight, M (effectively 0.028964 kg/mol/ K for air), and the substitution that density is mass over volume, rho = n M / V, the ideal gas law is changed to Equation 2: Density calculated from the ideal gas equation This equation could be applied separately to the tank variables or to the thrust variables. The second important relationship comes from figuring out what happens when gas in the tank or nozzle expands. When a gas expands, its internal energy is used to perform work on the surroundings, and the gas therefore tends to cool off. If the gas expands slowly, there is time for itmto absorb hest from its warmer surroundings and the expansion is essentially isothermal, meaning the temperature stays at its initial value or that of the surroundings. On the other hand, if a gas expands quickly its temperature will drop dramatically. This is called adiabatic expansion, where adiabatic means no noticeable heat transfer from the surroundings (i.e. the walls of the tank). In adiabatic expansion, the pressure drops more rapidly than it would for an isothermal (slow) expansion. Adiabatic expansion could haolen inside the tank if it is emptying rapidly, but this depends on the relative sizes of thr tank and nozzle. On the other hand, adiabatic expansion certainly occurs when a gas moves from the tank through the nozzle region. In other words, here the gas is moving quickly and therefore expanding quickly. The thermodynamic relationships for pressure and temperature for reversible adiabatic expansion of a constant heat capacity ideal gas are: Equation 3A: Adiabatic pressure and density relationship Equation 4A: Adiabatic temperature and density relationship where the subscript, “o” indicates the initial state of the gas before the expansion started. This means if we know how the density is changing from an initial state to some later state, we can compute P and T as well. In the case of the nozzle, we apply the above equations as the gas travels between the tank and the throat. In the case, they become Equation 3B: Adiabatic pressure and density relationship between tank and throat regions Equation 4B: Adiabatic temperature and density relationship between tank and throat regions The parameter, “gamma” , is the dimensionless ratio of specific heats ( gamma =. Cp / Cv ), and by statistical theory of gases, gamma = 7/5 = 1.4, for low temperature diatomic molecules, nitrogen (N2) and oxygen (O2) and so that value is used here. Next, we need to determine the gas density in the nozzle when the tank is at a specified conditions. Recall that that the nozzle is treated as if it instantaneously responds to whatever state the tank is in. A fuller discussion of the nozzle flow equations can be found in other sources like textbooks that cover ideal compressible flow in nozzles. Choked flow means that the flow is exactly at the speed of sound in the throat region. A higher speed cannot be achieved in the throat, regardless of upstream or downstream conditions. Thus, choked flow acts to limit how much gas flow can pass through a given size orifice, This is the reason why pressure relief valves on tanks must be properly sized to accommodate sufficient flow. Choked flow happens for a large pressure drop across the nozzle or orifice, specifically if the upstream tank pressure meets the following condition relative to atmospheric pressure downstream from the nozzle: Equation 5: Choked flow condition Equation 5 is the origin of the rule of thumb or approximation that choked flow occurs for upstream pressure that is more than twice the value of downstream pressure (absolute). If the tank pressure drops below this limit, the speed of gas in the throat is subsonic, and less gas will flow than in the choked flow regime. The solution to subsonic flow in the nozzle is complicated and is less important to know because it is at the end of the tank’s discharge when pressure is low, and so will be neglected here. The solution to choked flow in the throat region follows a simple relationship, derived from energy and mass balances: Equation 6: Throat to tank density ratio This can be substituted from Equation 3B and 4B to determine pressure and temperature in the throat in terms of tank conditions. For choked flow the throat velocity is exactly the speed of sound, which is what makes it easier to analyze. For ideal gases, speed of sound, c, is determined solely by temperature. Thus, we can relate throat velocity to throat temperature, and in turn to tank temperature: Equation 7: Speed of sound at the throat For example, if T_tank = 294 Kelvins, then c_o = 314 m/sec for air. Now we can determine the mass flow rate, “m_dot”, through the nozzle or orifice. This comes from the following standard relationship, applied at the throat, because that is where conditions are Equation 8: Mass flow,rate at the throat where “A_” is the throat cross-sectional area given by Equation 9: Area of a circle and where “d_” is throat diameter. Dimensionless parameter, Cd, in Equation 8 is the discharge coefficient, accounting for friction between fluid and walls and a phenomenon known as vena contracta. In essence, Cd, is needed in Equation 8 because the effective area for fluid at speed, v_o, is somewhat smaller than actual throat area. Cd would be equal to 1.0 for a perfect (frictionless or thermodynamically reversible) nozzle: in practice for a smoothly tapering nozzle it might be as high as 0.98, while for a sharp-edged orifice it might be as low as 0.60. Anything that causes separation of flow from the nozzle wall or increases frictional contact will decrease Cd. Making the appropriate substitutions into Equation 8 leads to an equation for mass flow in terms of readily determined quantities: Equation 10: Mass flow rate in terms of readily determined quantities Frequently in industrial situations, mass flow rates are expressed instead as volumetric flow rates corresponding to a gas at a standard temperature and pressure (even though the gas is not actually at that temperature and pressure). For instance, a mass flow meter used for gases may express mass flow as standard liters per minute (SLPM) or standard cubic feet per minute (SCFM). In other words, even though m_dot (mass flow) is the key value being measured, it is expressed as Equation 11: Standard volumetric flow and mass flow rate which requires knowing what rho_std value is programmed by the manufacturer into the flow meter. This can be determined from the ideal gas law, given specified P_std and T_std values. As an example, the American manufacturer, Omega, assumes a standard temperature “T_std” of 70 degrees Fahrenheit (294.26 Kelvins) and a standard pressure “P_std” of 1 atmosphere which equals 14.696 psia (101,325 Pscals) thus by the ideal gas law, the standard density “rho_std” would equal 1.2 kg/m3 for air (molecular weight 28.97 g/mole). Combining Equations 10 and 11 and the ideal gas law leads to Equation 12: Combining Equations 10 and 11 for standard volumetric flow rate where “c_std” is the speed of sound at the standard temperature: Equation 13: Standard volumetric rate and mass flow rate relationship Makers of valves and orifices may provide an experimentally determined size parameter known as flow coefficient, Cv. For gases this dimensionless parameter can be converted to CdA_* by Equation 14: Discharge area relationship4 to valve coefficient (metric units) The key design principles resulting from the above analysis are, provided tank pressure is large enough to generate choked flow, that (1) mass flow rate of a gas through an orifice is proportional to throat area and tank pressure and (2) flow rate does not depend on downstream pressure. Equation 10 gives the rate of mass loss from a tank at a given gas density and temperature. To determine how long it will take to depressurize the tank, we must do a transient mass balance on the tank. The ordinary differential equation for this is: Equation 15: Change of mass in time where “m_dot” comes from Equation 10 and “m” is the mass of gas in the tank. This in turn is: Equation 16: Mass in the tank where V_tank is the fixed tank volume. With these substitutions we get for the governing equation Equation 17: Mass flow rate from the tank To make things more manageable, let us create a discharge time constant called “tau” Equation 18: Time constant for blowdown of a tank where “c_o” is the speed of sound at the initial temperature “T_o” (i.e. at the beginning of blowdown) Equation 19: Speed of sound at initial conditions With this new time constant, Equation 17 becomes: Equation 20: Mass flow rate change in the tank The last thing to do before solving this equation is figure out what to do with T_tank. We have two options: Assume gas temperature in the tank does not change in time, based on blowdown taking a long time so that heat can be readily absorbed from the walls. Thus, T_tank = T_o. This leads to Equation 20 Equation 21: Tank density change in time which can be separated and integrated to give the solution Equation 22: Tank density as a function of initial conditions where “rho_o” is initial density in the tank. We then convert densities to pressure using the ideal gas equation. Equation 23: Tank pressure as a function of initial conditions The equation tells us how tank pressure varies with time, for an isothermal tank and choked exit flow. Assume the gas cools as it expands in the tank, due to no heat transfer from the walls, based on the blowdown taking a short time to complete. Thus, T_tank is given by Equation 4A. This leads to Equation 20 becoming Equation 24: Mass flow rate from the tank which can be separated and integrated to give a solution. Equation 25: Density of the tank as a function of time We then convert densities to pressures using Equation 3A for adiabatic expansion. Equation 26: Tank pressure as a function of time This equation tells us how tank pressure varies with time, for an adiabatic tank and choked exit flow. The tank temperature can likewise be predicted from Equation 4A. Equation 27: Tank temperature as a finction of time The isothermal and adiabatic models of tank blowdown can be considered two extremes, with the correct answer (i.e., with the true amount of heat transfer) lying somewhere in between them. Figure 2 shows an example of the respective blowdown curves (Equation 23 and 26). As noted previously, adiabatic tank conditions lead to more rapid pressure loss than do isothermal conditions. The curves predict that the tank will have lost 80% of its original pressure at a time in the range of 1.3tau < t < 1.6tau. This shows the value of evaluating the variable, tau, to get an approximation of the time it takes to depressurize the tank. Figure 2: Comparison of isothermal and adiabatic blowdown curves.	{"url":"https://www.rrs.org/tag/standard-flow-conditions/","timestamp":"2024-11-04T01:09:58Z","content_type":"text/html","content_length":"93244","record_id":"<urn:uuid:b0bdacfe-c161-42df-9fb4-bfcf69e0e27a>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00698.warc.gz"}
Tesla 18650, 2170 and 4680 Battery Cell Comparison Basics \| Torque News Greater capacity, more power, smaller size, lighter in weight, easier to manufacture on a mega scale and with less expensive components are the challenges of designing an EV battery. In other words, it comes down to cost and performance. Think of it as a balancing act where the kilowatt hours (kWh) achieved need to provide the most range, but at a reasonable manufacturing cost. Hence, you often seen a battery pack description listing its manufacture cost coming with numbers such as a range of $240-$280/kWh for example during production. Oh, and let’s not forget safety. Remember the Samsung Galaxy Note 7 fiasco a few years ago and the EV battery equivalents of vehicle fires and Chernobyl equivalent meltdowns. Spacing between cells in a pack and thermal controls to prevent one cell from igniting another cell, from igniting another cell, etc. in a runaway chain reaction disaster scenario adds to the complexity of battery development for EVs. Of which, even Tesla has had its share of problems. 3.2v Lifepo4 Battery While EV battery packs consist of three major parts: the battery cells, the battery management system(s), and a box or container of some sort to hold it all together, for now, we will take a look at just the cells and how they evolved with Tesla, but remains an issue for Toyota. The cylindrical 18650 cell is a lithium-ion type measuring 18mm in diameter and 65mm in length and weighs approximately 47 grams. At a nominal voltage of 3.7volts, each cell can be charged as high as 4.2 volts and discharged as low as 2.5 volts, with each cell storing up to 3500 mAh. Much like an electrolytic capacitor, Tesla’s EV battery cells consist of long sheets of anodes and cathodes separated by a charge-insulating material and are rolled up and packaged tightly into a cylindrical form to save space and pack as much energy as possible. Those sheets of cathode (negative charge) and anode (positive charge) each have tabs for connecting like charges between cells resulting in a powerful battery---the sum of many as one, if you will. Like a capacitor where its capacitance (power) is increased by decreasing the spacing between the anode and cathode sheets, changing the dielectric (the aforementioned insulating material between the sheets) to one of higher permittivity, and increasing the area of both the anode and cathode sheets, the next step up in Tesla’s EV cell was the 2170 which came in a cylinder slightly larger than the 18650 measuring at 21 millimeters by 70 millimeters, and weighed approximately 68 grams. At a nominal voltage of 3.7volts, each cell can be charged as high as 4.2 volts and discharged as low as 2.5 volts, with each cell storing up to 4800 mAh. There’s a tradeoff, however, primarily of which is more about resistance and heat than it was about the need for a slightly larger can. In the case of the 2170, the increase in the anode/cathode plate sizes resulted in a longer path for charge to travel which meant more resistance and thereby more energy escaping as heat from the cells as well as interfering with rapid charging requirements. To create a next generation battery cell with even greater power (but without increased resistance) Tesla engineers designed a significantly larger cell with what is called a “tabless” design that shortened the electrical path and thereby resulted in less heat generated from resistance. Much of this can be attributed to who is possibly the best battery researcher in the world. The 4680 cell is shingle-spiral form design that is simpler to manufacture and comes in a package size of 46 mm in diameter and 80 mm in length. The weight is not available but its other voltage characteristics are reportedly similar or the same; however, each cell is rated for around a whopping 9000 mAh, which is why the new Tesla tabless battery Is so good. Furthermore, its charging speed remained conducive to rapid requirements. So, What Does This All Mean? While going up in size rather than down in size with each cell seems counter to design desires in a battery cell, the improvements made in the power capacity and control of heat generation of the 4680 over both the 18650 and the 2170 resulted in basically fewer cells with more power per pack in the same size pack as used with earlier Tesla models powered with the 18650 and 2170 cells. To put this in a numerical perspective, that means only about 960 “4680” cells are needed to fill the same space as the 4,416 “2170” cells in the same amount of space, but with added benefits such as a lower cost per kWh production and a significant increase in power using the 4680 cell pack. As reported earlier about a comparison to the 2170 cell, the 4680 is expected to provide five times more energy storage with 6 times more power resulting in an increase from 82 kWh to 95 kWh in the newer Tesla’s, translating into an expected increase in road range of up to 16 percent. Bear in mind that this is just the basics on Tesla battery cells and that there is much more behind the tech. But it’s a good start for future articles, as we will take a look on how the battery packs are managed regarding power use, as well as safety issues with respect to controlling heat generation, lost power, and…of course…the risk of EV battery fires. If you are into All-Things-Tesla, here's your chance to buy a Hot Wheels RC version of the Tesla Cybertruck. Timothy Boyer is Torque News Tesla and EV reporter based in Cincinnati. Experienced with early car restorations, he regularly restores older vehicles with engine modifications for improved performance. Follow Tim on Twitter at @TimBoyerWrites for daily Tesla and electric vehicle news. The "whopping 9000 mAh" in the 4680 battery does not sound whopping at all considering the 2170 battery has 4800 mAh, which is more than 1/2 the energy but at less than 1/5 the size. I think there must be a mistake here as otherwise you'd need a battery module way larger with the 4680 to get the same amount of power as with the 2170. In reply to The "whopping 9000 mAh" in by MrCurious (not verified) The capacity of Tesla 4680 cell has been told "25Ah", not 9Ah. In reply to The "whopping 9000 mAh" in by MrCurious (not verified) A 21mm diameter cylinder with a height of 70mm equates to ~2,307mm³. A 46mm diameter cylinder with a height of 80mm equates to 5,777mm³. That means the 2170 is ~2.5 times smaller In volume. That is not less than 1/5th the volume, correct? Also the 2170 batteries need coolant jackets along the sides of the vertical batteries requiring for the to be spaces out and take up more room. The 4680 batteries need heat dissipated from the top and bottom allowing for them to be placed closer together and take up less room. Please let me know if my math and/or logic is off. In reply to A 21mm diameter cylinder with by Trenton (not verified) Volume is calculated by Pi x r² x height. I think you used r instead of r². The volume of the 46mm cylinder is 5.48times larger than the volume of the 21mm. 24,245mm³ vs 132,952mm³ So it's not a miracle, it's a 5 times larger cell with 5 times more capacity. If the makes everything easier and reduces costs has to be seen. In reply to The "whopping 9000 mAh" in by MrCurious (not verified) That was my first thought, too. In reply to The "whopping 9000 mAh" in by MrCurious (not verified) Less heat generated, longer lifespan or more charge cycles and much safer? Hi, well...the "whopping" may be a little on the hyperbole side, but as the resources I found state "...the 4680 is expected to provide five times more energy storage with 6 times more power resulting in an increase from 82 kWh to 95 kWh in the newer Tesla’s, translating into an expected increase in road range of up to 16 percent." That, and the information also reports that the number of 4680 cells to occupy the same space as the 2170 battery system in a Tesla is only 1/4 as many, but results in 6 times more power, I believe this is a significant improvement. An engineer could likely put this in a better and clearer perspective. Any engineers out there who would like to comment? All input is welcome. In reply to Hi, well...the "whopping" may by Timothy Boyer Maybe it is best to present a graph of power per unit weight/volume versus energy storage capacity per unit weight/volume for all three designs. In reply to Hi, well...the "whopping" may by Timothy Boyer None of the stated numbers agree with the results posited in the article. 9000 is not 6 times 4800. I've tried reconciling individual stats on each iteration with the improvement claims and these assertions simply don't add up. Something's my is amiss. In reply to Hi, well...the "whopping" may by Timothy Boyer Given the numbers you provided, 82kWh with 4x as many cells as the 4680 configuration at 95kWh, simple math puts that at 4.63 times more energy on a per cell basis. In reply to Hi, well...the "whopping" may by Timothy Boyer not an engineer but Just do the math pii x r squared x length 21mm x 70 mm = 96,931 cu mm 46mm x 80 mm = 531,539 cu mm 531,539/96931=5.48 so the 4680 is 5.48 times the volume of a 2170 highest capacity of a 2170 cell currently available is 5000mah @15amp max continuous discharge 5000 x 5.48= 27,400 mah required output of a 4680 to equal 2170 energy density. so a 4680 would have to have more than 27ah before is is more efficient than a 2170 As far as size goes there is no significant advantage to a larger size over a smaller size battery as the proportion of space between them remains the same. With equivalent chemistries they would occupy the same space per ah at scale. There are less batteries though so they could possibly be more reliable. But take up less space. No In reply to not an engineer but Just do by boo radley (not verified) I've been using those 18650 batteries for years now, and all the ones I get are 30-35 amps. As an aside, my oldest set is almost 10 years old, and still work perfectly even after thousands of charges. Does that amp range help the math? In reply to Hi, well...the "whopping" may by Timothy Boyer The space occupied comment is a little misleading. They may take up the same volume when assembled in a pack, however if you do the math no of cells x cell volume you will find the actual effective volume of the 4680's is around 17% bigger. This makes the extended range a little less impressive. Yeah, it's not a matter of simple arithmetic. You just don't have all of the data that Tesla has behind their battery---proprietary info you know. For example, the new battery cell may be designed to avoid losing a significant amount of power due to heat loss compared to the the earlier model of cell. But they are not going to reveal how, of course. The article info comes from last year's battery day in which Elon claimed 6X more power. In reply to Yeah, it's not a matter of by D. Banner (not verified) They have discussed how heat is managed with the cell, at least in part. The large array of tabs means less resistive heating of the tabs, which means an less power losses. Hmm.. the numbers don't make sense. 960 cells @ 9Ah each = 8640 Ah To get a 95 kWh battery, the V of each cell would need to be ~11V (95k/8640) NMC cells are ~4.25 V/cell, so that does not make sense. Are the new Silicon cells of a much higher voltage?? Can anyone tell me if this battery is the NMC cathode In reply to Can anyone tell me if this by Charlie (not verified) It seems clear that this new 4680 battery has a rated capacity in the 25AH range and they have eliminated cobalt from the design. Given the inherent space lost in a cylindrical shape (made up for in manufacturing efficiencies), the larger the diameter of a battery, the more efficiently it will fill a specific area. They are literally putting a round peg (lots of them) into a square space, so the fewer gaps you have in that space, while maintaining thermal stability, the better. That's the real advantage of what Tesla has achieved, here. They have increased the volumetric size of the battery (and hence the capacity) while controlling thermal properties by building a tabless design with very low, and very consistent, internal resistance. This new cell really is a game-changer. In reply to It seems clear that this new by Jason Broom (not verified) Well done Jason. Now can you tell me the volume loss for 500 4860's versus 2750 2170 cells ? In reply to Well done Jason. Now can you by royal gosser (not verified) multiply 500 x 5,48 for the equivalent number of 2170s = 2740 they would occupy the same physical space. look up circle stacking in wikipedia. But you already knew that didn't you. the six times more power from a 4680 is due to the lower internal resistance which lowers heat build up and allows higher continuous output. Energy density remains the same. In reply to Well done Jason. Now can you by royal gosser (not verified) Hexagonal lattice packing is the densest possible packing of circles in a plane, and it's independent of the diameter of the circle (or for cylinders standing on end); the packing density is ~90.69% of the area. The Tesla batteries are already using hexagonal lattice packing, so you're not going to get any significant amount of change in waste volume between the two. In reply to Hexagonal lattice packing is by Sean (not verified) While they may be hexagonal packed, each row of the smaller cells have cooling running between them, increasing the effective diameter by about 15%. Whereas the larger cells are cooled top &/or In reply to Can anyone tell me if this by Charlie (not verified) Yes they are NVM the data I've found is this Cathode. NVM Weight. 1355 g Size.46x80mm Capacity.9000 mah Total energy.96-99wh(estimated) I want to find out this info: Max capacity.?(per cell) Amp output.?(per cell) Voltage.?(per cell)Im very excited about these cells making they're way into the open market and being put to use for p.e.vs Cause I use the 21700 Panasonic's in my electric skate as 12s8p configuration from 2 12s4p batteries ran in parallel and it is able to max out at 80amps continuous discharge (bms max capacity not batteries)60mph and 80 miles of range per charge. So I can only imagine what the 4680s will accomplish and what new configuration shapes will be designed for best convinience of mounting said battery pack to bikes etc. Cause my 14sx4p on my ebike did 40mph and 25 miles of range a charge. And that was just a 300$ battery In other reports, there is presented capacity of 25000mAh per cell 4680. This is much more in accordance with 6 times increase against 21700. Whopping? That closes this article for me. One to the next one. doing the numbers the 4680 would need to produce over 25 maps to equal the energy density of the 2170. The was an article (can't find it now) that showed that when grouping cylinders efficiently there was no difference in proportion of space between cells regardless of size. e.g. bigger cells have bigger spaces between them. So the main advantage is cost to produce. (note: the battery number is the dia and length if you want to calc it yourself but it comes out that the 4680 is 5.48 times the volume of a 2170 I looked up available 2170 cells that range from 4000mah to 5000mah and choose one that was 500 and had a continuous discharge rating of 15 amp Remember its the energy density that is more important (I believe). Power alone only tells you the current capability (V*I actually with both have same voltage degradation curve) which is more important for charging maybe . So the 4860 has roughly the same energy density as the 2170 as mentioned above and with the total space loss the same, then it seems that the lower thermal resistance of the battery will be the main factor for better energy density......Yes? Change will to could and I will agree with your statement. However the only available specs do do not bear this out. I look forward to tests of actual 4680 samples when they become available Upon further reflection I realized that we need to define the metrics used to measure lithium cells. The three most common methods are capacity (energy density), power(continuous output in amps) and internal resistance. They are all related. Capacity and continuous output rating are inversely proportional and governed by the internal resistance which is related to the cathode size. This means that the less internal resistance the greater the continuous output can be. This is usually attained by a larger cathode which in turn reduces the volume of anodic material and therefore the capacity of the battery. All other parameters aside. The 4680 can be made with a physically larger cathode without affecting energy density which lowers internal resistance and therefore allows higher continuous output. This is important to a point as continuous output must match or exceed the output of the motors and accessory electronics. In summary the 4680 design offers a free boost in continuous output at the same energy density over 2170s. This is supported by the battery data charts which show 5,48 times the capacity and 6 times the continuous energy output. Harnessing this to the best advantage is another matter out of the realm of battery specs. e.g. Do you decrease the weight of the vehicle to increase the range by suing fewer batteries do you tweak the battery spec to produce less output over more capacity. It seems Musk has chosen to to stay with the same energy density and perhaps throttle the output through the current controllers already in the vehicles over tweeting the battery cells. But remember 5000 mah is 5000 mah so any range increases would come from the decrease in weight due of using fewer cells. In summary make the car go further pew kilowatt due to the decreased weight of the battery pack. I believe they said those saving were in the neighborhood of 6%. We'll just have to see how Musk and his engineers work all of this out. Please remember that I have come to these conclusions through my calculations and the sketchy data available and statements made by Musk in his battery day video which support my data. I may have missed some finer points of battery physics which could skew this data. If anyone has concrete data or knowledge that support or refute my conclusions I would be more than happy to hear them. In reply to Upon further reflection I by boo radley (not verified) Can I have one for my old TmS (2015)?? Cycle With Battery Torque News is an automotive news provider by Hareyan Publishing, LLC, dedicated to covering the latest news, reviews and opinions about the car industry. Our professional team of reporters have many years of experience covering the latest cars, trucks, upcoming new-car launches and car shows. They provide expertise, authority and trustworthiness in covering automotive news. Torque News provides a fresh perspective not found on other auto websites with unique pieces on design, international events, product news and industry trends. TorqueNews.com offers a new look at the world's love affair with cars! We are committed to the highest ethics, providing diverse voices, to accuracy, making corrections, and the best standards of automotive journalism. Copyright ©	{"url":"https://mgahv.in/blog/b3iy-tesla-18650-2170-and-4680-battery-cell-comparison-basics-torque-news/","timestamp":"2024-11-03T23:19:34Z","content_type":"text/html","content_length":"32094","record_id":"<urn:uuid:13bdf8af-5173-42ea-b057-d1502cf46cf3>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00407.warc.gz"}
Measuring Angles in Radians What is a Radian? A radian is an angle that subtends an arc whose length is equal to the radius of the circle. It is abbreviated as "rad." $$ 1 \ rad $$ Typically, if an angle is given as a single numeric value without any symbol, it is understood to be in radians. Given that the circumference of a circle with radius r is 2πr, we can deduce that a full circle measures 2π radians. Here, the symbol π, or pi, represents a constant approximately equal to $$ \pi = 3.14 $$. Proof. To determine how many times the radius fits into the circumference, we divide the circumference (2πr) by the radius. $$ \frac{2 \pi r}{r} = 2 \pi \ rad $$ The result is two pi (2π) radians. Therefore, we can express a full angle (360°) as 2 pi radians (2π). Similarly, a straight angle (180°) is pi radians (π). And so forth.	{"url":"https://www.andreaminini.net/math/measuring-angles-in-radians","timestamp":"2024-11-01T22:30:01Z","content_type":"text/html","content_length":"13091","record_id":"<urn:uuid:9d165240-b535-4fd5-bc24-a71feabb5338>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00686.warc.gz"}
Linear Algebra-Part 1 -College Mathematics The introduction to Linear Algebra starts with Matrices and Determinants. Learn about Determinants , Matrices and their applications-A College Mathematics course. Learn about cofactors, Laplace's expansion. Upper and lower triangular matrices are discussed here. You will learn about indempotent, singular matrices and how to multiply 2 matrices. How to solve problems on determinants is discussed. Transpose of a matrix, symmetric and skew symmetric matrices, Adjoint of a matrix are taught here. You will learn about rank of a matrix and properties of rank of a matrix. Elementary row and column operations are introduced. The lesson concludes with problems on determining the rank of a matrix.	{"url":"https://www.mathmadeeasy.co/post/linear-algebra-part-1-college-mathematics","timestamp":"2024-11-04T16:48:34Z","content_type":"text/html","content_length":"1050489","record_id":"<urn:uuid:de592c36-829b-40d0-82be-a34b061a591d>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00187.warc.gz"}
Chinese fēn Category: main menu • Portland cement menu • Chinese fēn Portland cement conversion Amount: 1 Chinese fēn (fēn) of mass Equals: 1.33 cups Metric (cup mtr. si) in volume Converting Chinese fēn to cups Metric value in the Portland cement units scale. TOGGLE : from cups Metric into Chinese fēn in the other way around. CONVERT : between other Portland cement measuring units - complete list. Conversion calculator for webmasters. General Portland cement General or common purpose Portland cement type (not any other weaker/cheaper cement replacement-version). It's the primary masonry binder hence bonding agent for mortars and concretes consisting of building sand, stones or other gravel aggregate, mixed with water. By standard practice, when freshly poured, Portland cement has unit volume mass of 94 lbs/cu-ft - 1506 kg/m3 (but it becomes denser as the storage time is prolonged, when it gets compressed or vibrated; in such situations its weight per volume can increase to as high as 104 lbs/cu-ft). This calculator is based on the fresh form Portland cement w/ the standard mass properties of 94 pounds to 1 cubic foot. Convert Portland cement measuring units between Chinese fēn (fēn) and cups Metric (cup mtr. si) but in the other reverse direction from cups Metric into Chinese fēn. conversion result for Portland cement: From Symbol Result To Symbol 1 Chinese fēn fēn = 1.33 cups Metric cup mtr. si Converter type: Portland cement measurements This online Portland cement from fēn into cup mtr. si converter is a handy tool not just for certified or experienced professionals. First unit: Chinese fēn (fēn) is used for measuring mass. Second: cup Metric (cup mtr. si) is unit of volume. Portland cement per 1.33 cup mtr. si is equivalent to 1 what? The cups Metric amount 1.33 cup mtr. si converts into 1 fēn, one Chinese fēn. It is the EQUAL Portland cement mass value of 1 Chinese fēn but in the cups Metric volume unit alternative. How to convert 2 Chinese fēn (fēn) of Portland cement into cups Metric (cup mtr. si)? Is there a calculation formula? First divide the two units variables. Then multiply the result by 2 - for example: 1.3282544803435 * 2 (or divide it by / 0.5) 1 fēn of Portland cement = ? cup mtr. si 1 fēn = 1.33 cup mtr. si of Portland cement Other applications for Portland cement units calculator ... With the above mentioned two-units calculating service it provides, this Portland cement converter proved to be useful also as an online tool for: 1. practicing Chinese fēn and cups Metric of Portland cement ( fēn vs. cup mtr. si ) measuring values exchange. 2. Portland cement amounts conversion factors - between numerous unit pairs. 3. working with - how heavy is Portland cement - values and properties. International unit symbols for these two Portland cement measurements are: Abbreviation or prefix ( abbr. short brevis ), unit symbol, for Chinese fēn is: Abbreviation or prefix ( abbr. ) brevis - short unit symbol for cup Metric is: cup mtr. si One Chinese fēn of Portland cement converted to cup Metric equals to 1.33 cup mtr. si How many cups Metric of Portland cement are in 1 Chinese fēn? The answer is: The change of 1 fēn ( Chinese fēn ) unit of Portland cement measure equals = to 1.33 cup mtr. si ( cup Metric ) as the equivalent measure for the same Portland cement type. In principle with any measuring task, switched on professional people always ensure, and their success depends on, they get the most precise conversion results everywhere and every-time. Not only whenever possible, it's always so. Often having only a good idea ( or more ideas ) might not be perfect nor good enough solution. If there is an exact known measure in fēn - Chinese fēn for portland cement amount, the rule is that the Chinese fēn number gets converted into cup mtr. si - cups Metric or any other Portland cement unit absolutely exactly.	{"url":"https://www.traditionaloven.com/building/masonry/cement/convert-china-fen-cement-to-cup-mtr-si-cement.html","timestamp":"2024-11-05T22:28:41Z","content_type":"text/html","content_length":"40096","record_id":"<urn:uuid:d8fb45e7-069d-4650-8dd8-fa4ed43a20f4>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00288.warc.gz"}
Game Design Novice random() (Game Maker) ( Game Maker, 6.1, 7 ) random - generate a random number rnum = random(x) • rnum = returned random real number • x = upper limit of random number. random() generates a random real number between 0 and less than x. It is produced as a decimal fraction, so if you want a whole number (integer), you should use floor() or ceil() in combination with random(). floor() is used most often. Simple Example After the code below is executed, rnum} will contain a random real number between 0 and less than 5. Remember, this number will be a number with a decimal point and not an integer. 50/50 Chance A 50/50 chance can be simulated this way : if (random(1) >= .5) //something happens Simulating Dice Rolls Standard 6-sided dice and other polyhedral dice rolls can be simulated by simply using random() to generate a number between 1 and the maximum number of the die. Don't forget the + 1. die = floor(random(6)) + 1 Related Pages page revision: 4, last edited: 30 Jun 2012 15:23	{"url":"http://gamedesign.wikidot.com/gamemaker:random","timestamp":"2024-11-04T14:07:40Z","content_type":"application/xhtml+xml","content_length":"34725","record_id":"<urn:uuid:c3cb5f6c-e6b4-4a29-837c-90e94911dd23>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00659.warc.gz"}
How Many Rounds Do you CC? Help Support Ruger Forum: Oct 15, 2024 7-15 depending on which EDC is on me. No extra mags because I don't want to carry them around. And in a self defense scenario on the street if one mag don't get it done, more won't help. I imagine that if I need extra mags I'm in a "hero situation" where I'm trying to stop a robbery with multiple targets, or something like that. I don't have any need to be a hero. Just to go home every night. I suppose if you live in a fairy isolated, low crime area the point of how many reloads is moot. On the other hand in ten minutes or less I can go from my fairly affluent, low crime area to some of the worst you'll find in my state. Just drive from one "nice" area to another Often requires passing through sketchy areas. If I should ever need a firearm again I can't predict how many shots will be fired. So I carry additional ammunition. And while ever handgun I carry has a proven track record of reliability, Murphy is always present so I usually carry backup. Dec 25, 2007 Many folks seem to be overconfident in their high stress shooting capabilities. I expect to miss and maybe a LOT. Nov 15, 2005 the best one can hope for is to practice and practice and when that awful time comes your training helps out.... I know just in shooting a lot I can be dead on accurate most of the time and then all of a sudden the damn bullets get a mind of their own and start going way off. Jul 4, 2023 I'm forced to change my answer today from a 9 round .38 super because I switched over to my 15 round S&W M&P's in .40 caliber. Nov 17, 2009 A gazzilion years ago when I was a young buck I was at a customer's house and the guy told me the reason he carried a gun was, "I'm too old and fat to fight." That is exactly where I am now........ I concur. I am too old to fight and get out of breath too quickly to run. I would like to see solid, verifiable statistics of details concerning self-defense shootings. How many per year? Day of week? Daylight or darkness? Location . . .rural, urban, "hood", etc? Age, race and gender of all involved? Number of assailants? Assailants' weapons? Number of assailants shot . . . wounded or killed? Bystanders shot . . . by either party . . . wounded or killed? Number of shots fired? Defensive weapon(s) employed? Reloads employed? Law enforcement involvement? Legal aftermath, charges filed, final results? Other considerations? IMHO, knowing all these situational details would assist one in determining his/her position on firearms as a defensive tool. All the statistics in the world don't mean a thing when the balloon goes up. All the statistics in the world don't mean a thing when the balloon goes up. ^^^ TRUE ^^^ But they might have helped you prepare for that unlikely eventuality. Dec 25, 2007 Yessir, all those statistics mean nothing if/when IT'S YOUR DAY. I'm a believer in statistics I have personally witnessed. Here are two examples. The M16 is worthless and fails when most needed. The 1911A1 is 100% effective. Beyond that regarding either weapons system it is all hearsay. Aug 5, 2007 I would like to see solid, verifiable statistics of details concerning self-defense shootings. How many per year? Day of week? Daylight or darkness? Location . . .rural, urban, "hood", etc? Age, race and gender of all involved? Number of assailants? Assailants' weapons? Number of assailants shot . . . wounded or killed? Bystanders shot . . . by either party . . . wounded or killed? Number of shots fired? Defensive weapon(s) employed? Reloads employed? Law enforcement involvement? Legal aftermath, charges filed, final results? Other considerations? IMHO, knowing all these situational details would assist one in determining his/her position on firearms as a defensive tool. I don't know of anywhere there is a detailed analysis of such statistics. If there were it would probably diminish many debates on gun forums. I don't know of anywhere there is a detailed analysis of such statistics. If there were it would probably diminish many debates on gun forums. If nothing else I believe it would allow realistic consideration of certain fallacies prevalent today. Might even keep some politicians closer to honest . . . maybe. Nov 15, 2005 Nope, we could have hard solid numbers and most of us would still 'discuss' it and probably disagree with them. Nope, we could have hard solid numbers and most of us would still 'discuss' it and probably disagree with them. Yep, nothing like facts to start a disagreement. Dec 3, 2021 A lot of the defense lawyer's job is to sway the jury's minds into their way of believing or thinking their client is not guilty, right? Not much different than a used car salesman. Some of those car salesmen can sell a pile of crap when they know it is a pile of crap into the best car ever. And a prosecutor's job is to convict, evidence be damned. Nov 17, 2009 Yep, nothing like facts to start a disagreement. So true but then where were the 'facts' from is another thing. If you are accessing 'facts' from Baltimore City I am sure they will tell a different story than from somewhere in the cornfields of So true but then where were the 'facts' from is another thing. If you are accessing 'facts' from Baltimore City I am sure they will tell a different story than from somewhere in the cornfields of Yep. That's why you read all the reports you can find to help sort out the truth from the crap. Believing the "I heard/read it somewhere . . ." reporting is worse than worthless. Aug 28, 2024 And a prosecutor's job is to convict, evidence be damned. That is the sad truth way too often. Dec 3, 2021 I would like to see solid, verifiable statistics of details concerning self-defense shootings. How many per year? Day of week? Daylight or darkness? Location . . .rural, urban, "hood", etc? Age, race and gender of all involved? Number of assailants? Assailants' weapons? Number of assailants shot . . . wounded or killed? Bystanders shot . . . by either party . . . wounded or killed? Number of shots fired? Defensive weapon(s) employed? Reloads employed? Law enforcement involvement? Legal aftermath, charges filed, final results? Other considerations? IMHO, knowing all these situational details would assist one in determining his/her position on firearms as a defensive tool. Does the assailant have a good relationship with the Police or town officials? Last edited:	{"url":"https://www.rugerforum.com/threads/how-many-rounds-do-you-cc.317370/page-6#post-3259963","timestamp":"2024-11-10T15:36:24Z","content_type":"text/html","content_length":"199581","record_id":"<urn:uuid:f7ddfad7-5a4b-47df-86e9-0c81ad38041d>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00465.warc.gz"}
Why do competitors put their stores next to each another? – A Deep Reinforcement Learning approach Have you ever wondered why competing physical stores locate themselves close to each other as a cluster? Since we live in the AnyLogic world, we will use simulations and artificial intelligence to analyze this mystery, but this question is a classical Game Theory problem, so let’s start by discussing this from a game theory perspective that will give us the theoretical grounds to develop a simulation model. Game Theory Perspective Let’s imagine two competitors soon to open a new store in a community in which customers are uniformly distributed in terms of location and interest for the product sold. If the stores cooperate with each other, they can locate themselves in positions that minimizes the average distance travelled by a customer, while at the same sharing 50% of the demand. This collaborative scenario is a social optimal solution and everybody would be happy with it. But after they give each other a handshake and chose the location of their respective stores, each one individually can decide to either cooperate, or betray. This can be represented by a table that shows the rewards of each store owner based on the decision they both make, alongside with the reward for the customers. If they both cooperate, each gets 50% of the customers, and the customers get maximum reward. If only one of them betrays, moving to the center of the city, it gets 60% of the customers and some customers have to travel more, reducing the customer reward to 80. If they both betray each other moving to the center of the city, they still get 50% of the customers but the social reward is at its lowest since people living in the edges of the city now have to travel more. If a store owner thinks about their own benefit, the following strategic mindset is presented. • If the other store cooperates, the maximum reward will be obtained by betraying. • If the other store betrays, the maximum reward will be obtained by betraying. From this perspective, it is always a better strategy to betray, as long as the store owner doesn’t care about social happiness. Both betraying each other is the Nash Equilibrium of the system. This is of course a simplified version of the world since it doesn’t consider the fact that they might lose customers by being too far, and we also don’t consider the psychology of the human mind in these scenarios. Simulation Model Ok, now that we covered the context, let’s try to find a way to make this happen in a simulation setup using AnyLogic. To do that, we need a business that is able to make decisions based on its own selfish interests; but this is not so simple to conceptualize if there are several stores in a big city with lots of customers. So, to avoid getting into the trouble of making an algorithm ourselves, we can use reinforcement learning (RL) with a reward equal to the number of sales made. This reward will create selfish businesses who don’t care about social optimization, but only about their own financial benefit, which is fine because that’s how store owners behaved in the game theory example. The city is simplified to be a rectangular area with businesses and houses randomly placed somewhere in that area. Each house has a random number of customers inside it. When a customer needs a product (which is decided by a simple rate of 1 every arbitrary time unit), they will move to the closest business and will always go back home with the product in their hands. So, with the general model created, now we need to make it RL-ready, and if you are familiar with RL, you know that we need to create an observed space, an action space and a reward. Let’s see each one of them separately. In all the following observations, you have a variable called performingAgent, which is equivalent to the id of the agent making the decisions. This is important since only 1 agent will be making decisions during the training while the others remain in fixed places (I will explain this further later). So, these are the observations: A reward of 1 is obtained every time a sale is made. Nine actions are defined: four of them are related to movements parallel to x and y axes, four of them to movements in diagonal and the last action is not to move at all. The distance moved by the agent after each action is fixed and arbitrarily chosen. Training using Pathmind As of the writing of this article, Pathmind doesn’t have a feature that allows independent trainings for multiple agents that are competing with each other with different and independent reward systems, so what we need to do, as previously explained, is to train one individual business while maintaining the others in a fixed position (or moving randomly). And if we want to use a competition setup with n competitors, we need to train the model, with an initial configuration that defines which business is going to make the decisions. We do this with a random variable as follows (representing the performingAgent parameter we talked about before): This is important for the training to work, because you need the agent to have a sense of self, based on its id. So, the model you will find in the cloud (see references at the end for the link) is the test environment, and not the training environment because we want to train agents individually with selfish behavior and not as a group, meaning that for training purposes, the number of controlled agents is only 1, but for testing purposes, the number of controlled agents can be higher. What we find using RL for this problem is that the businesses, have a constant incentive to move closer and closer to the other businesses as the best strategy to land more sales. And the position in which these businesses will cluster is close to the “center of mass” of the available customers within the city, which is near the city center if the house locations and customers per house are uniformly distributed. Which is great about this example is that we have found the Nash equilibrium using simulations and RL without any incentive other than sales, meaning that you can solve other very simple problems using RL without a lot of Research & Development efforts. I can’t finish this article without a homework for you to try. Imagine now a new situation in which businesses care about the social optimization and want to collaborate in order to have similar sales, while at the same time minimizing the distance travelled by customers. How would you do this? Would you still use Reinforcement Learning? Would you rather use the optimization experiment or your own optimization algorithm? Or maybe some other clever solution? If you do this homework share your AnyLogic Cloud solution in the comments section. You can check and download this model directly through the AnyLogic cloud link: For more details on the topic, watch the video available in the YouTube Noorjax Consulting channel: [https://www.youtube.com/watch?v=9JWZeQ9Pdzk ]	{"url":"https://noorjax.com/2022/05/29/why-do-competitors-put-their-stores-next-to-each-another-a-deep-reinforcement-learning-approach/","timestamp":"2024-11-07T15:48:58Z","content_type":"text/html","content_length":"62750","record_id":"<urn:uuid:6b2cafdf-cbfa-4958-82e3-025164e30f8f>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00206.warc.gz"}
Technical Analysis The core of Technical Analysis is a study of supply and demand in a market. Whether you use upper strategy or lower strategy, there are hundreds of different technical indicators, and some of them are more popular and commonly used. At the end of the day, they are all derived from the analysis of Price, Volume and Time. Even if you are looking at twenty different indicators, they are derived from the same data. These various indicators can be considered as a three-dimensional vector whose attributes are Price, Volume and Time. Once you realize this, you will understand that Technical Analysis is kind of a self-fulfilling prophecy. If everybody depends on indicators such as Fibonacci Retracements, their actions are going to be same and will eventually lead to the same results. As an example, if everybody using Fibonacci Retracements knows that a stock has a key support level as its value depreciates and reaches 50% retracement, its value is most likely to go up. Fibonacci sequence The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. A Sanskrit grammarian named Pingala, who lived sometime between the fifth century BC and the second or third century AD, is credited with the first mention of the Fibonacci sequence of numbers. It is named after the Italian mathematician Leonardo Pisano (also known as Fibonacci) who lived from 1170-1250, as it has he who introduced it to the Western civilization. Fibonacci numbers are of interest to biologists and physicists because they are observed to occur more frequently in nature. For instance, the branching patterns in trees and leaves and the distribution of seeds in a raspberry are based on Fibonacci numbers. Fibonacci numbers Tradespoon provides charts showing Fibonacci Retracements with each trade pick. Fibonacci retracements show horizontal lines which indicate areas of support or resistance which might precede reversals in price activity. Measuring a rally or decline and dividing the distance by ratios of 23.6%, 38.2%, 50%, 61.8% and 100% create these levels. Look at the time horizon of any technical charted package, and find the lowest point and highest point in the chart. By simply connecting those two dots and dividing the distance by ratios, you can draw your own Fibonacci Retracement. Our research at Tradespoon has shown that the probability of correctly predicting the position of a stock is highest between 50 to 75 days. This is why we favor charts that have 60 days worth of Every stock that we recommend and on every trade recommended, you will see 60 days’ worth of data plotted by finding the lowest and highest points, and doing Fibonacci Retracements where the key retracements are 32%, 50% and 68%. In Figure 35, you will notice that Las Vegas Sand sold off after their earnings announcement. Also, you will notice that 50% retracement is shown roughly at 59.5 meaning, 59.5 is a 50% retracement if there is no binary event for the next 10-20 days. In the absence of a binary event, it is most likely that Las Vegas Sand will not breach the overhead resistance at 59.5, meaning it will rebound and revert back to its mean as it approaches 59.5-so, this is your sell signal.	{"url":"https://www.tradespoon.com/blog/ebook/technical-analysis-fibonacci-retracements/","timestamp":"2024-11-04T15:45:48Z","content_type":"text/html","content_length":"81115","record_id":"<urn:uuid:030ec6ec-d74c-432c-84c3-78a4fcb1f558>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00234.warc.gz"}
For TI's - When a tandem student wont jump..... What you guys do every day, the things you say to students, the little things that you probably don't remember the next day or week, they matter to us. A nice little quote, something to think about as an instructor. DougH 270 I might print that out, that is exactly why I became a tandem instructor, and exactly what I always want to keep in perspective. "The restraining order says you're only allowed to touch me in freefall" normiss 736 shorehambeach 9 I think its easy and understandable for TI's to sometimes forget the impact for the 'passenger'. For some people it is life changing. I am 39 and did a tandem for my wife's 40th. In the past 12 months since doing the tandem I am now on my way to my A (even though i live in the UK and have never jumped here).... but more importantly.... My 11 years old daughter has now spent 30 minutes in the tunnel belly flying and will do AFF when she's 16. My boy is 3 and he wants to skydive...and he will when he's older. At the moment he jumps from the stairs with my benny helmet shouting "Skydive / Pull Parachute / Land" All this came from a brilliant TI who I met for 20 minutes in Vegas ! Bless you TI's :) SkymonkeyONE 4 I might print that out, that is exactly why I became a tandem instructor, and exactly what I always want to keep in perspective. What we must all understand is that skydiving is an infintesimallly small sport which almost nobody will experience in their life. We, as life-long instructors, must do everything in our power to alleviate these peoples' fears and get them to trust us. It's TREMENDOUSLY rewarding to me. D-12501, AFF/SL/TM-I, PRO, S&TA kflying 0 I'm just curious - with the evolution of tandems from a compressed FJC to a carnival jump - is there a correlation between the amount of time spent on the ground with the student versus the no time other than gearing up carnival rider and balking at the door? "old timers" - who remember when there was at least a 30 minute training class - your viewpoints would be appreciated! A male pilot is a confused soul who talks about women when he's flying, and about flying when he's with a woman. Artisan 0 Nightingale, that was an awesome story. Thank you for sharing that experience for a newbie like me to read. Outstanding post. Many kudos. Never force an unwilling student to go.! If they say no, it means NO. We give full refunds to the student. No plane ride fees, no TI fees, no video fees. Except for the TI, all others can jump for free. And then we bring the plane down with the TI and the "no go" student. Works for us no matter what aircraft we are flying. matt3sa 0 Personally if their feet are out they are going. I've got somewhere between 500 and 800 tandems and I would estimate that approximately 20 have said something along the lines of "I can't do this" or something that is a fearful response. Often they grab the door frame. However, if their feet are on the step, the last thing I'm going to do is make the pilot work harder while rubbing a 13000.00 tandem rig all over everything trying to haul a 175 to 220 person backwards into the aircraft. No thank you. As long as I can get their hands back onto their own harness they're going for a ride. I'll get the drogue out safely. 99 percent of them always thank me and do great once they are out. I've only had one person that truly didn't want to go and regretted going. I do however feel as though an Otter or larger turbine aircraft would change that for me with the additional space provided. airtwardo 7 I'm just curious - with the evolution of tandems from a compressed FJC to a carnival jump - is there a correlation between the amount of time spent on the ground with the student versus the no time other than gearing up carnival rider and balking at the door? "old timers" - who remember when there was at least a 30 minute training class - your viewpoints would be appreciated! Don't know what you're looking for but I'll chime in with my opinion. I got my tandem rating in the mid '80's, as a TI we packed, trained & jumped...usually out of Cessnas. It was a long hard day, you were beat after 5 jumps...the student retention rate was about 1 in 10. With economics of the carnival ride, things have sped up considerably...I would even say it's a lot more efficient. I took my son for a tandem a few weeks ago, I'm not currently a TI so I asked a friend to take him. He was trained with several other 'students' getting essentially the same information I taught years ago. I don't know what the retention rate is like these days...but as far as I'm concerned it doesn't matter. More people are being exposed to the sport in a relatively safe manner...the membership numbers are up so it must be working at least to some extent in regard to generating interest to possibly ~ If you choke a Smurf, what color does it turn? ~ diablopilot 2 I agree never force a student. Do you pay the TI for the job he's done however? You're not as good as you think you are. Seriously. DARK 0 So I am a new ti so this has only happened once to me and in all the years I have been in the sport I have only seen it happen a handfull of times. My student was a small asian girl, cool as a cucumber throughout the entire thing until she saw the tandem ahead of us go and as soon as that happened she freaked out. I kept us moving to the door but the closer we got the more cat like she got. we landed with the plane. So this is the part that I am wondering what other people think about. As I am a new instructor and because I felt like I 'gave in' too easily I told manifest that I was happy to go again if she wanted to. She said she wanted to try one more time but this time I asked her on the ground if she freaked out again did she want me to force her out. She said yes. So we went up again and she was terrified all the way up. Everyone on the plane knew what was going on and tried to calm her down which only made it worse. She wouldnt let go of my sleeve the entire ride and would just stare at the corner. We got geared up and this time she kept it together until we were right in the door and then she went cat like again so I turned around and made sure her arms and legs were not grabbing anything and I went out backwards. When the parachute opened it sounded like she was crying for about 30seconds which got me real worried but then she sobbed ' that was the best thing I have ever done thanks' It could easily have gone the other way I guess and she could have hated but what do you guys think? Student says yeah force me out, do you do it? Is it right to do it? DARK 0 Never force an unwilling student to go.! If they say no, it means NO. We give full refunds to the student. No plane ride fees, no TI fees, no video fees. Except for the TI, all others can jump for free. And then we bring the plane down with the TI and the "no go" student. Works for us no matter what aircraft we are flying. Do you pay the TI? The TI does not get paid. He takes "one for the team". However, he does get two fun jump tickets to full altitude. diablopilot 2 That's very kind of you. You're not as good as you think you are. Seriously. Mikeal 0 My first jump was at a carnival ride tandem mill while on vacation. Little or no instruction except how to stand in the door. I will say that it was amazing enough to make me pursue skydiving but it did not give me the experience that my SL Instructor/Coaches/DZO gave me on my way to my license at my now home DZ. It's not just TI's that have a impact on someones jumping career/life but any coach or instructor that has calmed me down and reminded me that we do this for fun. The little things matter! My SL instructor use to pick my up by the hip rings to show me I wouldn't fall out. Was my biggest fear. My favorite thing is right before climbing out the pilot leans over and tells me to have a good one ;) always puts a smile on my face. JohnMitchell 16 The TI does not get paid. He takes "one for the team". However, he does get two fun jump tickets to full altitude. At my DZ I don't get or expect even that. An occasional refusal is just part of the job. So far I've only had one and I didn't mind the free plane ride. If you are getting so many refusals it's seriously hurting your income, you should examine your "bedside manner."	{"url":"https://www.dropzone.com/forums/topic/60378-for-ti's---when-a-tandem-student-wont-jump...../page/2/?tab=comments#comment-4103397","timestamp":"2024-11-06T06:02:42Z","content_type":"text/html","content_length":"346492","record_id":"<urn:uuid:b5e7a026-671b-40df-a4a9-cdb9a7aeed6a>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00725.warc.gz"}
“Mathematics………The Poetry of Logical Ideas” Einstein “Mathematics is, in its way, the poetry of logical ideas.” Albert Einstein Since we all want to help our children learn math, it is often tempting to say, “The way you solved that problem was great, but now let me show you a faster way.” The most important thing to remember when engaging your children in mathematical problem solving is to support them to solve problems using their own strategies. This problem is an interesting context in which younger children can practice addition, and it can be solved in a variety of ways. USE THE NUMBERS 1-6 IN EACH SET OF CIRCLES BELOW. The sum of each side of the triangle should equal the number in the center of the triangular shape. For Your Youngest Children – you may want to cut out the numbers 1-6 as pieces. This will allow for easy manipulation of the numbers’ positions. WILL’S MARBLES involves complex reasoning about fractions that will challenge your children’s understandings of the concepts involved. It is a good example of how fractions relate to multiplication and division. ~Ages 7-11 Will and his friend Sam walked along the road together. Will had a big bag of marbles. Unfortunately, the bottom of the bag split and all the marbles spilled out. POOR WILL!! One third (13) of the marbles rolled down the hill too quickly for Will to pick them up. One sixth (16) of all the marbles disappeared into the rain-water drain! Will and Sam picked up all the marbles they could, BUT half (12) of the marbles that remained nearby were picked up by other children who ran off with them! Will counted all the marbles he and Sam had rescued. Will gave one third (13) of these to Sam for helping him pick them up. Will put his remaining marbles into his pocket. There were 14 of them. How many marbles were there in Will’s bag before the bottom split? What fraction of the total number that had been in the bag had he lost or given away? Getting Started – How many marbles did Will and Sam rescue? How might this help you to work out the number of marbles which Will had before the bag split? SOLVING – we need to work backwards, beginning with the last part, and ending with the first. 1. Will walks away with 14 marbles, 2/3 of what was recovered. His friend walks away with 1/3 of what was recovered. 14 is 2/3 so to find out 1/3 I then half 14, getting 7. Sam had 7 and Will had 14. A total rescued of 14 + 7 = 21.21 is half (1/2) of what was lying around on the ground, the other half having been taken by the children. To find how many were on the ground nearby, we need to double 21. NOW, we have an answer of 42! 1. 42 must be doubled to get the final answer, as 1/3 and 1/6 went down drains or hills (1/3 + 1/6 = 1/6 + 2/6 =1/2). 1. This gives us a final answer of 84 marbles in the bag. To find out what fraction of the marbles Andy had given away or lost you have to find the fraction of marbles he was left with. He was left with 14 out of 84 marbles (14/84). You then work out the fraction in its lowest form. Firstly divide 14 and 84 by 2 to get 7/42 then divide them by 7 to get an answer of 1/6. However 1/6 is what he is left with so he must have lost or given away 5/6 of his	{"url":"https://www.kathyaproberts.com/mathematics-the-poetry-of-logical-ideas-einstein/","timestamp":"2024-11-09T13:50:31Z","content_type":"text/html","content_length":"68723","record_id":"<urn:uuid:1bff0e90-e398-4caf-b30b-46c593214a9b>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00312.warc.gz"}
Platypus Innovation This is a maths post -- some technical notes on work we did for the Arab Social Media Report produced by The Dubai School of Govenment . Non-mathematicians should see that study instead. If you proceed, you have been warned: there will be equations. There were several challenges in using the Twitter API to meet the study's research goal. Here I look at population estimation: how to measure the population size by sampling. Capture/Recapture and the Lincoln-Petersen Formula Twitter themselves do not provide data on the geographical distribution of their userbase, and they're a little opaque about their true user population with dead accounts bolstering the numbers. What little official data there is, focuses on those countries with the highest per capita Twitter penetration. In other words, announcements have generally ignored the Arabian peninsula. At the highest level, estimating population size is a simple two step process due to a clever idea from ecological surveying called mark-recapture technique (also known as capture/recapture). Capture/recapture looks at the overlap between different samples in order to estimate the total size of a population. The degree of overlap tells you how complete your samples were, and hence the size of the population. We used a sampling process to collect a couple of samples -- sets of users for each country. The samples were obtained by the simple process of looking for people tweeting. In principle, this is all that is required in order to apply the standard Lincoln-Petersen formula for mark-recapture population estimation.[1] Not So Fast Mr Bond However, the Lincoln-Petersen formula relies on several assumptions: That the population does not significantly change between samples i.e. there aren't many people joining or leaving Twitter across the sampling period. That the sampling procedure does not have an effect on individual behaviours (in ecological sampling the act of capturing an animal might sometimes kill it). That all individuals in the population are equally likely to be captured. Assumption 1 is a reasonable approximation – although Twitter is growing, the change in the Twitter population over a short period will be relatively small. Assumption 2 is also valid as the sampling process is completely passive and cannot affect individual behaviours. However assumption 3 clearly does not hold for a message-based sampling technique. Different twitter users exhibit different patterns of activity: some post many times a day, others once a month. Such a population is said to be heterogenous. We have attempted to correct for this as follows. Correcting for heterogeneity The chances of being picked up in a sweep are linked to activity. More frequent twitter users are more likely to turn up in both sweeps. Activity levels are far from uniform (as confirmed here and in various studies, e.g. [2]). This has the effect that the standard Lincoln-Petersen formula will very significantly underestimate the population size. We correct for this by assigning a prior distribution for the likelihood of being seen. This allows a corrected formula to be calculated. This correction uses extra information about users supplied by Twitter, as described below. Note: given longer histories with more sweeps, there are other models which can be fitted for capture behaviour. See [3] for an overview of techniques. With two sweeps, it is necessary to use a prior distribution to model the heterogenity effect. Without an informative prior, the maximum likelihood estimator for population size with heterogenity is only the number of individuals seen. We assume that an individual's capture probability is linearly correlated with their average post frequency, which we can calculate from their Twitter profile. be the number of individuals captured in sweep 1 and 2 respectively, let be the number of marked individuals found in sweep 2 (the overlap) and let be the total population (which is what we wish to estimate). We divide the population into those caught in sweep 1, and those who were not captured in sweep 1. Let be the individuals captured and marked in sweep1, and the individuals not captured in sweep 1. These sub-populations have different probabilities of being captured in sweep 2, which we denote is the average posterior probability of capture given a previous capture, and is the average posterior probability of capture given no previous capture. , we could estimate \| \| = ( and hence = \| \| + But we don't have -- what we have is an estimator for So we have more work to do. be the tweet frequency distributions for , i.e. has the probability function P(frequency\| ). We measure directly, creating a histogram. We can then estimate the prior distribution for since P(frequency=f \| ) is proportional to ) by the link with tweet frequency. This estimate is unstable around low frequencies, so we set a minimum activity threshold of one tweet per fortnight. We use the prior as an estimator for . This is reasonable, but does have some bias towards higher frequencies, which will result in the final correction being smaller than it should be, and hence our result is below the ideal estimate. By the link with tweet frequency described above, we have ) and ) for some value And without further ado, this gives + ( Note that the Lincoln-Petersen formula is a special case of this equation, where . Which is to say, if you put the homogenity assumption back in, you'll get Lincoln-Petersen out. *The handful of lines shown here took some work, with help from the good Dr Halliwell, and some computational modelling work to double check the reasonableness of it all. Correcting for the unlocatable population A significant number of users choose to withhold their location, or provide non-geographical locations e.g. "wherever there is dancing". Because a country-based sampling process has to discard unresolved locations, without correction we would underestimate the population size. In order to correct for this, we estimated the size of this effect for each country surveyed. We searched for tweets with the location-identifying phrases, "I'm in X" and "here in X" for both the country name and large cities within that country. We performed these searches in both English and Arabic. These searches pick up a mixture of: Identifiable tourists and visitors (identified by the fact that they give their location as a different country). Identifiable local people (identified by their location). People who do not give out their proper location. Let's assume that: (a) the people who use such phrases do not have any bias for or against putting their proper location into their user description, and (b) the people who withhold their location are visitors or locals in proportion to the ratio of identified visitors and identified locals. Now we can estimate the proportion of locals who withhold their location. Putting these things together allowed us to go beyond sample measurements to estimate the underlying populations. Seber, G.A.F., The Estimation of Animal Abundance and Related Parameters. Caldwel,New Jersey: Blackburn Press. http://blogs.hbr.org/cs/2009/06/new_twitter_research_men_follo.html (10% of users create 90% of volume) Sophie Baillargeon Louis-Paul Rivest, Rcapture: Loglinear Models for Capture-Recapture in R	{"url":"https://platypusinnovation.blogspot.com/2011/09/","timestamp":"2024-11-14T12:01:58Z","content_type":"application/xhtml+xml","content_length":"62392","record_id":"<urn:uuid:d14017ca-af30-42c7-986d-3906a30d3126>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00500.warc.gz"}
Which WACC when? A cost of capital puzzle (revisited) Real or nominal? Pre-tax or post-tax? (Or even vanilla?) The number of ‘flavours’ for calculating the weighted average cost of capital is sometimes bewildering. It is often assumed that they all reach more or less the same conclusion, but is this always the case? Contrary to common belief among practitioners, different styles of calculation have a material impact on the value of cash flow to This article was originally published in September 2005. All 2015 commentary is from Oxera. How should a regulator estimate the weighted average cost of capital (WACC) of the companies it regulates? Twenty years of regulatory precedent have not managed to simplify the issue, and it remains central to any price-setting process. This article discusses the relationship between the cost of capital, inflation and tax in the context of utility regulation. However, the concepts are applicable whenever conversions between pre- and post-tax, or real and nominal costs of capital are required. For example, profitability analysis is frequently undertaken based on pre-tax cash flows, and benchmarked against a pre-tax cost of capital. As the article shows, it is easy to miscalculate the pre-tax cost of capital and thereby introduce bias into the analysis. Recently, attention has focused increasingly on precisely which version of the WACC should be used. Numerous possibilities exist, differing, in particular, in the way they approach two key issues. The first is the approach taken to compensating investors for the effects of inflation; the second is the way in which a company’s tax liability is remunerated. This article investigates why regulators are looking again at this issue. In the recent distribution price control review (DPCR4), Ofgem changed its approach to funding the tax liabilities of the distribution network operators; meanwhile, Network Rail’s interim review of track access charges has suggested a different approach to dealing with the effect of inflation.^1 It is recognised that the approach to both issues can affect, for example, the incentives on the capital structure of firms and the extent to which a price control package is believed to be ‘financeable’. There is, however, a bigger issue. It is often assumed that even when approaches to the WACC differ, the long-term effect is the same. That is, the revenues received by the company, and the cash flows they provide to investors, are the same under any of the approaches. As discussed in this article, this is not always the case. 1. Regulators account for the effects of tax and inflation in a variety of ways within their price-setting frameworks. 2. These differences can have an impact on factors such as financeability and the incentives to adopt particular capital structures. 3. It is assumed that the long-term result is the same regardless of which approach is taken. This is not always correct. First, inflation Inflation is central to regulation. It is a given, in the UK and abroad, that investors’ returns should allow for inflation, and that what matters are the real returns received by investors. Real returns The meaning of real returns depends on the inflation index that nominal returns are benchmarked against, and is ambiguous unless this index is specified. It is usual practice to use an index of consumer prices, and in many countries there is an obvious index to choose. For example, there is a harmonised methodology for calculating consumer price indices across EU countries. In the UK, there are two broad groups of consumer price indices—the Retail Prices Index (RPI) and the Consumer Prices Index (CPI)—along with variants of these such as RPIJ and CPIH. These were reviewed in a February 2015 Agenda article.^1 There are two ways in which this can be achieved. The first is typical of the majority of UK regulatory precedent. Inflation is compensated for through annual indexation and applied to the assets on which a real return is allowed. The second approach is to wrap expectations of inflation into the nominal WACC calculation. Here, the regulatory asset base (RAB) is not adjusted to allow for inflation; the necessary compensation is provided by the WACC calculation itself. If it is assumed for the moment that both approaches have the same long-term result, what factors influence the appropriateness of each approach? As mentioned above, the typical UK approach is for the RAB to be indexed by inflation and a real WACC to be used. This approach has one important advantage: in real terms, the regulatory depreciation allowance is constant in each year that the asset remains within the asset base (assuming straight-line depreciation). As a result, today’s customers and tomorrow’s customers pay an equal amount for the asset. This reflects the fact that both sets of customers derive benefit from the use of the asset. However, this approach also has a disadvantage. It can mean that the way the company remunerates its investors differs from the way consumers remunerate the company. Figure 1 shows why this is important. It assumes that a debt of £1,000 attracts a nominal interest rate of 6.6%, and that it is necessary to repay £100 of the principal in every year. But what if that debt was used to finance a £1,000 investment, depreciated over ten years, with a return of 4.0% allowed and the RAB indexed by inflation at 2.5%? The results are very different. When debt is raised, the interest paid is normally expressed on a nominal basis with no indexation of the principal. This results in interest costs having a relatively ‘front-end loaded’ profile, while the remuneration of the costs provided for in the regulatory settlement is ‘back-end loaded’. Figure 1 Interest costs and associated remuneration Source: Oxera analysis. This difference can have significant policy implications. In a regulatory environment in which, in many sectors (particularly the water sector), there is already considerable concern regarding the financeability of the regulatory package,^2 a regulatory policy that exacerbates the difference between costs being incurred and revenues for their remuneration provided—i.e. using indexing and real WACC—strikes some as curious. This was certainly the view of Network Rail during the 2003 interim review of track access charges, and it is also a point that has been raised (in a personal capacity) by Lord Currie, Chairman of Ofcom.^3 Although the ‘back-end loaded’ cash flow profile can exacerbate financeability problems, companies may be able to mitigate the mismatch between indexed revenues and nominal financing costs by issuing inflation-indexed debt and/or entering into inflation swaps. The ability to issue these instruments varies across national capital markets. Furthermore, such back-end loaded profiles may be attractive to the class of investors that look to hedge against long-dated inflation-linked liabilities. For example, pension funds have become more prominent as investors in utilities regulated under a real WACC, indexed RAB model. Second, tax The price control packages must also provide companies with sufficient revenue to meet their corporation tax liabilities. In the UK, this is paid on profits at a (statutory) rate of 30% after interest payments. Again, there are two approaches. The first is the ‘tax wedge’. Here, the cost of equity—that is, the return required by equity investors—is multiplied by a ‘wedge’. This converts the post-tax cost of equity, sufficient to meet the requirements of equity investors, to a pre-tax cost of equity. When this value is applied to the RAB, it provides sufficient revenues to meet the tax liabilities. After tax payments are made, it still provides sufficient returns to satisfy equity investors. Alternatively, some regulators prefer to use a ‘vanilla’ WACC. Here, the post-tax cost of equity is untouched. Instead, the assessment of likely corporation tax liabilities for a regulated company is managed as a cash-flow item and added to the operating costs of a business. The box below provides more detail on these calculations and their underlying formulae. Approaches to tax in setting the WACC The formula for the pre-tax cost of capital is: WACC (pre-tax) = g × Rd + 1/(1 – t) × Re × (1 – g) where g is gearing; Rd is the cost of debt; Re the post-tax cost of equity; and t is the corporation tax rate. This can be compared with the vanilla WACC, so called as it abstracts from all considerations of tax: WACC (vanilla) = g × Rd + Re (1 – g) The difference is the factor 1/(1 – t) applied to the cost of equity in the first calculation but not in the second. This factor (the tax wedge) is equal to approximately 1.42 at the UK statutory corporation tax rate of 30%. When the tax wedge is not applied (i.e. a vanilla WACC is used), it is necessary to fund the tax liabilities as part of the efficient operating costs of the business. Further complicating the issue is the post-tax WACC given by the formula: WACC (post-tax) = g × Rd × (1 – t) + Re (1 – g) This formula captures the tax benefit associated with gearing up (as interest is deducted before tax is calculated). However, as interest payable on debt is already factored into taxable profit, this calculation should not be used in the determination of prices. What factors determine which approach to take? The first point to note is that, actually, both approaches can be made equivalent. If detailed tax modelling is undertaken to estimate what the tax liability of a company will be during the price control period, a tax wedge to the post-tax cost of equity figure can be calculated, providing a revenue stream with the same net present value (NPV) as the NPV of the tax costs. However, the equivalence breaks down if precise liabilities are not calculated—indeed, in using a tax wedge, it is more common for a standard corporation tax rate of 30% to be applied. There are often good reasons for this approach, not least of which is the simplicity it introduces to the regulatory price-setting formula. Nonetheless, over any five-year period, the effective tax rate of the company in question can differ from the statutory rate. This can lead to companies being either under- or over-remunerated for their tax liabilities. Furthermore, in multi-company sectors, more problems can be created by using more than one generic figure. If a generic 30% tax wedge is used, it is often accompanied by another assumption—an industry-wide gearing figure. In other words, a pre-tax cost of capital is calculated to give sufficient revenues to meet the tax liabilities of a company taxed at 30% with, for example, 50% gearing. Even within a five-year period, this creates an incentive on the regulated company to raise its gearing levels above 50% to increase the benefit of the interest tax shield and therefore reduce its tax bill relative to that assumed by the regulator (assuming that the costs of financial distress do not increase). However, the incentive becomes even stronger when it is likely that the gearing assumption will not only stay fixed for a five-year period, but indeed might not change very much thereafter. The use of a vanilla WACC can help eliminate that incentive. It allows a split between the gearing assumption used in the WACC calculation and that used to calculate tax. So once a tax allowance is set, there is still an incentive for a company to gear up over the five-year period. But at the end of that period, the tax calculation at the next review can take account of the new higher gearing level without reference to a sector-wide gearing assumption. Do they all give the same answer? This article has so far considered the reasons for a regulator choosing to adopt either a nominal or real WACC, expressed on either a pre-tax or vanilla basis. As mentioned above, it is often considered that, at least in the long run, the balance between investor returns and consumers will be the same for each approach. In other words, it is argued that all approaches should provide the same NPV of cash flows to investors. Nominal and real WACCs in a pre-tax world Yet is this really the case? One reason to think that it may not be is that it is not clear which is the appropriate approach to calculating a particular real pre-tax cost of capital consistent with a nominal equivalent. Consider the example in Table 1 taken from Ofcom’s recent determination on the cost of capital for BT’s copper access network, which led to a nominal pre-tax cost of capital of close to 10%. Table 1 Ofcom’s parameter estimates for BT’s copper access WACC Notes: Figures taken from the high gearing scenario. All figures rounded to two decimal places in text but exact. ^1 Calculated using the Fisher relationship: ({1 + nominal}/{1 + inflation}) – 1. Source: Ofcom (2005), ‘Ofcom’s Approach to Risk in the Assessment of the Cost of Capital’, August. What is the real pre-tax WACC equivalent of the 9.99% pre-tax nominal WACC? One option, taken by many regulators,^4 would be to follow exactly the same building-block approach as used in the example above, but use the real risk-free rate estimate of 2.05%. This approach yields a real pre-tax estimate of 6.73%. However, an alternative approach, adopted on occasion by Ofcom, would be to take the outturn nominal pre-tax WACC of 9.99% calculated in Table 1 and use the Fisher relationship (see note to table) to derive the real equivalent. This yields a real pre-tax WACC of 7.31%. In the first case, a regulator taking this approach to estimating the real pre-tax WACC would be adjusting for inflation by using a real rather than a nominal risk-free rate, and would then make an adjustment for tax in the cost of equity calculation. The alternative approach would have the tax wedge applied to the cost of equity with a nominal risk-free rate. The adjustment for inflation is then made only at the end. It is clear that the sequence in which tax and inflation are dealt with can make a significant difference: in the numerical example above, the real pre-tax WACC changes by almost 60 basis points. So, which is the ‘correct’ answer? If it was thought that the answer should be given by the approach that ensures that the NPV of cash flows received by investors is exactly equal to the cost of that investment, it appears that the answer is likely to be … neither! This can be demonstrated with the example of a simple regulatory financial model, where the following assumptions are made: Over the years, a few sharp-eyed readers have pointed out that this conclusion is incorrect. In fact, there is a ‘correct’ answer—i.e. the ‘alternative’ approach described above. This is because tax is calculated based on nominal rather than real earnings, and therefore tax adjustments must be performed to the nominal, rather than the real, WACC. • an initial investment of £1,000 is made in year 0, financed, as in the WACC calculation in Table 1, by 35% debt and 65% equity; • the investment is depreciated over ten years; • it is assumed that all cash flows (both costs and revenues) arise at the same time, on one particular day within that year; • it is assumed that corporation tax of 30% is charged on profits, after the deduction of accounting depreciation, or capital allowances, which are calculated on a straight-line nominal basis, and interest payments, assuming that the debt attracts a nominal coupon; and • £35 of debt is repaid every year, so that by the end of the period the asset value and debt position are nil. Using these assumptions, the cash flows available to investors can be calculated as the sum of regulatory depreciation and allowed return, less corporation tax. As these are nominal, post-tax cash flows, it is appropriate to discount them using the nominal vanilla WACC of 7.58%. Table 2 sets out the application of these assumptions in the case where a nominal pre-tax WACC of 9.99% is used, and therefore the RAB is not indexed by RPI. Table 2 Calculation of cash flows to investors using nominal WACC (£) Source: Oxera analysis. The NPV of these cash flows to investors is precisely £1,000—exactly the value of the initial investment. This can be contrasted with the situation in which the RAB is indexed by inflation and a real pre-tax WACC, of either 6.73% or 7.31%, is used. The full cash-flow position is not set out here in as much detail as provided in Table 2, although the logic of the calculations is the same, simply with a different approach to calculating the total revenue line. The results are presented in Table 3. The results presented in Table 3 are sensitive to the modelling approach—in particular, whether the regulatory allowed return (estimated WACC) is applied to the opening RAB or the average RAB, and the intra-year timing of the inclusion of the annual inflation adjustment to the RAB. It can be shown that the NPV of cash flows in the second row is within 0.1% of the initial investment—rather than the 5% indicated—which is consistent with there being a single correct approach of applying the tax adjustment to nominal parameters. Table 3 Comparison of the impact on cash flows of nominal and real pre-tax WACCs Source: Oxera analysis. Compared with the nominal pre-tax approach, the higher real (alleged) equivalent leads to over-recovery. By contrast, the lower value actually leads to under-recovery. Further analysis can show that what really matters is the profile of the use of capital allowances/accounting depreciation relative to the regulatory depreciation allowance. In particular, the nominal WACC approach leads to precisely the ‘correct’ recovery of revenues because the profiles of regulatory depreciation and accounting depreciation are identical. By contrast, in situations where the accounting depreciation/ profile of capital allowance is front-end loaded relative to the regulatory depreciation approach—which, given existing UK regulatory and tax accounting treatment precedent, is the more likely situation—it can be shown that it will always be the case that one of the pre-tax real estimates will lead to over-recovery and the other to under-recovery.^5 In light of this, what should be the appropriate response from regulators? If they wish to continue to use the real pre-tax approach, it appears that some element of judgement—in addition to that required to derive each of the individual parameters—will be needed. Statements from regulators such as: Ofcom believes that the costs associated with setting too low a cost of capital are greater than those associated with setting it too high^6 may therefore point in the direction of using the higher of the two pre-tax real numbers, and hence, for some regulators, a policy change. However, a different means for approaching the WACC could be considered. As seen above, these assumptions, and using the nominal pre-tax approach, appear to provide for cash flows that exactly offset the initial investment. Alternatively, in DPCR4, Ofgem switched from a pre-tax to a vanilla approach. As such, the next section considers how this analysis fits into the vanilla WACC framework. Nominal and real WACC in a vanilla world Using exactly the same individual parameter values as set out in Table 1, it is possible to derive the vanilla WACC estimates in Table 4. Table 4 Different vanilla WACC estimates (%) Source: Oxera analysis. There is one key point to note here. In contrast to the pre-tax calculations, the vanilla framework reverses the effect of the different approaches. The approach favoured by Ofcom now leads to a lower figure than that favoured by other regulators. That is, using a nominal risk-free rate and adjusting for inflation after the nominal WACC has been calculated now leads to a lower value than using a real risk-free rate to derive a real WACC. Mathematically, this is a consequence of the fact that the multiplicative effect of the tax wedge is no longer factored into the calculations. The cash flows and internal rates of return (IRRs) that result from this alternative approach can be calculated in much the same way as before. The results are presented in Table 5. Table 5 Comparison of the impact on cash flows of nominal and real vanilla WACCs Source: Oxera analysis. As before, the nominal vanilla approach provides for an NPV of revenues exactly offsetting the initial investment. However, in contrast to the pre-tax results, the ‘Ofcom’ approach to setting the real vanilla WACC also achieves the same result. Only one approach ‘fails’—building up from a real risk-free rate calculation. In contrast to the pre-tax outcome, in this context it actually creates a slight over-recovery. As indicated in the balloons above, this is not a surprising result. Applying tax adjustments to the nominal rather than real WACC is the correct approach to converting between the vanilla and pre-tax WACC. The choice of how to adjust for tax and inflation within the regulatory price-setting formula is complex, and can have a variety of impacts on the regulated company. These may include the extent to which the price control package is ‘financeable’ and the incentives on the capital structure of the firm. However, in addition to many of these issues that have traditionally been considered relevant by UK regulators, it appears that the extent to which investors will under- or over-recover their investment must also be factored into this analysis. ^1 Ofgem (2004), ‘Electricity Distribution Price Control Review: Final Proposals’, November; and Network Rail (2003), ‘Response to Third Consultation Paper’, September. ^2 There is a concern that investors are being required to invest in companies whose current cash-flow position is relatively fragile, with the prospect of the return on their investment being generated a long way into the future. ^3 Currie, D. (2003), ‘Mutualisation and Debt Only Vehicles’, Competition and Regulation, Institute of Economic Affairs. ^4 For example, the Competition Commission, Ofgem (when it has used a pre-tax WACC), the Civil Aviation Authority, and the Office of Rail Regulation. ^5 Davies, K. (undated), ‘Access Regime Design and Required Rates of Return: Pitfalls in Adjusting for Inflation and Tax Effects’, working paper. ^6 Ofcom (2005), ‘Ofcom’s Approach to Risk in the Assessment of the Cost of Capital’, January. Unbalanced regional development is a common economic concern. It arises from ‘clustering’ of companies and resources, compounded by higher benefit-to-cost ratios for infrastructure projects in well developed regions. Government efforts to redress this balance have had mixed success. Dr Rupert Booth, Senior Adviser, proposes a practical programme to develop… Read More As sustainability continues to grow in importance for businesses, regulators are starting to provide guidance on how competition law applies to ‘green agreements’. In our recent article, written alongside Linklaters, we examine how the European Commission and the UK’s Competition and Markets Authority (CMA) are shaping their frameworks to account… Read More	{"url":"https://www.oxera.com/insights/agenda/articles/which-wacc-when-a-cost-of-capital-puzzle-revisited/","timestamp":"2024-11-07T09:08:15Z","content_type":"text/html","content_length":"102599","record_id":"<urn:uuid:e6669f2b-107d-41cc-9773-4b254b87717d>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00405.warc.gz"}
Coarse-graining of cellular automata, emergence, and the predictability of complex systems We study the predictability of emergent phenomena in complex systems. Using nearest-neighbor, one-dimensional cellular automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. The resulting coarse-grained CA that we construct are capable of emulating the large-scale behavior of the original systems without accounting for small-scale details. Several CA that can be coarse-grained by this construction are known to be universal Turing machines; they can emulate any CA or other computing devices and are therefore undecidable. We thus show that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even decidable at some level of description. The renormalization group flows that we construct induce a hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method. Finally we argue that the large-scale dynamics of CA can be very simple, at least when measured by the Kolmogorov complexity of the large-scale update rule, and moreover exhibits a novel scaling law. We show that because of this large-scale simplicity, the probability of finding a coarse-grained description of CA approaches unity as one goes to increasingly coarser scales. We interpret this large-scale simplicity as a pattern formation mechanism in which large-scale patterns are forced upon the system by the simplicity of the rules that govern the large-scale ASJC Scopus subject areas • Statistical and Nonlinear Physics • Statistics and Probability • Condensed Matter Physics Dive into the research topics of 'Coarse-graining of cellular automata, emergence, and the predictability of complex systems'. Together they form a unique fingerprint.	{"url":"https://experts.illinois.edu/en/publications/coarse-graining-of-cellular-automata-emergence-and-the-predictabi","timestamp":"2024-11-04T11:22:00Z","content_type":"text/html","content_length":"59790","record_id":"<urn:uuid:3bdeca67-406f-49f5-8cd8-0074589eec89>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00536.warc.gz"}
Rarita Schwinger (Spin 3/2) Fields Written: 05/12/2013 Last edited: 22/06/2018 Filed under: Specialist Topics, Quantum Physics Introduction and Representations In principle, analysis of the representation theory of the Lorentz group (or rather its double cover) allows arbitrary • scalar particles. Specifically the Higgs particle lives here. • or either of its two irreducible parts - so spin 1/2 Dirac (or Majorana, which are Dirac with a reality constraint) or Weyl spinors particles. All the known 'matter' particles live here - the quarks and leptons. • vector particles. The best known quantum forces are mediated by gauge bosons in these representations - gluons for QCD, the various weak bosons and the photon. • tensor particles. This decomposition makes up a symmetric, two-index tensor However, in studying supergravity - the supersymmetric completion of gravity - one needs a (massless) spin 3/2 particle to partner up with the graviton. This gravitino is naïvely taken to be a vector-spinor meaning that it has one index of each type, as in Computing the representation, however, we find that by tensoring together these representations we get more than we wanted. Firstly, note and now recall the In particular, we observe that there are components of the vector-spinor which transform as spin 1/2 fields, which is perhaps surprising or undesirable. However, it turns out that the massless theory is naturally described by a gauge theory. This is slightly surprising at first, finding a fermionic gauge redundancy, but on reflection this is simply because we've only looked at spin 1/2 fermions before, whereas we've come across spin 0, 1 and 2 bosonic fields. Amongst other things, it turns out that this gauge redundancy makes the spin 1/2 parts of the field go away - that is, they correspond to pure gauge. The Theory So what exactly is this theory? It is described by a field (Here the gamma matrices in 4D are used. The factor of 1/2 corrects the kinetic term for the smaller number of degrees of freedom - for the Majorana case the barred spinor is not independent of the unbarred one. The above Lagrangians are sensitive in their overall phases to sign conventions, and in overall constants to normalization - we won't worry about this.) There is an alternative version of this Lagrangian which avoids the obviously (due to the fifth gamma matrix and use of epsilon with four indices) four-dimensional nature of the above, given by where one denotes the antisymmetrized products of gamma matrices by This is obtained simply by working out an identity involving the gamma matrices. Equations of motion The equations of motion in the Dirac case are easy to deduce (and are identical in the Majorana case) - one finds two equivalent equations Gauge redundancy and degrees of freedom The interesting thing about these fields is that they have a gauge redundancy given by for any Dirac/Majorana (according to the nature of the spin 3/2 field) spinor field This precisely conspires to remove the spin 1/2 degrees of freedom spotted above, reducing the number of degrees of freedom (counting in the Majorana case where each component is real for simplicity) down from 16 to 12. One must also realize that the But also we find that the corresponding equation of motion is a constraint equation, imposing four further independent constraints, and leaving us with merely 4 degrees of freedom. Finally, the fact that the Lagrangian is first-order in derivatives also serves its usual purpose of halving the apparent degrees of freedom (in the sense that in the phase space momenta conjugate to a given component are given by another component of the field rather than derivatives thereof) so that we have only 2 degrees of freedom - exactly as required to give the two helicity states of such a massless particle in four dimensions. In terms of equations (see also Gauge Quantization for Spin 3/2 Fields by Das and Freedman), this goes as follows: • One should pick a gauge for the gravitino. There are choices analogous to the Lorenz and Coulomb choices in electromagnetism (respectively harmonic gauge. However, we shall use the latter here because it simplifies the analysis of degrees of freedom somewhat. One should note that this gauge choice is always achievable (which is easily checked by writing down an • The constraint equation ( • Also, we may now solve for the A quick remark on gauge fixing: our choice of gauge conditions, as usual, did not quite completely fix the ambiguity in the field, because if we choose The analogy here is with imposing, for instance, the Coulomb gauge condition Resulting theory Putting this all together, we have the constraints with the remaining gauge redundancy and the equation of motion (using the constraints) Curved Space Theory In curved spacetime, with metric and vielbein such that This is all fairly simple, since the spinor indices do not transform under general coordinate transformations. (Spinor fields are sections of the spinor bundle associated to the principal bundle, with indices living in this internal space rather than a spacetime one - local Lorentz transformations on the vielbein or equivalently on the flat space indices can act on the spinors, but not the spacetime transformations.) The upshot is that one can continue writing down a four-component spinor as just a list of four numbers without worrying about picking a basis corresponding to the spacetime coordinates in any sense. Curved space gamma matrices Firstly, one has gamma matrices with Lorentz vector indices μ and consequently one needs to make these covariant. Fortunately this is easily done using a vielbein; one defines This is part of a general prescription for changing between spacetime indices and vielbein indices; one always simply contracts with the vielbein or its inverse as appropriate. (Recall that the whole vielbein can be thought of as an n × n matrix in n dimensions.) Spin connection Slightly more subtle is choosing the correct covariant derivative to act on It turns out - by considering the effect of a transformation or otherwise - that the correct spin connection for derivatives of a spinor To form a fully covariant derivative acting on the spin 3/2 field, one should simply add the Christoffel symbol term one would if only the vector index was present. The end result Quantum Theory In the quantum version of the theory, the 12 redundant degrees of freedom have to be cancelled by ghosts. See also Ghost counting in supergravity (Nielsen). Rarita Schwinger (Spin 3/2) Fields An introduction to the strange things that are spin 3/2 fields	{"url":"https://suchideas.com/articles/physics/quantum/rarita-schwinger/","timestamp":"2024-11-12T08:43:14Z","content_type":"text/html","content_length":"27525","record_id":"<urn:uuid:139d9d35-fdbb-4e31-9863-f5059c805149>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00734.warc.gz"}
Re: [tlaplus] TLA+ logic On Sunday, December 6, 2015 at 11:43:02 PM UTC+2, leuschel wrote: Do you have a TLA+ spec of the flawed sorting algorithm ? No, but the algorithm, as well as a formal specification of the broken assumed invariants and an account of the bug and its discovery, can all be found I am also not sure what kind of symbolic execution you are after. The answer of Leslie Lamport refers to BDD-based symbolic model checking. I am not too sure either (as I am not well-versed in the taxonomy of formal methods), but the kind of symbolic execution used in :) I believe it is not the same as BDD model-checking. A tool that is able to automatically check sorting algorithms is a very powerful one to have in your toolbelt, as sorting algorithms -- like state machines -- are exemplars of a very large class of algorithms and data structures (heaps, B-trees and many other kinds of trees, other indexes in general), and if you can check them, you can probably check many interesting programs.	{"url":"https://discuss.tlapl.us/msg00656.html","timestamp":"2024-11-02T21:53:03Z","content_type":"text/html","content_length":"8431","record_id":"<urn:uuid:fe453144-7737-44a9-81ae-5710ea5b6d99>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00597.warc.gz"}
Congruence in geometry From Encyclopedia of Mathematics An equivalence relation on a set of geometrical figures (segments, angles, etc.). It is introduced either axiomatically (see Hilbert system of axioms) or on the basis of some group of transformations, most frequently of motions (cf. Motion). Thus, in Euclidean geometry (and more generally in the geometry of spaces of constant curvature), two figures are said to be congruent, or equal, if one can be taken to the other by a motion. How to Cite This Entry: Congruence in geometry. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Congruence_in_geometry&oldid=14112 This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098	{"url":"https://encyclopediaofmath.org/index.php?title=Congruence_in_geometry&oldid=14112","timestamp":"2024-11-13T01:54:35Z","content_type":"text/html","content_length":"14150","record_id":"<urn:uuid:dfbc9c5a-1851-4cde-b592-8792317f4bdb>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00572.warc.gz"}
466 research outputs found The Sp(2)-gauge fixing of N = 1 super-Yang-Mills theory is considered here. We thereby apply the triplectic scheme, where two classes of gauge-fixing bosons are introduced. The first one depends only on the gauge field, whereas the second boson depends on this gauge field and also on a pair of Majorana fermions. In this sense, we build up the BRST extended (BRST plus antiBRST) algebras for the model, for which the nilpotency relations, s^2_1=s^2_2=s_1s_2+s_2s_1=0, hold.Comment: 10 pages, no figures, latex forma The existence of a local solution to the Sp(2) master equation for gauge field theory is proven in the framework of perturbation theory and under standard assumptions on regularity of the action. The arbitrariness of solutions to the Sp(2) master equation is described, provided that they are proper. It is also shown that the effective action can be chosen to be Sp(2) and Lorentz invariant (under the additional assumption that the gauge transformation generators are Lorentz tensors).Comment: LaTeX, 13 pages, minor misprints correcte We show that any theory with second class constraints may be cast into a gauge theory if one makes use of solutions of the constraints expressed in terms of the coordinates of the original phase space. We perform a Lagrangian path integral quantization of the resulting gauge theory and show that the natural measure follows from a superfield formulation.Comment: 12 pages, Latexfil The role of one loop order corrections in the triplectic quantization is discussed in the case of W2 theory. This model illustrates the presence of anomalies and Wess Zumino terms in this quantization scheme where extended BRST invariance is represented in a completely anticanonical form.Comment: 10 pages, no figure The present paper is devoted to the study of geometry of Batalin-Vilkovisky quantization procedure. The main mathematical objects under consideration are P-manifolds and SP-manifolds (supermanifolds provided with an odd symplectic structure and, in the case of SP-manifolds, with a volume element). The Batalin-Vilkovisky procedure leads to consideration of integrals of the superharmonic functions over Lagrangian submanifolds. The choice of Lagrangian submanifold can be interpreted as a choice of gauge condition; Batalin and Vilkovisky proved that in some sense their procedure is gauge independent. We prove much more general theorem of the same kind. This theorem leads to a conjecture that one can modify the quantization procedure in such a way as to avoid the use of the notion of Lagrangian submanifold. In the next paper we will show that this is really so at least in the semiclassical approximation. Namely the physical quantities can be expressed as integrals over some set of critical points of solution S to the master equation with the integrand expressed in terms of Reidemeister torsion. This leads to a simplification of quantization procedure and to the possibility to get rigorous results also in the infinite-dimensional case. The present paper contains also a compete classification of P-manifolds and SP-manifolds. The classification is interesting by itself, but in this paper it plays also a role of an important tool in the proof of other results.Comment: 13 page We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The covariance of the construction with respect to the change of the constraint basis is provided by introducing a connection in the ``constraint bundle'', which becomes a key ingredient of the conversion procedure for the non-scalar constraints. Unlike in the case of scalar second-class constraints, no Abelian conversion is possible in general. Within the BRST framework, a systematic procedure is worked out for converting non-scalar second-class constraints into non-Abelian first-class ones. The BRST-extended system is quantized, yielding an explicitly covariant quantization of the original system. An important feature of second-class systems with non-scalar constraints is that the appropriately generalized Dirac bracket satisfies the Jacobi identity only on the constraint surface. At the quantum level, this results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page The multilevel geometrically--covariant generalization of the field--antifield BV--formalism is suggested. The structure of quantum generating equations and hypergauge conditions is studied in details. The multilevel formalism is established to be physically--equivalent to the standard BV--version.Comment: 10 pages, FIAN/TD/13--9 A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first- and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate-invariant way. The general hypergauge functions are shown to be antisymplectic first-class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BRST-type generalized transformations are defined and the functional integral is shown to be independent of the hypergauge variations admitted. In the case of reduced phase space the Dirac's antibrackets are used instead of the ordinary ones The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be equivalent perturbatively to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.Comment: 14 pages, LaTeX, no figure	{"url":"https://core.ac.uk/search/?q=authors%3A(Batalin%20I.%20A.)","timestamp":"2024-11-02T14:11:05Z","content_type":"text/html","content_length":"141344","record_id":"<urn:uuid:742edd44-8d80-4182-b528-a5df61a387b4>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00305.warc.gz"}
Internal rate of return in software project management Simply put, the internal rate of return (IRR) gives you the average annual rate of return of a project throughout its lifetime. Like the NPV, the IRR is a discounted 2 Jul 2019 IRR (Internal Rate of Return) is another fundamental tool of real estate fund managers and investors determine when a project is likely to The good news is that IRR is easily calculated using Excel, real estate software or a Some of the contents are adapted from “Software Engineering” by Theodore P. The Importance of Project Cost Management □Internal Rate of Return (IRR). 9 Oct 2016 your formula tells you the discount rate…at which you would break even on a given investment.…If the IRR formula returns a value greater than… 8 Dec 2017 A Project Management Information System (PMIS) like PMWeb not only enables the Assessing Project Internal Rate of Return (IRR) set of clearly defined methods of communication between various software components. 12 Apr 2016 The Internal Rate of Return (IRR) is the rate at which each invested dollar is projected to grow for each period it is invested. Internal Rate of Return may be defined as the interest rate at which a monetary investment will return a zero Net Present Value. Every project manager should be familiar with how IRR is used in project management , i.e., to determine the earliest time a project is able to get out of its debt phase. The Internal Rate of Return is one of the most common success measures of projects and investments. It is a profitability metric that can be used to assess and compare different project options even if their investment amounts, timeline and cash flow characteristics differ. The purchasing team calculates the net present value, payback period, and internal rate of return. They present a report to the management which includes an Internal Rate of Return (IRR) of 14%. The firm’s weighted average cost of capital (WACC) is 8.5%. Internal rate of return is the rate where net present value of project is zero, it is a discounting rate by which future cash flows are adjusted to determine the present value, at IRR it is the minimum required rate of return of project and internal rate of return is also used to determine the discounting rate by giving the net present value of zero. Example Results -. Highway Rehabilitation Project. Economic analysis over 30 years: NPV@12% per annum = $530m. IRR = 20% per annum. Modified Access the answers to hundreds of Internal rate of return questions that are A project's NPV profile will cross the horizontal axis at: a) the cost of debt. b) the cost Management Firm is considering an investment of $15,000 for a new software 11 Nov 2019 As a project manager, start with a cost plan and create cost projections for the Compare the IRR, MIRR, and Payback Period for each project. Internal rate of return (IRR) is all about figuring out how quickly (if at all), and at what The project management department believes that this would produce an extra calculation almost always done with a financial calculator or software. conventional cash flows is quite simple – accept (reject) the project if the IRR is greater are only able to calculate a single IRR or the financial calculators/ software the cost of capital precisely, as long as the project manager is sure that the. Some of the contents are adapted from “Software Engineering” by Theodore P. The Importance of Project Cost Management □Internal Rate of Return (IRR). 9 Oct 2016 your formula tells you the discount rate…at which you would break even on a given investment.…If the IRR formula returns a value greater than… Internal rate of return is the rate where net present value of project is zero, it is a or by the use of some software system programmed to calculate the IRR. Internal rate of return (IRR) is all about figuring out how quickly (if at all), and at what The project management department believes that this would produce an extra calculation almost always done with a financial calculator or software. conventional cash flows is quite simple – accept (reject) the project if the IRR is greater are only able to calculate a single IRR or the financial calculators/ software the cost of capital precisely, as long as the project manager is sure that the. Some of the contents are adapted from “Software Engineering” by Theodore P. The Importance of Project Cost Management □Internal Rate of Return (IRR). 9 Oct 2016 your formula tells you the discount rate…at which you would break even on a given investment.…If the IRR formula returns a value greater than… 8 Dec 2017 A Project Management Information System (PMIS) like PMWeb not only enables the Assessing Project Internal Rate of Return (IRR) set of clearly defined methods of communication between various software components. The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) Net Present Value (NPV) Net Present Value (NPV) is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present. If its internal rate of return (IRR) is 10%, that cash flow should be discounted to give a present value of £5000/1.331 = £3757 (rounded up to the nearest pound). Internal Rate of Return (IRR) is a financial measure used to evaluate projected cash flow results and to compare the feasibility of a project/investment. IRR is generally used with other financial measures such as Net Present Value (NPV) and Return on Investment (ROI). I initially wrote a draft version of this post that outlined a variety of wrong ways to evaluate projects, but I gave up on it because it was too depressing. Instead of that, let's get right to it. The best practical way to evaluate technology projects is to calculate the proposed project's internal rate of return. Definition: The internal rate of return (IRR) is the discount rate that results in a net present value of zero for a series of future cash flows. What it means: It's a cutoff rate of return; avoid Internal Rate of Return (IRR) is a financial measure used to evaluate projected cash flow results and to compare the feasibility of a project/investment. IRR is generally used with other financial measures such as Net Present Value (NPV) and Return on Investment (ROI). Internal rate of return (IRR) is the minimum discount rate that management uses to identify what capital investments or future projects will yield an acceptable return and be worth pursuing. The IRR for a specific project is the rate that equates the net present value of future cash flows from the project to zero. The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) Net Present Value (NPV) Net Present Value (NPV) is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present. Return on Investment (ROI) and Internal Rate of Return (IRR) are among the most popular success measures for projects and investments. They are also mentioned in the Project Management Institute’s Body of Knowledge (source: PMBOK, 6 th edition, part 1, ch. 1.2.6.4, p.	{"url":"https://bestcurrencyvgvr.netlify.app/chum37955by/internal-rate-of-return-in-software-project-management-gone.html","timestamp":"2024-11-05T17:24:09Z","content_type":"text/html","content_length":"34580","record_id":"<urn:uuid:37d4f545-8811-4209-8ebf-9dc6f3f3034c>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00249.warc.gz"}
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Gabriel Santiago, Kyle Shiells, Jinghong Yang, Generalized parton distributions through universal moment parameterization: non‐zero skewness case, JHEP 05 150 (Feb 2023)	{"url":"https://qgtcollab.github.io/publications.html","timestamp":"2024-11-13T12:52:35Z","content_type":"text/html","content_length":"27991","record_id":"<urn:uuid:9c68188b-f5c3-492d-b0c9-9692ef7a0f99>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00001.warc.gz"}
What's decidable about weighted automata? Weighted automata map input words to numerical values. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. In the 90's, Krob studied the decidability of problems on rational series, which strongly relate to weighted automata. In particular, it follows from Krob's results that the universality problem (that is, deciding whether the values of all words are below some threshold) is decidable for weighted automata with weights in ℕ ∪ {∞}, and that the equality problem is undecidable when the weights are in ℤ ∪ {∞}. In this paper we continue the study of the borders of decidability in weighted automata, describe alternative and direct proofs of the above results, and tighten them further. Unlike the proofs of Krob, which are algebraic in their nature, our proofs stay in the terrain of state machines, and the reduction is from the halting problem of a two-counter machine. This enables us to significantly simplify Krob's reasoning and strengthen the results to apply already to a very simple class of automata: all the states are accepting, there are no initial nor final weights, and all the weights are from the set {∈-∈1,0,1}. The fact we work directly with automata enables us to tighten also the decidability results and to show that the universality problem for weighted automata with weights in ℕ ∪ {∞}, and in fact even with weights in ℚ^≥0 ∪ {∞}, is PSPACE-complete. Our results thus draw a sharper picture about the decidability of decision problems for weighted automata, in both the front of equality vs. universality and the front of the ℕ ∪ {∞} vs. the ℤ ∪ {∞} domains. Publication series Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Volume 6996 LNCS ISSN (Print) 0302-9743 ISSN (Electronic) 1611-3349 Conference 9th International Symposium on Automated Technology for Verification and Analysis, ATVA 2011 Country/Territory Taiwan, Province of China City Taipei Period 11/10/11 → 14/10/11 Dive into the research topics of 'What's decidable about weighted automata?'. Together they form a unique fingerprint.	{"url":"https://cris.huji.ac.il/en/publications/whats-decidable-about-weighted-automata-13","timestamp":"2024-11-03T03:31:29Z","content_type":"text/html","content_length":"53206","record_id":"<urn:uuid:1d01d97a-94c0-41ad-bfa5-52f7dd186572>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00648.warc.gz"}
Frenkel, Yakov Ilyich \| Encyclopedia.com Frenkel, Yakov Ilyich Frenkel, Yakov Ilyich (b. Rostov, Russia, 10 February 1894; d. Leningrad, U.S.S.R., 23 January 1954) As a child Frenkel exhibited both interest and ability in music and painting; but later, in school, he was attracted to mathematics and physics. In 1911 he completed his first independent mathematical paper, in which he created a new type of calculus—but it proved to be already known under the name calculus of finite differences. In 1912 he independently developed a physical theory which he showed to A. F. Joffe, with whom he established a close relationship. In 1913 Frenkel entered the Physics and Mathematics Faculty of St. Petersburg University, from which he graduated with honors in 1916. In 1916–1917 he participated in a seminar led by Joffe at the Petrograd Polytechnic Institute, and in 1918 he taught at the newly created Tavrida University in Simferopol. Frenkel returned to Petrograd (Leningrad) in 1921 and worked at the Physico-Technical Institute, which was directed by Joffe, fur the rest of his life; he also taught theoretical physics at Leningrad Polytechnic Institute. In 1929 Frenkel was elected an associate member of the Academy of Sciences of the U.S.S.R. He spent 1930–1931 in the United States, where he lectured at the University of Frenkel published many scientific books and journal articles, and his research encompassed extremely varied fields of theoretical physics. He was one of the founders of the modern atomic theory of solids (metals, dielectrics, and semiconductors). In 1916 he conceived, on the basis of the Bohr model of the atom, the theory of the double electric layer on the surface of metals, which permitted the first evaluations of the surface tensions of metals and of the contact potential. In 1924, on the basis of virial theory, Frenkel demonstrated that during the condensation of a metal from vapor the valence electrons of the atoms must become itinerant, moving at a speed comparable to the rate of intra-atomic motion. This was a noteworthy contribution to the problem of the heat capacity of electrons in metals, which had been blocking progress of the theory. In 1927 Frenkel became the first to attempt to construct a theory of metals based on the representations of quantum wave mechanics and was able to explain quantitatively the large mean free paths of electrons in metals. In 1928 he developed a simple, elegant deduction of the Pauli theory of the paramagnetism of electrons in metals, used in the majority of textbooks. He also offered in that year the first quantum mechanical explanation of the nature of ferromagnetism, which was independently developed somewhat later in Werner Heisenberg’s theory. He simultaneously offered the theory of coercive force in metals. Using the virial theorem, Frenkel established the connection between the electron theory of metals, the Thomas-Fermi atomic model, as well as the theory of the nucleus and high-density stars. The general fundamental questions first raised in these works have not lost their significance. In 1930 Frenkel and J. G. Dorfman offered the first theoretical substantiation of the breakup of a ferromagnetic substance into separate domains and predicted the existence of single-domain particles. In 1930–1931 Frenkel made a detailed study of the absorption of light in solid dielectrics and semiconductors. He pointed out the possibility of the emergence of two different forms of excitation in a crystal. When light is absorbed, an excitation state without ionization may appear. Frenkel called this excitation state “exciton,” since such a state has the properties of a quasi particle distributed inside the dielectric or semiconductor. The second type of excitation generated by light in solid bodies, according to Frenkel’s theory, is associated with ionization, i.e., with formation of a free electron and a free hole. When bound together the electron and hole form a unique neutral system that possesses a discrete energy spectrum; this system is called Frenkel’s Frenkel’s work on the theory of electric breakdown in dielectrics and semiconductors (1938) has great significance. As early as 1926, in his work on thermal motion in solid and liquid bodies, Frenkel was the first to work out a model of a real crystal, in which a fraction of the molecules or ions oscillate around temporary equilibrium positions which are intermediate between lattice points and in which a fraction of the lattice points are correspondingly free; the vacancies thus formed (Frenkel’s defects) migrate throughout the crystal. In distinction to the generally held representation of the closeness of the liquid state to the gaseous, Frenkel put forward the new idea of an analogy between a liquid and a solid body. He considered a liquid to be a body possessing short-range but not long-range order. Frenkel’s theory of diffusion and viscosity, which was built on this model, proved to be exceedingly fruitful. Frenkel systematically developed his thory of the liquid state in the monograph Kineticheskaya teoria zhidkostey (“The Kinetic Theory of Liquids,”, 1945), which earned him the firstdegree State Prize in 1947. Frenkel paid considerable attention to the theory of the mechanical properties of solid bodies. In papers published in conjunction with T. A. Kontorova (1937, 1938) it was first demonstrated theoretically that in distortion-free lattices a special form of particle motion is possible—a gradual, mutually concordant shift from certain equilibrium positions to others, which leads to a gradual, mutual displacement of the rows of atoms. This theory permitted the explanation of several specific particulars of the plastic deformation and twinning of crystals. The theory of the elasticity of rubbery substances, developed by Frenkel and S. E. Bresler in 1939, proved to be in good agreement with experimental data. Frenkel’s research had an essential influence on the development of electrodynamics and the theory of electrons, as well as the theory of atomic nuclei. His 1926 study served as the basis for the investigation of many questions concerning the dynamics of a spinning electron before the appearance, in 1928, of Dirac’s theory of relativistic quantum mechanics. In Elektrodinamika, published by Frenkel in 1928, questions of classical electrodynamics were examined from a completely new point of view. In 1936 he was the first to attempt the construction of a statistical theory of heavy nuclei, considering the nucleus as a solid body and setting aside the individual motion of nucleons. In 1939, shortly after the discovery of the splitting of heavy nuclei by Otto Hahn and Fritz Strassman, Frenkel developed (independently of Bohr and J. A. Wheeler) a theory which explains the process of splitting as the result of the electrocapillary oscillation of electrically charged drops of nucleic liquid. Frenkel also solved many problems in meteorology and geophysics. Between 1944 and 1949 he proposed the theory of atmospheric electrification in which the close connection between the electrification of clouds and the existence of fields in cloudless atmosphere was established. In 1945 he formulated a new theory of geomagnetism. 1. Original Works. Frenkel’s writings include lehrbuch der Elektrodynamik, 2 vols. (Berlin, 1926–1928); Kinetic Theory of Liquids (Oxford, 1946); Wave Mechanics. Elementary Theory (New York, 1950); Wave Mechanics. Advanced General Theory (New York, 1950); Sobranie izbrannykh trudov (“Collection of Selected Works”), 3 vols. (Moscow–Leningrad, 1956–1958); Prinzipien der Theorie der Atomkerne (Berlin, 1957); and Statistische Physik (Berlin, 1957). II. Secondary Literature. Articles and books on Frenkel and his work (in Russian) are A. I. Anselm, “Yakov Ilyich Frenkel”, in Uspekhi Fizicheskikh nahk, 47 , pt. 3 (1952), 470; J. G. Dorfman, “Yakov Ilyich Frenkel”, in Frenkel’s Sobranie izbrannykh trudov, II (Moscow–Leningrad, 1958), 3–15; V. Y. Frenkel, Yakov Ilyich Frenkel (Moscow–Leningrad, 1966); and I. E. Tamm, “Yakov Ilyich Frenkel”, in Uspekhi fizicheskikh nauk, 76 , pt. 3 (1962), 327. J. G. 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Big O Notation In computer science, Big O notation is a mathematical notation used to describe the limiting behavior of a function as its argument tends towards a particular value or infinity. It is primarily used to characterize the complexity of algorithms, specifically their runtime or space requirements (memory usage) in relation to the input size. Formal Definition Let $f$ and $g$ be two functions defined on the set of real numbers. We say that $f(x) = O(g(x))$ (read as "f of x is big O of g of x") if there exist positive constants $c$ and $x_0$ such $\|f(x)\| \leq c * \|g(x)\| \quad \text{for all } x > x_0$ This means that, for sufficiently large values of $x$, the function $f(x)$ will grow no faster than a constant multiple of $g(x)$. Common Big O Classes Here are some of the most frequently encountered complexity classes in algorithm analysis, listed in order of increasing growth rate: • $O(1)$: Constant time - the algorithm's runtime does not depend on the input size. (Example: Accessing an element in an array by its index) • $O(\log n)$: Logarithmic time – the runtime grows proportionally to the logarithm of the input size. (Example: Binary search) • $O(n)$: Linear time – the runtime grows proportionally to the input size. (Example: Traversing a linked list) • $O(n \log n)$: Log-linear time – the runtime is a product of a linear and a logarithmic term. (Example: Efficient sorting algorithms like merge sort or heap sort) • $O(n^2)$: Quadratic time – the runtime grows proportionally to the square of the input size. (Example: Naive nested loop algorithms) • $O(n^c)$: Polynomial time (where c is a constant) – the runtime grows as a polynomial function of the input size. • $O(2^n)$: Exponential time – the runtime grows exponentially with respect to the input size. (Example: Solving the traveling salesman problem by brute-force) Importance in Algorithm Analysis Big O notation provides a simplified and standardized way to talk about algorithm efficiency: • Predicting performance: It helps estimate how an algorithm's runtime or memory usage will scale with input size, allowing the comparison of different algorithms. • Focusing on worst-case scenarios: Big O notation usually represents the worst-case time complexity, giving an upper bound on the algorithm's resource consumption. • Abstraction: By focusing on the dominant growth rate, Big O notation simplifies analysis and helps identify the core factors influencing an algorithm's performance. Consider a function that finds the maximum element in an array of size n. If the array is unsorted, we need to examine all elements. This algorithm has a runtime complexity of O(n), indicating that the runtime grows linearly with the input size. Big O notation is considered an upper bound for the following reasons: 1. Worst-Case Focus: • Big O notation expresses the maximum potential growth rate of an algorithm's runtime or resource usage. • It inherently captures the worst-case scenario of an algorithm's behavior, meaning the scenario where the algorithm takes the longest to run or consumes the most resources for a given input size. 2. Asymptotic Behavior: • Asymptotic analysis, of which Big O is a central part, focuses on the behavior of algorithms as the input size (n) approaches infinity. • For large input sizes, dominant terms in the algorithm's complexity function begin to overshadow constant factors and lower-order terms. Big O expresses this dominant term, giving a sense of how inefficient the algorithm can get as inputs grow. 3. Mathematical Definition: • Formally, a function f(n) is said to be O(g(n)) if there exist constants c and n₀ such that: f(n) ≤ c * g(n) for all n ≥ n₀ • This means that eventually (n ≥ n₀), the growth of f(n) is always less than or equal to a constant multiple of g(n). In other words, g(n) acts as a ceiling for f(n)'s growth. Consider an algorithm with a runtime complexity of T(n) = 3n² + 5n + 8. • Big O Representation: This algorithm would be represented as O(n²). This is because the n² term dominates the growth of the function as n gets large. • Upper Bound Reasoning: For sufficiently large input values, the lower-order terms (5n + 8) and the constant factor (3) become less significant compared to n². Thus, the function's growth can be bounded by a constant multiple of n². Why It Matters: By understanding the upper bound, you can: • Predict scalability: Assess how an algorithm's performance will degrade with increasingly large input sizes. • Compare algorithms: Make informed choices between algorithms based on their worst-case complexity, especially when dealing with large datasets. Important Note: Big O doesn't tell you the exact runtime of an algorithm. It provides a way to compare growth rates and reason about an algorithm's efficiency in the long run.	{"url":"https://blog.prepsphere.com/share/C4Xs4nwFlOys","timestamp":"2024-11-02T20:28:31Z","content_type":"text/html","content_length":"67629","record_id":"<urn:uuid:67097631-95ac-47d2-9c4a-dc88d9e5408c>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00200.warc.gz"}
Value difference between OPC Kepware and readBlocking Why there is a difference in value tag between OPC Kepware and the value read by the function readBlocking? Also, the value in the Designer is exactly like in the OPC. standard python behavior: Built-in Functions — Python 3.12.3 documentation >>> round(27.799999, 5) >>> round(27.799999, 6) 2 Likes For 32-bit floating point, 27.8 IS the same number as 27.799999. Nothing to do with Ignition at all. The least common denominator of any number ending in .8 is five. Which yields a repeating binary fraction. { If you convert to double, and show even more decimal places, it will look even weirder. Simply artifacts of binary fractions. } 2 Likes To illustrate Phil's point: (IEEE-754 Floating Point Converter) 4 Likes	{"url":"https://forum.inductiveautomation.com/t/value-difference-between-opc-kepware-and-readblocking/89531","timestamp":"2024-11-09T12:25:47Z","content_type":"text/html","content_length":"27355","record_id":"<urn:uuid:5edd30a2-3709-4b56-a329-a9ef80d5f2e2>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00282.warc.gz"}