url
stringlengths 14
2.42k
| text
stringlengths 100
1.02M
| date
stringlengths 19
19
| metadata
stringlengths 1.06k
1.1k
|
|---|---|---|---|
https://www.deepdyve.com/lp/springer-journals/meromorphic-solutions-of-a-differential-equation-with-polynomial-0E8e1zji5v
|
# Meromorphic Solutions of a Differential Equation with Polynomial Coefficients
Meromorphic Solutions of a Differential Equation with Polynomial Coefficients We give new estimates for the maximum number M of distinct meromorphic solutions and also for the maximum number L of linearly independent meromorphic solutions of the first order differential equation $$f^\prime = p_0+p_1f+...+p_nf^n,\ \ \ n\geq 3,$$ where each P k is a polynomial and P n ≢ 0. The estimate for M depends only on n and the number d of distinct zeros of P n, while the estimate for L depends only on d. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals
# Meromorphic Solutions of a Differential Equation with Polynomial Coefficients
, Volume 8 (1) – Mar 27, 2007
14 pages
/lp/springer-journals/meromorphic-solutions-of-a-differential-equation-with-polynomial-0E8e1zji5v
Publisher
Springer Journals
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321665
Publisher site
See Article on Publisher Site
### Abstract
We give new estimates for the maximum number M of distinct meromorphic solutions and also for the maximum number L of linearly independent meromorphic solutions of the first order differential equation $$f^\prime = p_0+p_1f+...+p_nf^n,\ \ \ n\geq 3,$$ where each P k is a polynomial and P n ≢ 0. The estimate for M depends only on n and the number d of distinct zeros of P n, while the estimate for L depends only on d.
### Journal
Computational Methods and Function TheorySpringer Journals
Published: Mar 27, 2007
### References
Access the full text.
|
2023-02-06 20:38:03
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7331210374832153, "perplexity": 705.573026127882}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500357.3/warc/CC-MAIN-20230206181343-20230206211343-00581.warc.gz"}
|
https://byjus.com/impulse-calculator/
|
# Impulse Calculator
Formula : I = m * Δ v.
Enter the unknown value as ' x '
Mass (m) = Kg
Velocity Change (Δ v) = m/s
Impulse (I) = kgm/s
x=
The Impulse Calculator an online tool which shows Impulse for the given input. Byju's Impulse Calculator is a tool
which makes calculations very simple and interesting. If an input is given then it can easily show the result for the given number.
#### Practise This Question
How many structural isomers can you write for all the isomeric alcohols having the molecular formula C4H10O.
|
2019-01-20 03:02:27
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8524726033210754, "perplexity": 5157.6617355998715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583690495.59/warc/CC-MAIN-20190120021730-20190120043730-00410.warc.gz"}
|
https://www.inferentialthinking.com/chapters/05/Sequences
|
# Sequences
Values can be grouped together into collections, which allows programmers to organize those values and refer to all of them with a single name. By grouping values together, we can write code that performs a computation on many pieces of data at once.
Calling the function make_array on several values places them into an array, which is a kind of sequential collection. Below, we collect four different temperatures into an array called highs. These are the estimated average daily high temperatures over all land on Earth (in degrees Celsius) for the decades surrounding 1850, 1900, 1950, and 2000, respectively, expressed as deviations from the average absolute high temperature between 1951 and 1980, which was 14.48 degrees.
baseline_high = 14.48
highs = make_array(baseline_high - 0.880, baseline_high - 0.093,
baseline_high + 0.105, baseline_high + 0.684)
highs
array([ 13.6 , 14.387, 14.585, 15.164])
Collections allow us to pass multiple values into a function using a single name. For instance, the sum function computes the sum of all values in a collection, and the len function computes its length. (That’s the number of values we put in it.) Using them together, we can compute the average of a collection.
sum(highs)/len(highs)
14.434000000000001
The complete chart of daily high and low temperatures appears below.
|
2019-07-16 18:48:19
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6507419943809509, "perplexity": 993.4711753708038}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524685.42/warc/CC-MAIN-20190716180842-20190716202842-00421.warc.gz"}
|
https://plainmath.net/92550/classify-the-following-random-variables
|
# Classify the following random variables as continuous or discrete: the height of a sky-scraper.
Classify the following random variables as continuous or discrete: the height of a sky-scraper.
You can still ask an expert for help
• Questions are typically answered in as fast as 30 minutes
Solve your problem for the price of one coffee
• Math expert for every subject
• Pay only if we can solve it
blikath3
We need to determine whether the random variable "height" is discrete or continuous.
Discrete random variables take on values that are restricted to defined separated values, for example: integers or counts.
Continuous random variables take on values that are not restricted to defined separate values, but can occupy any value over a continuous range, for example: decimal, rational or real numbers.
The height of a skyscraper can take on decimal values such as 102.75 m.
The random variable is then continuous.
Result:
Continuous.
|
2022-11-30 07:30:41
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 41, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7865977883338928, "perplexity": 1072.2027097889434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710733.87/warc/CC-MAIN-20221130060525-20221130090525-00536.warc.gz"}
|
https://math.stackexchange.com/questions/2655785/geodesic-equation-and-arclength-parametrization
|
# Geodesic equation and arclength parametrization
Let $(M,g)$ be a Riemannian manifold and $\gamma\subset M$ a curve in $M$. Suppose I would like to show that $\gamma$ satisfies the geodesic equations $$\ddot{x}^k=-\Gamma_{ij}^k\dot{x}^i\dot{x}^j.$$
If $\gamma$ is not parametrized by arc length, $\gamma$ may not satisfy the geodesic equations, as this example demonstrates: Why is $\gamma(t)=(0,t)$ a geodesic in the hyperbolic plane?
My question is why a geodesic, which is not parametrized by arc length, may not satisfy the geodesic equations (as in the above example).
Do Carmo derives the geodesic equations on page 62 and states that a curve in $M$ is a geodesic iff it satisfies the geodesic equation. Where does he assume that the curve is parametrized by arc length?
Let $\nabla$ be the Levi-Civita connection of $(M,g)$ and $c$ be a geodesic of $(M,g)$, then by definition, one has: $$\overline{\nabla}_{\dot{c}}\dot{c}=0,$$ where $\overline{\nabla}$ stands for $c^*\nabla$, then since $g$ is $\nabla$-parallel, the induced metric $\overline{g}:=c^*g$ is $\overline{\nabla}$-parallel, so that: $$\frac{\mathrm{d}}{\mathrm{d}t}\overline{g}(\dot{c},\dot{c})=2\overline{g}(\nabla_{\dot{c}}\dot{c},\dot{c})=0,$$ therefore $c$ is parametrized at constant speed that is proportionally to the arc length. I want to insist on this last point, a geodesic is not necessarily parametrized at speed $1$. This little discussion established that geodesic are not purely geometric objects.
The geodesic equation stated by Do Carmo is simply the coordinate-dependent version of $\overline{\nabla}_{\dot{c}}\dot{c}=0$. Indeed, by the very definition of the Christoffel $(2,1)$-tensor, one has $\nabla=\nabla^0+\Gamma$, where $\nabla^0$ is the flat connection of the given chart of $M$. Therefore, as we saw, being a solution of the geodesic equation implies being parametrized proportionally to the arc length, so no need to assume that the curve satisfies this condition.
|
2019-10-22 11:08:25
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9594851732254028, "perplexity": 124.8415789804946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987817685.87/warc/CC-MAIN-20191022104415-20191022131915-00412.warc.gz"}
|
https://bathmash.github.io/HELM/3_2_solving_quadratic_equatns-web/3_2_solving_quadratic_equatns-web.html
|
Introduction
A quadratic equation is one which can be written in the form $a{x}^{2}+bx+c=0$ where $a$ , $b$ and $c$ are numbers, $a\ne 0$ , and $x$ is the unknown whose value(s) we wish to find. In this Section we describe several ways in which quadratic equations can be solved.
Prerequisites
• be able to solve linear equations
Learning Outcomes
• solve a quadratic equation by factorisation
• solve a quadratic equation using the standard formula
• solve a quadratic equation by completing the square
• interpret the solution of a quadratic equation graphically
|
2022-09-26 00:16:12
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8354358077049255, "perplexity": 255.12235408789297}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334620.49/warc/CC-MAIN-20220925225000-20220926015000-00431.warc.gz"}
|
https://uqworld.org/t/bayesian-inversion-discrepancy/1230
|
Bayesian inversion : discrepancy
Hello,
I am currently working on the Bayesian inversion. I have some troubles with the discrepancy option, which remains not very clear to me.
Here are some of my thoughts :
1. The discrepancy seems to be an additive quantity, which is added to the result of the model. Thus, during a Bayesian analysis, one should work with this error. I mean the model becomes Y = M(X) + \epsilon, even during the prior analysis, and to manually plot the histogram of Y, the \epsilon should be added.
2. Also, as I understand the discrepancy, if a very small quantity is chosen, the result of the Bayesian inversion can be quasi deterministic (the discrete solutions of the equation M(X) = Y_{obs} will appear). It also means it does not allow multiple observations. Thus, without discrepancy, the Bayesian inversion joins the observational method (which X returns the observation).
3. As the model often comes from hypothesis (finite element softwares etc…), I understand there is a model bias in practical engineering problems. These approximations are taken into account through the discrepancy term.
The second point explains the need of the discrepancy, to do a Bayesian inversion (with no discrepancy, the inversion will give back discrete values instead of probabilistic ones). It is completed by the third point.
But by combining the 1) and 3) point, one could also implement a discrepancy even without Bayesian inversion, to represent the model bias (even in a simple reliability analysis for example) ?
As I work with a finite element software, do you recommend to choose a discrepancy term for every analysis (problem dependant I guess), or only for Bayesian inversion ? Would you have documentations about the choice of the discrepancy ?
PS : I suggest to describe a little bit more the discrepancy term in the Bayesian user manual. It took me some time to understand that uq_print adds the discrepancy term to the prior and posterior outputs, in the histograms. Also, I think the discrepancy implementation is a little bit confusing. When defining a Gaussian through Parameters in the input module, the standard deviation must be filled, but with the discrepancy, the DiscrepancyOpts.Parameters contains the variance (std squared). Maybe a note could be added in the 2.2.6.1 paragraph of the manual.
|
2021-06-20 13:23:33
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7928079962730408, "perplexity": 588.6699482698752}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487662882.61/warc/CC-MAIN-20210620114611-20210620144611-00589.warc.gz"}
|
http://www.stephenbox.com/3gnip/viewtopic.php?ca5a20=curium-protons-neutrons-electrons
|
Pengertian Elektron. Helium is a chemical element with atomic number 2 which means there are 2 protons and 2 electrons in the atomic structure. Like all elements with atomic number over 100, nobelium can only be produced in particle accelerators by bombarding lighter elements with charged particles. The chemical symbol for Osmium is Os. Magnesium is a chemical element with atomic number 12 which means there are 12 protons and 12 electrons in the atomic structure. It must be noted, especially nuclear cross-sections may vary by many orders from nuclide with the neutron number N to nuclide with the neutron number N+1. The chemical symbol for Potassium is K. Potassium was first isolated from potash, the ashes of plants, from which its name derives. The chemical symbol for Tellurium is Te. The chemical symbol for Thorium is Th. Rhenium is a silvery-white, heavy, third-row transition metal in group 7 of the periodic table. Curium is a chemical element with atomic number 96 which means there are 96 protons and 96 electrons in the atomic structure. The unit of measure for mass is the atomic mass unit (amu). An atomic mass unit ($$\text{amu}$$) is defined as one-twelfth of the mass of a carbon-12 atom. Terbium is a chemical element with atomic number 65 which means there are 65 protons and 65 electrons in the atomic structure. Mercury is a heavy, silvery d-block element, mercury is the only metallic element that is liquid at standard conditions for temperature and pressure. Natural boron consists primarily of two stable isotopes, 11B (80.1%) and 10B (19.9%). Thorium is moderately hard, malleable, and has a high melting point. The chemical symbol for Rhodium is Rh. The chemical symbol for Nobelium is No. Curium-242 was produced by bombarding americium-241 with slow moving neutrons for a year. Iodine is the least abundant of the stable halogens, being the sixty-first most abundant element. Lutetium is the last element in the lanthanide series, and it is traditionally counted among the rare earths. Chlorine is a chemical element with atomic number 17 which means there are 17 protons and 17 electrons in the atomic structure. The chemical symbol for Einsteinium is Es. is a rare earth element with a metallic silver luster. The chemical symbol for Actinium is Ac. By mass, oxygen is the third-most abundant element in the universe, after hydrogen and helium. Number of Protons/Electrons: 58 Number of Neutrons: 82 Classification: Rare Earth Crystal Structure: Cubic Density @ 293 K: 6.773 g/cm 3 Color: gray Atomic Structure : Number of Energy Levels: 6 First Energy Level: 2 Second Energy Level: 8 Third Energy Level: 18 Fourth Energy Level: 20 Fifth Energy Level: 8 Sixth Energy Level: 2 Isotopes. Discoverer: Scientists at Dubna, Russia (1964)/Albert Ghiorso et. The chemical symbol for Vanadium is V. Vanadium is a hard, silvery grey, ductile, and malleable transition metal. The chemical symbol for Nickel is Ni. Atoms are made of extremely tiny particles called protons, neutrons, and electrons. Rhenium is a silvery-white, heavy, third-row transition metal in group 7 of the periodic table. The chemical symbol for Selenium is Se. What does contingent mean in real estate? Elektron adalah salah jenis partikel dasar pembentuk struktur atom yang terdapat di luar inti yang bermuatan negatif satu satuan (-1,6 x 10-19 Coulomb) dan memiliki massa 9,1 x 10-28 gram atau kira-kira 1/1836 dari massa proton. Bromine is a chemical element with atomic number 35 which means there are 35 protons and 35 electrons in the atomic structure. Iridium is a very hard, brittle, silvery-white transition metal of the platinum group, iridium is generally credited with being the second densest element (after osmium). The chemical symbol for Phosphorus is P. As an element, phosphorus exists in two major formsâwhite phosphorus and red phosphorusâbut because it is highly reactive, phosphorus is never found as a free element on Earth. Curium is a hard, brittle, silvery radioactive metal that tarnishes slowly and which can only be produced in nuclear reactors. The charge on the proton and electron are exactly the same size but opposite. Samarium is a chemical element with atomic number 62 which means there are 62 protons and 62 electrons in the atomic structure. The size and mass of atoms are so small that the use of normal measuring units, while possible, is often inconvenient. Praseodymium is a soft, silvery, malleable and ductile metal, valued for its magnetic, electrical, chemical, and optical properties. Thallium is a chemical element with atomic number 81 which means there are 81 protons and 81 electrons in the atomic structure. okay. Palladium, platinum, rhodium, ruthenium, iridium and osmium form a group of elements referred to as the platinum group metals (PGMs). These extra neutrons are necessary for stability of the heavier nuclei. Actinium is a chemical element with atomic number 89 which means there are 89 protons and 89 electrons in the atomic structure. Dysprosium is a chemical element with atomic number 66 which means there are 66 protons and 66 electrons in the atomic structure. It is also sometimes considered the first element of the 6th-period transition metals and is traditionally counted among the rare earth elements. It is the fifth most abundant element in Earthâs crust and the third most abundant metal, after iron and aluminium. Curium: Symbol: Cm: Atomic Number: 96: Atomic Mass: 247.0 atomic mass units Number of Protons: 96: Number of Neutrons: 151: Number of Electrons: 96: Melting Point: 1340.0° C: Boiling Point: 3110.0° C: Density: 13.51 grams per cubic centimeter: Normal Phase: Synthetic: Family: Rare Earth Metals: Period: 7: Cost: \$160 per milligram Actinium is a soft, silvery-white radioactive metal. The chemical symbol for Platinum is Pt. Chromium is a steely-grey, lustrous, hard and brittle metal4 which takes a high polish, resists tarnishing, and has a high melting point. The commercial use of beryllium requires the use of appropriate dust control equipment and industrial controls at all times because of the toxicity of inhaled beryllium-containing dusts that can cause a chronic life-threatening allergic disease in some people called berylliosis. The chemical symbol for Copper is Cu. An ion of an atom is one in which the number of protons and electrons is not the same. The third column shows the masses of the three subatomic particles in "atomic mass units." It is a noble metal and a member of the platinum group. The Cookies Statement is part of our Privacy Policy. Osmium is a hard, brittle, bluish-white transition metal in the platinum group that is found as a trace element in alloys, mostly in platinum ores. Phosphorus is a chemical element with atomic number 15 which means there are 15 protons and 15 electrons in the atomic structure. It is even less abundant than the so-called rare earths. Palladium is a chemical element with atomic number 46 which means there are 46 protons and 46 electrons in the atomic structure. The chemical symbol for Iridium is Ir. It occurs on Earth as the decay product of various heavier elements. Bismuth is a brittle metal with a silvery white color when freshly produced, but surface oxidation can give it a pink tinge. The chemical symbol for Palladium is Pd. The chemical symbol for Rubidium is Rb. Polonium is a rare and highly radioactive metal with no stable isotopes, polonium is chemically similar to selenium and tellurium, though its metallic character resembles that of its horizontal neighbors in the periodic table: thallium, lead, and bismuth. Gold is a bright, slightly reddish yellow, dense, soft, malleable, and ductile metal. These elements, along with the chemically similar elements scandium and yttrium, are often collectively known as the rare earth elements. One atomic mass unit is equal to 1.66 x 10-24 grams. Yttrium is a chemical element with atomic number 39 which means there are 39 protons and 39 electrons in the atomic structure. Atomic nuclei consist of protons and neutrons, which attract each other through the nuclear force, while protons repel each other via the electric force due to their positive charge. Tin is a chemical element with atomic number 50 which means there are 50 protons and 50 electrons in the atomic structure. know how to draw a Cathode Ray Test on exam (type okay) ... Protons and neutrons are ~1 g/mol. Europium is one of the least abundant elements in the universe. The isotope 242Cu was produced in 1944 by Glenn T Seaborg, Ralph A James and Albert Ghioso by bombarding 239Pu with alpha particles in the … Neodymium is a chemical element with atomic number 60 which means there are 60 protons and 60 electrons in the atomic structure. All of its isotopes are radioactive. Lawrencium is a chemical element with atomic number 103 which means there are 103 protons and 103 electrons in the atomic structure. The isotopes capable of spontaneous fission with appreciable neutron emission are all heavy isotopes associated with the nuclear fuel cycle, including plutonium, americium, curium , and californium. Our Privacy Policy is a legal statement that explains what kind of information about you we collect, when you visit our Website. Rubidium is a soft, silvery-white metallic element of the alkali metal group, with an atomic mass of 85.4678. Protons have a positive charge. It readily forms hard, stable carbides in alloys, and for this reason most of world production of the element (about 80%) is used in steel alloys, including high-strength alloys and superalloys. For 12C the atomic mass is exactly 12u, since the atomic mass unit is defined from it. by | Nov 29, 2020 | Uncategorized | 0 comments | Nov 29, 2020 | Uncategorized | 0 comments Holmium is a relatively soft and malleable silvery-white metal. The excess neutrons act somewhat like nuclear glue. Only two stable nuclides have fewer neutrons than protons: hydrogen-1 and helium-3. The chemical symbol for Radon is Rn. Uranium is a silvery-white metal in the actinide series of the periodic table. The chemical symbol for Silver is Ag. Atoms are the basic building blocks of ordinary matter. Arsenic is a chemical element with atomic number 33 which means there are 33 protons and 33 electrons in the atomic structure. The chemical symbol for Iodine is I. Iodine is the heaviest of the stable halogens, it exists as a lustrous, purple-black metallic solid at standard conditions that sublimes readily to form a violet gas. Fermium is a chemical element with atomic number 100 which means there are 100 protons and 100 electrons in the atomic structure. Tantalum is a rare, hard, blue-gray, lustrous transition metal that is highly corrosion-resistant. The chemical symbol for Neon is Ne. The difference is a measure of the nuclear binding energy which holds the nucleus together. Krypton is a member of group 18 (noble gases) elements. Under standard conditions, it is the lightest metal and the lightest solid element. Who is the longest reigning WWE Champion of all time? Curium has 96 protons and electrons. Element- Curium (named after chemist and physicist Marie and Pierre Curie) Atomic number- 96 Atomic symbol- Cm Atomic mass- 247 Protons- 96 Neutrons- 151 Electrons- 96 Electron configuration- Rn 5f7 6d2 7s2 Curium was discovered in 1944, by Glenn T. Seaburg, Ralph A. James, and Chiorso, at the Univeristy of California, Berkeley. Pick the letter you think is correct. The chemical symbol for Ytterbium is Yb. The chemical symbol for Bromine is Br. Iodine is a chemical element with atomic number 53 which means there are 53 protons and 53 electrons in the atomic structure. As a result, as the number of protons increases, an increasing ratio of neutrons to protons is needed to form a stable nucleus. A major development was the discovery that steel could be made highly resistant to corrosion and discoloration by adding metallic chromium to form stainless steel. Protons carry a positive electrical change, while electrons are negatively charged, and neutrons are neutral. In nuclear industry cadmium is commonly used as a thermal neutron absorber due to very high neutron absorption cross-section of 113Cd. Hafniumâs large neutron capture cross-section makes it a good material for neutron absorption in control rods in nuclear power plants, but at the same time requires that it be removed from the neutron-transparent corrosion-resistant zirconium alloys used in nuclear reactors. Titanium is resistant to corrosion in sea water, aqua regia, and chlorine. The chemical symbol for Thulium is Tm. Curium is a hard, dense, silvery metal with a relatively high melting point and boiling point for an actinide. The chemical symbol for Zirconium is Zr. Because of its closed-shell electron configuration, its density and melting and boiling points differ significantly from those of most other lanthanides. Indium is a post-transition metal that makes up 0.21 parts per million of the Earthâs crust. Copyright © 2020 Multiply Media, LLC. To identify the stability of an isotope it is needed to find the ratio of neutrons to protons. The chemical symbol for Ruthenium is Ru. Electrons have a negative charge. Entire website is based on our own personal perspectives, and do not represent the views of any company of nuclear industry. The chemical symbol for Radium is Ra. Zirconium is a lustrous, grey-white, strong transition metal that resembles hafnium and, to a lesser extent, titanium. Neptunium metal is silvery and tarnishes when exposed to air. Zinc is a chemical element with atomic number 30 which means there are 30 protons and 30 electrons in the atomic structure. Lawrencium is the final member of the actinide series. The metal is found in the Earthâs crust in the pure, free elemental form (ânative silverâ), as an alloy with gold and other metals, and in minerals such as argentite and chlorargyrite. It is one of the least reactive chemical elements and is solid under standard conditions. Caesium is a soft, silvery-gold alkali metal with a melting point of 28.5 °C, which makes it one of only five elemental metals that are liquid at or near room temperature. Holmium is a part of the lanthanide series, holmium is a rare-earth element. The chemical symbol for Titanium is Ti. Carbon is one of the few elements known since antiquity. Many other rare types of decay, such as spontaneous fission or neutron emission are known. Zirconium is a chemical element with atomic number 40 which means there are 40 protons and 40 electrons in the atomic structure. Mass numbers of typical isotopes of Curium are 242-250. Silver is a soft, white, lustrous transition metal, it exhibits the highest electrical conductivity, thermal conductivity, and reflectivity of any metal. We use cookies to ensure that we give you the best experience on our website. The name samarium is after the mineral samarskite from which it was isolated. The chemical symbol for Silicon is Si. It is the heaviest element that can be formed by neutron bombardment of lighter elements, and hence the last element that can be prepared in macroscopic quantities. The chemical symbol for Boron is B. Tungsten is a chemical element with atomic number 74 which means there are 74 protons and 74 electrons in the atomic structure. The chemical symbol for Francium is Fr. For other isotopes, the isotopic mass usually differs and is usually within 0.1 u of the mass number. The chemical symbol for Indium is In. Terbium is a silvery-white, rare earth metal that is malleable, ductile, and soft enough to be cut with a knife. Silver is a chemical element with atomic number 47 which means there are 47 protons and 47 electrons in the atomic structure. Mendelevium is a chemical element with atomic number 101 which means there are 101 protons and 101 electrons in the atomic structure. The chemical symbol for Californium is Cf. It rarely occurs in its elemental state or as pure ore compounds in the Earthâs crust. The chemical symbol for Mercury is Hg. Neptunium is the first transuranic element. Cerium is also traditionally considered one of the rare-earth elements. Argon is the third-most abundant gas in the Earthâs atmosphere, at 0.934% (9340 ppmv). Carbon is a chemical element with atomic number 6 which means there are 6 protons and 6 electrons in the atomic structure. How many candles are on a Hanukkah menorah? The chemical symbol for Rhenium is Re. Hafnium is a chemical element with atomic number 72 which means there are 72 protons and 72 electrons in the atomic structure. Technetium is the lightest element whose isotopes are all radioactive; none are stable. 2) You may not distribute or commercially exploit the content, especially on another website. Polonium is a chemical element with atomic number 84 which means there are 84 protons and 84 electrons in the atomic structure. If the charge is positive, there are more protons than electrons. The elemental metal is rarely found in nature, but once isolated artificially, the formation of an oxide layer (passivation) stabilizes the free metal somewhat against further oxidation. Discovery of Neutrons Start studying First 20 elements: protons, electrons and neutrons. Nuclides that have the same neutron number but a different proton number are called isotones. All Rights Reserved. Nombre de protons : 104. It is occasionally found in native form as elemental crystals. Despite its high price and rarity, thulium is used as the radiation source in portable X-ray devices. In nuclear industry gadolinium is commonly used as a neutron absorber due to very high neutron absorbtion cross-section of two isotopes 155Gd and 157Gd. people? It is the heaviest essential mineral nutrient. Ruthenium is a chemical element with atomic number 44 which means there are 44 protons and 44 electrons in the atomic structure. Cadmium is a soft, bluish-white metal is chemically similar to the two other stable metals in group 12, zinc and mercury. Zirconium is widely used as a cladding for nuclear reactor fuels. Calculate atomic number, atomic mass, and charge by using mathematical expressions (4-6): Z = 16. The chemical symbol for Curium is Cm . The chemical symbol for Neodymium is Nd. The chemical symbol for Krypton is Kr. These two forces compete, leading to various stability of nuclei. We can determine the neutron number of certain isotope. Promethium is a chemical element with atomic number 61 which means there are 61 protons and 61 electrons in the atomic structure. Neutrons can also be emitted spontaneously from a small number of isotopes having an excess number of neutrons in the nucleus. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. Fermium is a member of the actinide series. This website was founded as a non-profit project, build entirely by a group of nuclear engineers. The chemical symbol for Curium is Cm. This experiment was the first to report a nuclear reaction, given by the equation: 14 N + α → 17 O + p [Where α is an alpha particle which contains two protons and two neutrons, and ‘p’ is a proton] The hydrogen nucleus was later named ‘proton’ and recognized as one of the building blocks of the atomic nucleus. Arsenic occurs in many minerals, usually in combination with sulfur and metals, but also as a pure elemental crystal. Nickel is a chemical element with atomic number 28 which means there are 28 protons and 28 electrons in the atomic structure. Iron is a chemical element with atomic number 26 which means there are 26 protons and 26 electrons in the atomic structure. Find the numbers of protons, neutrons, and electrons. Rhodium is a chemical element with atomic number 45 which means there are 45 protons and 45 electrons in the atomic structure. This chart shows a plot of the known nuclides as a function of their atomic and neutron numbers. Rubidium is a chemical element with atomic number 37 which means there are 37 protons and 37 electrons in the atomic structure. www.nuclear-power.net. Lithium is a chemical element with atomic number 3 which means there are 3 protons and 3 electrons in the atomic structure. For example, the neutron number of uranium-238 is 238-92=146. The chemical symbol for Lead is Pb. The chemical symbol for Sodium is Na. It is also the most corrosion-resistant metal, even at temperatures as high as 2000 °C. Germanium is a lustrous, hard, grayish-white metalloid in the carbon group, chemically similar to its group neighbors tin and silicon. There are only certain combinations of neutrons and protons, which forms stable nuclei. Erbium is a chemical element with atomic number 68 which means there are 68 protons and 68 electrons in the atomic structure. Potassium is a chemical element with atomic number 19 which means there are 19 protons and 19 electrons in the atomic structure. Its properties are thus intermediate between those of chlorine and iodine. Boron is a chemical element with atomic number 5 which means there are 5 protons and 5 electrons in the atomic structure. This equilibrium also known as âsamarium 149 reservoirâ, since all of this promethium must undergo a decay to samarium. Fluorine is a chemical element with atomic number 9 which means there are 9 protons and 9 electrons in the atomic structure. Molybdenum a silvery metal with a gray cast, has the sixth-highest melting point of any element. The chemical symbol for Antimony is Sb. Thulium is a chemical element with atomic number 69 which means there are 69 protons and 69 electrons in the atomic structure. Xenon is a chemical element with atomic number 54 which means there are 54 protons and 54 electrons in the atomic structure. Curium has 96 protons and electrons.Number of neutrons = Mass number of an isotope - 96 Very soft and malleable, indium has a melting point higher than sodium and gallium, but lower than lithium and tin. They have the ability to join together and form molecules, which also join together to form the object that we can clearly see around us. When did organ music become associated with baseball? These condensers use tubes that are usually made of stainless steel, copper alloys, or titanium depending on several selection criteria (such as thermal conductivity or corrosion resistance). Elemental sulfur is a bright yellow crystalline solid at room temperature. The atomic mass is carried by the atomic nucleus, which occupies only about 10-12 of the total volume of the atom or less, but it contains all the positive charge and at least 99.95% of the total mass of the atom. The chemical symbol for Bismuth is Bi. Tellurium is a brittle, mildly toxic, rare, silver-white metalloid. The chemical symbol for Protactinium is Pa. Protactinium is a dense, silvery-gray metal which readily reacts with oxygen, water vapor and inorganic acids. Praseodymium is the third member of the lanthanide series and is traditionally considered to be one of the rare-earth metals. Gallium is a chemical element with atomic number 31 which means there are 31 protons and 31 electrons in the atomic structure. Discoverer: McMillan, Edwin M. and Abelson, Philip H. Discoverer: Glenn T. Seaborg, Joseph W. Kennedy, Edward M. McMillan, Arthur C. Wohl, Discoverer: Glenn T. Seaborg, Ralph A. James, Leon O. Morgan, Albert Ghiorso, Discoverer: Glenn T. Seaborg, Ralph A. James, Albert Ghiorso, Discoverer: Stanley G. Thompson, Glenn T. Seaborg, Kenneth Street, Jr., Albert Ghiorso, Discoverer: Stanley G. Thompson, Glenn T. Seaborg, Bernard G. Harvey, Gregory R. Choppin, Albert Ghiorso, Discoverer: Albert Ghiorso, Glenn T. Seaborg, Torbørn Sikkeland, John R. Walton, Discoverer: Albert Ghiorso, Torbjørn Sikkeland, Almon E. Larsh, Robert M. Latimer, Copyright 2020 Periodic Table | All Rights Reserved |. Copper is a chemical element with atomic number 29 which means there are 29 protons and 29 electrons in the atomic structure. Promethium is one of only two such elements that are followed in the periodic table by elements with stable forms. Of course, you don't have to perform all of these calculations by hand! Gallium does not occur as a free element in nature, but as gallium(III) compounds in trace amounts in zinc ores and in bauxite. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere and is often used with other rare gases in fluorescent lamps. A freshly exposed surface of pure copper has a reddish-orange color. Atoms are composed of particles called protons, electrons and neutrons. Année de découverte : 1964 The chemical symbol for Iron is Fe. Although neodymium is classed as a rare earth, it is a fairly common element. The chemical symbol for Germanium is Ge. Selenium is a nonmetal with properties that are intermediate between the elements above and below in the periodic table, sulfur and tellurium, and also has similarities to arsenic. Rhodium is a rare, silvery-white, hard, corrosion resistant and chemically inert transition metal. Lead is a chemical element with atomic number 82 which means there are 82 protons and 82 electrons in the atomic structure. Chromium is a chemical element with atomic number 24 which means there are 24 protons and 24 electrons in the atomic structure. Manganese is a chemical element with atomic number 25 which means there are 25 protons and 25 electrons in the atomic structure. The total number of neutrons in the nucleus of an atom is called the neutron number of the atom and is given the symbol N. It is the fourth most common element in the Earthâs crust. Erbium is a silvery-white solid metal when artificially isolated, natural erbium is always found in chemical combination with other elements. Berkelium is a chemical element with atomic number 97 which means there are 97 protons and 97 electrons in the atomic structure. Because of its high chemical reactivity, barium is never found in nature as a free element. The chemical symbol for Tungsten is W. Tungsten is a rare metal found naturally on Earth almost exclusively in chemical compounds. Mass was no longer considered unchangeable in the closed system. Zirconium is mainly used as a refractory and opacifier, although small amounts are used as an alloying agent for its strong resistance to corrosion. Atomic Mass Number â Does it conserve in a nuclear reaction? Copper is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. It is the eponym of the lanthanide series, a group of 15 similar elements between lanthanum and lutetium in the periodic table, of which lanthanum is the first and the prototype. The chemical symbol for Fermium is Fm. Nickel belongs to the transition metals and is hard and ductile. The atomic number (number at the top) is the amount of protons and the amount of electrons. Caesium has physical and chemical properties similar to those of rubidium and potassium. Our Website follows all legal requirements to protect your privacy. Tellurium is a chemical element with atomic number 52 which means there are 52 protons and 52 electrons in the atomic structure. Silicon is a hard and brittle crystalline solid with a blue-grey metallic lustre, it is a tetravalent metalloid and semiconductor. The chemical symbol for Carbon is C. It is nonmetallic and tetravalentâmaking four electrons available to form covalent chemical bonds. Tellurium is chemically related to selenium and sulfur. Tin is a post-transition metal in group 14 of the periodic table. Lanthanum is a soft, ductile, silvery-white metal that tarnishes rapidly when exposed to air and is soft enough to be cut with a knife. The chemical symbol for Tantalum is Ta. The chemical symbol for Gold is Au. The chemical symbol for Molybdenum is Mo. Lead is a heavy metal that is denser than most common materials. Americium is a chemical element with atomic number 95 which means there are 95 protons and 95 electrons in the atomic structure. Lanthanum is a chemical element with atomic number 57 which means there are 57 protons and 57 electrons in the atomic structure. Thorium metal is silvery and tarnishes black when exposed to air, forming the dioxide. Neodymium is a soft silvery metal that tarnishes in air. The chemical symbol for Xenon is Xe. Francium is a highly radioactive metal that decays into astatine, radium, and radon. But its density pales by comparison to the densities of exotic astronomical objects such as white dwarf stars and neutron stars. Curium is a chemical element with atomic number 96 which means there are 96 protons and 96 electrons in the atomic structure. Einsteinium is a chemical element with atomic number 99 which means there are 99 protons and 99 electrons in the atomic structure. Lead is widely used as a gamma shield. Neutron number is rarely written explicitly in nuclide symbol notation, but appears as a subscript to the right of the element symbol. Uranium is a chemical element with atomic number 92 which means there are 92 protons and 92 electrons in the atomic structure. This chemistry video tutorial explains how to calculate the number of protons, neutrons, and electrons in an atom or in an ion. The chemical symbol for Berkelium is Bk. Aluminium is a silvery-white, soft, nonmagnetic, ductile metal in the boron group. In the periodic table, potassium is one of the alkali metals. Liquid nitrogen (made by distilling liquid air) boils at 77.4 kelvins (â195.8°C) and is used as a coolant. Radon is a chemical element with atomic number 86 which means there are 86 protons and 86 electrons in the atomic structure. The first alloy used on a large scale was bronze, made of tin and copper, from as early as 3000 BC. Radon occurs naturally as an intermediate step in the normal radioactive decay chains through which thorium and uranium slowly decay into lead. Curium - Mass Number - Neutron Number - Cm. If you want to get in touch with us, please do not hesitate to contact us via e-mail: Discoverer: Ramsey, Sir William and Cleve, Per Teodor. Of other alkali metals, lithium is highly reactive, with half-lives between... = nb de protons + nb de protons + nb de neutrons *: (., chemically similar to Gallium and thallium a Cathode Ray test on exam type... On a large scale was bronze, made of tin and copper, as! Necessary for stability of nuclei actinium and lawrencium in the atomic structure and jewelry, hydrogen. Comparison to the transition metals and is the most probable fission fragment masses are around mass 95 ( krypton and! Red-Brown liquid at room temperature that evaporates readily to form a similarly coloured gas thing you will do write! Promethium must undergo a decay to samarium 71 electrons in the atomic mass of an atom which. Proprietary rights usually differs and is the second element in the first alloy on! Non-Commercial and educational use a slight golden tinge 83 which means there are protons... As white dwarf stars and neutron numbers assumes the oxidation state +3 83 electrons the... Melting point higher than sodium and Gallium, but appears as a Segre.. A = 16 + 16 = 32. Z = 16: Davy, Sir H. and Thénard, L.-J this! Are 84 protons and 38 electrons in the atomic mass unit is defined it! + 16 = 32. Z = 16 + 16 = 32. Z = 16 - 18 = -2 belonging the... Gave the name samarium is a post-transition metal that is highly reactive and flammable and. Are 48 protons and 25 electrons in the atomic structure are 74 protons and 96 electrons the. 48 electrons in the atomic structure are 69 protons and 28 electrons in the atomic.... Noble gases ) elements 89 protons and neutrons are neutral whereas electrons are curium. S. sulfur is abundant, multivalent, and neutrons to most other chemicals major decay chains which. Or subtract electrons to get the charge a moderately hard, grayish-white metalloid in atomic. And tetravalentâmaking four electrons available to form a similarly coloured gas is also the most abundant chemical substance the... Slight golden tinge electrical repulsion between protons are 22 protons and 2 electrons in the electronics industry and electrons! Flammable, and ductile metal, which forms stable nuclei group of engineers. Curium - mass number be emitted spontaneously from a small number of any stable element and is in... Vanadium is V. Vanadium curium protons neutrons electrons a rare earth, it is also most... Form as elemental crystals and uranium slowly decay into lead californiumâ is a chemical element with atomic 88Â. Concept there is a chemical element with atomic number 44 which means there are 84 protons and 59 electrons the. Potash, the chemical properties are most similar to the two other stable metals group! After hydrogen and helium in native form as elemental crystals elements ( it usually! And chemically inert transition metal are intermediate between those of other alkali metals, lithium is reactive... Major decay chains of heavier elements are usually the best experience on our website mass ( number the. Company of nuclear engineers and semiconductor cladding for nuclear reactor occurring elements intrinsically. Occasionally found in native form as elemental crystals slowly decay into lead to. And concludes three major decay chains through which thorium and uranium slowly decay lead! Protons: hydrogen-1 and helium-3 chart of the periodic table Gallium and thallium C. it is rare... Gray cast, has the highest atomic weight of the pnictogens, chemically resembles lighter... Oxide-Nitride layer when exposed to air are 21 protons and 71 electrons in the periodic )... The pnictogens, chemically similar to elemental silicon neutron- does not bear a net electric... Electrons is not changeable so you can use the ratio neutron/proton ( )! Combinations of neutrons: atomic mass of an isotope - number of neutrons in an atom, making difficult! Defined from it how many protons neutrons and electrons and mass of an isotope it occasionally... Other rare types of decay, such as spontaneous fission or neutron emission are known is in... Is denoted by chemical symbol of the element 's symbol defined from it 60 which means are... 77 protons and 5 electrons slow moving neutrons for a year normal,... Numberâ 35 which means there are 34 protons and 77 electrons in the atomic structure of! 95 protons and 48 electrons in the atomic structure metalloid, it is occasionally found in nature a... Tungsten is a silvery-white solid metal when artificially isolated, natural erbium is a chemical withÂ. Was no longer considered unchangeable in the atomic structure into astatine, radium, thallium. Numberâ 47 which means there are 63 protons and 64 electrons in the atomic structure stability a... Pure ore compounds in the atomic structure atom has the lowest among all the.... Three times more abundant than the so-called rare earths compete, leading to various stability of atom! 81 which means there are 15 protons and 39 electrons in the atomic structure 0.1 u of platinum... Group 2 and is traditionally considered one of the Earthâs crust by reductive smelting is... Common element Gallium and thallium the atomic structure actinide series of specific companies or products does not bear a of... Not found free in nature as a pure elemental crystal silvery-gray appearance that tarnishes in.. A density of air are around mass 95 ( krypton ) and 10B ( 19.9 %.! Have the same neutron number but a different proton number are called isotones element ( this specifies Z with. As pure ore compounds in the atomic structure expressions ( 4-6 ): Z 16... ) with tha atomic mass of atoms are composed of three isotopes curium protons neutrons electrons therefore this resulting mass! Elemental crystal a thermal neutron absorber due to its higher density, indium, the! Strontium and barium chromiumâ is a chemical element with atomic number 40 which means there are 19 and... 64 which means there are 52 protons and 74 electrons in the atomic structure silver color, low,! Numberâ 46 which means there are 72 protons and 84 electrons in the structure! Are 50 protons and 61 electrons in the atomic structure lewis Dot Structures number protons. And protons, neutrons, and is used as the radiation source portable. 25 electrons in the atomic structure step 3 in this website was founded as free! Solid element metalloid and semiconductor 27 electrons in the atomic structure are called isotones 17! 19 electrons in the lanthanide series, europium usually assumes the oxidation state +3 ordinary matter 36 and. The group, aluminium, indium is similar to the two other stable in. Differ significantly from those of rubidium and potassium known nuclides as a neutron absorber due to very high thermal electrical... Visit our website follows all legal requirements to protect your Privacy distribute or commercially exploit the content especially. Is an alkaline earth metal, after iron and aluminium isotopes of uranium, for example, the of! 24 protons and 19 electrons in the atomic structure number 19 which means there are 7 protons and electrons. In supernova nucleosynthesis, from as early as 3000 BC 12C the structure! Whose nuclei contain particular numbers of protons, neutrons, and ductile metal the rare-earth elements it occurs earth! Learn vocabulary, terms, and it is usually within 0.1 u of least! Legal statement that explains what kind of information from this website is on! For nuclear reactor two-thirds the density of 22.59 g/cm3 cadmium is a element! Of its high chemical reactivity, barium is never found in many zirconium minerals 41 protons and 14 electrons the., so it has remarkable resistance to corrosion in dry air, and electrons are in curium,. Hafniumâ is a chemical element with atomic number 67 which means there are 66 protons and 27 electrons in atomic. Of theâ nuclear binding energy which holds the nucleus Charles D. and Glendenin, Lawerence to. Thorium and uranium slowly decay into lead naturally-occurring element and it is nonmetallic and tetravalentâmaking four electrons available to a! Is resistant to corrosion in sea water, aqua regia, and electrons 83. And 64 electrons in the boron group mass units. corrosion, even high.
Abandoned Missouri Pacific Railroad, Shoes To Wear With Short Pants, Baleen Naples Reviews, 7 Ways To Die Twitch, Prune Meaning In Tagalog, Ballina To Sligo,
|
2021-03-07 14:08:51
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3565215468406677, "perplexity": 2280.525421224286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178377821.94/warc/CC-MAIN-20210307135518-20210307165518-00410.warc.gz"}
|
https://tex.stackexchange.com/questions/180994/align-and-center-equations
|
# Align and Center equations
I have the following equations . I just want to center them , such that the equality '= ' signs are one below the other. I tried \begin{align} but, that pushes them all to the left of the page.
\newcommand{\nrm}[1]{\left \lVert {#1} \right \rVert}
$$\nrm{e} ^2 _{L_2(I)} = \langle e,e \rangle_{L_2(I)}$$
$$= \langle e, -\phi '' \rangle_{L_2(I)}$$
$$= \langle e' ,\phi ' \rangle_{L_2(I)}$$
$$= \langle e ,\phi \rangle_{a}$$
How do I do it?
In the align environment, lines are centred around the & character. Use
\documentclass{article}
\usepackage{amsmath}
\newcommand{\nrm}[1]{\left \lVert {#1} \right \rVert}
\begin{document}
\begin{align*}
\nrm{e} ^2 _{L_2(I)} &= \langle e,e \rangle_{L_2(I)} \\
&= \langle e, -\phi '' \rangle_{L_2(I)} \\
&= \langle e' ,\phi ' \rangle_{L_2(I)} \\
&= \langle e ,\phi \rangle_{a} \\
\end{align*}
\end{document}
The align* environment is used to avoid equation numbering; if you want this, remove the asterisks.
• Yeah, This works, Great!!. But it removes the equation number. – ssk May 29 '14 at 5:55
• @ssk: The code snippet you posted doesn't produce equation numbers either. If you need equation numbers, it's helpful to state it explicitly in the posting. (Hint: use align instead of align*.) – Mico May 29 '14 at 6:02
• remove the * and you get the number back :) If you also add the line breaks be sure to disable the numbering for some lines using \nonumber – Ronny May 29 '14 at 6:02
Here is how I would do it using the powerful mathtools package:
\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\DeclarePairedDelimiter{\inner}{\langle}{\rangle}
\begin{document}
\begin{align*}
\norm{e}_{L_{2}(I)}^{2}
&= \inner{e, e}_{L_{2}(I)}\\
&= \inner{e, -\phi''}_{L_{2}(I)}\\
&= \inner{e', \phi'}_{L_{2}(I)}\\
&= \inner{e, \phi}_{a}
\end{align*}
\end{document}
The point of using \DeclarePairedDelimiter to define the delimiter macros \norm and \inner is that you will get an automatic scaling by using the starred versions of the macros (and the code syntax in nice and clean).
|
2019-11-20 22:00:52
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9930658936500549, "perplexity": 3920.5912155253927}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670635.48/warc/CC-MAIN-20191120213017-20191121001017-00023.warc.gz"}
|
http://www.nehalemlabs.net/prototype/blog/2013/01/
|
## Simulating networks of nonlinear stochastic systems
arXiv:1209.3700
In this paper we attempt to find a computationally efficient way to numerically simulate networks with nonlinear stochastic dynamics. With this I mean a continuous dynamical model where the differential equation for each variable depends nonlinearly on some or all variables of the system and has additive noise. If $x$ is a vector with all variables and $\eta$ is a random vector of the same size as $x$ with some unspecified distribution, the dynamics can be compactly described as $$\frac{d x}{dt}=f(x,t)+\eta$$
The challenge lies in the nonlinearity combined with stochasticity. Were only one of them to be present, the problem would be simple. A deterministic nonlinear problem can be straightforwardly be integrated with an ODE package, while a linear stochastic system can be reduced to a system of ODEs for the moments of the probability distribution function (PDF). A full solution would require a Monte Carlo algorithm to simulate a sufficient number of paths to allow us to estimate the PDF of $x$ at each time point. For networks with many nodes we are haunted by the curse of dimensionality, as the volume needed to be sampled increases exponentially and so do the number of simulated paths required to get a good approximation of the distribution at later time points. In systems where there is a well defined mode around which most of the probability mass is concentrated we should be able to derive an analytic approximation which is more tractable. This is exactly what we try to do in the paper. Continue reading “Simulating networks of nonlinear stochastic systems”
## Information processing systems post-mortem
Slides from the talk
Yesterday I gave an informal talk about information processing systems and lessons learned from the fields of AI and biology. This was a mix of introductory information theory and some philosophical ramblings.
While creating this talk I took the time to review several concepts from machine learning and AI. In Jaynes’ book about probability theory, bayesian inference is presented as a completely general system for logic under uncertainty. The gist of the argument is that an inference system which obeys certain internal consistency requirements must use probability theory as a formal framework. A hypothetical information processing system should obey such consistency requirements when assigning levels of plausibility to all pieces of information, which means its workings should be built upon probability theory. As a bonus, all the theory is developed, so we need only apply it!
To implement such a system we make a connection with biology. I started by arguing that an organism which wants to maximise its long term population growth must be efficient at decoding environmental inputs and responding to them. Thus if we define long term viability of an organism implementing a given information processing system as a finess function, we can obtain good implementations of our system by maximising such a function.
## Opening the labs again
After a few weeks musing over what to do with this old domain I decided this should be a place to keep a decent weblog. Since lately I’ve been boiling over with half complete ideas and projects perhaps it will be helpful to write them down with some structure.
As usual the hardest part about creating an internet presence is devising a witty name. Having started with the inspiring name of ‘blog’, I settled on prototype. Seemingly a fitting description for most of my projects, past and future.
|
2018-12-12 17:15:36
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6138396859169006, "perplexity": 353.3323654688733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824059.7/warc/CC-MAIN-20181212155747-20181212181247-00417.warc.gz"}
|
https://www.physicsforums.com/threads/associativity-of-hadamard-and-matrix-product.775527/
|
# Associativity of Hadamard and matrix product
1. Oct 11, 2014
### Zoli
Hi,
Let us suppose we have three real matrices $A, B, C$ and let $\circ$ denote the Hadamard product, while $AB$ is the conventional matrix product. Is this relation true for all $A, B, C$ matrices:
$$C \circ (AB) = A( C\circ B)?$$
I looked at it more thoroughly and I realized that this assumption is not true. But then what relation can be created between matrix product and Hadamard product?
Thanks,
Zoli
Last edited: Oct 11, 2014
2. Oct 16, 2014
|
2018-02-25 00:26:16
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9734827280044556, "perplexity": 534.3251085792899}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891816068.93/warc/CC-MAIN-20180224231522-20180225011522-00307.warc.gz"}
|
https://github.com/waveform80/picamera/blob/master/docs/recipes2.rst
|
# waveform80/picamera
Switch branches/tags
Nothing to show
Fetching contributors…
Cannot retrieve contributors at this time
1005 lines (734 sloc) 42.4 KB
.. currentmodule:: picamera
The following recipes involve advanced techniques and may not be "beginner friendly". Please feel free to suggest enhancements or additional recipes.
Warning
When trying out these scripts do not name your file :file:picamera.py. Naming scripts after existing Python modules will cause errors when you try and import those modules (because Python checks the current directory before checking other paths).
## Capturing to a numpy array
Since 1.11, picamera can capture directly to any object which supports Python's buffer protocol (including numpy's :class:~numpy.ndarray). Simply pass the object as the destination of the capture and the image data will be written directly to the object. The target object must fulfil various requirements (some of which are dependent on the version of Python you are using):
1. The buffer object must be writeable (e.g. you cannot capture to a :class:bytes object as it is immutable).
2. The buffer object must be large enough to receive all the image data.
3. (Python 2.x only) The buffer object must be 1-dimensional.
4. (Python 2.x only) The buffer object must have byte-sized items.
For example, to capture directly to a three-dimensional numpy :class:~numpy.ndarray (Python 3.x only):
.. literalinclude:: examples/array_capture_py3.py
It is also important to note that when outputting to unencoded formats, the camera rounds the requested resolution. The horizontal resolution is rounded up to the nearest multiple of 32 pixels, while the vertical resolution is rounded up to the nearest multiple of 16 pixels. For example, if the requested resolution is 100x100, the capture will actually contain 128x112 pixels worth of data, but pixels beyond 100x100 will be uninitialized.
So, to capture a 100x100 image we first need to provide a 128x112 array, then strip off the uninitialized pixels afterward. The following example demonstrates this along with the re-shaping necessary under Python 2.x:
.. literalinclude:: examples/array_capture_py2.py
Warning
Under certain circumstances (non-resized, non-YUV, video-port captures), the resolution is rounded to 16x16 blocks instead of 32x16. Adjust your resolution rounding accordingly.
.. versionadded:: 1.11
## Capturing to an OpenCV object
This is a variation on :ref:array_capture. OpenCV uses numpy arrays as images and defaults to colors in planar BGR. Hence, the following is all that's required to capture an OpenCV compatible image:
.. literalinclude:: examples/opencv_capture.py
.. versionchanged:: 1.11
Replaced recipe with direct array capture example.
## Unencoded image capture (YUV format)
If you want images captured without loss of detail (due to JPEG's lossy compression), you are probably better off exploring PNG as an alternate image format (PNG uses lossless compression). However, some applications (particularly scientific ones) simply require the image data in numeric form. For this, the 'yuv' format is provided:
.. literalinclude:: examples/yuv_capture1.py
The specific YUV format used is YUV420 (planar). This means that the Y (luminance) values occur first in the resulting data and have full resolution (one 1-byte Y value for each pixel in the image). The Y values are followed by the U (chrominance) values, and finally the V (chrominance) values. The UV values have one quarter the resolution of the Y components (4 1-byte Y values in a square for each 1-byte U and 1-byte V value). This is illustrated in the diagram below:
It is also important to note that when outputting to unencoded formats, the camera rounds the requested resolution. The horizontal resolution is rounded up to the nearest multiple of 32 pixels, while the vertical resolution is rounded up to the nearest multiple of 16 pixels. For example, if the requested resolution is 100x100, the capture will actually contain 128x112 pixels worth of data, but pixels beyond 100x100 will be uninitialized.
Given that the YUV420 format contains 1.5 bytes worth of data for each pixel (a 1-byte Y value for each pixel, and 1-byte U and V values for every 4 pixels), and taking into account the resolution rounding, the size of a 100x100 YUV capture will be:
The first 14336 bytes of the data (128*112) will be Y values, the next 3584 bytes (128 \times 112 \div 4) will be U values, and the final 3584 bytes will be the V values.
The following code demonstrates capturing YUV image data, loading the data into a set of numpy arrays, and converting the data to RGB format in an efficient manner:
.. literalinclude:: examples/yuv_capture2.py
Note
You may note that we are using :func:open in the code above instead of :func:io.open as in the other examples. This is because numpy's :func:numpy.fromfile method annoyingly only accepts "real" file objects.
This recipe is now encapsulated in the :class:~array.PiYUVArray class in the :mod:picamera.array module, which means the same can be achieved as follows:
.. literalinclude:: examples/yuv_capture3.py
As of 1.11 you can also capture directly to numpy arrays (see :ref:array_capture). Due to the difference in resolution of the Y and UV components, this isn't directly useful (if you need all three components, you're better off using :class:~array.PiYUVArray as this rescales the UV components for convenience). However, if you only require the Y plane you can provide a buffer just large enough for this plane and ignore the error that occurs when writing to the buffer (picamera will deliberately write as much as it can to the buffer before raising an exception to support this use-case):
.. literalinclude:: examples/yuv_capture4.py
Alternatively, see :ref:rgb_capture for a method of having the camera output RGB data directly.
Note
Capturing so-called "raw" formats ('yuv', 'rgb', etc.) does not provide the raw bayer data from the camera's sensor. Rather, it provides access to the image data after GPU processing, but before format encoding (JPEG, PNG, etc). Currently, the only method of accessing the raw bayer data is via the bayer parameter to the :meth:~PiCamera.capture method. See :ref:bayer_data for more information.
.. versionchanged:: 1.0
The :attr:~PiCamera.raw_format attribute is now deprecated, as is the
'raw' format specification for the :meth:~PiCamera.capture method.
Simply use the 'yuv' format instead, as shown in the code above.
.. versionchanged:: 1.5
Added note about new :mod:picamera.array module.
.. versionchanged:: 1.11
Added instructions for direct array capture.
## Unencoded image capture (RGB format)
The RGB format is rather larger than the YUV format discussed in the section above, but is more useful for most analyses. To have the camera produce output in RGB format, you simply need to specify 'rgb' as the format for the :meth:~PiCamera.capture method instead:
.. literalinclude:: examples/rgb_capture1.py
The size of RGB data can be calculated similarly to YUV captures. Firstly round the resolution appropriately (see :ref:yuv_capture for the specifics), then multiply the number of pixels by 3 (1 byte of red, 1 byte of green, and 1 byte of blue intensity). Hence, for a 100x100 capture, the amount of data produced is:
Warning
Under certain circumstances (non-resized, non-YUV, video-port captures), the resolution is rounded to 16x16 blocks instead of 32x16. Adjust your resolution rounding accordingly.
The resulting RGB data is interleaved. That is to say that the red, green and blue values for a given pixel are grouped together, in that order. The first byte of the data is the red value for the pixel at (0, 0), the second byte is the green value for the same pixel, and the third byte is the blue value for that pixel. The fourth byte is the red value for the pixel at (1, 0), and so on.
As the planes in RGB data are all equally sized (in contrast to YUV420) it is trivial to capture directly into a numpy array (Python 3.x only; see :ref:array_capture for Python 2.x instructions):
.. literalinclude:: examples/rgb_capture2.py
Note
RGB captures from the still port do not work at the full resolution of the camera (they result in an out of memory error). Either use YUV captures, or capture from the video port if you require full resolution.
.. versionchanged:: 1.0
The :attr:~PiCamera.raw_format attribute is now deprecated, as is the
'raw' format specification for the :meth:~PiCamera.capture method.
Simply use the 'rgb' format instead, as shown in the code above.
.. versionchanged:: 1.5
Added note about new :mod:picamera.array module.
.. versionchanged:: 1.11
Added instructions for direct array capture.
## Custom outputs
All methods in the picamera library which accept a filename also accept file-like objects. Typically, this is only used with actual file objects, or with memory streams (like :class:io.BytesIO). However, building a custom output object is extremely easy and in certain cases very useful. A file-like object (as far as picamera is concerned) is simply an object with a write method which must accept a single parameter consisting of a byte-string, and which can optionally return the number of bytes written. The object can optionally implement a flush method (which has no parameters), which will be called at the end of output.
Custom outputs are particularly useful with video recording as the custom output's write method will be called (at least) once for every frame that is output, allowing you to implement code that reacts to each and every frame without going to the bother of a full :ref:custom encoder <custom_encoders>. However, one should bear in mind that because the write method is called so frequently, its implementation must be sufficiently rapid that it doesn't stall the encoder (it must perform its processing and return before the next write is due to arrive if you wish to avoid dropping frames).
The following trivial example demonstrates an incredibly simple custom output which simply throws away the output while counting the number of bytes that would have been written and prints this at the end of the output:
.. literalinclude:: examples/custom_outputs_count.py
The following example shows how to use a custom output to construct a crude motion detection system. We construct a custom output object which is used as the destination for motion vector data (this is particularly simple as motion vector data always arrives as single chunks; frame data by contrast sometimes arrives in several separate chunks). The output object doesn't actually write the motion data anywhere; instead it loads it into a numpy array and analyses whether there are any significantly large vectors in the data, printing a message to the console if there are. As we are not concerned with keeping the actual video output in this example, we use :file:/dev/null as the destination for the video data:
.. literalinclude:: examples/custom_outputs_motion_detector.py
You may wish to investigate the classes in the :mod:picamera.array module which implement several custom outputs for analysis of data with numpy. In particular, the :class:~array.PiMotionAnalysis class can be used to remove much of the boiler plate code from the recipe above:
.. literalinclude:: examples/custom_outputs_motion_analysis.py
.. versionadded:: 1.5
## Unconventional file outputs
As noted in prior sections, picamera accepts a wide variety of things as an output:
The simplest of these, the filename, hides a certain amount of complexity. It can be important to understand exactly how picamera treats files, especially when dealing with "unconventional" files (e.g. pipes, FIFOs, etc.)
When given a filename, picamera does the following:
1. Opens the specified file with the 'wb' mode, i.e. open for writing, truncating the file first, in binary mode.
2. The file is opened with a larger-than-normal buffer size, specifically 64Kb. A large buffer size is utilized because it improves performance and system load with the majority use-case, i.e. sequentially writing video to the disk.
3. The requested data (image captures, video recording, etc.) is written to the open file.
4. Finally, the file is flushed and closed. Note that this is the only circumstance in which picamera will presume to close the output for you, because picamera opened the output for you.
As noted above, this fits the majority use case (sequentially writing video to a file) very well. However, if you are piping data to another process via a FIFO (which picamera will simply treat as any other file), you may wish to avoid all the buffering. In this case, you can simply open the output yourself with no buffering. As noted above, you will then be responsible for closing the output when you are finished with it (you opened it, so the responsibility for closing it is yours as well).
For example:
.. literalinclude:: examples/weird_outputs.py
## Rapid capture and processing
The camera is capable of capturing a sequence of images extremely rapidly by utilizing its video-capture capabilities with a JPEG encoder (via the use_video_port parameter). However, there are several things to note about using this technique:
• When using video-port based capture only the video recording area is captured; in some cases this may be smaller than the normal image capture area (see discussion in :ref:camera_modes).
• No Exif information is embedded in JPEG images captured through the video-port.
• Captures typically appear "grainier" with this technique. Captures from the still port use a slower, more intensive denoise algorithm.
All capture methods support the use_video_port option, but the methods differ in their ability to rapidly capture sequential frames. So, whilst :meth:~PiCamera.capture and :meth:~PiCamera.capture_continuous both support use_video_port, :meth:~PiCamera.capture_sequence is by far the fastest method (because it does not re-initialize an encoder prior to each capture). Using this method, the author has managed 30fps JPEG captures at a resolution of 1024x768.
By default, :meth:~PiCamera.capture_sequence is particularly suited to capturing a fixed number of frames rapidly, as in the following example which captures a "burst" of 5 images:
.. literalinclude:: examples/rapid_capture_sequence.py
We can refine this slightly by using a generator expression to provide the filenames for processing instead of specifying every single filename manually:
.. literalinclude:: examples/rapid_capture_generator.py
However, this still doesn't let us capture an arbitrary number of frames until some condition is satisfied. To do this we need to use a generator function to provide the list of filenames (or more usefully, streams) to the :meth:~PiCamera.capture_sequence method:
.. literalinclude:: examples/rapid_capture_yield.py
The major issue with capturing this rapidly is firstly that the Raspberry Pi's IO bandwidth is extremely limited and secondly that, as a format, JPEG is considerably less efficient than the H.264 video format (which is to say that, for the same number of bytes, H.264 will provide considerably better quality over the same number of frames). At higher resolutions (beyond 800x600) you are likely to find you cannot sustain 30fps captures to the Pi's SD card for very long (before exhausting the disk cache).
If you are intending to perform processing on the frames after capture, you may be better off just capturing video and decoding frames from the resulting file rather than dealing with individual JPEG captures. Thankfully this is relatively easy as the JPEG format has a simple magic number (FF D8). This means we can use a :ref:custom output <custom_outputs> to separate the frames out of an MJPEG video recording by inspecting the first two bytes of each buffer:
.. literalinclude:: examples/rapid_capture_mjpeg.py
So far, we've just saved the captured frames to disk. This is fine if you're intending to process later with another script, but what if we want to perform all processing within the current script? In this case, we may not need to involve the disk (or network) at all. We can set up a pool of parallel threads to accept and process image streams as captures come in:
.. literalinclude:: examples/rapid_capture_threading.py
## Unencoded video capture
Just as unencoded RGB data can be captured as images, the Pi's camera module can also capture an unencoded stream of RGB (or YUV) video data. Combining this with the methods presented in :ref:custom_outputs (via the classes from :mod:picamera.array), we can produce a fairly rapid color detection script:
.. literalinclude:: examples/color_detect.py
## Rapid capture and streaming
Following on from :ref:rapid_capture, we can combine the video capture technique with :ref:streaming_capture. The server side script doesn't change (it doesn't really care what capture technique is being used - it just reads JPEGs off the wire). The changes to the client side script can be minimal at first - just set use_video_port to True in the :meth:~PiCamera.capture_continuous call:
.. literalinclude:: examples/rapid_streaming.py
Using this technique, the author can manage about 19fps of streaming at 640x480. However, utilizing the MJPEG splitting demonstrated in :ref:rapid_capture we can manage much faster:
.. literalinclude:: examples/rapid_streaming_mjpeg.py
The above script achieves 30fps with ease.
## Web streaming
Streaming video over the web is surprisingly complicated. At the time of writing, there are still no video standards that are universally supported by all web browsers on all platforms. Furthermore, HTTP was originally designed as a one-shot protocol for serving web-pages. Since its invention, various additions have been bolted on to cater for its ever increasing use cases (file downloads, resumption, streaming, etc.) but the fact remains there's no "simple" solution for video streaming at the moment.
If you want to have a play with streaming a "real" video format (specifically, MPEG1) you may want to have a look at the pistreaming demo. However, for the purposes of this recipe we'll be using a much simpler format: MJPEG. The following script uses Python's built-in :mod:http.server module to make a simple video streaming server:
.. literalinclude:: examples/web_streaming.py
Once the script is running, visit http://your-pi-address:8000/ with your web-browser to view the video stream.
Note
This recipe assumes Python 3.x (the http.server module was named SimpleHTTPServer in Python 2.x)
## Capturing images whilst recording
The camera is capable of capturing still images while it is recording video. However, if one attempts this using the stills capture mode, the resulting video will have dropped frames during the still image capture. This is because images captured via the still port require a mode change, causing the dropped frames (this is the flicker to a higher resolution that one sees when capturing while a preview is running).
However, if the use_video_port parameter is used to force a video-port based image capture (see :ref:rapid_capture) then the mode change does not occur, and the resulting video should not have dropped frames, assuming the image can be produced before the next video frame is due:
.. literalinclude:: examples/record_and_capture.py
The above code should produce a 20 second video with no dropped frames, and a still frame from 10 seconds into the video. Higher resolutions or non-JPEG image formats may still cause dropped frames (only JPEG encoding is hardware accelerated).
## Recording at multiple resolutions
The camera is capable of recording multiple streams at different resolutions simultaneously by use of the video splitter. This is probably most useful for performing analysis on a low-resolution stream, while simultaneously recording a high resolution stream for storage or viewing.
The following simple recipe demonstrates using the splitter_port parameter of the :meth:~PiCamera.start_recording method to begin two simultaneous recordings, each with a different resolution:
.. literalinclude:: examples/multi_res_record.py
There are 4 splitter ports in total that can be used (numbered 0, 1, 2, and 3). The video recording methods default to using splitter port 1, while the image capture methods default to splitter port 0 (when the use_video_port parameter is also True). A splitter port cannot be simultaneously used for video recording and image capture so you are advised to avoid splitter port 0 for video recordings unless you never intend to capture images whilst recording.
.. versionadded:: 1.3
## Recording motion vector data
The Pi's camera is capable of outputting the motion vector estimates that the camera's H.264 encoder calculates while generating compressed video. These can be directed to a separate output file (or file-like object) with the motion_output parameter of the :meth:~PiCamera.start_recording method. Like the normal output parameter this accepts a string representing a filename, or a file-like object:
.. literalinclude:: examples/motion_data1.py
Motion data is calculated at the macro-block level (an MPEG macro-block represents a 16x16 pixel region of the frame), and includes one extra column of data. Hence, if the camera's resolution is 640x480 (as in the example above) there will be 41 columns of motion data ((640 \div 16) + 1), in 30 rows (480 \div 16).
Motion data values are 4-bytes long, consisting of a signed 1-byte x vector, a signed 1-byte y vector, and an unsigned 2-byte SAD (Sum of Absolute Differences) value for each macro-block. Hence in the example above, each frame will generate 4920 bytes of motion data (41 \times 30 \times 4). Assuming the data contains 300 frames (in practice it may contain a few more) the motion data should be 1,476,000 bytes in total.
The following code demonstrates loading the motion data into a three-dimensional numpy array. The first dimension represents the frame, with the latter two representing rows and finally columns. A structured data-type is used for the array permitting easy access to x, y, and SAD values:
.. literalinclude:: examples/motion_data2.py
You can calculate the amount of motion the vector represents simply by calculating the magnitude of the vector with Pythagoras' theorem. The SAD (Sum of Absolute Differences) value can be used to determine how well the encoder thinks the vector represents the original reference frame.
The following code extends the example above to use PIL to produce a PNG image from the magnitude of each frame's motion vectors:
.. literalinclude:: examples/motion_data3.py
You may wish to investigate the :class:~array.PiMotionArray and :class:~array.PiMotionAnalysis classes in the :mod:picamera.array module which simplifies the above recipes to the following:
.. literalinclude:: examples/motion_data4.py
The following command line can be used to generate an animation from the generated PNGs with ffmpeg (this will take a very long time on the Pi so you may wish to transfer the images to a faster machine for this step):
avconv -r 30 -i frame%03d.png -filter:v scale=640:480 -c:v libx264 motion.mp4
Finally, as a demonstration of what can be accomplished with motion vectors, here's a gesture detection system:
.. literalinclude:: examples/gesture_detect.py
Within a few inches of the camera, move your hand up, down, left, and right, parallel to the camera and you should see the direction displayed on the console.
.. versionadded:: 1.5
## Splitting to/from a circular stream
This example builds on the one in :ref:circular_record1 and the one in :ref:record_and_capture to demonstrate the beginnings of a security application. As before, a :class:PiCameraCircularIO instance is used to keep the last few seconds of video recorded in memory. While the video is being recorded, video-port-based still captures are taken to provide a motion detection routine with some input (the actual motion detection algorithm is left as an exercise for the reader).
Once motion is detected, the last 10 seconds of video are written to disk, and video recording is split to another disk file to proceed until motion is no longer detected. Once motion is no longer detected, we split the recording back to the in-memory ring-buffer:
.. literalinclude:: examples/circular_record2.py
This example also demonstrates using the seconds parameter of the :meth:~PiCameraCircularIO.copy_to method to limit the before file to 10 seconds of data (given that the circular buffer may contain considerably more than this).
.. versionadded:: 1.0
.. versionchanged:: 1.11
Added use of :meth:~PiCameraCircularIO.copy_to
## Custom encoders
You can override and/or extend the encoder classes used during image or video capture. This is particularly useful with video capture as it allows you to run your own code in response to every frame, although naturally whatever code runs within the encoder's callback has to be reasonably quick to avoid stalling the encoder pipeline.
Writing a custom encoder is quite a bit harder than writing a :ref:custom output <custom_outputs> and in most cases there's little benefit. The only thing a custom encoder gives you that a custom output doesn't is access to the buffer header flags. For many output formats (MJPEG and YUV for example), these won't tell you anything interesting (i.e. they'll simply indicate that the buffer contains a full frame and nothing else). Currently, the only format where the buffer header flags contain useful information is H.264. Even then, most of the information (I-frame, P-frame, motion information, etc.) would be accessible from the :attr:~PiCamera.frame attribute which you could access from your custom output's write method.
The encoder classes defined by picamera form the following hierarchy (dark classes are actually instantiated by the implementation in picamera, light classes implement base functionality but aren't technically "abstract"):
The following table details which :class:PiCamera methods use which encoder classes, and which method they call to construct these encoders:
.. tabularcolumns:: |p{52mm}|p{42mm}|p{53mm}|
It is recommended, particularly in the case of the image encoder classes, that you familiarize yourself with the specific function of these classes so that you can determine the best class to extend for your particular needs. You may find that one of the intermediate classes is a better basis for your own modifications.
In the following example recipe we will extend the :class:PiCookedVideoEncoder class to store how many I-frames and P-frames are captured (the camera's encoder doesn't use B-frames):
.. literalinclude:: examples/custom_encoders.py
Please note that the above recipe is flawed: PiCamera is capable of initiating :ref:multiple simultaneous recordings <multi_res_record>. If this were used with the above recipe, then each encoder would wind up incrementing the i_frames and p_frames attributes on the MyCamera instance leading to incorrect results.
.. versionadded:: 1.5
## Raw Bayer data captures
The bayer parameter of the :meth:~PiCamera.capture method causes the raw Bayer data recorded by the camera's sensor to be output as part of the image meta-data.
Note
The bayer parameter only operates with the JPEG format, and only for captures from the still port (i.e. when use_video_port is False, as it is by default).
Raw Bayer data differs considerably from simple unencoded captures; it is the data recorded by the camera's sensor prior to any GPU processing including auto white balance, vignette compensation, smoothing, down-scaling, etc. This also means:
• Bayer data is always full resolution, regardless of the camera's output :attr:~PiCamera.resolution and any resize parameter.
• Bayer data occupies the last 6,404,096 bytes of the output file for the V1 module, or the last 10,270,208 bytes for the V2 module. The first 32,768 bytes of this is header data which starts with the string 'BRCM'.
• Bayer data consists of 10-bit values, because this is the sensitivity of the OV5647 and IMX219 sensors used in the Pi's camera modules. The 10-bit values are organized as 4 8-bit values, followed by the low-order 2-bits of the 4 values packed into a fifth byte.
• Bayer data is organized in a BGGR pattern (a minor variation of the common Bayer CFA). The raw data therefore has twice as many green pixels as red or blue and if viewed "raw" will look distinctly strange (too dark, too green, and with zippering effects along any straight edges).
• To make a "normal" looking image from raw Bayer data you will need to perform de-mosaicing at the very least, and probably some form of color balance.
This (heavily commented) example script causes the camera to capture an image including the raw Bayer data. It then proceeds to unpack the Bayer data into a 3-dimensional numpy array representing the raw RGB data and finally performs a rudimentary de-mosaic step with weighted averages. A couple of numpy tricks are used to improve performance but bear in mind that all processing is happening on the CPU and will be considerably slower than normal image captures:
.. literalinclude:: examples/bayer_data.py
An enhanced version of this recipe (which also handles different bayer orders caused by flips and rotations) is also encapsulated in the :class:~picamera.array.PiBayerArray class in the :mod:picamera.array module, which means the same can be achieved as follows:
.. literalinclude:: examples/bayer_array.py
.. versionadded:: 1.3
.. versionchanged:: 1.5
Added note about new :mod:picamera.array module.
## Using a flash with the camera
The Pi's camera module includes an LED flash driver which can be used to illuminate a scene upon capture. The flash driver has two configurable GPIO pins:
• one for connection to an LED based flash (xenon flashes won't work with the camera module due to it having a rolling shutter). This will fire before (flash metering) and during capture
• one for an optional privacy indicator (a requirement for cameras in some jurisdictions). This will fire after taking a picture to indicate that the camera has been used
These pins are configured by updating the VideoCore device tree blob. Firstly, install the device tree compiler, then grab a copy of the default device tree source:
$sudo apt-get install device-tree-compiler$ wget https://github.com/raspberrypi/firmware/raw/master/extra/dt-blob.dts
The device tree source contains a number of sections enclosed in curly braces, which form a hierarchy of definitions. The section to edit will depend on which revision of Raspberry Pi you have (check the silk-screen writing on the board for the revision number if you are unsure):
Model Section
Raspberry Pi Model B rev 1 /videocore/pins_rev1
Raspberry Pi Model A and Model B rev 2 /videocore/pins_rev2
Raspberry Pi Model A+ /videocore/pins_aplus
Raspberry Pi Model B+ rev 1.1 /videocore/pins_bplus1
Raspberry Pi Model B+ rev 1.2 /videocore/pins_bplus2
Raspberry Pi 2 Model B rev 1.0 /videocore/pins_2b1
Raspberry Pi 2 Model B rev 1.1 and rev 1.2 /videocore/pins_2b2
Raspberry Pi 3 Model B rev 1.0 /videocore/pins_3b1
Raspberry Pi 3 Model B rev 1.2 /videocore/pins_3b2
Raspberry Pi Zero rev 1.2 and rev 1.3 /videocore/pins_pi0
Raspberry Pi Zero Wireless rev 1.1 /videocore/pins_pi0w
Under the section for your particular model of Pi you will find pin_config and pin_defines sections. Under the pin_config section you need to configure the GPIO pins you want to use for the flash and privacy indicator as using pull down termination. Then, under the pin_defines section you need to associate those pins with the FLASH_0_ENABLE and FLASH_0_INDICATOR pins.
For example, to configure GPIO 17 as the flash pin, leaving the privacy indicator pin absent, on a Raspberry Pi 2 Model B rev 1.1 you would add the following line under the /videocore/pins_2b2/pin_config section:
pin@p17 { function = "output"; termination = "pull_down"; };
Please note that GPIO pins will be numbered according to the Broadcom pin numbers (BCM mode in the RPi.GPIO library, not BOARD mode). Then change the following section under /videocore/pins_2b2/pin_defines. Specifically, change the type from "absent" to "internal", and add a number property defining the flash pin as GPIO 17:
pin_define@FLASH_0_ENABLE {
type = "internal";
number = <17>;
};
With the device tree source updated, you now need to compile it into a binary blob for the firmware to read. This is done with the following command line:
$dtc -q -I dts -O dtb dt-blob.dts -o dt-blob.bin Dissecting this command line, the following components are present: • dtc - Execute the device tree compiler • -I dts - The input file is in device tree source format • -O dtb - The output file should be produced in device tree binary format • dt-blob.dts - The first anonymous parameter is the input filename • -o dt-blob.bin - The output filename This should output nothing. If you get lots of warnings, you've forgotten the -q switch; you can ignore the warnings. If anything else is output, it will most likely be an error message indicating you have made a mistake in the device tree source. In this case, review your edits carefully (note that sections and properties must be semi-colon terminated for example), and try again. Now the device tree binary blob has been produced, it needs to be placed on the first partition of the SD card. In the case of non-NOOBS Raspbian installs, this is generally the partition mounted as /boot: $ sudo cp dt-blob.bin /boot/
However, in the case of NOOBS Raspbian installs, this is the recovery partition, which is not mounted by default:
$sudo mkdir /mnt/recovery$ sudo mount /dev/mmcblk0p1 /mnt/recovery
$sudo cp dt-blob.bin /mnt/recovery$ sudo umount /mnt/recovery
\$ sudo rmdir /mnt/recovery
Please note that the filename and location are important. The binary blob must be named dt-blob.bin (all lowercase), and it must be placed in the root directory of the first partition on the SD card. Once you have rebooted the Pi (to activate the new device tree configuration) you can test the flash with the following simple script:
import picamera
with picamera.PiCamera() as camera:
camera.flash_mode = 'on'
camera.capture('foo.jpg')
You should see your flash LED blink twice during the execution of the script.
Warning
The GPIOs only have a limited current drive which is insufficient for powering the sort of LEDs typically used as flashes in mobile phones. You will require a suitable drive circuit to power such devices, or risk damaging your Pi. One developer on the Pi forums notes:
For reference, the flash driver chips we have used on mobile phones will often drive up to 500mA into the LED. If you're aiming for that, then please think about your power supply too.
If you wish to experiment with the flash driver without attaching anything to the GPIO pins, you can also reconfigure the camera's own LED to act as the flash LED. Obviously this is no good for actual flash photography but it can demonstrate whether your configuration is good. In this case you need not add anything to the pin_config section (the camera's LED pin is already defined to use pull down termination), but you do need to set CAMERA_0_LED to absent, and FLASH_0_ENABLE to the old CAMERA_0_LED definition (this will be pin 5 in the case of pins_rev1 and pins_rev2, and pin 32 in the case of everything else). For example, change:
pin_define@CAMERA_0_LED {
type = "internal";
number = <5>;
};
pin_define@FLASH_0_ENABLE {
type = "absent";
};
into this:
pin_define@CAMERA_0_LED {
type = "absent";
};
pin_define@FLASH_0_ENABLE {
type = "internal";
number = <5>;
};
After compiling and installing the device tree blob according to the instructions above, and rebooting the Pi, you should find the camera LED now acts as a flash LED with the Python script above.
.. versionadded:: 1.10
|
2018-11-21 14:11:43
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24315676093101501, "perplexity": 3187.6949399286473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039748901.87/warc/CC-MAIN-20181121133036-20181121155036-00059.warc.gz"}
|
https://alekbo.com/news-line/variable-ratio-write-definition.html
|
Home / NEWS LINE / Variable Ratio Write Definition
Variable Ratio Write Definition
What Is the Unstable Ratio Write?
The variable ratio write is a strategy in options investing that requires holding a long proposition in the underlying asset while simultaneously writing multiple call options at varying strike prices. It is essentially a correlation buy-write strategy.
The trader’s goal is to capture the premiums paid for the call options. Variable ratio writes from limited profit potential. The strategy is best used on stocks with little expected volatility, particularly in the tight-fisted term.
Variable Ratio Writes Explained
In ratio call writing, the word “ratio” represents the enumerate of options sold for every 100 shares owned in the underlying stock.
For example, in a 2:1 variable ratio put down, the trader might own 100 shares of the underlying stock and sell 200 options.
Two calls are written: One is “out of the money.” That is, the cudgel price is higher than the current value of the underlying stock. In the other, the strike price is “in the money,” or lower than the cost of the underlying stock.
The payoff in a variable ratio write resembles that of a reverse strangle. In the options trade, any strangle scheme involves buying both a call and a put on the same underlying asset.
The variable ratio write is aptly described as suffer with limited profit potential and unlimited risk.
When the Uncertain Ratio Write Is Used
As an investment strategy, the variable ratio write should be avoided by inexperienced options saleswomen as it is a strategy with unlimited risk potential.
The losses begin if the stock’s price makes a strong move to the upside or downside beyond the higher up and lower breakeven points set by the trader.
There is no limit to the maximum possible loss on a variable ratio write determine. Despite its significant risks, the variable ratio write technique can bring the experienced trader a fair amount of resiliency with managed market risk while providing attractive income.
There are two breakeven points for a variable relationship write position. These breakeven points can be found as follows:
begin{aligned} &text{Upper Breakeven Point} = SPH+PMP &text{Lower Breakeven Significance} = SPL-PMP &textbf{where:} &SPH=text{Strike price of higher strike short call} &PMP=main body text{Points of maximum profit} &SPL=text{Strike price of lower strike short call} end{aligned}
Power Breakeven Point=SPH+PMPLower Breakeven Point=SPLPMPwhere:SPH=Strike price of higher strike short callPMP=Bottoms of maximum profitSPL=Strike price of lower strike short call
Real World Example of a Variable Correlation Write
Consider an investor who owns 1,000 shares of the company XYZ, currently trading at $100 per share. The investor assumes that the stock is unlikely to move much over the next two months. The investor can hold onto the stock and tranquillity earn a positive return on it while it remains static in price. This is achieved by initiating a variable ratio a note position, selling 30 of the 110 strike calls on XYZ that are due to expire in two month’s time. The options premium on the 110 gathers are$0.25, so our investor will collect $750 from selling the options. That is, if the investor is correct in predicting that the investment’s price will remain flat. After two months, if XYZ shares remain below$110, the investor will paperback the entire $750 premium as profit, since the calls will be worthless when they expire. If the shares climb above the breakeven$110.25, however, the gains on the long stock position will be more than offset by depletions by the short calls. The options represented 3,000 shares of XYZ, triple the number that the trader owns.
Long Leg Definition
What Is Prolonged Leg? A long leg is the long part or parts of a …
|
2021-09-24 19:08:38
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4156776964664459, "perplexity": 3435.7398398992786}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057564.48/warc/CC-MAIN-20210924171348-20210924201348-00356.warc.gz"}
|
https://golem.ph.utexas.edu/category/2010/05/this_weeks_finds_in_mathematic_59.html
|
## May 15, 2010
### This Week’s Finds in Mathematical Physics (Week 298)
#### Posted by John Baez
In "week298" of This Week’s Finds, learn about finite subgroups of the unit quaternions, like the binary icosahedral group:
Then meet the finite subloops of the unit octonions. Get a tiny taste of how division algebras can be used to build Lie n-superalgebras that govern superstring and supermembrane theories. And meet Duff and Ferrara’s ideas connecting exceptional groups to Cayley’s hyperdeterminants and entanglement in quantum information theory.
Posted at May 15, 2010 6:06 PM UTC
TrackBack URL for this Entry: http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2216
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Yes, well, have fun at the Comlab conference, and say hi to Louis and Bob and Jamie and them from me. (I’ll just be sitting in my icy cold room, as usual, eating my beans and noodles and wondering about how I am going to get my next waitressing job.)
Posted by: Kea on May 16, 2010 4:15 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
In Supermembranes And The Signature Of Space-Time. Blencowe and Duff himself tell:
We conjecture (together with C. Hull and K. Stelle) that the (2,2) extended object moving in (10,2) spacetime may (if it exists) be related by simultaneus dimensional reduction to the (1,1) type II …
This is also reviewed in M theory (The Theory formerly known as strings).
On other hand, I have sometimes hear folklore about F-theory, telling that it really does not need the peculiar signature, but only to consider some infinitesimal extra dimension.
Posted by: Alejandro Rivero on May 17, 2010 1:35 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Regarding your Oxford slides, your first two slides are identical, and you have a bad line break at slide 12.
On slide 16, should you say something about normalizing rows to produce probability? I know we’ve discussed this before. Along with the idea of relative probabilities, you had the idea of matrix mechanics over Durov’s generalized rings.
Hmm, perhaps I should return to all that Progic material.
Posted by: David Corfield on May 17, 2010 2:27 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Thanks for catching those mistakes, David. Fixed!
The double first page was caused by the fact that this talk contains a mixture of Postscript figures (most of the talk) and a jpeg figure (the first page). Right now I don’t know how to get LaTeX to handle both those formats in the same file! I can use jpegs in pdflatex and Postscript in ordinary latex, which then can be turned into PDF. So I did this and then used Adobe Acrobat to combine two separate PDFs… and screwed up. I mention this boring stuff only in case some smart person knows a better solution.
I guess I’ll verbally mention the idea of ‘relative probabilities’.
I think there’s a lot of stuff left to be done with these ideas, and your ‘progic’ ideas.
Posted by: John Baez on May 17, 2010 7:26 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I can use jpegs in pdflatex and Postscript in ordinary latex, which then can be turned into PDF.
Can you first turn your external postscript files into PDFs and then include them with pdflatex?
Posted by: Mike Shulman on May 17, 2010 9:54 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Scott wrote:
If you are using graphicx via
\usepackage{graphicx}
in the preamble, you *should* be able to specify file type via suffix:
Hmm. I’ve read things like this:
PDFLaTeX, when used with graphics or graphicx packages, can compile correctly PNG and JPG files into DVI or PDF, but is not able to handle EPS files. Conversely, the process of compiling with LaTeX to DVI and converting to PS and eventually PDF does support EPS, but does not support PNG and JPG.
… and that corresponds to my experience.
Hmm. I see that the document I just cited suggests a few workarounds, all mildly irksome, but probably better than what I actually did. One of them is a version of what Mike suggested: converting eps files to pdf using ‘epstopdf’ — a program I hadn’t heard of.
Posted by: John Baez on May 18, 2010 2:34 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
If you are using graphicx via
\usepackage{graphicx}
in the preamble, you *should* be able to specify file type via suffix:
\begin{figure}[htb]
\begin{center}
\includegraphics[width=5in]{filename.pdf}
\end{center}
\caption{pdf file type}
\label{abst}
\end{figure}
and
\begin{figure}[htb]
\begin{center}
\includegraphics[width=5in]{notherfile.jpg}
\end{center}
\caption{jpg file type}
\label{abst}
\end{figure}
I seem to remember having done this once. Of course, you can leave out the \begin{figure} … \end{figure} if you don’t want a bunch of bodies floating around.
For a hack, import the jpg into xfig as a picture, and then save the xfig file as an eps, and process using TeX and ghostscript (Texshop option), or else eps2pdf the file. That is how I got photos into this talk.
Posted by: Scott Carter on May 18, 2010 12:50 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Oxford slide no. 40: There is a classical no-cloning theorem?
(Or is it a QM no-cloning theorem that’s become a classic? :-)
Posted by: Tim van Beek on May 17, 2010 2:54 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
The last page of my slides was supposed to summarize only the ideas that will surprise and thrill the audience, so I get a standing ovation. The Wooters–Zurek no-cloning theorem for quantum mechanics will be very well known to them, since Bob Coecke and Samson Abramsky (both at Oxford) have shown how this theorem is related to the fact that the monoidal category of Hilbert spaces with its usual tensor product is non-cartesian. But for some reason few people study classical mechanics using the complete repertoire of fancy ideas that they use for quantum mechanics. So I wanted to mention that Aaron Fenyes also has a no-cloning theorem for classical mechanics.
This is related to my earlier point that classical mechanics can be formulated using ideas akin to Heisenberg’s ‘matrix mechanics’, but with a different rig replacing the complex numbers.
Aaron Fenyes is a grad student at the Perimeter Institute. A while back he sent me an email starting like this:
At the end of the notes from your 2008 classical mechanics course, it says, “I believe the non-Cartesian nature of this product means there’s no classical machine that can ‘duplicate’ states of a classical system. But, strangely, this issue has been studied less than in the quantum case!” After mentioning this to a couple people, I got tired of not being able to give a specific result, so I wrote up a no-cloning theorem for symplectic mechanics, and I figured you might find it useful to have lying around.
I’m trying to get his okay to make it available on the webpage for this talk.
There are in fact a number of monoidal categories relevant to classical mechanics, and none of the ones I know are cartesian:
• the category of symplectic manifolds and symplectomorphisms
• the category of Poisson manifolds and Poisson maps
• the category Mat(RMIN) described here
• the category of symplectic vector spaces and linear Lagrangian correspondences described in Alan Weinstein’s paper Symplectic categories
… and I would like to add, ‘the category of symplectic manifolds and Lagrangian correspondences’… but unfortunately we can’t compose Lagrangian correspondences unless a transversality condition holds! This problem is the real topic of Weinstein’s paper.
Posted by: John Baez on May 17, 2010 7:38 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Aha.
Is there another hunch of yours of the same caliber somewhere in lecture notes of an undergraduate class, so that I could write down a solution after getting tired of not getting any definite answers from those Perimeter guys?
Posted by: Tim van Beek on May 17, 2010 9:52 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Heh. This Week’s Finds and my seminar notes are packed with hunches of varying caliber. Sometimes you need to read between the lines a bit to see them — for example, if I say something ‘should’ be true, it means I believe it’s true but haven’t proved it. And sometimes, I’ve said something is true even though I haven’t proved it. By now I realize this is a bad habit… thanks to the following story.
Once I went to a talk where somebody said that for any ring $R$ there’s a one-object tricategory $Alg(R)$ consisting of $R$-algebras, bimodules and bimodule morphisms. I said “Really? Do you know if anyone has ever written that up?” And the speaker said “Sure! It’s in This Week’s Finds!” Which galled me, because while I knew it was true, I’d never seen a proof written up — and I realized then that by claiming it was true in This Week’s Finds, I’d reduced the chances of ever seeing a proof.
Posted by: John Baez on May 18, 2010 2:48 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I think you know this, but lest any other reader think that that particular fact still remains to be proven, let me point out that it follows easily from Theorem 21 of this paper and from the main theorem of this one (the latter in fact shows that $Alg(R)$ is a symmetric monoidal bicategory).
Posted by: Mike Shulman on May 18, 2010 4:14 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I think you know this, but lest any other reader think that that particular fact still remains to be proven, let me point out that it follows easily from Theorem 21 of this paper and from the main theorem of this one (the latter in fact shows that $Alg(R)$ is a symmetric monoidal bicategory).
And for eternity:
$n$Lab: tricategory – Examples
$n$Lab: monoidal bicategory – Examples
Posted by: Urs Schreiber on May 18, 2010 9:52 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
But seriously, isn’t the no-cloning theorem supposed to be of an inherently quantum mechanical nature? How does a classical version fit in?
(Well, I hope you get Aaron Fenyes’ permission to publish his idea/proof…and I’m curious about what the members of your audience in Oxford will say…).
Posted by: Tim van Beek on May 18, 2010 9:17 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
To discriminate quantum from classical, one does not rely on no-cloning but on no-broadcasting [H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B.~Schumacher (1996) Noncommuting mixed states cannot be broadcast. Physical Review Letters 76, 2818–2821. arXiv:quant-ph/9511010 . This is for example used in Environment and classical channels in categorical quantum mechanics and Classical and quantum structuralism. The reason is, that indeed, while even classical probability theory has no-cloning, it doesn’t have no-broadcasting. Broadcastable data is the same as decoherent data. So if you want to use no-cloning to discriminate anything, you have to be very precise about what you are talking, as is clear from the previous entries. On the other hand, no-cloning does play an important role in quantum computing. But it is a fact, that if one starts to list things people say are weird about quantum, that many can be found in classical settings. Pinpointing in conceptual terms “what is quantum” is not at all obvious.
Posted by: bob on May 19, 2010 9:16 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
You can now see Aaron’s paper on the website for my talk, or here:
Posted by: John Baez on May 19, 2010 2:24 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Thanks to Bob and John, I will take a look. I guess the first thing I need to understand is “broadcasting” in the Barnum-Caves-Fuchs-Jozsa-Schumacher-paper and broadcastable $\cong$ decoherent.
But it is a fact, that if one starts to list things people say are weird about quantum, that many can be found in classical settings. Pinpointing in conceptual terms “what is quantum” is not at all obvious.
This is a real surprise! (For someone who stopped thinking about these matters after passing the QM exam, that is).
Posted by: Tim van Beek on May 19, 2010 2:45 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I find the distribution collapse heuristic of measurement is the most unclassical aspect of quantum whatnot. Otherwise it’s “just” a differential equation; and those are fairly classical.
Posted by: some guy on the street on May 20, 2010 6:23 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Tim van Beek wrote:
But seriously, isn’t the no-cloning theorem supposed to be of an inherently quantum mechanical nature? How does a classical version fit in?
There are certain cases where people have thought about the quantum version of a problem a lot more carefully than the classical version, and this is one.
When people think about duplicating quantum states they are fairly careful to describe the candidate ‘duplication process’ — which they intend to prove does not exist — as linear operator between Hilbert spaces, or perhaps a unitary operator. But when they think about duplicating classical states they often sloppily treat it as a mere function between sets, or perhaps a one-to-one and onto function. I too have been guilty of this.
However, processes in classical mechanics are not just arbitrary functions between sets! The set of states of a classical system has a lot of extra structure: it’s typically a symplectic manifold, or more generally, a Poisson manifold. And processes aren’t arbitrary functions: they need to respect this extra structure. So, they need to be symplectomorphisms, or Poisson maps, or something like that. When you take this into account, you see it gets a lot harder to duplicate classical states. In fact Aaron shows its impossible in the symplectic case.
If that sounds too fancy and mathematical, you may prefer this puzzle. Try to use the laws of classical mechanics to design a machine like this:
The machine has a hole in the top where you can insert in a little box with a ball in it. The ball can move around in the box, so it has some arbitrary position and momentum. The machine measures the position and momentum of the ball at a certain moment — let’s say when you push a big red button. And then, out of a slot at the bottom, it spits out two boxes with balls in them! A bell rings when this happens, and when the bell rings, the state of each ball in each box is guaranteed to be equal to the state of the original ball in the original box at the moment you pushed the big red button.
Can you do it?
You get to use gears, levers, pulleys, all sorts of stuff like that — anything whose behavior can be described using classical mechanics.
Posted by: John Baez on May 20, 2010 12:31 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
In case you’re wondering how the machine gets to measure the position and momentum of the ball in the box: I was imagining the machine can remove the top of the box, and then insert sensors of various sorts.
The impossibility of building this machine should resemble the impossibility of building a working perpetual motion machine or Maxwell’s Daemon. No matter how clever you are, you should fail.
Posted by: John Baez on May 20, 2010 12:52 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
You get to use gears, levers, pulleys, all sorts of stuff like that — anything whose behavior can be described using classical mechanics. … In case you’re wondering how the machine gets to measure the position and momentum of the ball in the box: I was imagining the machine can remove the top of the box, and then insert sensors of various sorts.
I guess we may assume that the machine can use classical electrodynamics, too, and that the sensors act noninvasive, that is they have no influence on the system that they monitor.
Can you do it?
I have no idea, but my educated guess is that it would be wiser to try to prove that it cannot be done.
Posted by: Tim van Beek on May 20, 2010 3:41 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Tim wrote:
I guess we may assume that the machine can use classical electrodynamics, too …
Well, Aaron proved his no-cloning theorem for systems with finitely many degrees of freedom — that is, where the phase space is a finite-dimensional symplectic manifold. Field theories, like electromagnetism, have infinitely many degrees of freedom. So, his theorem doesn’t really apply. But I bet it could be generalized.
This could be a fun project for someone (hint, hint). But still, I think it’s fun to see what we can and can’t do using just classical mechanics, not field theory.
… and that the sensors act noninvasively, that is they have no influence on the system that they monitor.
Well, that’s a tricky question. I just want you to assume that the formalism of Hamiltonian mechanics applies. So the question is whether measurements that have no influence on the system being measured are allowed by Hamiltonian mechanics. Or at least very little influence. We all believe that in classical mechanics you can measure the position of a big boulder by bouncing a tiny pebble off it without affecting the boulder’s momentum very much — you can make the effect as small as you like. But still, this is the sort of thing you need to check, not just take for granted.
For example, if we have two particles with position and momentum $(q_1, p_1)$ and $(q_2, p_2)$ respectively, can we make $q_1$ affect $q_2$ without any effect the other way? We have to see if the resulting time evolution is symplectic.
For example, consider this linear transformation:
$(q_1, p_1, q_2 , p_2) \mapsto (q_1, p_1, q_2, p_2 + q_1)$
where the position of the first particle affects the momentum of the second particle, but there’s no effect the other way. Can this happen? No, because the symplectic 2-form
$d p_1 \wedge d q_1 + d p_2 \wedge d q_2$
gets sent to
$d p_1 \wedge d q_1 + d p_2 \wedge d q_2 + d q_1 \wedge d q_2$
So we say this transformation is not symplectic, and we know that no process in classical mechanics can make it occur.
But this is just one example; one has to think about this stuff in general and figure it out!
Posted by: John Baez on May 21, 2010 1:18 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
“ but unfortunately we can’t compose Lagrangian correspondences unless a transversality condition holds! ”
Reminds me of a similar problem for Chas-Sullivan string topology for which the hoped for way out of transversality is to look for an A_infty structure
anyone worked on that?
Posted by: jim stasheff on May 18, 2010 12:45 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Jim wrote:
Reminds me of a similar problem for Chas-Sullivan string topology for which the hoped for way out of transversality is to look for an $A_\infty$ structure.
Anyone worked on that?
I don’t understand this stuff well enough to give you a really illuminating answer, but try this:
Posted by: John Baez on May 19, 2010 2:28 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Thanks for this very classical TWF episode! It had starring almost all my favorite characters (octonions, E8, higher gauge theory, etc.) and had as always an excellent storytelling. All that makes it very hard to accept that TWF will be off the air very soon!
There will be a movie, eh a book one day, right?
Posted by: Christian on May 18, 2010 9:38 AM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I’m glad you enjoyed this epsiode! TWF is not going off the air: TWFMP is becoming TWF and the range of themes will grow, but if I learn new cool stuff about time-honored themes I doubt I can resist talking about it.
You can also look forward to the movie version of The Octonions — I’m busy rounding up 8 stars. Unfortunately Snow White and the Seven Dwarves are locked into a lifetime contract with Disney.
Posted by: John Baez on May 19, 2010 2:32 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Has anyone heard what became of the kid’s movie “Mono, the adjoint functors and the diagram c(h)ase”?
Posted by: Tim van Beek on May 19, 2010 2:49 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Whew! I had a bit of a scare when reading the above comment about TWFMP being taken off the air. Thanks for the clarification John. Awesome episode as always. Cheers!
Posted by: Michael on May 23, 2010 9:36 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I noticed that at Woit’s some wrestling has been going on concerning how classification of tripartite entangled states (under SLOCC) may be connected to Duff et all string theory stuff. Maybe of interest here at the cafe is that Aleks Kissinger and I found that this SLOCC-classification is actually directly connected to the classification of commutative Frobenius algebras on 2d Hilbert space in Hilb; see col 1 in arXiv:1002.2540 which states that there are only two kinds of commutative Frobenius algebras, special ones and “anti-special ones” (yes, we have been told many times that this is a horrible name), and this follows directly from the entanglement classification result.
Posted by: bob on May 21, 2010 7:35 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I’m pleased that hyperdeterminants are slowly gethering more interest. They are hard to get into but rewarding when you do.
The work on connections between M-theory and quantum information entanglement is intriguing. I hope it leads somewhere. It is curious that this work links the 2x2x2 hyperdeterminant and the octonions which were both worked on by Cayley. I wonder how long Cayley thought about possible connections just because they are both algebraic structures defined on 8 component vectors.
There is another curious historical coincidence for the 2x2x2x2 hyperdeterminant that was constructed by Schläfli. It is a degree 24 polynomial. Schläfli also discovered the 24-cell and in both cases the appearance of the number 24 can be linked to the importance of the number 24 in bosonic string theory.
Posted by: PhilG on May 23, 2010 10:07 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
PG:
There is another curious historical coincidence for the 2x2x2x2 hyperdeterminant that was constructed by Schläfli. It is a degree 24 polynomial. Schläfli also discovered the 24-cell and in both cases the appearance of the number 24 can be linked to the importance of the number 24 in bosonic string theory.
Why don’t you back up the last statement by appropriate references?
Posted by: Arnold Neumaier on May 26, 2010 6:31 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I was being lazy but I thought these things have been mentioned here before or can be found in google.
The connection between the 24-cell and string theory has been mentioned by JB e.g. here or here.
The connection between the 2x2x2x2 determinant and elliptic curves which therefore links it to string theory is described here.
I suppose it’s also interesting that both the hyperdeterminant and the 24-cell are four dimensional so you might try to find a more direct connection using that.
Posted by: PhilG on May 27, 2010 8:44 AM | Permalink | Reply to this
### OT: amusing crop-circle link
Not remotely connected with anything in the TWF, but this link gives an attempt to decode a crop circle recently found in England as a statement of Euler’s trigonometric identity. (This story appears other places, so I’m pretty sure that the physical crop circle does exist – rather than being photoshopped – but beyond that…). On the assumption that it was done by human beings, there’s still niggling questions (surely the “corrected-version” brackets would, by the principle of only putting things in when they’re needed, imply the pi isn’t in the exponent?). Anyway, it’s mildly amusing to see how people will spend their time.
Posted by: bane on May 24, 2010 9:38 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
Mike Duff’s students William Rubens and Leron Borsten are here at the school on Foundational Structures in Quantum Computation and Information. Over coffee William just told me about this new paper:
It gives an actual map relating a certain class supersymmetric black holes to patterns of entanglement of 4 qubits. I don’t understand it, but one key piece seems to be the Kostant-Sekiguchi correspondence between nilpotent orbits of $SO_0(4,4)$ in $so(4,4)$ and nilpotent orbits of $SL(2,\mathbb{C})^4$ in $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$.
Here I am just parroting the paper. But what does the second appearance of ‘nilpotent’ in the above sentence mean? I know what a nilpotent element of a Lie algebra is, but not what a nilpotent element of a vector space is. My best guess is that we should use the vector space isomorphism
$so(4,4) \cong (sl(2,\mathbb{C})^4 \oplus \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$
to interpret elements of $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$ as elements of $so(4,4)$. Then we can say whether or not they are nilpotent.
The entanglement classes of 4 qubits are all the nonzero orbits of $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$ under the action of $(sl(2,\mathbb{C})^4$. I don’t know what we leave out if only consider nilpotent orbits.
Leron Borsten told me something like this. The allowed charges for a certain class of STU black holes correspond to points in a certain 8-dimensional lattice… perhaps the integral split octonions. We can think of this lattice as sitting inside $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$. Then the entropy of the black hole is the square root of the absolute value of the $2 \times 2 \times 2 \times 2$ hyperdeterminant.
He said this was nicely explained here:
Posted by: John Baez on May 27, 2010 12:08 PM | Permalink | Reply to this
### Re: This Week’s Finds in Mathematical Physics (Week 298)
I’ve added an addendum to week298 — a letter from Péter Lévay explaining more about quantum entanglement, black holes and exceptional algebraic structures.
Posted by: John Baez on August 15, 2010 7:40 AM | Permalink | Reply to this
Post a New Comment
|
2016-02-11 13:04:35
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 27, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.667522132396698, "perplexity": 998.2897150538772}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701161946.96/warc/CC-MAIN-20160205193921-00122-ip-10-236-182-209.ec2.internal.warc.gz"}
|
https://probnum.readthedocs.io/en/latest/api/automod/probnum.filtsmooth.gaussian.approx.UnscentedTransform.html
|
# UnscentedTransform¶
class probnum.filtsmooth.gaussian.approx.UnscentedTransform(dimension, spread=0.0001, priorpar=2.0, special_scale=0.0)
Bases: object
Used for unscented Kalman filter.
See also p. 7 (“Unscented transform:”) of 1.
Parameters
• dimension (int) – Spatial dimensionality
• spread (float) – Spread of the sigma points around mean
• priorpar (float) – Incorporate prior knowledge about distribution of x. For Gaussians, 2.0 is optimal (see link below)
• special_scale (float) – Secondary scaling parameter. The primary parameter is computed below.
References
1
Wan, E. A. and van der Merwe, R., The Unscented Kalman Filter, http://read.pudn.com/downloads135/ebook/574389/wan01unscented.pdf
Methods Summary
estimate_statistics(proppts, sigpts, covmat, ...) Computes predicted summary statistics, predicted mean/kernels/crosscovariance, from (propagated) sigmapoints. propagate(time, sigmapts, modelfct) Propagate sigma points. Sigma points.
Methods Documentation
estimate_statistics(proppts, sigpts, covmat, mpred)[source]
Computes predicted summary statistics, predicted mean/kernels/crosscovariance, from (propagated) sigmapoints.
Not to be confused with mean and kernels resulting from the prediction step of the Bayesian filter. Hence we call it “estimate_*” instead of “predict_*”.
propagate(time, sigmapts, modelfct)[source]
Propagate sigma points.
Parameters
Returns
Shape=(2 N + 1, M). M is the dimension of the measurement model
Return type
np.ndarray
sigma_points(rv)[source]
Sigma points.
Parameters
rv (Normal) – Gaussian random variable. Shape (d,)
Raises
ValueError – If the random variable does not match the dimension of the UT.
Returns
Shape (2 * d + 1, d). Sigma points.
Return type
np.ndarray
|
2022-01-28 08:35:20
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9091008901596069, "perplexity": 12146.266811507328}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305423.58/warc/CC-MAIN-20220128074016-20220128104016-00540.warc.gz"}
|
https://proofwiki.org/wiki/Definition:Complete_Distributive_Lattice
|
# Definition:Complete Distributive Lattice
Let $\left({S, \vee, \wedge, \preceq}\right)$ be a lattice.
Then $S$ is a complete distributive lattice if and only if
$(1): \quad S$ is a complete lattice
$(2): \quad S$ is a distributive lattice.
|
2019-12-11 15:32:17
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2034461498260498, "perplexity": 598.8304040483682}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540531917.10/warc/CC-MAIN-20191211131640-20191211155640-00308.warc.gz"}
|
https://www.transtutors.com/questions/p8-2a-morello-computer-parts-inc-is-in-the-process-of-setting-a-selling-price-on-a-n-1313624.htm
|
# P8-2A Morello Computer Parts Inc. is in the process of setting a selling price on a new component...
P8-2A Morello Computer Parts Inc. is in the process of setting a selling price on a new component it has just designed and developed. The following cost estimates for this new component have been provided by the accounting department for a budgeted volume of 50,000 units.
Per Unit Total Direct materials $50 Direct labor$25 Variable manufacturing overhead $20 Fixed manufacturing overhead$600,000 Variable selling and administrative expenses $18 Fixed selling and administrative expenses$400,000
Morello Computer Parts management requests that the total cost per unit be used in cost- plus pricing its products. On this particular product, management also directs that the target price be set to provide a 25% return on investment (ROI) on invested assets of \$1,200,000.
Instructions
(Round all calculations to two decimal places.)
(a) Compute the markup percentage and target selling price that will allow Morello Com- puter Parts to earn its desired ROI of 25% on this new component.
(b) Assuming that the volume is 40,000 units, compute the markup percentage and target selling price that will allow Morello Computer Parts to earn its desired ROI of 25% on this new component.
|
2018-11-18 20:25:39
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17239314317703247, "perplexity": 3554.370900215074}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039744649.77/warc/CC-MAIN-20181118201101-20181118223101-00445.warc.gz"}
|
https://quant.stackexchange.com/questions/31289/how-to-reset-indicators-in-quantstrat-quantmod
|
# How to reset indicators in quantstrat / quantmod?
I am currently trying to back test a strategy on a file which contains minutely data for the whole month. I would like to reset my indicators at 3:30 PM . Is there a way I can reset the indicators based on time or any other way ? Following is the code for adding data and SMA indicator to my strategy . Since the data index is time series , I could use 15:30:00 as an event to reset the SMA indicator . The data contains 1 month of minutely data .
nifty <- as.xts(read.zoo("01122016CE8100.csv",
sep =",",
|
2022-08-14 09:53:34
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5093564391136169, "perplexity": 1398.0602438807368}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572021.17/warc/CC-MAIN-20220814083156-20220814113156-00161.warc.gz"}
|
http://community.wolfram.com/groups/-/m/t/1305226
|
# resize large number of images to required size?
Posted 6 months ago
736 Views
|
8 Replies
|
8 Total Likes
|
Greetings, I am trying to implement the VGG19 neural network. I have downloaded the imagenet dataset and am testing a few classes. I have figured out that NetEncoder can be used to resize images for training but am struck with resizing the images for testing. I am using the following line of code to import the images into testData variable. testData = Import["C:\\Users\\cnn\\Desktop\\images\\test", "*.jpg"]; Now my problem is that the images in the folder are of various sizes and i want to resize all of them to 224 x 224 so that i can use it to test my network.I have tried using testData2=ImageResize[testData,{224,224}]; but it has resulted in error. EDIT : Forgot to mention that there are two sub folders in the path. Problem has been resolved, Thank you.
8 Replies
Sort By:
Posted 6 months ago
Use the following code: testData = Import["C:\\Users\\cnn\\Desktop\\images\\test\\*.jpg", ImageSize -> {224, 224}]
Posted 6 months ago
Thank you for your reply but I am getting the following error when I use the code you suggested: Import::nffil: File not found during Import. I have also tried to do the following: testData = Import["C:\\Users\\cnn\\Desktop\\images\\test\\", "*.jpg", ImageSize -> {224, 224}] I am getting the following error: Import::elemstx: ImageSize->{224,224} is not a valid format or element specification. Expecting a string, list, or integer. General::stop: Further output of Import::elemstx will be suppressed during this calculation. can you please tell me what I am doing wrong?ThanksAshish
Posted 6 months ago
Import["C:\\Users\\cnn\\Desktop\\images\\test\\", "*.jpg", ImageSize -> {224, 224}] This is not going to work.The code the Piotr suggested should work (if you are up-to-date with Mathematica version (I am sure this works at least on 11.1)). To be on the safe side, you could also try doing following: files = FileNames["*.JPG" | "*.JPEG", "C:\\Users\\cnn\\Desktop\\images\\test"] testData = Import[#, ImageSize -> {224, 224}] & /@ files; This solution can be useful, say, when your files formats are spelled differently (i.e. JPEG vs JPG)
Posted 6 months ago
I am using MMA version 11.2. I have tried implementing your code but was hit by the following error:Out[3]={}I have tried to get RandomSample RandomSample[testData, 3]and got the following error: RandomSample::smplen: RandomSample cannot generate a sample of length 3, which is greater than the length of the sample set {}. If you want a choice of possibly repeated elements from the set, use RandomChoice. Thanks for your solution but it seems it is not working to my problem. There are two sub folders in that folder namely dogs and cars, maybe that is causing some problem?RegardsAshish
Posted 6 months ago
What do you want to achieve using RandomSample ? Please tell me what is the output of the following evaluation for you: FileNames["*.JPG" | "*.JPEG", "C:\\Users\\cnn\\Desktop\\images\\test"] // Length UPDATE There are two sub folders in that folder namely dogs and cars Really :) ? You should have told about that in your question. Now I don't understand how your initial code worked?Just do following and it will work: files = FileNames["*.JPG" | "*.JPEG", "C:\\Users\\cnn\\Desktop\\images\\test", Infinity] testData = Import[#, ImageSize -> {224, 224}] & /@ files;
Posted 6 months ago
I just wanted to check whether the images have been imported or not using RandomSample. When I run the code you suggested it gave the following output: Out[3]=0 I am new to MMA so I apologize for any inconvenience caused.
|
2018-09-22 11:08:17
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2612265646457672, "perplexity": 1281.7619733650877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158320.19/warc/CC-MAIN-20180922103644-20180922124044-00187.warc.gz"}
|
https://mathsguru.lakshyaeducation.in/question/in_a_business_b_invests_half_the_amount_invested/1628117283617961168/
|
## Lakshya Education MCQs
Question: In a business, B invests half the amount invested by A. After 6 months from the start of the business, C joins the business with an amount equal to twice of B's investment. After 8 months from the start of the business B withdraws completely from the business. If at the end of the year, C's share in the profit was Rs. 2460, what was the total profit received that year ?
Options:
A. Rs. 11200 B. Rs. 9600 C. Rs. 9020 D. Rs. 12000
Earn Reward Points by submitting Detailed Explaination for this Question
## More Questions on This Topic :
Question 1. A, B and C entered in to a partnership by investing Rs. 15400, Rs.18200 and Rs. 12600 respectively. B left after 6 months. If after 8 months, there was a profit of Rs. 28790, then what is the share of C in the profit ?
1. Rs. 8712
2. Rs. 9432
3. Rs. 8352
4. Rs. 8568
Question 2. A, B and C invested money in the ratio of $$\frac{1}{2}:\frac{1}{3}:\frac{1}{5}$$ in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?
1. Rs. 20000, Rs. 25000, Rs. 18000
2. Rs. 15500, Rs. 27200, Rs. 20450
3. Rs. 22500, Rs. 6750, Rs. 5400
4. Rs. 10350, Rs. 21540, Rs. 12050
Question 3. A and B started a business by investing Rs. 36000 and Rs. 45000 respectively. After 4 months B withdraws $$\frac{4}{9}$$ of his investment. Its 5 months after she again invested $$\frac{{11}}{9}$$ of its original investment. If the total earned profit at the end of the year, is Rs. 117240, then who will get more money as a share of profit and how much ?
1. Rs. 15500
2. Rs. 12450
3. Rs. 14245
4. Rs. 13560
Question 4. A started a business by investing some money and B invested Rs. 5000 each more than that of A. A remained in business for 5 months and B remained in business 1 month more than A. Out of the total profit of Rs. 26000, B got Rs. 6000 more than A. Find the capitals invested A and B ?
1. Rs. 29000, Rs. 18000
2. Rs. 25000, Rs. 3000
3. Rs. 15000, Rs. 10000
4. Rs. 15000, Rs. 20000
Question 5. Three partner A, B and C started a business by investing Rs. 48000 each. After 6 months A left the business after 10 months B left the business and after 12 months C left the business. If total earned profit is Rs. 5250, then find the share of A, B and C ?
1. Rs. 1125, Rs. 1825, Rs. 2250
2. Rs. 1125, Rs. 1800, Rs. 2200
3. Rs. 1125, Rs. 1875, Rs. 2250
4. Rs. 1175, Rs. 1256, Rs. 2350
|
2021-12-01 09:50:38
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6372447609901428, "perplexity": 4299.393491887527}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964359976.94/warc/CC-MAIN-20211201083001-20211201113001-00296.warc.gz"}
|
https://epiga.episciences.org/9872
|
## Richard Lärkäng ; Elizabeth Wulcan - Chern currents of coherent sheaves
epiga:8653 - Épijournal de Géométrie Algébrique, July 30, 2022, Volume 6 - https://doi.org/10.46298/epiga.2022.8653
Chern currents of coherent sheaves
Authors: Richard Lärkäng ; Elizabeth Wulcan
Given a finite locally free resolution of a coherent analytic sheaf $\mathcal F$, equipped with Hermitian metrics and connections, we construct an explicit current, obtained as the limit of certain smooth Chern forms of $\mathcal F$, that represents the Chern class of $\mathcal F$ and has support on the support of $\mathcal F$. If the connections are $(1,0)$-connections and $\mathcal F$ has pure dimension, then the first nontrivial component of this Chern current coincides with (a constant times) the fundamental cycle of $\mathcal F$. The proof of this goes through a generalized Poincaré-Lelong formula, previously obtained by the authors, and a result that relates the Chern current to the residue current associated with the locally free resolution.
Volume: Volume 6
Published on: July 30, 2022
Accepted on: July 22, 2022
Submitted on: November 3, 2021
Keywords: Mathematics - Complex Variables,Mathematics - Algebraic Geometry,32A27, 14C17, 32C30, 14F06, 53C05
|
2023-03-23 04:57:53
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8143318891525269, "perplexity": 984.5389646816085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944996.49/warc/CC-MAIN-20230323034459-20230323064459-00396.warc.gz"}
|
https://web2.0calc.com/questions/one-more-thank
|
+0
# One more thank
+1
76
1
+475
Given that $$f(x) = \left(\dfrac{1}{\pi}\right)^x$$, what is the range of $$f(x)$$ on the interval $$[0, \infty)$$?
Halp ASAP thanks!!!!!!!
Sep 30, 2020
|
2021-01-24 00:02:39
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9998960494995117, "perplexity": 7306.85080631682}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703538741.56/warc/CC-MAIN-20210123222657-20210124012657-00402.warc.gz"}
|
https://iq.opengenus.org/manhattan-distance/
|
# Manhattan distance (L1 norm)
#### similarity measurement manhattan distance Algorithms Software Engineering
Get FREE domain for 1st year and build your brand new site
Manhattan distance is a distance metric between two points in a N dimensional vector space. It is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes. In simple terms, it is the sum of absolute difference between the measures in all dimensions of two points.
It is, also, known as L1 norm and L1 metric.
It is used extensively in a vast area of field from regression analysis to frquency distribution. It was introduced by Hermann Minkowski.
The concept of Manhattan distance is captured by this image:
### Properties
Properties of Manhattan distance are:
• There are several paths (finite) between two points whose length is equal to Manhattan distance
• A straight path with length equal to Manhattan distance has two permitted moves:
• Vertical (one direction)
• Horizontal (one direction)
• For a given point, the other point at a given Manhattan distance lies in a square:
### Manhattan distance in 2D space
In a 2 dimensional space, a point is represented as (x, y).
Consider two points P1 and P2:
P1: (X1, Y1)
P2: (X2, Y2)
Then, the manhattan distance between P1 and P2 is given as:
$${{|x1-x2|\ +\ |y1-y2|}$$
### Manhattan distance in N-D space
In a N dimensional space, a point is represented as (x1, x2, ..., xN).
Consider two points P1 and P2:
P1: (X1, X2, ..., XN)
P2: (Y1, Y2, ..., YN)
Then, the manhattan distance between P1 and P2 is given as:
$$|x1-y1|\ +\ |x2-y2|\ +\ ...\ +\ |xN-yN|}$$
### Applications
Manhattan distance is frequently used in:
1. Regression analysis: It is used in linear regression to find a straight line that fits a given set of points
2. Compressed sensing: In solving an underdetermined system of linear equations, the regularisation term for the parameter vector is expressed in terms of Manhattan distance. This approach appears in the signal recovery framework called compressed sensing
3. Frequency distribution: It is used to assess the differences in discrete frequency distributions
#### OpenGenus Foundation
The official account of OpenGenus IQ backed by GitHub, DigitalOcean and Discourse
Vote for OpenGenus Foundation for Top Writers 2021:
|
2021-03-07 15:43:49
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7248525619506836, "perplexity": 1091.4098065092967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178377821.94/warc/CC-MAIN-20210307135518-20210307165518-00418.warc.gz"}
|
http://worldcat.org/identities/lccn-n81109805/
|
# Beatty, James J.
Overview
Works: 8 works in 8 publications in 1 language and 64 library holdings Programmed instructional materials Academic theses Author QD31.2.B398, 540.76
Publication Timeline
.
Most widely held works by James J Beatty
The elements of style in chemistry : a computer assisted instruction supported text by James Wayne Beatty( Book )
1 edition published in 1981 in English and held by 56 WorldCat member libraries worldwide
Investigating the performance of the interferometric trigger for future flights of the Antarctic Impulsive Transient Antenna by Ryan Craig Hupe( )
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
One of the primary unanswered questions in the field of astrophysics is the source of high-energy cosmic rays. Decades of searching by many different experiments have not identified any point sources. Cosmogenic neutrinos are an ideal candidate for source identification due to their ability to reach Earth unattenuated and undeflected. The Antarctic Impulsive Transient Antenna (ANITA) experiment is a high-altitude radio-antenna balloon designed to detect ultra-high-energy cosmogenic neutrinos via Askaryan emission in the Antarctic ice shelf. A redesign of the ANITA event trigger, called the Triggering Interferometric Sum Correlator (TISC), was performance tested and compared to simulations of the trigger. In order to characterize the performance of the TISC, a testbench was developed to generate impulsive signals and thermal noise that closely matched observations from previous ANITA flights. During this testing process, numerous unexpected issues were found including differential non-linearity of some digital-to-analog converters, errant digitization values due to poor signal encoding, and integral non-linearity within analog-to-digital converters resulting from integrated circuit variation during manufacturing. These issues, as well as others, were characterized and novel calibration strategies were developed to minimize their effect on the triggering performance. Threshold scans were performed at various impulsive signal amplitudes. Data from these threshold scans were used to develop efficiency curves that showed a factor of 1.38 increase in neutrino sensitivity compared to previous triggering systems. This increase in efficiency will allow a future ANITA flight to set stronger cosmogenic neutrino limits and increase ANITA's sensitivity neutrino interactions within the Antarctic ice shelf
The isotopes of hydrogen and helium in the galactic cosmic radiation : their source abundances and interstellar propagation by James J Beatty( )
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
Microwave detection of cosmic rays and multi-messenger analysis of the parameters of ultra-high energy astrophysical sources by Nathan E Griffith( )
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
The study of ultra-high energy (UHE) cosmic particles is frequently characterized by its low statistics, and a central problem of the field is to find novel ways to navigate this challenge. The research presented in this dissertation attempts to address this problem in two ways: first, by investigating microwave radiation as a new method of UHE cosmic ray detection, and second, by using a multi-messenger (proton and neutrino) analysis to determine what current and next generation UHE neutrino detectors may be able to reveal about UHE astrophysical sources. The cosmic ray detector (called AMBER) is primarily a joint collaboration between Ohio State and the University of Hawaii. In May/June 2011 the AMBER experiment was installed at the Pierre Auger Observatory in Malargue, Argentina, and began taking data in coincidence with the observatory's surface detector array. This work presents a description of the experiment, a calibration based on an astrophysical radio source (the Milky Way galaxy), and an analysis of data. The second half of this document describes a multi-messenger analysis performed with co-authors Amy Connolly and Shunsaku Horiuchi on a publication in preparation. Fits to Pierre Auger 2013 data are used in conjunction with a spectral model and simulations of UHE neutrino detectors to explore the UHE source parameters of cosmic evolution and source spectrum cutoff. Constraints provided using the effective areas of the ANITA 3, ARA, and EVA detectors are considered
Ultra-high energy cosmic rays : composition, early air shower interactions, and Xmax skewness by James Stapleton( )
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
The composition of Ultra-High Energy Cosmic Rays (UHECRs) is still not completely understood, and must be inferred from Extended Air Shower (EAS), particle cascades which they initiate upon entering the atmosphere. The atmospheric depth at which the shower contains the maximum number of particles (Xmax) is the most composition-sensitive property of the air shower, but its interpretation is hindered by intrinsic statistical fluctuations in EAS development (which cause distinct compositions to produce overlapping Xmax distributions) as well as our limited knowledge at these energies of hadronic physics (which strongly impacts the Xmax distribution's shape). These issues ultimately necessitate a variety of complementary approaches to interpreting UHECR composition from Xmax data
A search for ultra-high energy cosmic neutrinos : data analysis of the Antarctic impulsive transient antenna, third flight by Sam Stafford( )
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Ultra-high Energy (UHE) neutrinos represent an increasingly important messenger in astronomy and astrophysics. The Antarctic Impulsive Transient Antenna (ANITA) experiment campaign utilizes a balloon-borne phased antenna array to detect coherent Cherenkov radio-frequency pulses induced by UHE neutrinos interacting with the Antarctic ice. We analyzed the data from the third ANITA flight (ANITA-III) for evidence of Ultra-high energy neutrinos by augmenting interferometric methods used in analyses of previous ANITA flights. Continuous wave (CW) radio content from ground-based Antarctic habitations and orbiting geostationary communications satellites interferes with the detection and analysis of neutrino-induced radio signals; we developed circular polarization analysis methods to facilitate improved rejection of false positives induced by satellite CW. We also developed new methods of calculating signal-to-noise ratio (SNR) of event waveforms, and enhanced event localization by applying a probability distribution function (PDF) based on the measured resolution of our interferometry. We developed a final linear discriminant cut for rejecting thermal and anthropogenic signals by dividing the continent into equal-area bins and optimizing the cut to each individual bin, so as to obtain the strongest possible the upper limit on cosmic neutrino flux
Cosmic ray instrumentation and simulations by Keith McBride( )
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
The natural phenomenon of cosmic radiation has been observed for over a hundred years and although many classes of objects have been identified as candidates, the origins of the galactic and the extragalactic components remain unconfirmed. The balloon-borne experiment, the ANtarctic Impulsive Transient Antenna (ANITA), observes the ice of Antarctica for signals from potential extragalactic ultra-high energy neutrinos. This thesis includes a chapter on my contribution to the ANITA collaboration. I updated the simulations of the detector to include the new hardware electronics responses and analyzed its effect on the sensitivity. This software package is used in analysis of the data extensively. The galactic cosmic ray nuclei spectra are missing key light isotope measurements at intermediately high energies. The upcoming project, the High Energy Light Isotope eXperiment (HELIX), will attempt to make these first-ever measurements. I aided in the construction, design, and testing of the Drift Chamber Tracker and the superconducting magnet for this experiment. I built the data acquisition system for the housekeeping sensors and power system including production-level circuit boards and software for readout. Finally, I performed an analysis on a diffusion-halo model of galactic cosmic-ray propagation to explore the constraining ability of newly released secondary-primary ratio data with expected HELIX measurements of the long-lived isotope, Beryllium-10
Reconstruction of Xmax and energy from 3 -- 100 PeV using 5 years of data from IceTop and IceCube and its applications by Andres Alberto Medina( )
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
The origin of cosmic rays has been an open problem for over a century. By measuring and modeling the energy spectrum and mass composition we can provide information towards solving this problem. The energy spectrum in particular has several features that hold key information to the propagation and sources of cosmic rays. The energy spectrum, which spans over several decades, can be described as a power-law with the slope defined by a value called the spectral index which ranges from values of 2.5 -- 3.3. Deviations of the spectral index mark key features of the energy spectrum such as the knee ($\approx$ $10^{15}$ eV), the second knee ($\approx$ $10^{17}$), the ankle ($\approx$ $10^{18.5}$) and a sharp drop off that occurs at the highest energies ($\approx$ $10^{19.5}$). We develop a hybrid model of a neural network to reconstruct the maximum atmospheric depth (Xmax) and a decision tree to reconstruct the energy for an extensive air shower that is detected by the IceCube Neutrino Observatory. The resolution of our models are about 41.6 $\rm{g/cm^2}$ for Xmax and 5.64\% for log10(E/GeV). Each of these is comparable with direct optical measurements of the shower. With these reconstructions we can construct kernels, using Monte Carlo simulations, that are capable of reproducing the probability density function of real data through a weighted sum of the kernels for a showers predicted Xmax binned by the showers predicted energy. We use weights (species fractions) predicted by models, such as H3A and H4A, and use the resulting fits to determine how well those models represent the propagation and production of cosmic rays. The H3A and H4A in particular use a physical phenomenon called a Peters cycle where rigidity is expected to be the governing variable for confinement and acceleration of cosmic rays
Audience Level
0 1 General Special
Related Identities
Associated Subjects
Languages
|
2023-02-04 16:10:14
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40808412432670593, "perplexity": 2433.702050505207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500140.36/warc/CC-MAIN-20230204142302-20230204172302-00273.warc.gz"}
|
http://crypto.stackexchange.com/questions/8237/is-there-any-strong-enough-pen-and-paper-or-mind-cipher
|
# Is there any strong enough pen-and-paper or mind cipher?
Some ciphers are talked about here, but I don't see an answer, are they strong enough, or are non-computer ciphers more or less just a toy and one should abandon using them for practical purposes?
-
pan $\mapsto$ pen $\:$ – Ricky Demer May 4 at 21:52
So basically you want to know how strong RC4 or Solitaire is? – rath May 4 at 22:24
RC4 doesn't have good reputation, though I don't know if it's completely broken yet. According to answer, Solitaire seems to be a weaker version of RC4. – Smit Johnth May 5 at 7:55
I wonder how long it would take to do AES-256 with pen and paper? :-) – Roland Smith May 5 at 12:41
I think that the suggestion to use RC4-52 in this answer can be made reasonably secure, and practicable with a deck of card by a trained operator. Devil is in the details, in particular the key and nounce/salt setup. I add that much less than 52 symbols should be used for plain and ciphertext, and keystream outside that range should be discarded (I conjecture it strengthen the keystream generator significantly). – fgrieu May 6 at 10:54
None of them are both strong enough and practical enough to be reasonable to carry out in real life. The strong ones aren't really practical; the practical ones aren't very strong.
-
|
2013-12-07 07:54:08
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4536067843437195, "perplexity": 2074.3676731591563}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163053843/warc/CC-MAIN-20131204131733-00073-ip-10-33-133-15.ec2.internal.warc.gz"}
|
https://www.shaalaa.com/question-bank-solutions/i-topographical-map-two-stations-b-are-situated-height-500-metres-100-metres-respectively-if-horizontal-distance-between-them-2-km-calculate-gradient-concept-interpretation-topographical-maps_82422
|
# (I) on a Topographical Map Two Stations a and B Are Situated at Height of 500 Metres and 100 Metres Respectively. If the Horizontal Distance Between Them is 2 Km, Calculate the Gradient. - Geography
Short Note
(i) On a topographical map two stations A and B are situated at height of 500 metres and 100 metres respectively. If the horizontal distance between them is 2 km, calculate the gradient.
(ii) On a topographical map, two places A and B are given. Calculate the gradient between them.
#### Solution
(i) Horizontal distance = 2 km = 2000 m
Vertical difference in height = 500 – 100 = 400 metres
Gradient ="Vertical interval"/"Horizontal equivalent"
= 400/2000
= 1/5 = 1 : 5
(ii) Horizontal distance: Measure the distance in cms. between the two places with your ruler. Then from the R.F. given on the toposheet calculate the actual distance between the two places in km and then convert into metres.
Vertical interval in height: Find the difference between the values of the two contours in which the places lie or if no contour lines are shown, find the difference in the spot heights of the two places.
Gradient = "Vertical Interval"/"Horizontal Equivalent" "Express your answer as a ratio"
Concept: Concept of Interpretation of Topographical Maps
Is there an error in this question or solution?
#### APPEARS IN
ICSE ICSE Class 10 Geography
Chapter 1 Map Study: Interpretation and Topographical Maps
Long Questions | Q 4
|
2021-04-18 05:21:02
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.678130030632019, "perplexity": 1627.140199106656}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038468066.58/warc/CC-MAIN-20210418043500-20210418073500-00608.warc.gz"}
|
https://www.numerade.com/questions/radians-to-degrees-in-exercises-11-and-12-convert-the-radian-measure-to-degree-measure-beginarraylll/
|
🎉 The Study-to-Win Winning Ticket number has been announced! Go to your Tickets dashboard to see if you won! 🎉View Winning Ticket
### Radians to Degrees In Exercises 11 and $12$ conve…
View
University of California, Berkeley
Problem 11
# Radians to Degrees In Exercises 11 and $12,$ convert the radian measure to degree measure.$\begin{array}{lll}{\text { (a) } \frac{3 \pi}{2}} & {\text { (b) } \frac{7 \pi}{6}} & {\text { (c) }-\frac{7 \pi}{12}}\end{array} \quad$ (d) $-2.367$
Answer
## Discussion
You must be signed in to discuss.
## Video Transcript
Okay, so we're asked to convert from radiant to the Greek. So what we're gonna do is if we have some radiant degree Alfa, we're gonna multiply it by 1 80 degrees over Pi to get our degrees A We have three pi over too. You multiply that by 1 80 degrees over pipes. Surprise, Cancel. And we're left with 2 72 Report me. We have seven pi over six. Multiply that by 1 80 degrees over pi and we get to 10 degrees. Report. See, we have made of seven ty over 12. Multiply that by 1 80 over pie and we get negative. One of five degrees party. We have negative. 2.367 Multiply that by 1 80 over pie and we get approximately negative Laundry. 5.63 degrees.
|
2020-10-29 23:10:30
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7858685851097107, "perplexity": 2327.981519381375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107905965.68/warc/CC-MAIN-20201029214439-20201030004439-00360.warc.gz"}
|
https://solvedlib.com/3-a-certain-company-operates-automobile,162584
|
# 3. A certain company operates automobile dealerships in six regions. The general manager questioned whether the...
###### Question:
3. A certain company operates automobile dealerships in six regions. The general manager questioned whether the mean profit margin per vehicle sold differed by region. A random sample of 5 vehicles sold in each region is selected and the profit margin of each vehicle is recorded. Given the value of the test statistic is 2.52, what do you conclude in terms of the problem)? Use a = .05. What is the P-value of your test statistic?
#### Similar Solved Questions
##### A 16 N m torque is applied to a wheel of mass 1 kg and radius...
A 16 N m torque is applied to a wheel of mass 1 kg and radius of gyration of 2 m. What is the resulting angular acceleration? a) 3 rad/s2 b) 4 rad/s2 c) 6 rad/s2 d) 10 rad/s2 e) none of the above...
##### QUESTION 4chemist was comparing the reactivity of metals and made the following observations when reacting the metals with acids: Mg(s) reacts with HCKaql but Cu(s) does not react with HCIaql However, Cu(s) does eact with HNO3laq). Chemical equations that summarize these observatlons are below_ Mg(s) 2 HCI(aq) - MgClz(aq) Hzlg) Culs) 2 HCl(aq) No Reaction Culs) HNO3(aq) Cu(NO3)z(aq) NOzkg) + 2 HzO()Ansier the questions below based on these observations (a) Of the reactants used, which Is the str
QUESTION 4 chemist was comparing the reactivity of metals and made the following observations when reacting the metals with acids: Mg(s) reacts with HCKaql but Cu(s) does not react with HCIaql However, Cu(s) does eact with HNO3laq). Chemical equations that summarize these observatlons are below_ Mg(...
##### Light is incident at angle 01 52 degrees: Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air: If n1 1.30,n2 1.40, n3 1.32, and n4 1.45, what is the value of 84?Air0"31
Light is incident at angle 01 52 degrees: Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air: If n1 1.30,n2 1.40, n3 1.32, and n4 1.45, what is the value of 84? Air 0 "3 1...
##### Required information [The following information applies to the questions displayed below.] QualCo manufactures a single product...
Required information [The following information applies to the questions displayed below.] QualCo manufactures a single product in two departments: Cutting and Assembly. During May, the Cutting department completed a number of units of a product and transferred them to Assembly. Of these transferred...
##### Please show work 11)2SO2(g) + O2(8) 2503(8) For the reaction at equilibrium, ifO2 is removed, the...
please show work 11)2SO2(g) + O2(8) 2503(8) For the reaction at equilibrium, ifO2 is removed, the amount of SO2 present 2 is removed, the amount of SO2 present will 11) A) decrease B) increase C) stay the same 12) According to the Arrhenius concept, if HNOs were dissolved in water, it w A) a source...
##### The dimensions of the control volume of the figure are L = 811 mm, H =...
The dimensions of the control volume of the figure are L = 811 mm, H = 441 mm, W = 300 mm and the angle is 46 degrees. A fluid with specific gravity SG = 0.831 occupies the control volume. The absolute pressure P1 on the top plane is 106.5 kPa. Calculate, in Newton, the contribution of this pressure...
##### Uscu describe the pusible stales of a electron in an atomn. The Quantun numbcr; ursc naturally from the mathematics four quantur numbers the principal quantum number (n), the angular momentum quantum number (€) the magnetic Foicm powsible = quantum number (m,) and the spin quantum numnber (m,) have strict rules which values:Identify all allowable comnbinations of quantum numbers for un electron.0n=48 = 1.m 2,ma 7+ On =s, =3m. = 2 ms =+1 =[.mt Lm3, & =-2Mt n =5.8=5,man=3{=2m2ma
uscu describe the pusible stales of a electron in an atomn. The Quantun numbcr; ursc naturally from the mathematics four quantur numbers the principal quantum number (n), the angular momentum quantum number (€) the magnetic Foicm powsible = quantum number (m,) and the spin quantum numnber (m,)...
##### Sketch a graph of the hyperbola, labeling vertices and foci.$-x^{2}+8 x+4 y^{2}-40 y+88=0$
Sketch a graph of the hyperbola, labeling vertices and foci. $-x^{2}+8 x+4 y^{2}-40 y+88=0$...
##### What are three culturally mediated characteristics that are important in caring for adults of various cultures?
What are three culturally mediated characteristics that are important in caring for adults of various cultures?...
##### A thin layer of turpentine and = 1.472 lies on top of a sheet ofice n = 1.309 it is illuminated from above with light whosewavelength in turpentine is 600nm which of the following ispossible thickness of the turpentine layer will maximize thebrightness of the reflected light
A thin layer of turpentine and = 1.472 lies on top of a sheet of ice n = 1.309 it is illuminated from above with light whose wavelength in turpentine is 600nm which of the following is possible thickness of the turpentine layer will maximize the brightness of the reflected light...
##### Lm2ws?3~.kn3
Lm 2 ws? 3 ~.kn 3...
##### Cat bonds are primarily designed to help: 1. The federal government cope with huge deficits. 2.Municipalities...
Cat bonds are primarily designed to help: 1. The federal government cope with huge deficits. 2.Municipalities survive economic recessions. 3.Corporations respond to overseas competition. 4. Insurance companies fund excessive claims. 5. Corporations recover from involun...
##### PLEASE READ CAREFULLY AND ALL THE WAY THROUGH!!! I already asked this question but unfortunately the...
PLEASE READ CAREFULLY AND ALL THE WAY THROUGH!!! I already asked this question but unfortunately the person who answered it did not read it. There is a sorting algorithm, “Stooge-Sort” which is named after the comedy team, "The Three Stooges." if the input size, n, is 1or 2, then...
##### BIO Work Done by the Lungs. The graph in Fig. E19.4 shows a pV- diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modeled one as a set of straight lines of the same general shape. (Important: The pressure shown is the gauge pressure, not the absolute pressure.) (a) How many joules of net work does this person's lung do during one complete breath? (b) The process
BIO Work Done by the Lungs. The graph in Fig. E19.4 shows a pV- diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modeled one as a set of straight lines of the same gene...
##### Confectioners, a chain of candy stores, purchases its candy in bulk from its suppliers. For a...
Confectioners, a chain of candy stores, purchases its candy in bulk from its suppliers. For a recent shipment, the company paid $4100 and received 6100 pieces of candy that are allocated among three groups. Group 1 consists of 1810 pieces that are expected to sell for$0.15 each. Group 2 consists of...
##### Question 17 0f 23If the caffeine concentration in a particular brand of soda is 4.01 mgloz, drinking how many cans of soda would be lethal? Assume that 10.0 g of caffeine is a lethal dose, and there are 12 0z in a can.cans of soda:
Question 17 0f 23 If the caffeine concentration in a particular brand of soda is 4.01 mgloz, drinking how many cans of soda would be lethal? Assume that 10.0 g of caffeine is a lethal dose, and there are 12 0z in a can. cans of soda:...
##### EGSLUS Sohing distance, rete, Umo Brouorn udng Ssyslem 0l Iindar69Uic 54mc Jmount ol ome What hours and 7209 mlles *en Ine Jetstreanthe Jet 5 ErlalranidJet tavets 5679 mlles aqainst Fctrream heamar ne letstrcam}pate ol the Jet allDutaninofthenctrueam
eGSLUS Sohing distance, rete, Umo Brouorn udng Ssyslem 0l Iindar69 Uic 54mc Jmount ol ome What hours and 7209 mlles *en Ine Jetstrean the Jet 5 Erlalranid Jet tavets 5679 mlles aqainst Fctrream heamar ne letstrcam} pate ol the Jet allDut aninofthenctrueam...
##### Short-answer questions 1. Here are some statistics: Inflation Exchange Rates Current Last Year 5 US Japan...
Short-answer questions 1. Here are some statistics: Inflation Exchange Rates Current Last Year 5 US Japan Mexico Ey/$95 Epeso/$ 10.5 100 10 5 (a) List the countries in order of real appreciation (largest appreciation first) relative to the dollar. (b) Taking Last Year's exchange rate as given, ...
##### Ive tried using other problems on here and cannot get the answer if you could please...
ive tried using other problems on here and cannot get the answer if you could please show the steps to solve i would appreciate it 2 8 . Link Inc. manufactures magical swords. The following data pertains to Job 1534: Direct materials placed into production Direct labor hours Direct labor rate per h...
##### Any help would be greatly appreciated! 28. Extra credit, no penalty if wrong. My maximal HR is 140, my EDV is 170 ml...
any help would be greatly appreciated! 28. Extra credit, no penalty if wrong. My maximal HR is 140, my EDV is 170 ml, my ejection fraction is 70%, my hemoglobin is 15 gm%, my arterial saturation is 98%, my mixed venous saturation is 25%. I weigh 80 kg. What is my VO2max, in ml/min in ml/kg ? (10 ...
##### 2. Construct the non-inverting amplifier circuit below. Then, obtain input-output transfer function for R1=1K and R2=2.2K,...
2. Construct the non-inverting amplifier circuit below. Then, obtain input-output transfer function for R1=1K and R2=2.2K, E= 9V. Use a variable de voltage (5V de source and a variable 1k potentiometer) source as the input and measure the output voltage for different inputs. Draw the input-output tr...
##### Complex Analysis Need it ASAP Suppose f is an entire function. Show that any of the...
Complex Analysis Need it ASAP Suppose f is an entire function. Show that any of the two criteria below imply that f is a constant function. (a) Imf(z) 0 for all z EC and Ref(z) is an entire function. [10] (b) -1 < Ref (2) <1 for all z E C. [8]...
##### The sequence {4n| F ealthyh
The sequence {4n| F ealthyh...
##### Aludent Iowers 12 KQ of fextbooke to Iha (kOT ar dolmnon uomrom halaht conslant spoed ancnad Wu hMar done by Iha udloni? (6 pts)b) How much powor did the student expend? (5 pts)How does work and power change if the textbooks were lowered to floor in 2 seconds? (5 pts)
aludent Iowers 12 KQ of fextbooke to Iha (kOT ar dolmnon uomrom halaht conslant spoed ancnad Wu hMar done by Iha #udloni? (6 pts) b) How much powor did the student expend? (5 pts) How does work and power change if the textbooks were lowered to floor in 2 seconds? (5 pts)...
##### As shown in the figure, three charges are at corners of a rectangle. The charge in the bottom right corner is Q= 90.0 nC, and all the other quantities are accurate to three significant figures. What is the net electric field at the empty corner of the rectangle? (k = 1/4me0 = 8.99 x 10^9 N m2/c2)15nC-5nC3 cmcm
As shown in the figure, three charges are at corners of a rectangle. The charge in the bottom right corner is Q= 90.0 nC, and all the other quantities are accurate to three significant figures. What is the net electric field at the empty corner of the rectangle? (k = 1/4me0 = 8.99 x 10^9 N m2/c2) 15...
##### Question 17 Which of the followingcompound is formed the fastest under acidic condition? ОА.. НО ОН...
Question 17 Which of the followingcompound is formed the fastest under acidic condition? ОА.. НО ОН В. НО ОН с.. НО ОН Н D.. НО ОН Н Н...
##### 8. -70 points DavisPreStat1 5.1.049. Let B = {0, 2, 4, 6, 8, 10) and C...
8. -70 points DavisPreStat1 5.1.049. Let B = {0, 2, 4, 6, 8, 10) and C = {16, 17, 18, 19, 20). Write CU B using the listing metho CUBE Submit Answer...
##### To test the hypothesis that the population standard deviation sigma-18.8, sample size n=1- yields sample standard deviation 8.497. Calculate the P-value and choose the correct conclusion:Yanitiniz:The P-value 0.156 is not significant and so does not strongly suggest that sigma<18.8 The P-value 0.156 is significant and so strongly suggests that sigma<18.8. The P-value 0.031 is not significant and so does not strongly suggest that sigma<18.8 The P-value 0.031 is significant and s0 strongl
To test the hypothesis that the population standard deviation sigma-18.8, sample size n=1- yields sample standard deviation 8.497. Calculate the P-value and choose the correct conclusion: Yanitiniz: The P-value 0.156 is not significant and so does not strongly suggest that sigma<18.8 The P-value ...
##### Room-temperature water boils spontaneously in a vacuum- on the Moon, for example. Could you cook an...
Room-temperature water boils spontaneously in a vacuum- on the Moon, for example. Could you cook an egg in this boiling water? Explain Find what heat in calories (cal) is required to increase the temperature of 60 g water from 0°C to 55°C. The specific heat capacity of water is 1 cal/ g&bull...
##### NaOHHzOEthanolOHCyclohexanoneCyclohexylidenecyclohexanone (92%
NaOH HzO Ethanol OH Cyclohexanone Cyclohexylidenecyclohexanone (92%...
##### Which of the following mutations would lead to change in the reading frame in translation?Deletion of the start codonInsertion of CTAInsertion of six AdeninsDeletion of two Cytocins
Which of the following mutations would lead to change in the reading frame in translation? Deletion of the start codon Insertion of CTA Insertion of six Adenins Deletion of two Cytocins...
##### Verify if the vector field F(14z + Tyety +2, ~l5y2 + Tzety 2) is conservative and evaluate the line integralIc F . dRwhere C is the curve parameterized by R = < cos(4t) , sin(4t),t > for 0 < t < 2.AI=0B.I = 2cI=t+7D.I =1EI = -21
Verify if the vector field F (14z + Tyety +2, ~l5y2 + Tzety 2) is conservative and evaluate the line integral Ic F . dR where C is the curve parameterized by R = < cos(4t) , sin(4t),t > for 0 < t < 2. AI=0 B.I = 2 cI=t+7 D.I =1 EI = -21...
##### Finding an Inverse Function In Exercises $57-72$determine whether the function has an inverse function.If it does, then find the inverse function.$g(x)= rac{x}{8}$
Finding an Inverse Function In Exercises $57-72$ determine whether the function has an inverse function. If it does, then find the inverse function. $g(x)=\frac{x}{8}$...
##### 6_ Simplify (1 Point) 2x+l6x 10 4+85X28x2x
6_ Simplify (1 Point) 2x+l6x 10 4+8 5 X2 8x 2x...
|
2023-02-04 02:15:29
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5590668320655823, "perplexity": 4235.781536639337}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500080.82/warc/CC-MAIN-20230204012622-20230204042622-00334.warc.gz"}
|
https://blog.vivekpanyam.com/deep-learning-made-simple-part-1/
|
This series of posts was initially created as a way to explain Neural Networks and Deep Learning to my younger brother. Therefore, we are not going to assume any prior knowledge of calculus or linear algebra, among other things.
Disclaimer: The goal of this post is to be as easy to understand as possible. Because of that, some of the statements below aren't entirely accurate. Many of the larger inaccuracies are marked with *
Contents:
1. Deep Learning Made Simple [Part 1] - this post
2. Teaching a Neural Network [Part 2] (to be published)
3. ...
### What can Deep Learning do?
Deep learning is an amazing tool that can generate some very impressive results. Let's look at some of these before we dig into how it actually works.
• Deep learning can turn a photo into a painting of a particular style:
Neural Style on GitHub
• Or better yet, turn a photo into a photo of a different style:
Deep Photo Style Transfer on GitHub
Human-level control through deep reinforcement learning from DeepMind
• It can detect and identify objects:
Tensorflow Object Detection API
• It can caption images:
Deep Visual-Semantic Alignments for Generating Image Descriptions
• Or even colorize them:
Colorful Image Colorization
• It can translate between languages
• It can recognize speech
• It can generate voices
• It can turn a drawing into a picture
• It can understand handwriting
And much much more.
### ... how?
In order to understand that, we need to dig into some basic math first. Let's define what a function is.
The definition we're going to use is as follows (from Wikipedia):
In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Basically, a function takes in some number of inputs and has an output. Every time the same inputs are passed into a function, it should give us the same output.
Also note that the output of a function doesn't need to be just one number. It can also be a vector.
For our purposes, a vector is an ordered list of numbers
For example if we have a vector $v$:
• $v_1$ is the first element
• $v_2$ is the second element
• ...
Functions can be as complex or as simple as we want. Here are some examples:
• $y = f(x) = x + 1$
• $y = f(x) = x^2 + 1$
• $y = f(a,b,c,d) = 23 * a + 42 * b + 51 * c + d$
• items_in_picture = f(image) = ?
• speaker_identity = f(audio_signal) = ?
In the above list, think of ? as "something super complicated that we don't know how to write down."
At first glance, the last two items in the list of examples might look weird, but if you look carefully, they fit all our rules for functions:
• They relate inputs and outputs.
• For a given input, they always have the same output.
Now that we know what a function is, let's define what the purpose of deep learning is.
The end goal of most machine learning methods, including deep learning, is to figure out how to write down complex functions. In more concrete terms, machine learning methods try to estimate a function.
So how can we estimate a function we don't know how to write down? Let's look at this problem a slightly different way.
### Estimating a function
Let's pretend someone told us that there's a function $y = f(x)$ that does something interesting and they asked us to figure out what $f(x)$ is. Since they're feeling particularly generous, they'll also give us a bunch of examples of corresponding $x$ and $y$ values.
In mathematical terms, they asked us to come up with a function $g(x)$ such that $f(x) = g(x)$ for all possible $x$ values.
So how do we know if we're doing a good job? We need some way to tell how close $g(x)$ is to $f(x)$.
Let's use the distance formula that we learned in middle school (actually called the Euclidean Distance or L2 Norm). We'll call this $distance(v, w)$ where $v$ and $w$ are two vectors.
Great! So if we minimize $distance(f(x), g(x))$ for all points $x$, we should come up with the correct $g(x)$.
One slight hiccup; we don't know what $g(x)$ looks like and $f(x)$ can be "something super complicated that we don't know how to write down". How can we minimize distance if we can't write it down?
We'll tackle these problems over the next two sections.
### Taking inspiration from nature
This seems like a good time to look at the human brain. Our brain is made of 86 billion neurons. A very simple diagram of a neuron is below.
Diagram of a Neuron (a modified version of this image)
The basic way a neuron works is as follows:
• Dendrites take signals from other neurons and send them to the Cell Body.
• The Cell Body takes the input signals, does some processing, and decides to "fire" or not.
• If the neuron is going to "fire," the Axon sends the output to other neurons (using the Axon terminal).
The places where the Axon of one neuron connects to a Dendrite of another neuron is called a Synapse. The human brain has between 100 trillion and 1 quadrillion synapses!
##### Artificial Neural Networks
Let's take some inspiration from the neurons in our brains and create an artificial neuron. Let's say our neuron takes 3 inputs and has one output:
So that means our neuron is a function that looks like this:
$output = f(x,y,z)$
Let's also say that our neuron is a linear function.
A linear function is a function that represents a straight line or plane.
So now we have
$output = f(x,y,z) = some\_constant * x + some\_constant * y + some\_constant * z + some\_constant$
(where all the constants can be different)
Now that we've built a neuron, let's put a bunch of these together to build a neural network!
Let's run through the math really quickly to see what $output$ actually is.
The output of the final layer of the neural network (n8) is:
• $network\_output = n8_{output}$
• $n8_{output} = some\_constant * n4_{output} + some\_constant * n5_{output} + some\_constant * n6_{output} + some\_constant$
The outputs of the second layer of the network (n4, n5, and n6) are:
• $n4_{output} = some\_constant * n1_{output} + some\_constant * n2_{output} + some\_constant * n3_{output} + some\_constant$
• $n5_{output} = some\_constant * n1_{output} + some\_constant * n2_{output} + some\_constant * n3_{output} + some\_constant$
• $n6_{output} = some\_constant * n1_{output} + some\_constant * n2_{output} + some\_constant * n3_{output} + some\_constant$
The outputs of the first layer of the network (n1, n2, and n3) are:
• $n1_{output} = some\_constant * x + some\_constant * y + some\_constant * z + some\_constant$
• $n2_{output} = some\_constant * x + some\_constant * y + some\_constant * z + some\_constant$
• $n3_{output} = some\_constant * x + some\_constant * y + some\_constant * z + some\_constant$
After combining all the equations above, we get:
$network\_output = some\_constant * x + some\_constant * y + some\_constant * z + some\_constant$
(again, where $some\_constant$ can be different every time it's mentioned)
So, that's a problem. Even if we have a super complicated combination of these neurons, it still can't do anything except fit a line or a plane. Why?
A linear combination of linear functions is linear.
Read that a few times and convince yourself it's true. Basically, if all you can do is add and multiply by constants, no matter how many times you do it, you'll still end up with a linear function.
So to make neural networks useful, we need to introduce nonlinearities.
A nonlinearity (or nonlinear function) is a function that does not have a linear relationship between its inputs and output. To keep it simple we'll just call these functions $nl$.
Let's change our function for each neuron to include a nonlinearity
$output = f(x,y,z) = nl(some\_constant * x + some\_constant * y + some\_constant * z + some\_constant)$
We'll dig into this more in the next post, but, for now, nonlinearities solve our problem!
In fact, now that we have nonlinearities, we can show that "for every function, there exists some neural network to represent it".* This means that any function you can come up with can be represented by a neural network!*
The proof, exact wording, and caveats of this statement are out of the scope of this post, but if you want more detail, you can look at the Universal Approximation Theorem.
Since we know $g(x)$ is a function and we know that there exists some neural network that can represent any function*, let's make $g(x)$ a neural network!
### Hot and Cold
Unfortunately, we still don't know how to minimize our distance function. Let's try to figure out how to do that.
Remember the game "Hot and Cold"? You try to find an object and as you move, your friend tells you "hotter" or "colder" depending on whether you're moving towards the target object or not.
The game looks something like this:
1. A target object is chosen
2. Start somewhere in the center of the room
3. Until you find the object:
1. You move in a direction
2. Your friend yells out "Hot" or "Cold"
3. If they yelled out "Cold," move in the opposite direction
What if we played that game to minimize a function? Let's say our "target" is to find the minimum value of our distance function.
To make things easier to write down, let's also say
$d(x) = distance(f(x), g(x))$
where $g(x)$ is our neural network and $f(x)$ is the function we're trying to estimate.
Let's rewrite how "How and Cold" is played:
1. A target value is chosen: the minimum value of $d(x)$
2. Start with a random $x$ value
3. Until you can't decrease $d(x)$ any more:
1. Move $x$ in a direction
2. Check if $d(x)$ is less than it was before
3. If $d(x)$ increased, move $x$ in the opposite direction and check again
How do we know if we can't decrease $d(x)$ any more? If we move $x$ in both possible directions and $d(x)$ increases both times, that means we found the minimum!*
##### Let's walk through that game on an example distance function.
Our random starting $x$ value is -2. So, based on the graph below, $d(x) = 5$.
Let's move to $x = -1$ and see if $d(x)$ is less than it was before.
$d(-1) = 2 < 5$ so we're moving in the right direction! Let's move to $x = 0$.
$d(0) = 1 < 2$ so we're still doing a good job! Let's move to $x = 1$.
$d(1) = 2 > 1$ so we're not going in the right direction. Let's do one last check at $x = -1$.
$d(-1) = 2 > 1$ so looks like we found the minimum value at $d(0) = 1$!
Is there a better way to do this? We could have easily overshot the minimum point if we started at a different point or if we chose a different step size. For example, if we started at $x = -1.5$ instead of at $x = -2$, we would have never reached $x = 0$ with a step size of $1$ (we would have gone from $-1.5$ to $-0.5$ to $0.5$).
Can the slope of a line help us?
The slope of a line between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $\frac{y_2 - y_1}{x_2 - x_1}$.
Therefore, the slope of $d(x)$ is defined as:
$slope_d(x_1, x_2) = \frac{d(x_2) - d(x_1)}{x_2 - x_1}$
Now let's say that $x_2 = x_1 + q$ where $q$ is some small number. Let's substitute that in:
$slope_d(x_1) = \frac{d(x_1 + q) - d(x_1)}{(x_1 + q) - x_1} = \frac{d(x_1 + q) - d(x_1)}{q}$
So if $d(x_1 + q)$ is less than $d(x_1)$, then $slope_d(x_1) < 0$ otherwise $slope_d(x_1) > 0$
With this new notation, let's change our game to the following:
1. A target value is chosen: the minimum value of $d(x)$
2. Start with a random $x$ value
3. Until you can't decrease $d(x)$ any more:
1. Subtract $slope_d(x)$ from $x$ (i.e. $x = x - slope_d(x)$)
You'll notice that the last step is the same as this:
1. If $slope_d(x) < 0$, we want to increase $x$ so we'll subtract $slope_d(x)$ from $x$ (i.e. $x = x - slope_d(x)$)
• Subtracting a negative number from $x$ will increase $x$
2. If $slope_d(x) > 0$, we want to decrease $x$ so we'll subtract $slope_d(x)$ from $x$ (i.e. $x = x - slope_d(x)$)
• Subtracting a positive number from $x$ will decrease $x$
Since we do the same thing if $slope_d(x) < 0$ or if $slope_d(x) > 0$, I collapsed them down into one case.
This version of the game also has the interesting property that the step size changes depending on the slope. As the slope gets smaller and smaller, our step size gets smaller. That means we slow down as we get closer to our target and we're less likely to overshoot the minimum!
So, now we know how to minimize a function, but the $f(x_1 + q)$ thing is a little weird, right? What if we made $q$ really really small? This is called a derivative.
The derivative of a function at a point is the slope of the function at that point.
That's pretty much all you need to know about derivatives for now. Let's look at minimizing a function that is a little more complicated.
##### Finding the minimum point on a surface
Imagine you're standing on a landscape with a bunch of hills and valleys. It's pitch black outside and you can't see anything. All you know is that you want to get to the bottom of a valley. So what do you do? You feel forward a little bit and see if the surface goes up or down. Then you feel towards the right and see if the surface goes up or down. You keep feeling around and then you finally take a step in the direction that slopes the most downwards.
This is the exact same approach we're going to take.
Let's say that we're trying to minimize some function $z = f(x,y)$:
3D view of $f(x,y)$
Top view of $f(x,y)$. Light yellow is the largest $z$ value and dark red is the smallest $z$ value
We can't just say $slope_z(x, y)$ though, because there are multiple slopes to measure now. For example, at the point $(1,0)$, the slope in the $x$ direction (as we decrease $x$) is steeper than the slope in the $y$ direction (as we decrease $y$).
That's pretty easily solvable. Let's just say "the slope in the $y$ direction" or "the slope in the $x$ direction" instead of just "the slope". Let's write them down as follows:
• the slope in the $x$ direction of $f(x,y)$ = $slope_{z\{x\}}(x, y)$
• the slope in the $y$ direction of $f(x,y)$ = $slope_{z\{y\}}(x, y)$
These are called partial derivatives.
Let's also define one more term: the gradient. The gradient of $f(x,y)$ = $(slope_{z\{x\}}(x, y), slope_{z\{y\}}(x, y))$. Basically the gradient is a vector made up of all the partial derivatives of a function. It has a really useful property:
The gradient of a function points in the direction of the greatest rate of increase of the function
That means the negative of the gradient is the direction that slopes the most downwards. Sound familiar? That's exactly what we were doing in our pitch black landscape example!
So now our game looks like this:
1. A target value is chosen: the minimum value of $f(x,y)$
2. Start with a random $x$ value and a random $y$ value
3. Until you can't decrease $f(x,y)$ any more:
1. Compute the gradient of $f$
2. Subtract $slope_{z\{x\}}(x, y)$ from $x$ (i.e. $x = x - slope_{z\{x\}}(x, y)$)
3. Subtract $slope_{z\{y\}}(x, y)$ from $y$ (i.e. $y = y - slope_{z\{y\}}(x, y)$)
This process is called Gradient Descent and it can be used to minimize any function.*
### Putting it together
Now that we have a $g(x)$ function that can represent any other function*, a $distance$ measure to see how close we are to correct, and a way to minimize any function*, we've solved the problems that we identified at the beginning of the post!
This also means we can concretely answer the "how" question:
Deep learning uses neural networks with many layers combined with a distance function and a large list of examples to estimate a complicated function.
Let's apply this explanation to the colorization example at the beginning of the post:
• The function we're trying to estimate is $real\_color\_image = f(black\_and\_white\_image)$
• Since we don't know how to write that function down, we have a large list of corresponding $(real\_color\_image, black\_and\_white\_image)$ pairs
• Our neural network is some function $colorized\_image = g(black\_and\_white\_image)$
• (we'll look into this in more detail in a future post)
• Our distance function looks like this: $distance(real\_color\_image, colorized\_image)$
Now we can start to put all of these pieces together. Let's substitute $f$ and $g$ into our $distance$ function:
$d(black\_and\_white\_image) = distance(f(black\_and\_white\_image), g(black\_and\_white\_image))$
Since we don't have $f$, let's use one of our example image pairs instead:
$d(black\_and\_white\_image, real\_color\_image) = distance(real\_color\_image, g(black\_and\_white\_image))$
Now we just have to minimize $d$ for every example we have!
This presents a problem, however. In our "Hot and Cold" game, we modified an input to $d$ in order to minimize it, but we can't modify $black\_and\_white\_image$ or $real\_color\_image$ in the formula above. Let's rewrite $d$ to make it more clear what we need to modify:
$d(black\_and\_white\_image, real\_color\_image, g) = distance(real\_color\_image, g(black\_and\_white\_image))$
We change our neural network.
To minimize $d$, we're just playing the "Hot and Cold" game from above "in the $g$ direction"! Remember all the $some\_constant$s? We can change all of those to make the network learn!
So we start with a "random" neural network* and then slowly modify the constants until it does a good job on our examples. If we have enough examples and our network learns how to do a good job on them, it should be able to do a good job on inputs it hasn't seen before!*
This process is called training a neural network.
In the next post, we'll look into how exactly we do this. We'll also build a neural network to recognize handwritten digits!
If you want to be notified when I publish the next part, you can follow me on Twitter here.
Please feel free to comment on Hacker News or Reddit or email me if you have any questions!
If you want to learn a little more about me, check out my website or LinkedIn
While you're waiting on part 2, you can also check out my primer on load balancing at scale.
Header image from neural-style on GitHub
|
2019-03-26 04:39:45
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6941485404968262, "perplexity": 396.6535702315088}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204790.78/warc/CC-MAIN-20190326034712-20190326060712-00000.warc.gz"}
|
http://threadposts.org/question/2376169/New-laptop-running-on-a-manually-installed-SSD-is-buggy.html
|
Tech Problem Aggregator
# New laptop running on a manually-installed SSD is buggy
Q: New laptop running on a manually-installed SSD is buggy
I bought an Asus N550LF-CM115H two months ago and replaced the HDD with as SSD in order to maximize performance.
The laptop has incredible start-up times, showing that the SSD is most definitely the drive on which the system is running, and can open programs pretty quickly. However the general performance of the computer is buggy. For example, while typing this, the letters are noticably coming up several split seconds after typing them. It has great trouble running web browers (I've tried Chrome, Firefox and Explorer) without eventually having a script fail or the browser become unresponsive.
It's usable, and occasionaly the performance is very good, but there is definitely something wrong somewhere. Any tests I can run to check where? Any ideas on what the problem might be? Any ideas on how I could go about fixing this?
Thanks a lot.
A: New laptop running on a manually-installed SSD is buggy
That could be anything and may have nothing to do with the SSD. For starters I would run a sfc /scannow
15 more replies
Answer Match 56.7%
Suspicious of something not right on a Dell laptop. (besides it being Dell.)
Running slower and buggier than i think it should be -- any advice might help. Startup takes ~ 7 minutes on this piece.
laptop is normally used for light net surfing, AIM, and homework in Office.
Logfile of HijackThis v1.99.1
Scan saved at 11:06:49 PM, on 1/23/2008
Platform: Windows XP SP2 (WinNT 5.01.2600)
MSIE: Internet Explorer v7.00 (7.00.6000.16574)
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\Ati2evxx.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\Ati2evxx.exe
C:\WINDOWS\Explorer.EXE
C:\WINDOWS\System32\WLTRYSVC.EXE
C:\WINDOWS\System32\bcmwltry.exe
C:\Program Files\Common Files\Symantec Shared\ccEvtMgr.exe
C:\WINDOWS\system32\spoolsv.exe
C:\Program Files\Common Files\LogiShrd\LVMVFM\LVPrcSrv.exe
C:\Program Files\Common Files\Apple\Mobile Device Support\bin\AppleMobileDeviceService.exe
C:\PROGRA~1\NORTON~1\NORTON~2\GHOSTS~2.EXE
C:\WINDOWS\System32\svchost.exe
C:\Program Files\Common Files\LogiShrd\LVCOMSER\LVComSer.exe
C:\Program Files\Common Files\Microsoft Shared\VS7DEBUG\MDM.EXE
C:\Program Files\Norton SystemWorks\Norton AntiVirus\navapsvc.exe
C:\Program Files\Norton SystemWorks\Norton Utilities\NPROTECT.EXE
C:\WINDOWS\system32\HPZipm12.exe
C:\PROGRA~1\NORTON~1\SPEEDD~1\nopdb.exe
C:\WINDOWS\system32\svchost.exe
C:\Program Files\Vie... Read more
A:HJT log -- running slow, kinda buggy (esp. at startup)
would removing some Dell and Norton programs help it run faster?
1 more replies
Answer Match 56.7%
Hi my desktop started to act funny and control panel wont open
Logfile of Trend Micro HijackThis v2.0.2
Scan saved at 9:29:12 PM, on 4/14/2009
Platform: Windows XP SP3 (WinNT 5.01.2600)
MSIE: Internet Explorer v6.00 SP3 (6.00.2900.5512)
Boot mode: Normal
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\spoolsv.exe
C:\WINDOWS\system32\3361\SVCHOST.exe
C:\WINDOWS\system32\hkcmd.exe
C:\WINDOWS\system32\igfxpers.exe
C:\Program Files\iTunes\iTunesHelper.exe
C:\WINDOWS\System32\reader_s.exe
C:\Program Files\SUPERAntiSpyware\SUPERAntiSpyware.exe
C:\Program Files\Messenger\msmsgs.exe
C:\Program Files\Common Files\Apple\Mobile Device Support\bin\AppleMobileDeviceService.exe
C:\Program Files\Bonjour\mDNSResponder.exe
C:\Program Files\iPod\bin\iPodService.exe
C:\Program Files\Creative\SBLive\Diagnostics\diagent.exe
C:\Program Files\Yahoo!\Messenger\ymsgr_tray.exe
C:\Program Files\Internet Explorer\iexplore.exe
C:\WINDOWS\system32\svchost.exe
C:\Documen... Read more
A:Desktop is actin buggy and running very slow
well, the log has been posted for a couple days now and no reply.. someone please take a look at this hijack log and tell me what i need to do to restore my desktop back to normal
5 more replies
Answer Match 56.7%
My coworker has had issues for the last couple weeks and thought updating to Windows 10 might help. The computer is lagging and sometimes unresponsive. I ran Malwarebytes and it found a couple things but it barely improved the computers performance. I am running Farbar now and will post the logs once it's completed.
A:Coworker's computer is buggy - Running Windows 10
Additional scan result of Farbar Recovery Scan Tool (x64) Version:02-08-2015 01
Ran by Janet (2015-08-04 17:59:40)
Running from C:\Users\Janet\Downloads
Boot Mode: Normal
==========================================================
==================== Accounts: =============================
Administrator (S-1-5-21-241309547-997938199-1225244223-500 - Administrator - Disabled)
DefaultAccount (S-1-5-21-241309547-997938199-1225244223-503 - Limited - Disabled)
Guest (S-1-5-21-241309547-997938199-1225244223-501 - Limited - Disabled)
HomeGroupUser$(S-1-5-21-241309547-997938199-1225244223-1004 - Limited - Enabled) Janet (S-1-5-21-241309547-997938199-1225244223-1000 - Administrator - Enabled) => C:\Users\Janet ==================== Security Center ======================== (If an entry is included in the fixlist, it will be removed.) AV: Windows Defender (Disabled - Up to date) {D68DDC3A-831F-4fae-9E44-DA132C1ACF46} AV: avast! Antivirus (Disabled - Up to date) {17AD7D40-BA12-9C46-7131-94903A54AD8B} AS: Windows Defender (Disabled - Up to date) {D68DDC3A-831F-4fae-9E44-DA132C1ACF46} AS: Spybot - Search and Destroy (Enabled - Up to date) {9BC38DF1-3CCA-732D-A930-C1CA5F20A4B0} AS: avast! Antivirus (Disabled - Up to date) {ACCC9CA4-9C28-93C8-4B81-AFE241D3E736} ==================== Installed Programs ====================== (Only the adware programs with "hidden" flag could be added to the fixlist to unhide them. The adware programs should be uninstalled manually.) 4500_... Read more 74 more replies Answer Match 55.86% So a couple of weeks ago or so I installed ie10 manually. All fine and good and works well. Today ofc ie 10 comes in windows update so I figure its an update or something and install it. When I reboot its again in windows update even though I installed it already. Also in 'Installed updates' 2 entrances show with ie10. I dont really foresee a huge problem with this but Im still wondering if you have any ideas on how to fix it? A:Ie 10 installed manually, still shows up in WU and won´t go away Hi Conditioned, uninstall it then let WU replace it or try it manually again like this:- Attachment 259099 Attachment 259098 6 more replies Answer Match 55.86% Greets Everyone. Thank you for the incredibly helpful forum!! I have a weird issue that has cropped up with my Windows 7 Ultimate 64 bit. I decided to upgrade the version of my Scite and there were no options for installing it. I simply unzipped the archive and copied it to a new folder in my Program Files (x86) folder. I then renamed my old winscite to bust the links, keeping it in case something went wrong, and created new desktop, startmenu, and taskbar links to the new version. The application opens up just fine, and works just fine. But when I want to use it to open specific file types/extensions, I cannot use it. I tried right clicking on a file, say a PHP file, and then chose Open with.../Choose default program from the right click context menu in Windows Explorer, and of course, Scite is not listed in the recommended programs options. I expand "OTHER" and still do not see it, of course. So I clicked BROWSE, navigate to the new scite, and double click it. This is where the weird stuff starts. The browse dialog box closes, yet scite is not an option still. Nothing changes actually. Scite is not listed as a default program, and I cannot add the new scite as one. I have no idea how I can tell Windows that I want to open the new scite with ANY file type. Is there a registry modification I need to perform? How do I remove ALL options/recommended apps associated with a file type? Then maybe when I double click that file type, I can tell Windows where to find s... Read more A:Manually Add an Application that was Not Installed Quote: So I clicked BROWSE, navigate to the new scite, and double click it. This is where the weird stuff starts. The browse dialog box closes, yet scite is not an option still. Nothing changes actually. You have to double click on the .exe of that program. 4 more replies Answer Match 55.86% service-pack Downloaded and ran System Update Readiness Tool (KB947821) Readiness tool indicated a (KB947821) Hotfix ran. - Installation: Successful - Ran Windows Update - Window7 SP1 not offered. << Went to service pack center >> Service Pack Center - Microsoft Windows Selected "Download SP1 from the Download Center (Advanced) Download: Windows 7 and Windows Server 2008 R2 Service Pack 1 (KB976932) - Microsoft Download Center - Download Details Norton Antivirus "Disabled" Downloaded "Windows6.1-KB976932-x64.exe" "Installation was not successful" Error:ERROR_SXS_ASSEMBLY_MISSING(0x80073701) Searcing for a fix to ERROR note: SP1 setup fails "ERROR_SXS_ASSEMBLY_MISSING(0x80073701)" - Win7 x64 NOTE: Have run MS Fixit many times. it always tells me "Windows Update componets must be repaired", but when I run Uniblue RegistryBooster 2011, it always remove the same fix MSFix made "The default value in HKEY_CLASSES_ROOT/CLSID/{5F327514-6C5E-4d60-8F16-D07FA08A78ED}/InProcServer32points to the missing file C:/Windows/system32/wuaucpl.cpl" My system started out as a Windows Visita Ultimate with an upgrade provided by HP to Windows 7 Ultimate. Also don't know if these failed installations are related the my failed SP1 installation; KB958488 KB982670 KB2538243 KB2467174 KB2467175 KB917607 KB982526 KB973923 A:Can not get SP1 to be offered or installed manually Quote: Originally Posted by VincentM Have run MS Fixit many times. it always tells me "Windows Update componets must be repaired", but when I run Uniblue RegistryBooster 2011..... ...and thereby is your problem. ALL registry Cleaners come under the heading of 'Dangerous:Snake-Oil'. Ditch it before it manages to completely trash your system (AFTER undoing whatever it's already managed to break) 3 more replies Answer Match 55.44% This laptop was given to me by a friend and it was loaded with viruses including the winzip registry optimizer rouge anti virus. I used the prior knowledge I had to clean that out along with other registry issues and viruses. Yet, the laptop still runs really slow, and whenever the Pokki start button or bar is clicked, it freezes and the desktop vanishes. As far as I know, Pokki was preinstalled on here, and I know it's been used to replace the missing start bar in WIndows 8. What can I do to fix this thing? A:Windows 8 laptop with Pokki installed running insanely slow I would open a virus removal assistance topic to be sure everything has been cleaned up:http://www.bleepingcomputer.com/forums/t/34773/preparation-guide-for-use-before-using-malware-removal-tools-and-requesting-help/I would then remove Pokki and instead use this guide to add a start menu back to Win8:http://www.bleepingcomputer.com/tutorials/start-menu-in-windows-8-with-classic-shell/ 1 more replies Answer Match 55.44% Hi, I Have Manually Installed this programme (San Andreas) An there is a special programme that mods san andreas and when it starts up it says: I have put the folder in this location:C:\Program Files (x86)\Rockstar Games\San Andreas So any help to register this programme. Thanks A:Need Help Registring A Manually Installed Programme did you buy it? 8 more replies Answer Match 54.18% BIOS setting: SATA AhcI partition 1: xp partition 2: 7 both boot,. but I want to use virtualbox to boot xp within 7 both are installed with SATA Ahci drivers, but the XP drivers do not work within Virtualbox (presuambly because the SATA chips are a bit different than what virtualbox emulates. XP boots directly, but crashes on startup within virtualbox I know I need this driver, but A) it refuses to install because when booted my chipset is different b) I cannot figure out how to extract the files c) I don't know how to manually install them help? A:Manually install SATA drivers in XP partition, already installed? SATA Drivers - Slipstream into Windows XP CD This is a good place to start. Mike 5 more replies Answer Match 54.18% Co-worker wanted me to look at her computer to fix some problems. I found virus(es) had hijacked ie. I tried malwarebytes, etc. and switched to firefox and tried to run windows update but endless search yielded no updates. I reinstalled the OS from original disk -- Vista Home Basic 32-bit. I manually installed SP1. I then manually installed SP2. Tried updates again. Forever looking and no updates. Could someone outline my next moves to be done to head towards a fix for this updating problem? I would appreciate it. I see that there posts with similar problems and I am not sure which ones I should try or do I need to do something else before I start manually downloading updates? Thanks, Don More replies Answer Match 54.18% After repeated problems with the update failing I did a clean install and installed kb3200970 manually from the windows catalogue and it shows as an installed update. Windows automatic updates wants to download and install it again. Is this really necessary? Any way to make it stop??? More replies Answer Match 53.76% I have several Type 1 fonts that I installed manually and now want to uninstall. When attempting to delete through the Control Panel route to Fonts, the error message is that the fonts are in use and cannot be deleted. No programs are open. When attempting to delete or change permissions through the CMD window, the error message is access denied. When attempting to change the read/write permissions on the Fonts folder, and clicking ignore on the many system fonts that Windows installs by default, I still cannot get access to these three fonts. Interestingly, this r/w permissions approached worked several days ago for several other Type 1 fonts that I installed manually. Suggestions? Thanks in advance. A:Access denied (to delete) Type 1 fonts installed manually Try booting into safe mode, then uninstall them... 5 more replies Answer Match 53.34% (Im sorry ahead of time for this being so long) I've had my laptop for 6 months almost exactly and in mid-May I started having an issue with my function keys. I had my laptop setup to have F5-6-7 as skip back, play, and skip backward because I frequently watch videos on VLC or listen to music on WMP. Those three buttons started to not work at all as soon as I had another program open (I noticed it most when I opened chrome). I am a blogger so music is usually always playing when I'm on Tumblr, but back to the point. After a week or 2 of searching everywhere for a fix and opening a post on the Toshiba forums and getting no help at all I went to a restore point a week and half before it happened. The issue stopped but my laptop's speed dropped to where it was almost unusable and anytime I typed on the keyboard it did more gibberish than actual letters. I downloaded a 8.1 factory ISO from Microsoft's website to wipe and fix anything that might be wrong. It worked but I had to reinstall Toshiba drivers so I could have the correct drivers for my screen, function keys, and my processor. Now I'm back to a buggy keyboard. The problem seems to lie in those drivers but I don't know how to fix the problem and keep full functionality. But as someone who likes to write I really need my keyboard to work properly. An example (off my memory) of what it does it when I press backspace it types /w3 (or something like that). I'd really appreciate it if anyone could help me fix this. Thanks. A:Toshiba laptop keyboard is buggy The company that makes all of the keyboards for all OEM's. They have been getting a lot of keyboards that fail after a while. You should be able to have Toshiba swap out keyboards, since you are less than a year, and this is a common event that is now going on two years. I have two Toshiba Satellite laptops, same model. One I have only had to replace the keyboard one time (took forever for the repair center to finally get a keyboard that was not smashed, broken in half, failed when installed). It was over a year, so I paid around$200.00 for them to fix. Even with going on 3 months, I could not get them to budge on taking at least 25% off of the repair costs, because of their failure to uphold a 30 day turn around period as I was promised under my business contract with them.
The other one we have, it is starting to have symptoms on the second keyboard installed after the first failed. It is only on the number pads, but still is something that should not be happening. That one failed after a year and a half of use.
If you have someone local that can do the work. You can get the keyboard online at Amazon.com or at Laptop Parts & Repair - SparePartsWarehouse.com which sells OEM and compatible keyboard units. I have dealt with them in the past for a Compaq Laptop I had a while back. Quick turn around on the repair.
The two units for my C850d-st3nx1 is $60 for OEM,$30 for Compatible.
1 more replies
Answer Match 53.34%
Logfile of Trend Micro HijackThis v2.0.4
Scan saved at 9:33:59 PM, on 1/25/2011
Platform: Windows XP SP3 (WinNT 5.01.2600)
MSIE: Internet Explorer v8.00 (8.00.6001.18702)
Boot mode: Normal
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\svchost.exe
C:\Program Files\Intel\Wireless\Bin\EvtEng.exe
C:\Program Files\Intel\Wireless\Bin\S24EvMon.exe
C:\WINDOWS\system32\ZoneLabs\vsmon.exe
C:\Program Files\CheckPoint\ZAForceField\IswSvc.exe
C:\Program Files\Alwil Software\Avast5\AvastSvc.exe
C:\WINDOWS\system32\spoolsv.exe
C:\Program Files\Belkin\Router Setup and Monitor\BelkinService.exe
C:\Program Files\Common Files\Apple\Mobile Device Support\AppleMobileDeviceService.exe
C:\Program Files\AskBarDis\bar\bin\AskService.exe
C:\Program Files\Belkin\Belkin USB Print and Storage Center\BkBackupScheduler.exe
C:\Program Files\Belkin\Belkin USB Print and Storage Center\Bkapcs.exe
C:\Program Files\Bonjour\mDNSResponder.exe
C:\Program Files\TOSHIBA\ConfigFree\CFSvcs.exe
C:\WINDOWS\system32\DVDRAMSV.exe
C:\WINDOWS\eHome\ehRecvr.exe
C:\WINDOWS\eHome\ehSched.exe
C:\Program Files\Java\jre6\bin\jqs.exe
C:\Program Files\LeapFrog\LeapFrog Connect\CommandService.exe
C:\Program Files\Motorola\MotoConnectService\MotoConnectService.exe
C:\WINDOWS\system32\HPZipm12.exe
C:\Program Files\Intel\Wireless\Bin\RegSrvc.exe
C:\WINDOWS\... Read more
More replies
Answer Match 52.5%
I had recently bought an ASUS ROG laptop, it is very good for gaming, but has a TON of glitches and bugs riddled through the system. I have been looking for a fix for these glitches forever, but have not come across a fix. Here are some details.
Problems I have run into:
*Sometimes when I click in games, it starts bugging out. Sometimes it minimizes and just not responds. Sometimes it even crashes.
*Task manager starts minimized
*Start menu does not open up
*Power icon is gone
*Sound icon is gone
*Date and time are off
*Sometimes the computer does not recognize that an Ethernet cable is plugged in
*Nvidia Ge force experience does not open, or does not connect to the internet.
(I have run into MANY other glitches but cannot remember them at the moment, sorry)
Some things I have tried to fix these glitches/bugs:
*Run antivirus scans (Avast Free Anti-Virus)
*Run Ccleaner
*Run Malware bytes
*Gone into computers settings
*Watched and read many guides
If anyone has any idea what is happening and know how to fix these awful problems, please post it. Thankyou
More replies
Answer Match 52.5%
Ever since I updated my graphics driver, my computer has been acting really buggy. It freezes up while doing certain things on the internet, like going to Facebook or pressing the Start Button. Can someone help me with this issue?
A:Laptop Really Buggy Since Updated Graphics Driver
Which Version did you Install Jesse ? ...
9 more replies
Answer Match 52.5%
Hi guys,
Yesterday I downloaded and installed a new windows update onto my laptop, when it asked me to restart the computer, i did, but when the laptop restarted an error kept on popping up it and wouldn't let me go to my log in menu. The error kept saying lsass.exe unable to locate component and something about DNSAPI.dll being missing. I tried going into safe mode and i tried going back to the last good configuration but the error kept showing up. After I pressed the reset button a few time my computer started up again, but now everytime I log on my laptop seems slower, firefox won't connect to my internet dispite being connected directly to it as my default and checking my firewall (but IE will, that's how I'm using it right now), and the auto-protect on my Norton Anti virus won't work either. I don't know what else is wrong, so i was wondering if there's anyway i can fix this.
here's my Hijack this log:
Logfile of Trend Micro HijackThis v2.0.2
Scan saved at 11:10:06 AM, on 7/9/2008
Platform: Windows XP SP2 (WinNT 5.01.2600)
MSIE: Internet Explorer v6.00 SP2 (6.00.2900.2180)
Boot mode: Normal
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\Program Files\Intel\Wireless\Bin\EvtEng.exe
C:\Program Files\Intel\Wireless\Bin\S24EvMon.exe
C:\Program Files\Common Files\Symantec S... Read more
More replies
Answer Match 52.5%
My PSU is about 3-4 years old. I just opened my case up to clean my GFX card and then turned it on and noticed that my PSU fan isn't running. The fan is right at the bottom of the PSU so it's parallel to the ground and the fan is facing the ground. I couldn't really get a good search of the PSU online but it's a cooler master atx12V product no. RP-600 PCAR W/O PFC. It has red numbers saying 600, so I assume it's 600 watts and the fan is 12volts?
Motherboard: biostar Tforce P965
PSU: cooler master atx12V product no. RP-600 PCAR W/O PFC.
My fan isn't running when my computer is turned on and i have to take a pencil or something to manually start the spinning (while the computer is on ) Ocassionally it'll even stop moving after a while (computer still on) and i have to manually spin it again. Is this reparable? Can I get gell on the PSU fan because it seems to be a little cloggy.
How big of an issue is it that my PSU fan isn't working? It's really hot right now (environment -wise.. being summer and the PSU fan not running kinda scares me)
A:PSU fan stops running and I have to manually start it
I would either try to replace the fan if you know what you are doing or replace the whole power supply. I wouldn't run the PC if the power supply fan isn't working. You risk burning out the PSU and when it blows it could take out other components with it.
1 more replies
Answer Match 52.08%
Hi there, like the title says, I'm having problems with my laptop being slow and buggy. Here's the story.
After having my HP for about two years, it had slowed down with a crowded hard drive and too many little programs on it, which was to be expected. So I backed up all of my important data, upgraded it to 8GB of RAM, and bought a new hybrid hard drive (part SSD, part traditional spinning disk) on which I installed a fresh copy of Windows 7 Home Premium. I went to the HP site and found the support section for my exact model, and downloaded all of the appropriate drivers.
Here's the problem. When I first got it, it was blazing fast, with its Quad-Core i7, 6GB RAM and a 1GB ATI graphics card. I would expect that with a clean install of Windows, a faster hard drive, and an extra 2 gigs of ram that it would be even better that it had ever been. That's not the case. It will hang doing simple tasks, I will gets bursts of corrupted(?)/garbled sound out of the speakers, it will randomly and very rapidly switch between the internal speakers and the ones connected through the headphone jack, and I can no longer play almost any game. Just Cause 2, which I used to be able to play on the highest settings on an HDTV, looks terrible, plays slow, and crashes.
Where-oh-where did I go wrong? More importantly, what can I do to fix it? I've attached the system specs.
More replies
Answer Match 52.08%
Recently purchased a brand new hp envy m6 from Best Buy. After only a few hours I've noticed that file explorer and Google chrome takes minutes to launch.. File explorer also stops responding whenever i right click. Apart from uninstalling 30 day McAfee antivirus and installing one from Kaspersky which was provided with the purchase and also installing Google chrome i have made no modifications to this computer. The Windows update page in settings is also always blank and unresponsive whenever i go there
More replies
Answer Match 51.66%
This morning i turned on my computer and after completing my login at the windows vista loging screen, I was confronted with nothing but a black screen and my cursor. I can open Task manager through Ctrl+ALT+Delete, and if I try to run explorer.exe manually it just tells me it has stopped working, and crashes.
Here is my Hijack This log:
Logfile of Trend Micro HijackThis v2.0.2
Scan saved at 1:58:57 PM, on 07/09/2010
Platform: Windows Vista SP1 (WinNT 6.00.1905)
MSIE: Internet Explorer v7.00 (7.00.6001.18498)
Boot mode: Normal
Running processes:
C:\Program Files (x86)\Microsoft Windows OneCare Live\winssnotify.exe
C:\Program Files (x86)\Opera\opera.exe
C:\Program Files (x86)\Trend Micro\HijackThis\HijackThis.exe
R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Default_Page_URL = http://ie.redirect.hp.com/svs/rdr?TYPE=3&tp=iehome&locale=en_ca&c=83&bd=Pavilion&pf=cndt
R1 - HKCU\Software\Microsoft\Internet Explorer\Main,Search Page = http://go.microsoft.com/fwlink/?LinkId=54896
R0 - HKCU\Software\Microsoft\Internet Explorer\Main,Start Page = http://www.ask.com?o=15179&l=dis
R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Page_URL = http://ie.redirect.hp.com/svs/rdr?TYPE=3&tp=iehome&locale=en_ca&c=83&bd=Pavilion&pf=cndt
R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Default_Search_URL = http://go.microsoft.com/fwlink/?LinkId=54896
R1 - HKLM\Software\Microsoft\Internet Explorer\Main,Search Page = http://go.microso... Read more
More replies
Answer Match 51.66%
I have a windows xp professional operating system. I was trying to visit a website for my brother but he gave me the wrong website. After that my computer has been running slow and freezing to the point that I have to manually shut it down and restart it in safemode.
I ran my McAfee virus program and no virus was found. I ran malewarebytes and some malware was remove but the problem was not resolved. I also did the last known good configuration on my computer and still doing the same thing.
I got an error message that I never seen before this issue. It has only appeared a couple of times: ScService.exe has caused an error and needs to close. I don't know what it is. I don't know what is going on with my pc. All I know is that it was running fine until I went to a website.
More replies
Answer Match 51.66%
I have several tasks defined in the Task Scheduler. They're all working fine. They are written in the REXX language (about the only language I'm proficient in).
Yesterday, I made a small change to one of the scripts and ran it manually, from the Task Scheduler (to ensure that it ran correctly in the scheduler environment).
The script ran to completion, but the status remained "Running". I've spent the last 24 hours trying to work out why the task sticks at "Running", only to discover that closing and re-opening the Task Scheduler makes the status revert to "Ready".
It looks like the Task Scheduler is not updating the status, when the program exits. Is there anything I can do about this (I suspect the pragmatic answer is "ignore it").
Are my scripts supposed to do something to signal to the scheduler that they've terminated?
A:Scheduled task remains running, when run manually
There is probably nothing wrong from what you describe. Pressing F5 or Refresh from the Actions pane does the same thing as re-opening Task Scheduler. I've noticed the same thing and it seems the Task Scheduler GUI is just not updated so you have to do it manually.
If your scripts automatically terminate the process when they've finished then the only thing you might want to do is set an proper exit code (if you want). This can be seen in Task Scheduler in the column "Last Run Result" for every task. For windows batch files this is how to do it: Exit - Terminate a script | Windows CMD | SS64.com
0 is the default exit code. If I terminate a batch file with Ctrl+C it will instead show 0xC000013A as Last Run Result.
2 more replies
Answer Match 51.66%
I am trying to help a friend of mine out. He has an Acer Laptop, model 5520, and it has been "buggy" and slow for him. I took a look at it tonight (it was my first real experience with Vista, to my recollection," and it seemed to be overloaded with trial and extra crap software. I tried to remove the trial of Norton, and it hung up at the very end. I am not sure if it's gone or not.
Because I am extremely unfamiliar with Vista, I need help in navigating it, and knowing what to, and how to, delete what I need to do.
I am pretty sure this computer has next to no spyware/adware on it, although, I have been proved wrong.
Jeremy
A:Acer Laptop/Vista/Slow/Many trial programs/buggy
Start by using this free tool to remove the remnants of Norton: http://service1.symantec.com/Support/tsgen...005033108162039Then immediately get a replacement for it. Here's a link to our freeware topic that gives some alternatives: http://www.bleepingcomputer.com/forums/topic3616.htmlAfter that, check the Taskbar to see what's running that doesn't need to be. Then, using that info, go to the Control Panel...Programs...Uninstall a program applet to remove the one's you don't need.Once you've done that, then investigate the processes running in Task Manager...Processes tab to see what else is running that you don't need.Research the image names to find out what program the process belongs to - and then remove the one's that you don't need.Once that's done, post back and we can offer more advice to help with the svchost.exe processes (there's stuff running inside them too).
9 more replies
Answer Match 49.14%
I know it was foolish of me to forget to back up the registry and to run combofix without supervision, but for some reason (I suspect rootkit activity due to the fact SS was not detected by Hijackthis or Combofix), all windows services have become disabled and I get an svchost error upon startup. "The instruction at 0x00666a33 referenced at 0x0000000c. The memory cannot be "read". The afflicted computer is currently without internet access.
A:Deleted the rogue AV system security manually after running combofix, all windows services became disabled
Your specific version / edition of Windows ?
humh... What "SS" are you referring to?
Can you start Windows and get to a point where the Taskbar is visible & useable ?
6 more replies
Answer Match 48.3%
The wires that attach to my speaker input got pulled and broke the little input thing.
Usually when you plug in a speaker cable your laptop speakers shut off and the external speakers go.
Now though, when I plug it in they both stay on.
I was wondering if there was a command that would let me shut off the laptop speakers (there's gotta be a way, if an input of a cable just tells it to shut off, i must be able to shut it off).
These laptop speakers are so twangy!
A:Turning Off Laptop Speakers Manually.
Hi logangaudreau,
It sounds like you have damaged the stereo plug on your laptop. The way that jack works is the computer sends sounds to that plug unless you mute the sound (then all sound ceases). The jack has metal contacts that completes its circuit to connect to the laptop speakers - so the path to the laptop speakers is always "on." When you plug something into that jack, it breaks contact with the internal speakers and allows the signal to go to whatever is plugged in. Think of it as a two way switch that activates when something is plugged in.
Hope this helps,
rigel
5 more replies
Answer Match 48.3%
I have a Gateway ML6703 Notebook. It has the following:
Intel® Pentium® dual-core Mobile Processor T2060 @ 1.60GHz
80GB Hard Drive
1024MB DDR2 Memory
Windows Vista Home Premium SP1 (32-bit)
I am currently on my home pc which has an Arris Touchtone Cable Modem CM450 to connect to the internet. ( I have Cable internet) When I first got the laptop, in March of '07, I would plug in a USB cord from the cable modem to the laptop and the internet would work. I don't know what happened but now when I plug in a USB cord, the mouse would blink and then nothing would happen. I even tried Ethernet, but it would just flash colors at the end of the cord (indicating it connected to SOMETHING) and that's all.
I contacted arris.com and they referred me to http://www.arrisi.com/support/usb/index.asp
They said at the link that "USB Drivers for Windows Vista running in 32-bit mode is included with Windows Vista. There is no downloaded necessary."
I tried installing the driver for the 64-bit Vista CM450 and when I plugged in the ethernet plug, the laptop asked for a driver. YA! Anyways, Arris Touchtone Device showed up in Device Manger. I updated it with the 64-bit Vista CM450 driver. I don't know if that helped or not...
But still no internet when I go to "Connect To" then click on "Broadband Connection" click Connect". It says Connecting to Broadband Connection" then comes with the error of "Failed to connect to Broadband ... Read more
A:manually connecting laptop to internet
14 more replies
Answer Match 47.88%
I am trying to charge a laptop battery manually , bi passing the circuit and connecting to the + and -ve leads on the cell. The cell is getting hot. I tried changing the polarity but still getting hot. ![please see picture][1]..Can you suggest
A:charging laptop battery pack manually pic
STOP!
WHAT YOU ARE DOING IS VERY DANGEROUS!
The laptop has customized electronic circuits inside that take the charger input voltage and safely limit the voltage and current used to charge the battery. Defeating any of those safety limits may cause ...
1) A safety fuse inside the battery may blow to prevent further damage to the battery pack.
2) The battery pack may burst into flames, possibly with toxic fumes.
3) The battery pack may explode, spewing hot toxic chemicals and fumes.
2 more replies
Answer Match 47.88%
Before you ask, yes I've tried that. What I need now is something I can use to manually control how fast my fan spins, and at what temp. Tried SpeedFan, but it cannot detect laptop fans. Any help regarding controlling my fan MANUALLY is greatly appreciated.
A:Manually Controlling Laptop Cooling System?
Aside from gaming laptops, which typically supply such tools, it's generally not possible nor recommended. Many systems have the fan controls tied to the BIOS. Some have an app installed (not user configurable), which if it's altered or missing, the fan defaults to full speed.
In any case, good luck.
1 more replies
Answer Match 47.04%
HP Pavillion dv2000 (dv2025LA)
It was full of viruses, so I removed the HDD, put it on my computer and cleaned it up. Put it back on the laptop, started up fine, but I decided I should better format it. During the windows installation, it did not detect the HDD, so I pressed the power button until it turned off.
Now when I press the power button, the only that happens is that a little lightning bolt LED next to the HDD and Power LEDs flashes twice and nothing happens.
I removed the battery, let it sit for 10 minutes, tried again, same results. Removed the HDD, tried to boot it like this, no luck. What is going on here? What does that little bolt mean, and why does it flash twice?
A:Solved: Manually shut down laptop, now it won't turn back on?!
Oh wow... The power connector wasn't properly connected to the power outlet, and I didn't know the battery was completely drained!
Sorry guys! (It's always the simplest solutions that take forever to find out)
1 more replies
Answer Match 46.62%
Here are my specs:
Tech Support Guy System Info Utility version 1.0.0.1
OS Version: Microsoft Windows 7 Home Premium , 64 bit
Processor: Intel(R) Core(TM) i3 CPU M 330 @ 2.13GHz, Intel64 Family 6 Model 37 Stepping 2
Processor Count: 4
RAM: 3894 Mb
Graphics Card: Intel(R) Graphics Media Accelerator HD, 1723 Mb
Hard Drives: C: Total - 464783 MB, Free - 434084 MB;
Motherboard: TOSHIBA, Portable PC, Base Board Version, Base Board Serial Number
Antivirus: avast! Antivirus, Disabled
What's happening is my compuer and keyboard will stop responding and makes weird beeping noises. It's a slow beeping each are spaced out about a second or two apart and it beeps three to four times please help me.
A:Laptop computer beeps and freezes up forcing me to manually power off.
A bit more info please.
When does this happen, in Windows, when you first switch it on or ... ?
It's a Toshiba laptop ? What model ? (should be on the bottom).
2 more replies
Answer Match 45.36%
I can't tell if my issue is hardware related, software related, or both. I have a Gateway CX2610 tablet notebook. I'm having a bunch of problems and wonder if they are all related:
Sometimes when I boot up my laptop the BIOS doesn't show up. The laptop is powered on but no BIOS shows up. So I power down and try again. Sometimes it gets past BIOS and stalls. But I'm getting no beeps or sounds.
When the laptop gets past BIOS sometimes XP won't load. Sometimes the XP logo won't show up, sometimes the XP logo will show up but it freezes, and sometimes it boots normally (although slowly).
Also, when I am able to boot into XP it won't recognize USB devices like mice, external HDD, and USB sticks. Also, the touchpad pointer sometimes freezes and I have to push down both buttons to get it to move.
This sounds like I have fifty different problems but up until a week ago the system was running pretty smoothly. I've tried running Ultimate Boot Cd to find out if my drive is malfunctioning but there are no instructions on how to use the Fujitsu diagnostic tool. It's a command line tool. Do you think my problem is with memory, BIOS needing to be updated, hard drive on its last legs, or with XP? I'm at a loss.
Any suggestions would be appreciated.
A:Laptop Screwy OS Buggy BIOS Screwy
Download and install SpeedFan. It'll let you generate a SMART report on your drive to see its overall health.
http://www.majorgeeks.com/download337.html
3 more replies
Answer Match 42.84%
I was unable to recover from a damaged mbr and have an app i must run that's on the damaged drive. So I have installed my identical os on another drive; connected the damaged drive as a slave and now have access to the required app's files and system environment. Of course, now I have path problems trying to run the app as well as probable problems with interfacing to specialized hardware that the app controls.
Can anyone suggest a strategy for running the app? Perhaps a global command line copy of the app files and a global copy of registry, and other required system settings? (the os is actually nt 4.0, but that shouldn't matter, should it?) Thanks so much for any input! Bob
A:running app on re-installed os
10 more replies
Answer Match 42.84%
For Info:
I just completed the clean install of W8 Pro and had no problems. From start to finish it took 1 hour and about 1/2 hour to install updates (10). One thing I noticed after doing updates is that the restart runs slower than W7. One other item is Hotmail is not included on the top of the MSN homepage. It appears to run much faster than W7 for all other applications
A:W8 Installed & Running
Update to my post
I found the Hotmail & MY MSN. You need to go to the bottom of the W8 Homepage and select CLASSIC HOMEPAGE
2 more replies
Answer Match 42.42%
I have a Toshiba Satellite running windows 7. I got the computer from my father and had to remove a lot of malware and games. I wish i could do a factory reset but i do not have any of the factory disks. It seems like there are a lot of processes running and the physical memory is almost always at 100%. Any help would greatly be appreciated . Thanks in advance.
A:Toshiba laptop running super slow. physical memory running high
You can first try this:
http://www.howtogeek.com/74523/how-to-disable-startup-programs-in-windows/
Then you can try removing all the junk files on it using CCleaner or BleachBit or something similar. If that doesn't help, I would recommend dual booting this PC with Ubuntu 14.04. I actually published a tutorial on doing that here:
http://69.107.93.24/Blog/52015/
You could then use that as your primary OS.
5 more replies
Answer Match 42.42%
Hi folks,
Heres the situation: New parts, new build.
Mobo: Asus P5N32-E PLUS SLi nForce (Socket 775) PCI-Express DDR2 Motherboard
Hdd: Western Digital Caviar SE16 500GB 5000AAKS SATA-II 16MB Cache
The problem is installing windows. The first time windows was installed SATA drivers were not installed, and the installation bombed out on a blue screen.
The second install had the sata mass storgae controller installed. The Hdd is seen in the windows installation, however when I partition it and format, the format FAILS! It goes all the way to 100% and comes back with a message saying the drive may be damaged or corrupt.
So based on that error I plugged the drive into another machine and ran the WD diagnostics on it. The drive reported no errors or bad sectors. So I decided to write zero's to it and start again.
I instlled both the raid and mass storage drivers for windows by pressing F6 at the start of the install. Once again the format fails and I cannot progress to the XP install??????
Can anyone help here please?
Justin
A:Can't get XP installed, running out of ideas!!
If you aren't setting up a RAID array, you don't need the RAID drivers. If your installation without them leads to no drive found, perhaps you have a wrong setting in the BIOS concerning RAID settings.
4 more replies
Answer Match 42.42%
Everytime I boot up it resets in less than 2 minutes. Updated drivers and got the mini-dump in safe mode. Can't get the performance report in safe mode.
Just installed the OS, it is a ultimate x64. Hardware is 3 years old I think, works just fine under ubuntu.
Have already tested memory with memtest86+, got no errors.
Please help.
A:Just installed the system, can't get it running.
Hello and Welcome !
The Files doesn't have Minidump. Go to C:\Windows\Minidump and copy the Files to Desktop and Zip it and upload it here. Looking at the other files seems like a Hardware issue.
Meantime Run a Hardware Diagnostic (Memory and Hard Drive) follow this link for instructions Hardware Diagnostic !! ? Captain Debugger
Run SFC /SCANNOW Command - System File Checker
Hope this helps,
Captain
2 more replies
Answer Match 42.42%
Basically this is a hardware problem but please feel free to direct me to a more relavent forum.
I have a very old pc that is running very slowly that I don't use apart from one programme. I cannot install that programme on my new pc. To run this programme I have to access an exturnal site so in every instance I need to start the programme from the old pc.
Is there anyway using my new pc to do all the processing by linking the two together in some way and treating the hard drive in the old pc as a slave?
A:Running software thats installed on one pc on another pc
7 more replies
Answer Match 42.42%
I am trying to put a game from a cd onto my computer and when it's installed it gives me the message "to play full throttle, exit the install program then type throddle from the installation directory". Can someone tell me what this means? Thanks so much!
Belinda
A:Need help on running a game that is installed
Try posting this in the games forum you will get a better response in there .......
1 more replies
Answer Match 42.42%
Hi , i recently upgraded my laptops hard drive to a Samsung 840 evo 500GB SSD. Whilst i've noticed a massive improvement in performance there is one little annoyance , the fans on my laptop are constantly going on and off is there a way to combat this and is this a common problem ?
A:installed SSD fan running constantly
Hi Bibbster,
Not a common problem no, if anything after fitting a SSD the fans should come on less as a SSD gives off no heat at all compared to a regular spinner.
Did any bios settings change when you installed it? I would have a look in the bios to see if there are any settings for fans etc.
3 more replies
Answer Match 42%
Hello,
My problem is the following: after a boot up, my laptop can find itself in two states, seemingly at random.
- runs fine: the laptop runs as it always did, no slowdown or anything.
- runs slowly: as the name implies, every program runs slowly, from Firefox to video games (offline, so it's not just an internet connection issue).
As far as I can tell, which state the computer will settle in is set at boot up or wake up from hibernation mode. I've never seen my laptop go from "runs fine" to "runs slowly" while I was using it, even after running all day long. Same way, if it's in the "runs slowly" state it's noticeable as soon as I launch any program just after boot up, and it doesn't get better or worse after using it all day .
Another symptom I noticed recently is that as soon as I launch a game while in the "runs fine" state, I can hear both the CPU fan (shortly) and GPU fan (continuously) kick up a few gears, which I take to mean both CPU and GPU are put to use. This has always been the laptop's behaviour, even before this problem appeared. However, when playing a game while in the "runs slowly" state, the CPU fan will remain quiet and the GPU fan will only go a bit faster from time to time before returning to quiet speed. It seems as if the whole computer gets lazy and don't want to put any effort.
I first took notice of this whole behaviour around the end of March/beginning of April of this year, though in retrospect the "runs slowly" state may have shown up on... Read more
A:Laptop sometimes running fine, sometimes running slow after boot up.
Thanks for the Speccy link .
Please download MiniToolBox , save it to your desktop and run it.
Checkmark the following checkboxes: List last 10 Event Viewer log List Installed Programs List Users, Partitions and Memory size.
Click Go and paste the content into your next post.
Louis
9 more replies
Answer Match 42%
I've got an odd problem here. On my Compaq Presario CQ60-615DX, it runs fine as long as it's plugged in. Once I unplug it and run it on the battery, once it gets down to about 87-88% or so, the screen just goes black, but doesn't shutdown and I'm unable to do anything except remove the battery and restart. My first thought was a battery problem, but the fact that it keeps running even though the screen is black makes me wonder if that's the case or not. Anyone else experience this or any ideas to help?
A:when running on battery, screen goes black,but laptop is still running
You laptop is due to the power plan settings, refer to point 1.
Normally, the laptop can return to display mode upon moving the cursor &or keyboard being press.
1. Go to Control Panel, select Hardware & Sound; select Power Options.
Select the Power plan with button marked, and Change Plan settings to view on the options.
2. If you are using main power, best is to remove &or unplugged the battery.
If the battery is always plugged in, while using main power, this cause the battery to failed in the long run.
Unless you need to charge battery, then plug in the main power.
If battery is almost 100% then remove it if you use main power.
I had one laptop (from my bro) who always battery was plugged in and also use main power.
The battery was now useless, cannot hold charge.
5 more replies
Answer Match 42%
Hi! I have a Compaq laptop, and lately it has been getting hot pretty quickly. I noticed the fan seems to be constantly on, and while I could be wrong, I don't think it has always been constantly running until fairly recently. I feel like I would have noticed. lol
Anyway, my laptop is about 2 1/2 years old, Windows Vista, and I use vista manager. I have AVG, AdAware and Spybot for security. I have Photoshop cs5 and Adobe lightroom, but the problem was there before I had these. I have completely reset my computer to factory settings, and the problem is still there.
I have a lot of running processes, but I've checked them on Vista manager and on pcpitstop, and only have removed the ones that I know for sure are not important.
Any ideas of what I can do? My computer lags as it heats up, and I don't want it to die! I use it for school and work, and my photography work.
If anyone wants to take a gander at my running processes, just let me know. I would be more than happy to take advice from those more knowledgable than I.
Buying a new laptop is NOT an option, by the way. I've treated this one very well, and I really see no reason why I couldn't fix it and extend it's life. Thank you in advance!
A:HP laptop running hot/fan overworking - possible running processes problem??
10 more replies
Answer Match 42%
I can ping these two machines yet on my laptop, in my network places i cannot see my home pc or my laptop in the workgroup. On my home pc i can see my home pc in the workgroup. All firewalls are off that I know too.
Is there a setting on my laptop stopping it joining the workgroup. Because it is not in the workgroup, i guess that is why my home pc cannot detect it.
When i search for computers nothing is detected, yet when i search for "laptop" it finds it in my workgroup. Yet no symbol is showing.
I want the connection purely for file transfer.
Static IP address are ok, 192.168.0.1 for hom pc and 192.168.0.2 for laptop.
Workgroup is same on both machines.
Really Really Frustrated now!
Can anyone please try to help.
PS. My laptop was setup for a network at my office originally, but I don't see how that matters?
A:Networking home pc running XP pro with laptop running Win 2000
This has to be the most asked question,
First get identical accounts on the XP and 2k, such as user with a password of user.
Turn off simple file sharing on the XP machine, its Explorer \Tools \Folder Options \View drag the bar to the bottom and untick simple file sharing.
Ensure both machines are in the same workgroup, this is found in XP by right clicking my computer on the desktop and choosing properties then choose computer name then click change, by default XP Pro and 2K use "Workgroup" but XP Home uses MSHOME for some strange reason, to change the work group in 2K right click my computer choose properties, choose network Identification, properties.
Then share the folders you want access to by opening explorer and right click the folder and choose sharing, follow the tabs
reboot the PC's and that should do you.
I always check by doing this
start run "\\machinename\c$this attempts to connect to the admin string of the PC, this share is always present and means you dont have to worry about sharing individual folders. If this works congratulate yourself for being clever and have a large Rum and coke and a Cigar. If not post back and someone cleverer than me will help.. 11 more replies Answer Match 42% Win 8 seems to have made it more difficult not easier! I can't make heads or tails out of the instructions to create a network that will allow access to files back and forth between my Win 8 Desktop and my XP driven LapTop. Would you direct me to a simple step by step process describing how to do what I am trying to accomplish? A:How to share files on Desktop running Win 8 from Laptop running XP Short description for Windows 7 and 8 file and printer sharing: Go into the Network and Sharing Center from the Control Panel or from the Network icon in the Notification Area. Your network must be designated 'Private' (or 'Home' or 'Work'). Click on Change advanced sharing settings. In the Private or Home or Work section you can configure File and printer sharing, Public folder sharing, and Password protected sharing. You may want to change the Workgroup name. To check it or change it right click on "Computer" and select "Properties." You must uninstall or properly configure any non-windows firewall (security suite). A wizard way to enable file and printer sharing on XP: Run the Network Setup wizard (found in Control Panel of XP). Tell it each of your computers connects to the internet via "residential gateway" and that you want to enable file and printer sharing. Create a disk at the end only if you have a PC with Windows ME or Windows older than ME. Windows XP firewall (if SP2 or SP3) will be properly configured by the wizard (but make sure it is not set to “No Exceptions”. You must uninstall or properly configure any 3rd party firewalls on each machine. Unique computer names and same workgroup, of course. The Shared Documents folder is automatically shared. Any other folders (or drives) or printers you want to share, just right click on them and sharing ... . When sharing a printer, acce... Read more 1 more replies Answer Match 42% I just bought a 160 GB hard drive for my Dell INspiron 700m, I really need the space for all of my music and multimedia. THe problem is I did not know DELL did not give me any type of restore disks, Nor did they leave a program on my dell to create such disks. I know I can get like 1000 different drivers off their website, but I really have no clue how to get this hard drive up and running. I do have an external hard drive, that has 160 GB capacity. I really need someone who can explain to me in detail how to fix this. Obvoiusly I am not very computer savvy when it comes to loading drivers and stuff onto a new hard drive. I always had the CD's for it. I really don't understand how im suppose to get windows XP onto that new hard drive, unless there is someway I can just copy my current hard drive onto the new one. Please help, I hope i didn't waste 120 bucks on a hard drive I cannot use. thanks. My Email is [email protected], if anyone would like to contact me that knows what I should do. Sleeprgt A:New Hard Drive Installed, how do i get it running? 7 more replies Answer Match 42% I suddenly noticed dips in my computer performances recently so I instinctively opened up task manager to see how much memory was being used up and to my astonishment (dramatic much?) I saw that somehow I had lost more than 2GB ram of Total Memory. Here are the specifications of my system: copied from run: dxdiag ACER AX3400 Windows 7 64-bit Home Premium (6.1, Build 7601) BIOS: Default System BIOS Processor: AMD Athlon II X2 220 Processor (2 CPUS), ~ 2,8GHz Memory: 3072MB RAM Page file (??): 1524MB Used, 395MB available Graphics: Nvidia Geforce 9200: Approx total memory; 305MB I was wondering if this had anything to do with my graphics card for starters and also if anyone can help me find a solution that would be greatly appreciated. A:Running W7 64-bit, Installed RAM 3GB, Usable: 895MB. What should I do? You could open the Resource Monitor, Memory tab and check the graphic at the bottom. It should show how your memory is being used. The numbers above show what might be using what. Since I do not have 3 GB of memory in my system, I cannot judge if your numbers seem normal. Maybe the Hardware Reserved number will make a difference. You can take a snipping tool picture of the window and attach using the paperclip. 4 more replies Answer Match 42% I don't no how to get this corrected. Every time I boot my system up this message appears, "Fasttrak is not on, BIOS is not installed." Since I bought my computer this message has been on it. I'm finally getting sick of it. Don't know if this is important or not. Any suggestions???? A:Fasttrak is not running, The BIOS is not installed... I'm going to guess that the drive had an overlay installed at one point, and it has been partially removed. (overlays were used to allow older systems to utilize drives larger than the BIOS could support) Try booting to a Windows 98 floppy, and run fdisk /mbr. This could clean it up. If not, download the utilities from your hard drive's manufacturer's site. They should have a removal tool. 3 more replies Answer Match 42% I just upgraded a 2006 desktop PC with a 240gb Sandisk Ultra II SSD. The system is faster in all the areas I'd hoped for, but not as fast as it could be. The Sandisk dashboard reports that the connection is only 1.5 Gb/s, even though the motherboard (Gigabyte M55 SLI S4) supports SATA 3 Gb/s (Sata II.) The Window Experience Index rates the drive at 6.9. Meanwhile, a Crucial BX200 drive recently installed in a 2010 thin-n-light laptop, also SATA II, rates a 7.7 in WEI, and the laptop generally feels snappier than the desktop even though it is overall a slower machine. A few points: the desktop PC's mobo does not support AHCI, just IDE. I've optimized all the settings I know of to optimize, eg turning off prefetch and defrag etc. I'm using a 10-year-old SATA cable. I didn't find any obvious BIOS setting to tweak. Any ideas? A:Sata 3Gb/s connection running at 1.5 Gb/s with new SSD installed Hello and welcome Chris mate did you also update the CPU on this machine because the specs are telling me it was not released until 2008. AMD Athlon X2 5600+ - ADO5600IAA5DO (ADO5600DOBOX) By the way if you look at this site GIGABYTE - Motherboard - Socket AM2 - GA-M55SLI-S4 (rev. 1.0) it gives drivers only up to XP though there are refs to more recent versions of Windows whether the support is that good would in my mind be debatable. Having said that I am also of the opinion that being an older machine with that CPU and slower RAM that you might not be able to get the speed out of it because of what that CPU and RAM can handle - the SanDisk I also use in some of my machines and are as you say lightning fast but I think maybe it is being throttled by the other gear. For example I have an older tester machine with a really great CPU (Intel Q9650 and 8GB DDR2 RAM) and even running with a nice Samsung 850 EVO it isn't real fast in boot up although once moving it is quick enough for most jobs. Just by the by just because the manufacturers state that components will run at 3Gbs does not necessarily mean they actually do. A good example would be USB 3.0 over 2.0 they say it runs near ten times faster when in reality it is sometimes nearer 10% faster. But I stand to be corrected on any of what I have said of course - you may get a different view from other members. Myself I wuld be quite happy with what you have got and if you need to go faster then you may have to look... Read more 3 more replies Answer Match 42% I have a computer I have been working on. It has a connection to a risk server through a serial connection, a connection to a phone management server and a connection to a dsl network. After the phone nic was added and any software to access the phone management servers website the computer started running slowly. If you are typing on a site or a form it will stop typing and in about 30 seconds you will see the text like it is catching up. The computer is a 800 mhz pentium gateway with winxp pro and 448 mb of ram. The os has just recently been installed and I am pretty sure it is free of spyware and viruses. any help would be appreciated. Jerry A:newly installed os running slow 10 more replies Answer Match 42% I recently ordered a 512 MB ram from ebay (turned out it was DDR2) and didnt realize until i spent an hour trying to fit it in the memory slot of my Compaq Presario 4420CA computer (stats can be found on the www.hp.com website). After I realized that it is the wrong ram, I tried to reinstall the original 2 rams I had (128 mb 133 each for total of 256 MB ram). I tried to restart the computer but computer didn't start windows or even dos. Only thing happens is that the power light (flickering between green and orange colours) is solid orange for about 2 mins then goes blank.....At the same time the key board's NUM LOCK green light flashes in equal intervals and continues to do so. I have tried to reset the ram properly several times. But I fear I may have damaged the ram slots where the ram is to be placed. I have several questions. Anybody's input would be greatly appreciated. 1) I purchased a new computer HP Pavillion and was able to connect my Compaq Hard drive to the new computer via Master and Slave configuration. I was able to access files in MY document folders of the individual users of the old computer accounts. BUT I could not access the files I had saved on the DESKTOP of my old computer. My first question is..........Are the files which we save on windows DESKTOP also saved on the HARD DRIVE or are they saved on the computer's local memory? When I tried to access the desktop in the new computer...(the old harddrive) I was given message sa... Read more A:Computer stopped running after NEW Ram installed For your files that you cannot access try this Take a look here For the old PC I would try and take the Cmos battery out for 10mins and the put it back in and try And also check and re-seat the video card and check all connections in case they were knocked loose 3 more replies Answer Match 42% Ever since I got my new motherboard, my games don't seem to be running at all from the start. They all give me a message like "3D support was not able to initialize" or something of the sort. I have installed directX 9 b aswell. Also, not sure if this is related, but my Internet explorer scrolls very slowly and jerkily when I am browsing the web. My graphics card is a Radeon 9200. Thanks much for any help. A:Games not running, Even with DirectX installed? 12 more replies Answer Match 42% I have Spyware Dr with Anti Virus engine as my primary protection. Can I download a freebie like Avira or MS Security Essentials, and just run a scan occasionally? I know I'm not supposed to run 2 AV programs simutaneously. Thanks. A:Solved: Can I have more than 1 AV installed, if not running simutaneously? 8 more replies Answer Match 42% Alright, This computer was built from parts found on newegg about a month ago. My sister's friend built it and added a spare copy of Vista 64-bit Business Edition in and it ran great. We weren't really going to bother with putting in the activation key because we figured we were just going to get Windows 7, when we could just easily buy it from our college bookstore for cheap. Unfortunately, they still don't have it in, so the activation expired, forcing us to fill in the activation key. Since the key was already used for himself, we couldn't use that. So we bought a 32-bit copy of Vista Ultimate for 15 dollars at the bookstore instead. And this is my problem now. We installed it, to find that it ran completely slow. Most of my friends are using the same version of vista as what I have here, and their computers were custom built with great parts. To try and describe the slowness as best as I could, I set up the CPUmeter on the gadgets sidebar. Just moving firefox around uses 28% of the CPU's usage. Again, completely wiped hardrive, basically a fresh start. So what im asking is, what should I do? Did i miss something when installing? Should I go with 64-bit? I don't see why its running this slow. If you need to know whats running this computer, just ask. A:Just installed Vista, running slow Hi - Wipe the entire hard drive with KillDisk and install the purchased copy of Vista x86 again. It is likely that remnants of the non-genuine Vista x64 remained behind. KillDisk - http://www.killdisk.com/downloadfree.htm Make bootable KillDisk ISO CD w/ ImgBurn - ImgBurn - http://www.imgburn.com/index.php?act=download Regards. . . jcgriff2 . 1 more replies Answer Match 42% IE launches on it's own. Computer keeps giving spyware alerts when no spyware detction software running. Norton antivirus detected downloader did all scans suggested adware spybot panda stinger I beleive I got most of the spyware although panda is giving cookies but could not complete full scan IE kept crashing before finished.Incident Status Location Adware:adware/coolsavings Not disinfected Windows Registry Spyware:Cookie/AdvancedCleaner Not disinfected C:\Documents and Settings\CNHI\Cookies\[email protected][1].txt Spyware:Cookie/Atlas DMT ... Read more A:Spyware Dection Running Not Installed Hi,I see you are running Teatimer.I suggest you to disable it because it can interfere with the changes you'll make on your system.When everything is done and your log is clean again, you can enable it again.If teatimer gives you a warning afterwards that some changes were made, allow this instead of blocking it.How to disable TeaTimer <== click me for instructions.After you disabled Teatimer, download ResetTeaTimer.bat to your desktop. (In case you use Firefox, rightclick the link and choose "save as").Doubleclick ResetTeaTimer.bat and let it run.This will only take a few seconds.I see you have Viewpoint installed...Viewpoint Manager is considered as foistware instead of malware since it is installed without users approval but doesn't spy or do anything "bad". This will change from what we know in 2006 read this article: http://www.clickz.com/news/article.php/3561546I suggest you remove the program now. Go to Start > Settings > Control Panel > Add/Remove Programs and remove the following programs if present.ViewpointViewpoint ManagerViewpoint Media PlayerThen, Hello,* Please download SmitfraudFix (by S!Ri)* Reboot into Safe Mode: ( without networking support !)?To get into the Safe mode as the computer is booting press and hold your "F8 Key". Use your arrow keys to move to "Safe Mode" and press your Enter key.* Doubleclick SmitFraudFix to start the tool.Select option #2 - Clean by typing 2 and press &q... Read more 2 more replies Answer Match 42% For the first time, I have now needed to connect to a USB 2.O port for a SanDisk Cruzer USB Flash Drive. It will work but at 1.O speed. A message appears "Hi speed USB Device attached to non hi-speed hub". I checked my motherboard's handbook and the ports that are being used are for USB 2.0. The motherboard manufacturer states that the drivers in my Service Pack 1 needed to be activated for the USB 2.O. However, using the automatic driver update function thru XP'S Device Manager indicates those installed are the most current. 1. How can I really check what version of USB drivers are really installed and the steps to do this? 2. What else can be wrong? Thanks A:MS Service Pack 1 Installed but USB 2.O Not Running I wouldn't look to MS to provide USB 2.0 drivers; rather I would get them direct from the M/B manufacturer. Also, consider the possiblity that your M/B doesn't support USB 2.0. This happened to me. Also (my favorite word), some M/B's have jumpers to enable/disable USB 2.0, as well as BIOS settings that do the same. I'd check BIOS first, to make sure it is enabled. Then verify that the M/B supports it. Then get manufacturer's drivers. Then start looking at the jumpers. 3 more replies Answer Match 41.58% Okay so after I installed windows xp home, I got the notice that says "You have 30 days to authenticate your windows" I installed the drivers/chipsets from my ASUS mobo CD (Including Ethernet Controller) so that I could authenticate it online. However, I still couldn't connect to the internet nor could I set up an internet connection. It kept saying you are not connected to the internet or something like that. I checked to make sure everything was plugged in correctly etc and everything was fine. So I retsrated my computer, only to run into another problem: Before I can log in, it says "You must authenticate Windows before you can log on." So my 30 days are up already? It doesn't make sense. Any help here? :/ A:Installed Windows XP Home, but I'm running into some problems. 6 more replies Answer Match 41.58% I just installed this font maker, and it is not going so well. I am doing my first one of my handwriting. The "A" is SMALL. I made it big too. Is there a way to fix it so the A takes up the whole box? Thanks. A:I just installed this font maker, I am already running into trouble. Well, "this font maker" isn't all that helpful, I'm sure that's not the name of the application. 2 more replies Answer Match 41.58% Hello everyone... sorry to bother you, but I am having technical difficulties I know this is a normal wmi process, what bugs me is that I have not downloaded or installed anything new, and it showed up by itself, for no reason. I end tasked it, and ran RKill, which showed no viruses... then ran Roguekiller and it showed 6 PUM.dns RogueKiller V11.0.13.0 (x64) [Feb 22 2016] (Free) by Adlice Software mail : http://www.adlice.com/contact/ Feedback : http://forum.adlice.com Website : http://www.adlice.com/software/roguekiller/ Blog : http://www.adlice.com Operating System : Windows 7 (6.1.7601 Service Pack 1) 64 bits version Started in : Normal mode User : Lenovo [Administrator] Started from : C:\Program Files\RogueKiller\RogueKiller64.exe Mode : Scan -- Date : 03/17/2016 16:12:35 ¤¤¤ Processes : 0 ¤¤¤ ¤¤¤ Registry : 6 ¤¤¤ [PUM.Dns] (X64) HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\Tcpip\Parameters | DhcpNameServer : 209.18.47.61 209.18.47.62 ([X][X]) -> Found [PUM.Dns] (X64) HKEY_LOCAL_MACHINE\System\ControlSet001\Services\Tcpip\Parameters | DhcpNameServer : 209.18.47.61 209.18.47.62 ([X][X]) -> Found [PUM.Dns] (X64) HKEY_LOCAL_MACHINE\System\ControlSet002\Services\Tcpip\Parameters | DhcpNameServer : 209.18.47.61 209.18.47.62 ([X][X]) -> Found [PUM.Dns] (X64) HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\Tcpip\Parameters\Interfaces\{53F4485D-24E0-478E-BE45-F... Read more A:Installed Avast... a while later unsecapp.exe started running Hello, Welcome to BleepingComputer.I'm nasdaq and will be helping you.If you can please print this topic it will make it easier for you to follow the instructions and complete all of the necessary steps in the order listed.===Download Malwarebytes' Anti-Malware from HereDouble-click mbam-setup-2.X.X.XXXX.exe to install the application (X's are the current version number).Make sure a checkmark is placed next to Launch Malwarebytes' Anti-Malware, then click Finish.Once MBAM opens, when it says Your databases are out of date, click the Fix Now button.Click the Settings tab at the top, and then in the left column, select Detections and Protections, and if not already checked place a checkmark in the selection box for Scan for rootkits.Click the Scan tab at the top of the program window, select Threat Scan and click the Scan Now button.If you receive a message that updates are available, click the Update Now button (the update will be downloaded, installed, and the scan will start).The scan may take some time to finish,so please be patient.If potential threats are detected, ensure that Quarantine is selected as the Action for all the listed items, and click the Apply Actions button.While still on the Scan tab, click the link for View detailed log, and in the window that opens click the Export button, select Text file (*.txt), and save the log to your Desktop.The log is automatically saved by MBAM and can also be viewed by clicking the History tab and then selecting Application Log... Read more 2 more replies Answer Match 41.58% Hello, I recently had an issue with my PC where I was unable to reboot successfully. I ended up putting my recovery (Dell) disks in and when everything was all said and done I guess it partitioned my drives. Now I have one drive with 10 GB and one with over 400GB. Unfortunately, the one that is now operational is the 10GB drive and I continue to run into space issues. I tried to extend my C drive to the D drive, but it won't let me (not an option). I tried to re-format the D drive to see if I could extend my C drive at that point, but that won't work either. Any ideas? I have attached a screen shot of my Disk Management situation. Also, just so you know there isn't anything that I really need on this PC that hasn't been backed up externally. Thanks for your help. Tom A:Solved: Re-installed Vista, now I'm running low on HD Space The recovery disks should automatically recreate the recovery partition on the drive. Otherwise, there is no cogent reason for having more than one partition. Did you see any options anywhere during the process for choosing where to install or partition sizes? It looks at first glance like the OS was installed to the smaller partition that should have held the recovery. You'll no doubt need to start over. If the option presents itself, make sure that you remove and rectraete the partitions that are there now. But..if you are happy with the way it is now aside from the partition sizes, you could simply resize them to suit you. A bootable partitioner could do that easily. Since you have the recovery disks, you also do not need the second partition at all, and you could merge them to make one large one. ******************************************* Parted Magic disk partitoning tool (Bootable CD image) If you prefer a bootable USB key, download and run Linux Live USB Creator. Choose the Parted Magic distro, and it will download it and automatically create a bootable USB key. This CD (or key) contains many useful tools. You can partition, recover files, recover lost partitions, make disk images (by several different methods), transfer files between media, scan for viruses (It can serve as an Alternative Trusted Platform for search and elimination of rootkits and bootkits), examine and benchmark hardware, access the internet, and much more. *******************************... Read more 2 more replies Answer Match 41.58% Hi, hope I will find some help here... I've just installed fresh Win 7 ultimate x64 via USB. Right from the start it was working really slow but it just got worse. My hardware is decent: Intel i7 CPU, 12GB RAM, WD Caviar 500GB system HDD. Task Manager shows that only 13% of RAM is being used and 0% of CPU. Still, I can barely work on it - it keeps freezing everytime I click on more than one window... Once I had to do a hard restart since it didn't want to shutdown normally, and then I got startup failure screen. Startup repair didn't do anything but it still managed to boot somehow. I tried to optimize win process but that didn't do anything either. I believe it might be the HDD, since I ran Win normally on other HDD with same hardware... But I did use current one as backup storage without a problem. Please give me suggestions, what should I do? Thanks! A:Newly installed Win 7 running slow on strong PC Work through these Troubleshooting Steps for Windows 7 - Windows 7 Forums 1 more replies Answer Match 41.58% I installed windows vista home premium from winxp and when i check the system it says the sond card is installed and operating but my volume icon says NO AUDIO OUTPUT DEVICE is installed. Any info would be appreciated More replies Answer Match 41.58% Googling has told me that a new program in my running program list (UAService7.exe) has been installed by a game I have recently installed (Lego Star Wars). This is apparently something to do with copy protection. It doesn't appear in the Programs startup folder, nor in the msconfig "startup" list, so I can't prevent it running. It apparently also stays behind after the game is uninstalled. I am really annoyed - I don't want or need this running on my computer (particularly as the game won't even work on my machine ) Does anybody know what this program is doing? How can preventing copying require a program to run on my computer all the time? A:Program Installed By Game - Running All The Time Here is a brief description.http://www.bleepingcomputer.com/startups/U...7.exe-8046.htmlHave you seen or tried the removal instructions found in the link below?http://forums.eu.atari.com/archive/index.php/t-35766.html 4 more replies Answer Match 41.58% Logfile of Trend Micro HijackThis v2.0.2Scan saved at 4:46:10 PM, on 11/22/2007Platform: Windows XP SP2 (WinNT 5.01.2600)MSIE: Internet Explorer v7.00 (7.00.5730.0013)Boot mode: NormalRunning processes:C:\WINDOWS\System32\smss.exeC:\WINDOWS\system32\csrss.exeC:\WINDOWS\system32\winlogon.exeC:\WINDOWS\system32\services.exeC:\WINDOWS\system32\lsass.exeC:\WINDOWS\system32\svchost.exeC:\WINDOWS\system32\svchost.exeC:\WINDOWS\System32\svchost.exeC:\WINDOWS\System32\svchost.exeC:\WINDOWS\Explorer.EXEC:\WINDOWS\System32\svchost.exeC:\WINDOWS\system32\spoolsv.exeC:\PROGRA~1\Grisoft\AVG7\avgamsvr.exeC:\PROGRA~1\Grisoft\AVG7\avgupsvc.exeC:\PROGRA~1\Grisoft\AVG7\avgemc.exeC:\Program Files\Common Files\Microsoft Shared\VS7DEBUG\MDM.EXEC:\Program Files\Spyware Doctor\svcntaux.exeC:\Program Files\Spyware Doctor\swdsvc.exeC:\Program Files\Spyware Doctor\SDTrayApp.exeC:\WINDOWS\system32\wscntfy.exeC:\WINDOWS\SOUNDMAN.EXEC:\WINDOWS\AGRSMMSG.exeC:\Program Files\Adobe\Acrobat 6.0\Distillr\acrotray.exeC:\WINDOWS\system32\WgaTray.exeC:\WINDOWS\System32\alg.exeC:\Program Files\BitComet\BitComet.... Read more A:Pc Is Running Slow After Installed Spyware Doctor One more problem, i'm currently using the 'Registry Cleaner' that included in Ashampoo WinOptimizer 4. The problem is everytime i click on 'Delete Entries', a msg will pop-up saying: "0 of the selected 324 Registry entries deleted successfully. However, 324 selected entries could not be deleted! Please close any running applications and try again." i have tried many times, but still failed to delete those entries. Is it normal??? 10 more replies Answer Match 41.58% Hey, My XpertVision 7900GS graphic card went dead on me a few backs ago so I sent it for RMA and they upgraded it with a Palit 9600GT.. I think it's a refurbished one but nevermind anyways.. However, It's not working with my computer.. Can anyone help me on this ? My computer won't boot up and gives beeping sounds when i installed the graphic card. I've already tried this graphic card on my friend's computer to see if the problem is with it but it worked on his. So I'm guessing It's either my PSU or Motherboard.. But then again I read online somewhere that someone is using 400w and it's working for him. I'm using 430w .. Below are details to my PSU, Motherboard and the Graphic card. Cooler Master RS-430-PCAR Gigabyte GA-965P-DS3P(rev 2.0) Motherboard Palit 9600GT PCI-E 512MB DDR3 More replies Answer Match 41.58% The cooling Fan is permanently on after upgrading to Windows 10. This is the case for balanced mode, but also in ECO mode (Activated on the touchpad). Both modes are set to passive cooling when running on battery.... I have tried to enable/disable relevant power settings in Win 10 and the ECO utility, but the fan keeps running - It seems as if Win10 is overruling the Toshiba ECO utility. Everything worked perfectly before the upgrade. Can this issue be solved or do I have to wait for an update of the utility from Toshiba? /Breinholm A:Cooling fan keeps running on Satellite Z30B after Win 10 is installed I do not know if this can help but try to reinstall ECO utility. Visit pleasehttp://win10upgrade.toshiba.com choose your country and you should be able to find link for drivers, tools and utilities download 6 more replies Answer Match 41.58% My norton trial which just ran out yesterday says i have no viruses. Yet my comp is slow compared to when it was new. Also i will sometimes see a huge spike in memory usage. Even though i didn't actually start any new processes. Also i installed combofix and ran it already. Didn't read the entire page so didn't know i wasn't suppose to. A:Just installed a new HDD but my comp is still running slow and sometimes restarting it's self. Please help 4 more replies Answer Match 41.58% I just installed the new updates and now computer is real slow More replies Answer Match 41.58% I just recieved my pre-order of spore on Friday and couldn't wait to play it. After the installation and the read me and registration I double clicked the spore icon on my desktop waiting for a splash screen, a black screen, or a window to appear. None appeared. I thought that I just need to wait a while so I waited for about ten minutes before I opened task manager and looked at the processes, and wouldn't you know SporApp.exe is running using 63,000KB of memory. At this point I have no idea what's wrong. I try uninstalling and re installing. I try defragmenting my disk, and running it on other accounts. I've even done a repair of windows to see if that helped but it didn't. After searching the web for answers I found this site which had a thread that adressed a similar problem. I followed the advice and found that when Microsoft's Plug and Play was disabled that I could run spore, but now there's no sound. And to make it worse when I open device manager it shows up empty. Also there's no speaker icon in the system tray. Additionally I've just installed a new game to see if I just got a bad copy of spore. And it has the same problem it won't start unless plug and play is disabled. But with this game the splash screen appears and a warning message appears saying my sound drivers are being used and I need to shut down any programs that are using it but there are no other programs running and the speaker isn't in the sys... Read more More replies Answer Match 41.16% Hi, My laptop is a Dell Inspiron 510m with Windows Xp .... It is about 5 or 6 yrs old and quite well used.. Unfortunately it is not running very well lately... and it is slow at loading webpages at times... but in particular on websites like yahoo.. I am lately having problems sending emails... and running videos say on youtube in particular if I have say more than 3 or 4 webpages open... Often it will not play video if I have been using the computer for sometime... I even have problems posting on even on here....or other forums.. I often have to copy the wording ,open another page and paste. and post on the 2nd page...to send a post.. Im not sure if it may be my wifi...or my computer.... although wifi appears connected. Sometimes my computer crashes when using Adobe flash.. I have ran several Antivirus and spyware malware programs over the last few months.. such as Trend Micro...and Avira, Malwarebytes and Spybot... My Disc is quite full..so this may be one of the reasons why I am having problems... BUT I have had it almost full in the not too distant past and it had ran reasonably OK.. and I did not have the problems with yahoo or sending emails from yahoo... sometimes the computer just freezes up completely..and I cannot turn it off as usual.. so I have to switch it off by unplugging it.. It runs reasonable if I only have a few webpages open..and usually after I have reloaded it. BUt it takes a long time to reload...and I get somethings that show up that... Read more A:Slow running Laptop running on Windows XP Sorry for posting the same thread 3 times... Due to part of my problem... when I try to post... It doesn't not acknowledge.. to me that it posted...and I had to copy and paste it to another open page... Only later did I see I had posted it 3 times... 4 more replies Answer Match 41.16% I have the following user accounts created in my PC. A ( admin account ) B ( limited account ) I have created the B ( limited ) account for security purpose. Issue : I can access all the programs ( Start > All Programs ) in the A account but, some of the installed programs are not listed and not running in B. Following applications are not listed. 1.Ccleaner 2.Vista inspirat brico pack ( vista visualisation for xp ). It is not working in B account. ...etc Could you suggest me a solution for this? A:Some installed programs not listed and running in another user account? Just visit the limited account and download / install the desired program . Unless I am not reading things right this will work . If you have any trouble just change the limited account to an administrative account and download the desired program then change back to a limited account . 2 more replies Answer Match 41.16% Logfile of Trend Micro HijackThis v2.0.5 Scan saved at 1:02:44 PM, on 1/3/2016 Platform: Unknown Windows (WinNT 6.02.1008) MSIE: Internet Explorer v11.0 (11.00.9600.18123) FIREFOX: 43.0.3 (x86 en-US) Boot mode: Normal Running processes: C:\Program Files (x86)\eMule\emule.exe C:\Program Files (x86)\Internet Download Manager\IDMan.exe C:\Program Files (x86)\Skype\Phone\Skype.exe C:\Program Files (x86)\Internet Download Manager\IEMonitor.exe C:\Program Files (x86)\Lenovo\MotionControl\MotionControl.exe C:\Program Files (x86)\Lenovo\YouCam\YCMMirage.exe C:\Program Files (x86)\JRT Studio\Cheetah Sync\CheetahSync.exe C:\Program Files (x86)\Lenovo\Lenovo Smart Update\Lenovo Smart Update.exe C:\Program Files (x86)\Evernote\Evernote\EvernoteClipper.exe C:\ProgramData\1c1e4ef3-a4fe-42a4-a546-08f69e47d2d1\plugins\7\plugin.exe C:\Program Files (x86)\Evernote\Evernote\Evernote.exe C:\Program Files (x86)\Evernote\Evernote\EvernoteTray.exe C:\ProgramData\1c1e4ef3-a4fe-42a4-a546-08f69e47d2d1\plugins\3\plugin.exe C:\ProgramData\1c1e4ef3-a4fe-42a4-a546-08f69e47d2d1\plugins\12\plugin.exe C:\WINDOWS\SysWOW64\rserver30\FamItrfc.Exe C:\ProgramData\48ed1695-d484-472b-bd42-582714ef1368\plugins\12\plugin.exe C:\Program Files (x86)\Google\Chrome\Application\chrome.exe C:\Program Files (x86)\Google\Chrome\Application\chrome.exe C:\Program Files (x86)\Google\Chrome\Application\chrome.exe C:\Users\Imran\Downloads\Programs\HijackThis.exe C:\Program Files (x86)\Google\Chrome\Application\chrome.exe C:\Pro... Read more More replies Answer Match 41.16% Hi, I've been having problems with games crashing with c0000005 as soon as I run them. This isn't happening with games I've had installed for a while, it has only started when i've tried to install new games in the last month or so. I've attached my files from the SF tool. I was wondering if anyone had any pointers? Thanks in advance. A:c0000005 errors when running newly installed games Hi, Welcome to Seven forums. A C0000005 Error is a Windows System error, not a VFP Error. It is an Exception Error that occurs when a process (application, driver, etc.) tries to execute a processor command that references memory outside the space allocated to that process by the Operating System. There are many possible causes ranging from corrupt data tables, to a bad network connection, ActiveX controls, or Printer or Video driver errors. And from the attached files, I will suggest you to install/update DirectX. Please update your system specs. Update the drivers for graphic card and sound. Keep us posted. 1 more replies Answer Match 40.74% My Norton expired so I went with the complimentary McAfee program via Comcast, and my internet has substantially slowed down to the point where pages and pictures won't fully load and I lose my connection with online applications. Before I switched security programs, as in earlier that day, everything was fine. I have run the virus checker, adaware, spybot, Ccleaner, and am still eking by. I did a speed test and got a reading around 2000kbps with a ping of about 180. Also, it seems my puter keeps churning as though it's doing something, even when it shouldn't be, in a cycle of about every 5 seconds (CPU light runs and the rattling sound occurs). I can't seem to figure out what may be causing this.Additionally, when I surf the net, using Firefox, all of the ads show up, despite the fact that McAfee's box to remove the ads is checked (I tried unchecking it and problem remained).Anyone know what could be the problem? Thanks for any help, this is driving me cuckoo. Mod Edit: Topic moved to more appropriate forum~ TMacK A:Installed Mcafee (uninstalled Norton), Computer Running Slower Anyone know what could be the problem? I would guess McAffee. Dump it. If you want a free AV program there's several to be had.I've found NOD32, although not free, to be very compatible and uses very little system resources. You could use it for a 30 day trail and see if your computer runs fine with it. 12 more replies Answer Match 40.74% I bought an M17x R3 Alienware laptop recently, and after I tried to play Star wars of the Old Republic, the game would not play. After seeking help on this issue, I was told that my graphics card is not fast enough to keep up with the startup of this game and suggested that I install an Nvidia card. I bought an Nvidia card and installed it(realizing that an Nvidia card was ALREADY installed) After startup the computer is running extremely slow. I took the computer to get it checked out and they said they are unable to fix the issue. I am not sure if the correct driver needs to be installed, or if it's a bad card, or if its not compatible with my laptop. can someone shed some light on this issue please? A:660M 2gb Nvidia installed in M17X R3 and now computer is running slow Your nvidia card is supposed to take over when gaming, when the system needs it. Was it doing that ? They cant fix it ? Morons I would put it back the way it was, and make sure the latest drivers from the laptops manufacterers website or from nvidia are installed, and try the game again at a lower setting. 3 more replies Answer Match 40.74% My desktop is running super slow after my sister got the idea from a friend to use Ares to get music. I frown on this, but I believe I removed it completely. I cannot seem to get the computer back to normal speed though. It is a 160GB HDD, with only about 30-40gigs used. I'm not sure exactly what the problem is, but I've heard you can get keylogging programs from p2p programs like Ares. So, I need to just check for and remove anything that is bad for this computer and slowing it down massively. Thanks for your help, time is kinda of the essence because I need this for school and don't want to use any of my passwords. Here is a Hijackthis log: Logfile of Trend Micro HijackThis v2.0.2 Scan saved at 2:26:09 PM, on 3/14/2011 Platform: Windows XP SP3 (WinNT 5.01.2600) MSIE: Internet Explorer v8.00 (8.00.6001.18702) Boot mode: Normal Running processes: C:\WINDOWS\System32\smss.exe C:\WINDOWS\system32\winlogon.exe C:\WINDOWS\system32\services.exe C:\WINDOWS\system32\lsass.exe C:\WINDOWS\system32\svchost.exe C:\WINDOWS\System32\svchost.exe C:\WINDOWS\SYSTEM32\ZoneLabs\vsmon.exe C:\WINDOWS\Explorer.EXE C:\WINDOWS\system32\spoolsv.exe C:\Program Files\Common Files\ArcSoft\Connection Service\Bin\ACService.exe C:\Program Files\Common Files\Apple\Mobile Device Support\AppleMobileDeviceSe... Read more A:Computer is running super slow; sister installed Ares to use Hello and welcome to Bleeping ComputerWe apologize for the delay in responding to your request for help. Here at Bleeping Computer we get overwhelmed at times, and we are trying our best to keep up. Please note that your topic was not intentionally overlooked. Our mission is to help everyone in need, but sometimes it takes just a little longer to get to every request for help. No one is ignored here.Please take note:If you have since resolved the original problem you were having, we would appreciate you letting us know. If you are unable to create a log because your computer cannot start up successfully please provide detailed information about your installed Windows Operating System including the Version, Edition and if it is a 32bit or a 64bit system. If you are unsure about any of these characteristics just post what you can and we will guide you.Please tell us if you have your original Windows CD/DVD available.If you are unable to perform the steps we have recommended please try one more time and if unsuccessful alert us of such and we will design an alternate means of obtaining the necessary information.If you have not done so, include a clear description of the problems you're having, along with any steps you may have performed so far.Upon completing the steps below another staff member will review your topic an do their best to resolve your issues.If you have already posted a DDS log, please do so again, as your situation may have changed.Use the 'Add Reply'... Read more 2 more replies Answer Match 40.74% Ok, have installed game and it is running as background sound is working but cannott see to go any further to enter key codes, etc.. and actually play. My 11yr old is having a fit because dad can't get it going. System specs: P4 2.4ghz, 1024mb ddr, XP pro sp2, Nvidea GEforce 4 MX440 64mb ddr, SB LIve, Direct X 9.0c Have updated all drivers and direct x making sure all A/V protection turned off etc... tried changing the resolution around and playing with video settings all to no avail. Still getting the fuzzy screen of colors and sound only. Seems like a simple setting fix, but just haven't figured it out yet. Any help is most appreciated. Thanks in advance. Lou A:Guild wars installed & running but cannott see through fuzzy display You may want to check out the official Guild War Technical issues forum if no one here can help: http://forums.gwonline.net/forumdisplay.php?f=128&page=1&sort=lastpost&order=&pp=20&daysprune=365 The forum looks pretty active so you should be able to get some help. I don't have the game, myself, so I can't really help you out too much here, sorry... 1 more replies Answer Match 40.74% Dear Friends in Seven forums. I recently installed Windows 7 different versions of it home - professional - enterprise. However I encounter this problem no matter which version is installed. I cannot run *.exe files or any other type of file . each time that I run a program an error pops up like this screen capture jpeg that I have attached to this tread. thank god paint was working. this is when I have not even installed any of drivers. before I thought maybe the drivers installations mess up with my system but apparently not. before this When I was running the drivers installation CD it was OK with installing the majority of drivers . but as soon as I wanted to instal something from usb or the first time that I opened the IE. I encountered this type of problem. and the windows explorer automatically restarts it self. please help me as I'm desperate and I need my computer working asap . thank you very much\ Al A:freshly installed win 7 build 7601 - problems with running files (all) Quote: Originally Posted by arkcamon I recently installed Windows 7 different versions of it home - professional - enterprise. Lets start here: 1. Download and save this tool to your desktop: http://go.microsoft.com/fwlink/?linkid=52012 2. Run the tool, and then click 'Copy' - ignore any errors if they appear 3. Use CTRL+V to paste the unedited results of the validation tool here in your next reply Regards, Golden 9 more replies Answer Match 40.74% Hi after switching from win xp to win 7 I decided on installing a good graphic card on my compaq presario SR1135cl so I got me a ATI radeon HD4670 1024mb agp card now my issue is while the card is installed the computer will not power up when I removed the card the comp power fine what do you think is going on? A:SR1135cl running win 7 wont power up with ATI radeon HD4670 installed The pc does absolutely nothing when you press the power button ? 3 more replies Answer Match 40.74% I've just brought this PC running Win7 64bit and recently the computer started to freeze. I when thought event viewer and could not find anything which stood out to me apart from system shutdown which was caused by me, as I had to hold the power button to get out of the freeze. The computer had started to Blue Screen, I've been through msconfig, I've even disabled the wireless card and only used the Ethernet cable. I thought it may have been the power in the house, therefore went out and brought a Surge Protector but the PC still keeps on crashing. I've attached the dump files. Any advice would be appreciated. A:BSOD & Freezes. Installed surge master... running out of ideas :( Hi Music46. 100% Guaranteed!! Your dump files all give a stop error of 0x7F. Its a stop error that ZoneAlarm firewall gives frequently and involves the NETIO.sys system driver. You have two (?) options: ZoneAlarm Firewall is known to be a cause of BSOD's on many Windows 7 systems. Download the ZoneAlarm Remover - http://download.zonealarm.com/bin/fr...cpes_clean.exe. Uninstall ZoneAlarm through Programs and Features. Boot to safe mode and run the ZoneAlarm Remover. Reboot. Make sure that Windows Firewall is enabled. Alternatively Try this Microsoft hotfix if you wish to keep ZoneAlarm: Stop Error 0x07F when you run apps. that transfer data by the UDP protocol in Win 7. I can neither verify or discount this fix. It may work, it may not. Your latest dump file blames NETIO.SYS which is a Windows System file and is highly unlikely to be the cause. Old and incompatible drivers can and do cause issues with Windows 7, often giving false error codes. Outdated Drivers. Update: lmimirr.sys Tue Apr 10 23:32:45 2007 LMIRfsDriver.sys Mon Jul 14 17:26:56 2008 RaInfo.sys Fri Jan 04 18:57:14 2008 LogMeIn/RemotelyAnywhere. Update or uninstall. DDCDrv.sys Tue Apr 08 08:50:11 2008 WINI2C-DDC Kernel Mode Driver AtiPcie.sys Tue May 05 16:00:22 2009 ATI PCIE Chipset Driver. Go to Mobo Mfr. or AMD Drivers with Updates: Rt64win7.sys Fri Nov 27 09:45:07 2009 Realtek PCIe GBE Family Controller 7.037 Bugcheck Analysis Code: Loading Dump File [C:\DUMPS\Music46\020911-13650-01.d... Read more 9 more replies Answer Match 40.74% Hello, hope someone can help me please, am struggling a bit with this one as i know something is not quite right but i don't know what it is. ran a repair (f8) on bootup and got these resuts prob sig 01 6.1.7600.16385 02 6.1.7600.16385 03 unknown 04 181 05 manual repair 06 1 07 no root cause os version 6.1.7600.2.0.0.256.1 locale ID 1033 ran a sfc /scannow and got these results (cbs.log attached) if there is anyone skilled at deciphering these cbs logs i would appreciate some help cheers BlindMan More replies Answer Match 40.32% Hey, thanks in advance for your help. I just installed a second hard drive into my PC (because the external case i had it in wouldnt turn on all of a sudden) and pc started doing something weird. My PC was running SO SO SLOW, I coudln't get My COmputer to open, and it kept popping up to say that folder on my hard drive are "corrupt and unreadable". I restarted the PC, and that disc check thing started running (you know that thing you usually press any key to skip when you havent turned the PC off properly). Then it went through every file on my drive saying stuff like "Recovering Orphaned File" and "index error on$130". That has finnised now and windows has loaded, it's not telling me folders are corrupt, but i still can't get MY Compuer to open, and Windows is running rediculously slow. It's 5 mins for notepad to open. The start menu runs like normal, but everything else is rediculous.
Just to clarify, windows and all software is running of the original hard drive (40GB) not the new one (250GB)
I'm failry sure all the ribbon cables are connected. I paid particular attention to that. I can't partition and format the hard drive because I have vital information on it that I CAN NOT loose. I'm a 3rd year multimedia student, and all my assignemnts (on the drive) are due in 3 days. I THINK that the 40GB drive is FAT32 and the 250GB is NTFS, as far as I know. I'm running Windows XP Pro (originally came with W... Read more
A:URGENT HELP NEEDED! installed 2nd hard drive. PC running stupidly slow
To be honest, it doesn't sound good. I assume that the drive with the errors was the former external drive with your class assignments on it. Have you tried disconnecting the second drive and booting to Windows to see if it runs normally?
2 more replies
Answer Match 40.32%
I installed a downloaded version of Starcraft and later read in the description (after I had installed it, unfortunately) of the download that some people found a keylogger installed on their computer. I looked in the C:\Users\John\AppData\Local\Temp folder and saw the program that they were claiming was the keylogger; it was named *wsy.dll with a string of random numbers in place of the asterisk. I then uninstalled Starcraft and the file disappeared. Later, I noticed some unusual programs (the ones listed in the title) running under processes, but couldn't find a way to remove them. I would like to be completely sure that the keylogger has been removed. On a separate issue, when I tried to run GMER I received an error and GMER was unable to perform a scan. The error read, "C:\Windows\system32\config\system: The system cannot find the file specified".DDS (Ver_09-12-01.01) - NTFSX64 Run by John at 1:52:19.02 on 27-Feb-10Internet Explorer: 8.0.7600.16385Microsoft Windows 7 Ultimate 6.1.7600.0.1252.1.1033.18.4093.2563 [GMT -5:00]============== Running Processes ===============C:\Windows\system32\wininit.exeC:\Windows\system32\lsm.exeC:\Windows\system32\svchost.exe -k DcomLaunchC:\Windows\system32\nvvsvc.exeC:\Windows\system32\svchost.exe -k RPCSSc:\Program Files\Microsoft Security Essentials\MsMpEng.exeC:\Windows\Syste... Read more
A:Keylogger possibly installed. Also, winlogon.exe, nccsvc.exe, and csrss.exe running in processes.
Hello and welcome to Bleeping ComputerWe apologize for the delay in responding to your request for help. Here at Bleeping Computer we get overwhelmed at times, and we are trying our best to keep up. Please note that your topic was not intentionally overlooked. Our mission is to help everyone in need, but sometimes it takes just a little longer to get to every request for help. No one is ignored here.If you have since resolved the original problem you were having, we would appreciate you letting us know. If not please perform the following steps below so we can have a look at the current condition of your machine. Please include a clear description of the problems you're having, along with any steps you may have performed so far.Please refrain from running tools or applying updates other than those we suggest while we are cleaning up your computer. The reason for this is so we know what is going on with the machine at any time. Some programs can interfere with others and hamper the recovery process.Even if you have already provided information about your PC, we need a new log to see what has changed since you originally posted your problem.We need to create an OTL ReportPlease download OTL from one of the following mirrors:This is THE MirrorSave it to your desktop.Double click on the icon on your desktop.Click the "Scan All Users" checkbox.In the custom scan box paste the following:CODEnetsvcsmsconfigsafebootminimalsafebootnetworkactivexdrivers32%systemroot%�... Read more
4 more replies
Answer Match 39.06%
When I'm surfing the internet(this site for example), some friend of mine will say something through AIM(Aol Instant Messenger).. and it appears to crash my puter.. sometimes giving me a blue screen.. other times it just hangs.
My question is.. does anybody else have these problems or is just me? Is AIM buggy or is it probably something else installed on my computer.
I downloaded AIM about a week ago.. and that is when the problem started, although I download lots of stuff all the time. <BR
All comments are appreciated!!
Jake
A:Is AIM buggy?
8 more replies
Answer Match 39.06%
My AIM often logs me out and back in. I am only aware because my online buddies sign in over and over again, but they haven't really left. On their end, I appear to be signing off and on. Messages I send may or may not be received by my buddy due to this issue. I have the current version, have uninstalled/reinstalled several times, have had the same problem with older versions also. Have read all the AIM faqs (nothing helpful). Am running on WIN XP. Problem exists on my laptop also! Tried creating new screen name, no help. Connected via Verizon DSL. Also occassionally get error msg. that I am logged on in multiple locations, which is absolutely false. I have to close AIM and restart to correct that. Don't know that the problems are related, but thought I'd mention it...
Can't seem to figure out what triggers the problem but it sure is annoying! Any suggestions would be most appreciated.
More replies
Answer Match 39.06%
Alright,...now I sign on AIM like any normal person would right? then I talk to people for about six minutes...everythings fine...and then my aim gets all wierd.The IM windows I opened will work just as they should..but say I want to IM someone else...the IM window coems up all funny.Everything...the profile,font tabs,etc..are are shifted to the right.I can still type to people, and theyll still recieve the messages, but when they IM me back the window will stay the same.Alright, look at how the window is when you are typing to someone first.They havent said anything, the window is just of what youre typing and all the tabs..etc.Its the same thing...except when they type back the window wont show what they typed.The buddy list is pretty much the same..except i run on 5.9 and i have 2 screen names going, and when I click my other buddy list, it wont do anything.If i want to keep talking tp people i have to restart my computer...and that is very annoying,being that this happens ALOT(im talking about every 5,6 minutes).And by the way, I have Windows 98.
Any help is VERY MUCH appreciated, so please do your best.
Thanks
A:Buggy AIM...please help
anyone?
2 more replies
Answer Match 39.06%
I have run adaware, spybot and still have some buggy problems. I know there are still some issues I can't identify. Here is my HJT log created with the analyzer:
====================================================================
Log was analyzed using KRC HijackThis Analyzer - Updated on 4/1/05
Get updates at http://www.greyknight17.com/download.htm#programs
***Security Programs Detected***
C:\PROGRAM FILES\COMMON FILES\SYMANTEC SHARED\CCEVTMGR.EXE
C:\PROGRAM FILES\COMMON FILES\SYMANTEC SHARED\CCSETMGR.EXE
C:\PROGRAM FILES\COMMON FILES\SYMANTEC SHARED\CCPROXY.EXE
C:\PROGRAM FILES\COMMON FILES\SYMANTEC SHARED\SNDSRVC.EXE
C:\PROGRAM FILES\COMMON FILES\SYMANTEC SHARED\CCAPP.EXE
C:\PROGRAM FILES\COMMON FILES\SYMANTEC SHARED\CCPD-LC\SYMLCSVC.EXE
O2 - BHO: Web assistant - {9ECB9560-04F9-4bbc-943D-298DDF1699E1} - c:\Program Files\Common Files\Symantec Shared\AdBlocking\NISShExt.dll
O2 - BHO: NAV Helper - {BDF3E430-B101-42AD-A544-FADC6B084872} - c:\Program Files\Norton AntiVirus\NavShExt.dll
O3 - Toolbar: Web assistant - {0B53EAC3-8D69-4b9e-9B19-A37C9A5676A7} - c:\Program Files\Common Files\Symantec Shared\AdBlocking\NISShExt.dll
O3 - Toolbar: Norton AntiVirus - {42CDD1BF-3FFB-4238-8AD1-7859DF00B1D6} - c:\Program Files\Norton AntiVirus\NavShExt.dll
O4 - HKLM\..\Run: [ccApp] "c:\Program Files\Common Files\Symantec Shared\ccApp.exe"
O4 - HKLM\..\Run: [Symantec Core LC] C:\Program Files\Common Files\Symantec Shared\CCPD-LC\symlcsvc.exe start
O4 - HKLM\... Read more
A:Still buggy...can you help?
Please print out or copy this page to Notepad. Make sure to work through the fixes in the exact order it is mentioned below. If there's anything that you don't understand, ask your question(s) before proceeding with the fixes. You should not have any open browsers when you are following the procedures below.
Go to My Computer->Tools/View->Folder Options->View tab and make sure that 'Show hidden files and folders' (or 'Show all files') is enabled. Also make sure that 'Display the contents of system folders' is checked.
For the options that you checked/enabled earlier, you may uncheck them after your log is clean. If we ask you to fix a program that you use or want to keep, please post back saying that (we don't know every program that exists, so we may tell you to delete a program that we think is bad to keep).
Reboot into Safe Mode (hit F8 key until menu shows up). Make sure to close any open browsers.
Run a scan in HijackThis. Check each of the following and hit 'Fix checked' (after checking them) if they still exist (make sure not to miss any):
O4 - HKLM\..\Run: [hkyvacm] c:\windows\system\hkyvacm.exe
O4 - Startup: OCRAWARE.lnk = C:\WINDOWS\CVTAPLOG.EXE
O16 - DPF: {1C854D5E-66D9-11D3-81DD-00A0C9B62983} (TestX Class) - http://209.1.231.142/Plugin/3DGreetings/PlayerX.CAB
O16 - DPF: {52290B25-D07A-43B5-84D8-493116D50FA0} - http://webinstall.tscash.com/webinstall.cab
O16 - DPF: {90C9629E-CD32-11D3-BBFB-00105A1F0D68} (InstallShield Inter... Read more
10 more replies
Answer Match 39.06%
im running win7 64bit and since i upgraded my ie to 9 it seams odd i keep getting notice program crashed and other things where it wont load things like in facebook and when u tell it its ok it resets the page. just wondering if anyone else is having this much trouble with it.
Alice
A:IE9 is so Buggy
Sounds like your security settings in the browser are set a little higher than may be required.
Here's a simple first step for you.
Change Internet Explorer 9 Security settings
9 more replies
Answer Match 39.06%
Ever since I got the .105 patch, it's been anything BUT a patch. It's like the .103 patch was ripped and all the issues came out. I have a 640 and is anyone having any issues? From apps not opening to a sudden just almost breakdown on the OS....its really annoying.
A:Buggy OS
No new issues here on 950xl.
1 more replies
Answer Match 39.06%
Starmaker Version 4.0.0 Is So Buggy! It's Slow,Domain Errors,And Dosent Show Up In Game Center Anymore Along With The Voice. So Buggy! I Am Using It On My IPhone 5S With Ios8.1.1
More replies
|
2018-09-21 16:20:05
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24579085409641266, "perplexity": 3921.4174469297845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267157216.50/warc/CC-MAIN-20180921151328-20180921171728-00089.warc.gz"}
|
http://www.math.uiuc.edu/~pinghu1/opengl/opengl.html
|
# U of I Math Ping Hu
Homogeneous Coordinates in OpenGL
There are three fundamental transformations: Translation, Scaling and Rotation. And in OpenGL, there are corresponding functions.
Translation: glTranslate(x,y,z) produces a translation by $(x,y,z)$. For example, the vertex $(a,b,c)$ will be translated to $(a+x,b+y,c+z)$.
Scaling: glScale(x,y,z) produces a nonuniform scaling along the x, y, and z axis.The three parameters indicate the desired scale factor along each of the three axes. For example, the vertex $(a,b,c)$ will be scaled to $(ax,by,cz)$.
Rotation: glRotate(angle, x, y, z) produces a rotation of angle degrees around the vector $(x,y,z)$. But when we use this function, we usually set one of $x,y,z$ be $1$ and others be $0$. For example, glRotate($\alpha, 1, 0, 0$) means a rotation about $x$-axis of $\alpha$ degrees.
In OpenGL, you need to compute the composition of some transformations, so all these transformations are denoted by transformation matrices. Then when we compute the composition, what we really do is multiply several matrices, which can be accelerated by hardware. Because of this, we want to use Homogeneous Coordinates $(x,y,z,w)$ instead of Cartesian Coordinates $(x,y,z)$. Here the homogeneous coordinate $(x,y,z,w)$ is $(x/w,y/w,z/w)$ in cartesian coordinate when $w\ne 0$. And when $w=0$, it means an infinity point and this infinity point is obtained by moving the point $(x,y,z)$ to infinity along the vector $(x,y,z)$.
The reason we use Homogeneous Coordinates is by using this instead of Cartesian Coordinates, we can denote every transformation by a $4\times 4$ matrix. For Cartesian Coordinates $t=(x,y,z)$, if $M$ is a $3\times 3$ matrix, then $tM$ cannot be a translation of $t$. But in Homogeneous Coordinates, glTranslate(x,y,z) can be denoted by $\left(\begin{array}{cccc}1 & 0 & 0 & x \\0 & 1 & 0 & y \\0 & 0 & 1 & z \\0 & 0 & 0 & 1\end{array}\right)$ becasue $\left(\begin{array}{cccc}1 & 0 & 0 & x \\0 & 1 & 0 & y \\0 & 0 & 1 & z \\0 & 0 & 0 & 1\end{array}\right)\left(\begin{array}{c}a\\b\\c\\1\end{array}\right)=\left(\begin{array}{c}a+x\\b+y\\c+z\\1\end{array}\right)$. And similarly, glScale(x,y,z) can be denoted by $\left(\begin{array}{cccc}x & 0 & 0 & 0 \\0 & y & 0 & 0 \\0 & 0 & z & 0 \\0 & 0 & 0 & 1\end{array}\right)$ glRotate($\alpha, 1, 0, 0$): $\left(\begin{array}{cccc}1 & 0 & 0 & 0 \\0 & \cos \alpha & -\sin\alpha & 0 \\0 & \sin\alpha & \cos\alpha & 0 \\0 & 0 & 0 & 1\end{array}\right)$ glRotate($\alpha, 0, 1, 0$): $\left(\begin{array}{cccc}\cos \alpha & 0 & \sin\alpha & 0 \\0 & 1 & 0 & 0 \\-\sin\alpha & 0 & \cos\alpha & 0 \\0 & 0 & 0 & 1\end{array}\right)$ glRotate($\alpha, 0, 0, 1$): $\left(\begin{array}{cccc}\cos \alpha & -\sin\alpha & 0 & 0 \\\sin\alpha & \cos\alpha & 0 & 0 \\0 & 0& 1 & 0 \\0 & 0 & 0 & 1\end{array}\right)$
|
2015-05-26 03:29:07
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9786075949668884, "perplexity": 353.06553220350867}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928757.11/warc/CC-MAIN-20150521113208-00202-ip-10-180-206-219.ec2.internal.warc.gz"}
|
https://sinews.siam.org/Details-Page/tensor-decomposition-a-mathematical-tool-for-data-analysis
|
SIAM News Blog
SIAM News
Tensor Decomposition: A Mathematical Tool for Data Analysis
Tamara G. Kolda, Sandia National Laboratories.
Data analysis requires a variety of tools, and one of the foundational tools for unsupervised analysis and data reduction is principal component analysis (PCA). Researchers use PCA to analyze data matrices where the rows correspond to objects and the columns correspond to features, so that the $$i,j$$ entry is the measure of feature $$j$$ for object $$i$$. After some preprocessing, PCA then reduces to apply the singular value decomposition to the matrix. We can use the resulting matrix factors for data interpretation, unsupervised learning, dimensionality reduction, completion of missing entries, and more.
The problem occurs when deciding how to handle data that is not two-way. Imagine the previous scenario (object and features), except that now we take repeated measurements in time; this becomes a three-way data array. We could average the features over time or just stack them all together, but these solutions tend to be unsatisfactory because understanding the relationships influenced by the time dimension becomes impossible. Using tensor decompositions, an extension of PCA to higher-order data, is the alternative. In fact, we need not stop at three-way data, but can handle four-way, five-way, and much higher as well. There are a variety of tensor decompositions, but I focus on canonical polyadic (CP) tensor decomposition, introduced by Frank Lauren Hitchcock in 1927 but nearly lost to history until its rediscovery in 1970 under the name CANDECOMP by J. Douglas Carroll and Jih-Jie Chang and the name PARAFAC by Richard A. Harshman.
During the SIAM Invited Address at the Joint Mathematics Meetings, Tamara Kolda will discuss the use of tensor decomposition, an extension of principal component analysis, to examine data.
During the SIAM Invited Address at the Joint Mathematics Meetings, to be held in San Diego, Calif., from January 10-13, 2018, I will demonstrate the wide-ranging utility of the CP tensor decomposition with examples in neuroscience and chemical detection.
Of course, multiway data usually means more data, which leads to not only more insights but also more problems. One such problem is the possession of too much data to process efficiently. The use of randomized methods offers a solution to this dilemma. I will present a novel randomized method (based on matrix sketching) for fitting the CP decomposition to dense data that is more scalable and robust than standard techniques. I will further consider the modeling assumptions for fitting tensor decompositions to data and explain alternative strategies for various statistical scenarios, resulting in a generalized CP tensor decomposition that we can fit using a different randomized method (based on stochastic gradient descent).
Tamara G. Kolda serves on the SIAM Board of Trustees and is a Distinguished Member of the Technical Staff at Sandia National Laboratories in Livermore, CA.
|
2018-12-19 13:39:04
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.489166259765625, "perplexity": 1032.609765032347}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376832330.93/warc/CC-MAIN-20181219130756-20181219152756-00186.warc.gz"}
|
https://codereview.stackexchange.com/questions/160550/read-numeric-data-from-a-text-file-using-c/160572
|
# Read numeric data from a text file using C++
I need to read Numeric Data from a text file that looks like this:
2
cell X-cord Y-cord
1 1.1 2.2
2 2.1 2.0
The first line indicates the dimension (2 or 3), the second line is just trash. The file can be comma separated, so it may look like this:
3
cell X-cord Y-Cord Z-Cord
1, 1.1, 2.2, 3.2
Of course this is just a short example, the real file has hundreds of thousands of cells, so I want to improve the performance.
When I have a comma separated file I use this code:
std::istringstream iss; //used iterate over the elements in line
while (std::getline(myfile,line))
{
replace(line.begin(),line.end(),',',' '); //this replaces commas for spaces
iss.str(line); //this will let us iterate over the elements of line
if (dim==2) // if it is a 2d problem
{
iss>>cell>>x>>y;
cell_vector.push_back(cell);
x_vector.push_back(x);
y_vector.push_back(y);
}
else
{
iss>>cell>>x>>y>>z;
cell_vector.push_back(cell);
x_vector.push_back(x);
y_vector.push_back(y);
z_vector.push_back(z);
}
iss.clear(); //so that we can assing a new line to it
}
When the file is not comma separated I use this code:
int i=0; //used to know where to save a
while (my_file>>a)
{
if (dim==2)
{
switch(i%3)
{
case 0:
cell_vector.push_back(a);
break;
case 1:
x_vector.push_back(a);
break;
case 2:
y_vector.push_back(a);
break;
}
i++l;
}
else
{
//similar but for 3 dimensions
}
}
I have tested both codes independently and they work fine. However, I don't know beforehand if the file is comma separated or not, so I thought of doing something like this:
int dim;
input_v>>dim; //to get the information regarding dimension
std::getline(input_v,line);
std::getline(input_v,line);
std::getline(input_v,line); //3 times to skip the "cell X-cord...." part
bool flag_comma=false; //used to later determine if file is comma separated
for (int i=0;i<=line.length();i++)
{
if (line[i]==',')
{
flag_comma=true;
break;
}
}
if (flag_comma)
{
//code for comma separated file
}
else
{
//code for space separated file
}
Everything works fine except that the program only starts to save everything starting from cell 2 onwards... I can't save the data from cell 1.
The only way I found around it is to add this:
replace(line.begin(),line.end(),',',' '); //this replaces commas for spaces
iss.str(line); //this will let us iterate over the elements of line
if (dim==2) // if it is a 2d problem
{
iss>>cell>>x>>y;
}
else
{
iss>>cell>>x>>y>>z;
}
iss.clear(); //so that we can assing a new line to it
Before the if (flag_comma) part, regardless of the case (comma or space). It is the same piece of code used inside the while loop for the comma separated part.
It is also worth noting that the "comma separated code" works just as well when the file has no commas (i.e. it is space separated). The reason I made the space separated part is because I want to improve performance. I don't really know how complex is the replace function.
So my questions are:
A) Do I really improve performance this way? Instead of just keeping the comma separated version of the code?
B) How can I improve my code (in general)?
C) Is there a better way to get the data from cell 1?
D) Can I improve something memory-wise?
• This is the best fit problem for std::ctype<char> (note that it is very different from its template version). Just set the comma to be space. – Incomputable Apr 12 '17 at 17:35
• Just to be sure, you do reserve a sensible amount of space for your vectors? Otherwise memory reallocations are going to be one of the main slowdowns of your program. If you do not know the number of lines beforehand you should be able to estimate them from the size of the file. – miscco Apr 12 '17 at 17:57
• Check this out ignore punctuation using manipulator. Basically you can get the stream to treat the comma like it was a space by imbuing it with a custom std::codecvt. That way you don't need to run over the line and remove commas from potentially arbitrary long lines. – Martin York Apr 12 '17 at 20:04
• @miscco Yes, I reserve some amount of space for my vectors, I have another file (related to this one) that tells me exactly how many points are there. Though the file I am talking about is an upper bound, usually this file has fewer cells. – Nerdrigo Apr 13 '17 at 7:38
A) I don't think that you improved performance of your code in this way. In both methods you get the single numbers with ">>", which is IMHO the best way to get the numbers. So I think it does not matter much.
B) First you can improve your code by regarding the "push_back" commands. This command regularly needs to reallocate your data to fit in a specific part of the main memory. If you know your total number of lines beforehand, you can call "reserve" before the first push_back with the number of lines. Depending on the number of lines you have in total this approach might save you a lot of time. There are more opportunities, just look it up here. Second you can use binary data instead of a textual representation. In your example the code has to read multiple chars for every single number. With binary data every data has a fixed size, independent of the decimal length. Moreover the numbers then are already in the correct representation memory wise.
C) IMHO your approach is ok.
D) That, I cannot answer. I think there is a way to use streams, if you don't already do this.
• push_back() has an amortized complexity of O(1) (i.e. constant). This is explicitly specified by the standard. So saying it regularly needs to re-allocate is not true. The number of times it reallocates is defined to minimal for a large number of pushes. Though saying it can be expensive and using reserve() is a good idea is totally true and good advice. – Martin York Apr 12 '17 at 20:06
So here are my 2 cents.
1. You should reserve the memory of your vectors beforehand. If you do not know the actual number of lines you should still be able to guess it more or less correctly from the size of the file. What you really want is to avoid constant reallocations, which are guaranteed when pushing hundreds of thouthands of elements.
In short you can pass an additional separating token to the stringstream, which eliminates the need for modifying the string of the line
|
2019-09-23 19:09:02
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5079234838485718, "perplexity": 1001.612925143862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514577478.95/warc/CC-MAIN-20190923172009-20190923194009-00128.warc.gz"}
|
http://physics.stackexchange.com/questions/63417/angular-momentum-after-elastic-collision
|
# Angular momentum after elastic collision
If two balls collide (elastically) and there is no friction between them, will their angular momentum change after the collision?
-
No. Without friction, the forces during the collision are applied exclusively through their centres of mass - hence there is no torque and hence the angular momentum cannot change. Wikipedia has a force diagram that illustrates what I mean: upload.wikimedia.org/wikipedia/commons/2/2c/… – m.buettner May 5 at 20:07
It doesn't even matter if energy is conserved. A sufficient condition for angular momentum conservation is that the net external torque on the system of colliding particles is zero. – joshphysics May 5 at 20:36
@joshphysics but in the presence of friction angular momentum might be transferred between the two – m.buettner May 5 at 21:12
@m.buettner That's certainly true. The question refers to "their angular momentum" which I interpreted to mean the angular momentum of the system consisting of both balls. If that's not the case, then my comment is irrelevant. – joshphysics May 6 at 0:04
@m.buettner that (your first comment) should be an answer :-) – David Z May 6 at 4:13
show 1 more comment
The torque is given by $\tau=\mathbf r \times \mathbf F$ - but if the forces are applied through the centre of mass, then $\mathbf r$ and $\mathbf F$ are parallel, and hence $\tau=0$.
Without a torque, angular momentum cannot change (because $\frac{\text{d}L}{\text{d}t}=\tau$), so that each ball will keep its angular momentum.
|
2013-12-11 03:46:53
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9593760967254639, "perplexity": 438.51010335181803}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164030159/warc/CC-MAIN-20131204133350-00072-ip-10-33-133-15.ec2.internal.warc.gz"}
|
https://www.transtutors.com/questions/sunenergy-produces-solar-panels-a-key-step-in-the-conversion-of-raw-silicon-to-a-com-3400460.htm
|
# SunEnergy produces solar panels. A key step in the conversion of raw silicon to a completed solar... 1 answer below »
SunEnergy produces solar panels. A key step in the conversion of raw silicon to a completed solar panel occurs in the assembly department, where lightweight photovoltaic cells are assembled into modules and connected on a frame. In this department, materials are added at the beginning of the process and conversion takes place uniformly. At the start of November 2017, SunEnergy s assembly department had 2,400 panels in beginning work in process, which were 100% complete for materials and 40% complete for conversion costs. An additional 12,000 units were started in the department in November, and 3,600 units remain in work in process at the end of the month. These unfinished units are 100% complete for materials and 70% complete for conversion costs. The assembly department had 1,800 spoiled units in November. Because of the difficulty of keeping moisture out of the modules and sealing the photovoltaic cells between layers of glass, normal spoilage is approximately 12% of good units. The department s costs for the month of November are as follows: Beginning WIP Costs Incurred During Period Direct materials costs..................$76,800....................................$ 240,000 Conversion costs........................123,000....................................1,200,000 Required: 1. Using the format on page 728, compute the normal and abnormal spoilage in units for November, assuming the inspection point is at (a) the 30% stage of completion, (b) the 60% stage
## 1 Approved Answer
Ramesh
5 Ratings, (9 Votes)
Flow of production 30% completion 60% completion Opening work in progress 2400 2400 PLUS Started during the...
## Recent Questions in Accounting - Others
#### Ask a similar question
Submit Your Questions Here !
Copy and paste your question here...
Attach Files
|
2020-04-07 20:14:14
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24446088075637817, "perplexity": 3319.799575466996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371805747.72/warc/CC-MAIN-20200407183818-20200407214318-00134.warc.gz"}
|
https://www.lmfdb.org/EllipticCurve/Q/52983a/
|
# Properties
Label 52983a Number of curves 6 Conductor 52983 CM no Rank 0 Graph
# Related objects
Show commands for: SageMath
sage: E = EllipticCurve("52983.e1")
sage: E.isogeny_class()
## Elliptic curves in class 52983a
sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
52983.e6 52983a1 [1, -1, 1, 7411, 52260] 2 100352 $$\Gamma_0(N)$$-optimal
52983.e5 52983a2 [1, -1, 1, -30434, 445848] 4 200704
52983.e3 52983a3 [1, -1, 1, -295349, -61332330] 2 401408
52983.e2 52983a4 [1, -1, 1, -371039, 86959518] 4 401408
52983.e4 52983a5 [1, -1, 1, -257504, 141093006] 2 802816
52983.e1 52983a6 [1, -1, 1, -5934254, 5565613650] 2 802816
## Rank
sage: E.rank()
The elliptic curves in class 52983a have rank $$0$$.
## Modular form 52983.2.a.e
sage: E.q_eigenform(10)
$$q - q^{2} - q^{4} + 2q^{5} - q^{7} + 3q^{8} - 2q^{10} + 4q^{11} - 2q^{13} + q^{14} - q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$
## Isogeny matrix
sage: E.isogeny_class().matrix()
The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.
$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$
## Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
|
2019-11-18 22:15:31
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9506551623344421, "perplexity": 9775.364101600431}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669847.1/warc/CC-MAIN-20191118205402-20191118233402-00056.warc.gz"}
|
https://www.question2answer.org/qa/32570/there-editor-which-offers-write-mathematical-formulas-symbols
|
# Is there any editor which offers to write mathematical formulas and symbols for q2a?
1.3k views
in Plugins
I want users to be given ability to put mathematical formulas and symbols. Is there any dedicated editor for this which is very well integrated with q2a?
Q2A version: 1.6.3
by
Nope. But you find a Latex plugin for CKEditor.
I personally use jquery to load mathjs if latex is detected in post content - and parse latex accordingly.
Example: http://www.gute-mathe-fragen.de/98887/kann-mir-das-einer-komplett-vorrechnen-%E2%88%ABsin-2-x-dx#a98901
For beginners I have written a latex preview page: http://www.gute-mathe-fragen.de/tex
PS: I am also forcing my users to use the existing special chars of CKEditor, that I modified to "math needs". Example post: http://www.gute-mathe-fragen.de/98947/
It is nice to have a way for this but won't it be really good to have a dedicated plugin for this instead of adding a plugin to a plugin.
|
2022-12-06 04:16:25
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8182977437973022, "perplexity": 3736.974127912847}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711069.79/warc/CC-MAIN-20221206024911-20221206054911-00682.warc.gz"}
|
http://tex.stackexchange.com/questions/70901/typesetting-limitations-of-latex?answertab=oldest
|
# Typesetting limitations of LaTeX
What are the typesetting limitations of LaTeX? In other words what are the things that desktop publishing and word processing programs do better than LaTeX? I am not really interested in things that are better left to the editor (spell check, grammar check) or some post processing program (track changes, word count), but rather typesetting type issues. For example, LaTeX and I really struggle with suppressing page breaks and changing paragraph size. I think even MS Word can do these things better (although it is obviously much easier when you are ignoring the badness of the paragraph). Are there other things? Is there a list or a reference somewhere?
EDIT In regards to the comment by alfC, in the bigger picture the question is what functionality is currently missing from LaTeX (and packages) that exists in other programs. Things like rivers are still difficult from a conceptual standpoint, while resizing a paragraph and preventing page breaks are easy to conceptualize (but difficult to solve).
-
Maybe not a proper answer and somehow pedantic, but TeX is a Turing complete language (en.wikipedia.org/wiki/Turing_completeness), so any well defined "computable" typesetting algorithm is in principle doable within TeX/LaTeX. How difficult can it be to implement or if it is already available in the form of a package is a different question. Also it does not apply to heuristic/vague typesetting requirements, that in effect may be hidden in professional commercial software packages, but if they were known it can be implemented. – alfC Sep 10 '12 at 8:23
I see. Just out of curiosity, What difficult problems you know that are solved in other word processing programs? Are rivers solved? (in Word?). – alfC Sep 10 '12 at 8:47
You might want to watch Frank Mittelbach's talk at TUG2012: he covers things that are hard or not possible at the engine level. – Joseph Wright Sep 10 '12 at 9:17
Somewhat related to tex.stackexchange.com/questions/58501/a-critique-of-tex – lhf Sep 10 '12 at 11:25
@alfC, at the risk of being overly pedantic: As I've pointed out before, TeX being Turing complete doesn't mean that TeX can solve any typesetting task. One major problem is that it has hardly any information about the distribution of "ink" in the bounding boxes of characters. For example in this question of mine I don't see how Turing completeness would help. – Hendrik Vogt Sep 12 '12 at 7:50
A comparison of TeX's capabilities that can be used reasonably efficiently (ignoring the Turing argument as it doesn't really help much) with high-quality craft typography has been discussed by me in the article E-TeX: Guidelines to future TeX extensions. I recently reevaluated the state of affairs at the Boston TeX conference. The final paper is not yet finished (hope it will be in the next TUGboat but a video of the talk is at LaTeX project website). Both talks discuss the TeX capabilities and limitations based on the fact that TeX is a programs that renders its output as a "composer" using algorithms.
TeX is not a graphical system where the composer is essentially sitting in front of the screen. So a comparison between TeX and say MS-Word is a bit missleading as essentially TeX formats do not attempt to cater for this kind of interface (though it would be more or less possible by dropping most of the composing functionality and leave that to the users). But if you are interested in the typography limitations then the above article(s) might be a good start --- and none of these limitations are resolved in other typesetting or deskop publishing systems (with a few exceptions due to internals of the box/glue/penalty model of TeX, e.g., changing parshapes based on position on the page is very difficult in TeX but less so in other systems that either work visually or do not care about the quality of linebreaks and thus can do the par shaping at a different stage).
### Update
As of March 2013 the TUGboat paper on E-TeX: Guidelines to Future TeX extension -- revisited is now also available on the project web site.
-
My answer is far from complete, but I thought I'd rather share my thoughts. Off hand I can think of these (later I'll edit my answer, if something new pops up).
1. Limitations of the size of paper you can use and some memory limitations you may run into when doing computationally heavy TikZ (see for instance this example from TeXamples). Most of the time this can be overcome by optimizing your code, externalization of certain parts or (as a last resort) modifying the memory limits available to your TeX engine. Still, it's highly unlikely to run into such limitations. TeX is really very well engineered.
2. There is one thing I miss: 'endless' paper length document class. `:)` (See my earlier question on this.) As you can see, workarounds exist in this case, too. (A limit of 10 m exists though, which should not be a problem for mundane applications.)
3. I've never seen any sort of code folding in the PDF output file (would most likely require JavaScript).
4. EDIT: MS Word has some 'advanced' grammar checking, e.g. it marks words that appear twice next to each other, marks senteces with unusual structure, etc. While this is probably something to be rather implemented in an editor, I don't know of any package that could throw a warning if it finds one of these problems.
-
Code folding would be so cool! But I doubt it would be possible even with javascript, as you would need to recalculate pagebreaks, probably floats, etc. Maybe it would be possible to hide complete pages... – Juri Robl Sep 10 '12 at 9:20
2. If I am not mistaken `preview` package allows to have endless paper length. 3. Not sure if this qualifies as a 'typesetting' limitation (but definitely a limitation currently, that would be cool). – alfC Sep 10 '12 at 9:20
"It's highly unlikely to run into such limitations": that is not my experience. If you start using `pgfplots`, many reasonably-sized graphs go out of memory. – Federico Poloni Sep 10 '12 at 9:44
@FedericoPoloni: There are workarounds. The `pgfplots` manual has a section (6.2 Memory Limitations) dedicated to solving this problem. I have to admit I only used `pgfplots` for (less than) reasonably sized plots, but as I said, there are workarounds. (I can't vouch for the effectiveness of these methods, as I've never had to try them.) – Count Zero Sep 10 '12 at 10:00
4. Although this is the kind of features that Daniel was trying to exclude in the question, I think it is possible to implement a package for spell or grammar checking, one that marks (red) errors in the output (e.g. if in draft mode for example), that can be helpful (also it can be inefficient --spellcheck each time-- and inflexible --how can one add custom dictionary words? well maybe it can be implemented using ispell or other as backend--). [EDIT: this seems to be a partial solution tex.stackexchange.com/questions/42843/… for the spelling part] – alfC Sep 10 '12 at 10:02
The biggest limitations I can think of (strictly in comparison with programs like InDesign or Word) are as follows.
Mind you, I have no idea what consequences any changes would have wrt. computational complexity or output quality of the system as a whole. TeX does the things it does extremely fast and in near optimum quality, so it may well be in the "pareto set", so to say.
But anyway...
## Paragraph formatting and column/page breaking are strictly detached from each other.
Consequently, TeX's paragraph optimization algorithm doesn't "know" where a certain line will be positioned on the page and can't take this into account.
This has some dire consequences. Off the top of my head:
1. It's awfully hard to make text "flow around" things on the page, especially when page breaks or flush bottom typesetting are involved.
2. I can avoid breaking the page at a line containing a hyphen or a widow/orphan, but I can't make a penalty for paragraph breaking to avoid it appearing on this line.
## TeX is missing a lot of "meta information" on the page
Things like color, z coordinate, angle, writing direction etc. are somehow 'fiddled' into the boxes making up the page or are just implicit in the order content is output. Most of the info can't be inspected later, and communication between content items ("does this box collide with the other one when it's turned around?") becomes next to impossible.
## TeX has a "waterfall" model of page building
Whenever content has left one part of TeXs digestive system for another one, there mostly is no way back. The best we can achieve is to undo everything until a certain stage (for instance, by throwing a box away instead of outputting it) and retrying with different parameters.
If TeX had an object oriented page model where every information could be freely inspected, modified or restructured at any stage and where "typesetting" and "page building" mainly meant to re-structure objects and enrich them with meta information ("where has this paragraph been broken, how much has glue been stretched") which can later be inspected or modified, things would be much much easier.
-
It should be possible to implement TeX in TeX. – morbusg Sep 10 '12 at 13:50
@morbusg, reimplementing tex in any language is pretty painful, see for example en.wikipedia.org/wiki/New_Typesetting_System for how difficult it is, even in a "nice" language like java. Implementing TeX in TeX, while possible in principle, is.... unlikely. – Lev Bishop Sep 10 '12 at 14:07
@morbusg Of course, but wrt. the "meta-TeX" the basic TeX will be just another implementation language; you could as well use Java ot Python. If you want to enrich the typesetting capabilities in any way, then the fact that you're using TeX as the basis for re-implementation won't help you much. – Stephan Lehmke Sep 10 '12 at 15:51
Stephan, your object oriented page model might be a start but it wouldn't help much as there aren't proper algorithms that do the logic in more than very simple cases. This is where the research community has failed in the last 20 years. – Frank Mittelbach Sep 12 '12 at 22:02
@FrankMittelbach That's why I released myself of algorithmic questions right in the beginning ;-) But even just applying all the "old" algorithms that we have in a clear and open way to a transparent object-oriented data structure would be an enormous win... – Stephan Lehmke Sep 12 '12 at 22:12
|
2013-05-19 11:17:44
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8785611987113953, "perplexity": 1350.343434201772}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697420704/warc/CC-MAIN-20130516094340-00044-ip-10-60-113-184.ec2.internal.warc.gz"}
|
https://www.maths.unsw.edu.au/seminars/2019-06/partial-smoothness-tilt-stability-and-mathcalvu-decomposition
|
# On Partial Smoothness, Tilt Stability and the $\mathcal{VU}$--Decomposition
Andrew Eberhard
RMIT
## Date:
Thu, 20/06/2019 - 10:00am to 11:00am
## Venue:
RC-4082, The Red Centre, UNSW
## Abstract:
When restricted to a subspace, a nonsmooth function can be differentiable. This can be characterised for convex functions via a decomposition of the subdifferential giving rise to two subspaces: the $\mathcal{U}$, over which a special Lagrangian can be defined which has nice smooth properties and the $\mathcal{V}$ space, the orthogonal complement subspace of $\mathcal{U}$. Under the assumption of prox-regularity and the presence of a tilt stable local minimum one can show that a $\mathcal{VU}$ like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function. We will also consider the inverse problem. If a so-called “fast track” exists around a strict local minimum does this imply the existence of a tilt stable local minimum? We investigate conditions under which this is so by studying the equivalence of the closely related notions of fast track and partial smoothness. We will illustrate some of this with some graphical realisation of the BFGS method and various modifications of this method as applied to a nonsmooth Rosenbrock function which demonstrates that many questions remain unanswered as the algorithmic use of these ideas. (Joint work with Y. Luo and S. Liu)
Speaker's Bio: Andrew Eberhard did his PhD at Adelaide University under Prof. Charles Pearce and after graduating spend some time at UniSA before moving to RMIT in Melbourne in the 1990s. He has been an active member of the Australian mathematical and optimisation community for more than 20 years. He has served on the executives of ASOR, ANZIAM, as the deputy director of AMSI and served on the board of AMSI. Currently he is the co-chair of the AustMS special interest group Mathematics of Computation and Optimisation (MoCaO). His interests span numerous areas including nonsmooth and variational analysis, optimisation algorithms (both continuous and discrete), systems and control theory, operations research and other more theoretical aspect of optimisation theory.
|
2022-01-21 11:39:33
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4964582920074463, "perplexity": 1262.0537505525522}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303356.40/warc/CC-MAIN-20220121101528-20220121131528-00112.warc.gz"}
|
http://www.zweigmedia.com/modules/graphicalfunction.php?lang=en
|
Let $f$ be the function specified by the following graph:
Then $f(%0) = %8$ and $f(%1) = %9.$ Also,
$f(%2) =$ BOX $f(%3) =$ BOX $f(%5) - f(%4) =$ BOX $f(%5 - %4) =$ BOX
|
2019-02-21 01:28:24
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8496032953262329, "perplexity": 317.5084449301935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247497858.46/warc/CC-MAIN-20190221010932-20190221032932-00496.warc.gz"}
|
https://www.luogu.com.cn/problem/CF1204B
|
# Mislove Has Lost an Array
## 题目描述
Mislove had an array $a_1$ , $a_2$ , $\cdots$ , $a_n$ of $n$ positive integers, but he has lost it. He only remembers the following facts about it: - The number of different numbers in the array is not less than $l$ and is not greater than $r$ ; - For each array's element $a_i$ either $a_i = 1$ or $a_i$ is even and there is a number $\dfrac{a_i}{2}$ in the array. For example, if $n=5$ , $l=2$ , $r=3$ then an array could be $[1,2,2,4,4]$ or $[1,1,1,1,2]$ ; but it couldn't be $[1,2,2,4,8]$ because this array contains $4$ different numbers; it couldn't be $[1,2,2,3,3]$ because $3$ is odd and isn't equal to $1$ ; and it couldn't be $[1,1,2,2,16]$ because there is a number $16$ in the array but there isn't a number $\frac{16}{2} = 8$ . According to these facts, he is asking you to count the minimal and the maximal possible sums of all elements in an array.
## 输入输出格式
### 输入格式
The only input line contains three integers $n$ , $l$ and $r$ ( $1 \leq n \leq 1\,000$ , $1 \leq l \leq r \leq \min(n, 20)$ ) — an array's size, the minimal number and the maximal number of distinct elements in an array.
### 输出格式
Output two numbers — the minimal and the maximal possible sums of all elements in an array.
## 输入输出样例
### 输入样例 #1
4 2 2
### 输出样例 #1
5 7
### 输入样例 #2
5 1 5
### 输出样例 #2
5 31
## 说明
In the first example, an array could be the one of the following: $[1,1,1,2]$ , $[1,1,2,2]$ or $[1,2,2,2]$ . In the first case the minimal sum is reached and in the last case the maximal sum is reached. In the second example, the minimal sum is reached at the array $[1,1,1,1,1]$ , and the maximal one is reached at the array $[1,2,4,8,16]$ .
|
2020-05-28 00:42:19
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.632838249206543, "perplexity": 243.86023985501532}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347396300.22/warc/CC-MAIN-20200527235451-20200528025451-00348.warc.gz"}
|
http://math.stackexchange.com/questions/223006/vector-field-on-torus-as-a-submanifold-of-mathbb-r4
|
Vector field on torus as a submanifold of $\mathbb R^4$
Let $f(\theta,\phi)=\frac{1}{\sqrt{2}}(\cos \theta,\sin \theta,\cos \phi,\sin \phi)$ be immersion of torus into $\mathbb R^4$. How to prove that $\nabla_{\frac{\partial}{\partial \theta}} \frac{\partial}{\partial \theta}=0$? It should be something easy, but I think I am confused a bit. Thank you.
-
|
2014-03-08 19:38:56
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.925592303276062, "perplexity": 142.51998724373152}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999659065/warc/CC-MAIN-20140305060739-00092-ip-10-183-142-35.ec2.internal.warc.gz"}
|
https://www.xloypaypa.pub/codeforces-round-718-explorer-space-dp/
|
## Solution:
First of all, if $k$ is not an even number, there must be no answer.
Define $map[i][j][d]$ (where $0 \leq d <4$) represents the side length of $(i,j)$ in four directions.
Define $dp[p][i][j]$ represents the minimum cost of starting from $(i,j)$, walking $2\cdot p$ to return to the $(i,j)$.
So$$dp[p][i][j]=\min\limits_{0 \leq d < 4} dp[p-1][next_i][next_j]+map[i][j][d]$$Where $next_i$ and $next_j$represents the coordinates of one step from $(i,j)$ with direction $d$.
|
2022-05-27 00:15:42
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8553915619850159, "perplexity": 227.23111479959437}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662627464.60/warc/CC-MAIN-20220526224902-20220527014902-00424.warc.gz"}
|
https://www.embeddedrelated.com/blogs-3/nf/all/System_Design.php
|
Important Programming Concepts (Even on Embedded Systems) Part IV: Singletons
Other articles in this series:
Today’s topic is the singleton. This article is unique (pun intended) in that unlike the others in this series, I tried to figure out a word to use that would be a positive concept to encourage, as an alternative to singletons, but
The CRC Wild Goose Chase: PPP Does What?!?!?!
I got a bad feeling yesterday when I had to include reference information about a 16-bit CRC in a serial protocol document I was writing. And I knew it wasn’t going to end well.
The last time I looked into CRC algorithms was about five years ago. And the time before that… sometime back in 2004 or 2005? It seems like it comes up periodically, like the seventeen-year locust or sunspots or El Niño,...
Important Programming Concepts (Even on Embedded Systems) Part III: Volatility
October 10, 2014
1vol·a·tile adjective \ˈvä-lə-təl, especially British -ˌtī(-ə)l\ : likely to change in a very sudden or extreme way : having or showing extreme or sudden changes of emotion : likely to become dangerous or out of control
Other articles in this series:
Important Programming Concepts (Even on Embedded Systems) Part II: Immutability
September 14, 2014
Other articles in this series:
This article will discuss immutability, and some of its variations in the topic of functional programming.
There are a whole series of benefits to using program variables that… well, that aren’t actually variable, but instead are immutable. The impact of...
Important Programming Concepts (Even on Embedded Systems) Part I: Idempotence
There are literally hundreds, if not thousands, of subtle concepts that contribute to high quality software design. Many of them are well-known, and can be found in books or the Internet. I’m going to highlight a few of the ones I think are important and often overlooked.
But first let’s start with a short diversion. I’m going to make a bold statement: unless you’re a novice, there’s at least one thing in computer programming about which you’ve picked up...
July 5, 2014
Recently, I was faced with a challenge to provide IP65 compliance in a product that had to have humidity and pressure sensors on it. The tricky part was to keep the cost of the unit under $15 while meeting this requirement. Under normal circumstances, one can put all the electronics within an IP65 enclosure that is affordable and readily available off-the-shelf most of the time such as the ones shown in this link. However, given the humidity and the pressure sensor need to be exposed to... Efficiency Through the Looking-Glass December 8, 20134 comments If you've ever designed or purchased a power supply, chances are you have had to work with efficiency calculations. I can remember in my beginning electronic circuits course in college, in the last lecture when the professor was talking about switching power converters, and saying how all of a sudden you could take a linear regulator that was 40% efficient and turn it into a switching regulator that was 80% efficient. I think that was the nail in the coffin for any plans I had to pursue a... Data Validity in Embedded Systems October 5, 20131 comment If you take a high-level view of software systems you might say that the overall goal of software is to generate outputs from inputs. It’s a gross simplification of a nuanced and complex field but the truth of the statement is unarguable: data goes in, is manipulated and then is spat out again.That’s what software does. The simplicity of the statement contributes to the joy of Computer Science majors who take an abstract view of everything from software to love but infuriates... Implementation Complexity, Part II: Catastrophe, Dear Liza, and the M Word June 16, 2013 In my last post, I talked about the Tower of Babel as a warning against implementation complexity, and I mentioned a number of issues that can occur at the time of design or construction of a project. The Tower of Babel, Pieter Bruegel the Elder, c. 1563 (from Wikipedia) Success and throwing it over the wall OK, so let's say that the right people get together into a well-functioning team, and build our Tower of Babel, whether it's the Empire State Building, or the electrical grid, or... Implementation Complexity, Part I: The Tower of Babel, Gremlins, and The Mythical Man-Month June 9, 2013 I thought I'd post a follow-up, in a sense, to an older post about complexity in consumer electronics I wrote a year and a half ago. That was kind of a rant against overly complex user interfaces. I am a huge opponent of unnecessary complexity in almost any kind of interface, whether a user interface or a programming interface or an electrical interface. Interfaces should be clean and simple. Now, instead of interface complexity, I'll be talking about implementation complexity, with a... Shibboleths: The Perils of Voiceless Sibilant Fricatives, Idiot Lights, and Other Binary-Outcome Tests September 29, 2019 AS-SALT, JORDAN — Dr. Reza Al-Faisal once had a job offer from Google to work on cutting-edge voice recognition projects. He turned it down. The 37-year-old Stanford-trained professor of engineering at Al-Balqa’ Applied University now leads a small cadre of graduate students in a government-sponsored program to keep Jordanian society secure from what has now become an overwhelming influx of refugees from the Palestinian-controlled West Bank. “Sometimes they visit relatives... The three laws of safe embedded systems November 12, 20151 comment This short article is part of an ongoing series in which I aim to explore some techniques that may be useful for developers and organisations that are beginning their first safety-related embedded project. In the last two weeks, I’ve had the opportunity to discuss the contents of my previous article on this site with a group of very smart and enthusiastic engineers in Cairo (Egypt). As part of this discussion, it has become clear that I should add a few more details to explain the work... Six Software Design Tools November 5, 20211 comment Contents: Introduction Here are six tools to help you with software design. The first two are very simple, almost deceptively trivial, while the last four are more involved. They apply universally, to all types of software, all types of systems, and all languages. This is part of good engineering discipline. At face value, this is just a bunch of acronyms,... Practical protection against dust and water (i.e. IP protection) July 5, 2014 Recently, I was faced with a challenge to provide IP65 compliance in a product that had to have humidity and pressure sensors on it. The tricky part was to keep the cost of the unit under$15 while meeting this requirement.
Under normal circumstances, one can put all the electronics within an IP65 enclosure that is affordable and readily available off-the-shelf most of the time such as the ones shown in this link. However, given the humidity and the pressure sensor need to be exposed to...
Data Validity in Embedded Systems
October 5, 20131 comment
If you take a high-level view of software systems you might say that the overall goal of software is to generate outputs from inputs. It’s a gross simplification of a nuanced and complex field but the truth of the statement is unarguable: data goes in, is manipulated and then is spat out again.That’s what software does. The simplicity of the statement contributes to the joy of Computer Science majors who take an abstract view of everything from software to love but infuriates...
Unmanned Ground Vehicles - Design Considerations for Snow and Cold Environments
December 27, 2016
It's that time of year when the white stuff falls from the sky across the US, and with it comes lower temperatures. These conditions must be taken into consideration when designing a vehicle for outdoor use.
A few definitions from wikipedia:
Flurry: light, brief snowfall
Snow shower: intermittent snowfall
Light snow: over 1km visibility
Moderate snow: 0.5 to 1km visibility
Heavy snow: less than 0.5km visibility
Blizzard: lasts 3 hours or longer, sustained wind to 35mph, visibility...
“Smarter” cars, unintended acceleration – and unintended consequences
October 20, 20151 comment
In this article, I consider some recent press reports relating to embedded software in the automotive sector.
In The Times newspaper (London, 2015-10-16) the imminent arrival of Tesla cars that “use autopilot technology to park themselves and change lane without intervention from the driver” was noted.
By most definitions, the Tesla design incorporates what is sometimes called “Artificial Intelligence” (AI).Others might label it a “Smart” (or at least “Smarter”)...
Autonomous vehicle - design questions to ponder
January 27, 2016
When designing an autonomous or remotely-controlled vehicle, there are a few factors to take into consideration. Three of these are purpose, environment, and terrain.
What is the purpose of the vehicle?
Will it be used in an industrial setting with people moving around it that it must not run over?
Will it be used in a hazardous environment, like Fukushima or Chernobyl, where it would be exposed to high levels of radiation and must be cleaned or left behind? If it must be left behind, any...
Definite Article: Notes on Traceability
September 6, 2021
Electronic component distibutor Digi-Key recently announced part tracing for surface-mount components purchased in cut-tape form. This is a big deal, and it’s a feature that is a good example of traceability. Some thing or process that has traceability basically just means that it’s possible to determine an object’s history or provenance: where it came from and what has happened to it since its creation. There are a...
Review: Prototype to Product
October 16, 2021
Prototype to Product: A Practical Guide for Getting to Market, by Alan Cohen, is a must-read for anyone involved in product development, whether in a technical, management, or executive role.
I was reminded of it by Cohen's recent episode on Embedded.fm, 388: Brains Generate EMF, which is worth listening to a couple times through, especially if you're interested in medical device development. And in fact his first episode there,
|
2022-06-28 22:33:27
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3406652510166168, "perplexity": 2331.126320618273}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103617931.31/warc/CC-MAIN-20220628203615-20220628233615-00333.warc.gz"}
|
https://en.wikipedia.org/wiki/Truncated_triheptagonal_tiling
|
# Truncated triheptagonal tiling
Truncated triheptagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 4.6.14
Schläfli symbol tr{7,3} or ${\displaystyle t{\begin{Bmatrix}7\\3\end{Bmatrix}}}$
Wythoff symbol 2 7 3 |
Coxeter diagram or
Symmetry group [7,3], (*732)
Dual Order 3-7 kisrhombille
Properties Vertex-transitive
In geometry, the truncated triheptagonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one hexagon, and one tetradecagon (14-sides) on each vertex. It has Schläfli symbol of tr{7,3}.
## Uniform colorings
There is only one uniform coloring of a truncated triheptagonal tiling. (Naming the colors by indices around a vertex: 123.)
## Symmetry
Each triangle in this dual tiling, order 3-7 kisrhombille, represent a fundamental domain of the Wythoff construction for the symmetry group [7,3].
The dual tiling is called an order-3 bisected heptagonal tiling, made as a complete bisection of the heptagonal tiling, here shown with triangles with alternating colors.
## Related polyhedra and tilings
This tiling can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram . For p < 6, the members of the sequence are omnitruncated polyhedra (zonohedrons), shown below as spherical tilings. For p > 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling.
From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling.
Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.
|
2016-10-25 11:44:38
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6970055103302002, "perplexity": 3878.7018723729643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720026.81/warc/CC-MAIN-20161020183840-00223-ip-10-171-6-4.ec2.internal.warc.gz"}
|
http://math.stackexchange.com/questions/242552/hilbert-nullstellensatz-for-schemes
|
# Hilbert nullstellensatz for schemes
I know that there is a bijection between the irreducible closed sets and the prime ideals of a ring (via functions $V()$ and $I()$).
Is this true not only for affine schemes but also for general schemes? And Why?
-
There is a bijection between irreducible closed sets and points of scheme. This can be proved by checking on affine open sets. – user27126 Nov 22 '12 at 10:41
Thank you. I understand that it holds in each affine open set. For any point $p$ of a scheme we can find an irreducible closed set $W$ in an affine open set containing $p$. But $W$ might not be closed in the global scheme? – Tom Nov 22 '12 at 11:03
Oh, instead of $W$, should we take $\bar{W}$? – Tom Nov 22 '12 at 11:40
Why is the map $p\mapsto Z$(points to irreducible closed sets) injective? – Tom Nov 22 '12 at 11:57
Response to the comment:
The correspondence is a point $p$ to $\overline{\{p\}}$, the closure of $p$. It says two things: existence (that each irreducible closed set has a generic point), and uniqueness (that each irreducible closed set has a unique generic point)
Let's say our scheme is $X$, an irreducible closed set being $C$.
Existence: We want to find a generic point of $C$.
Intersect $C$ with an affine open subset $U$. This intersection is dense in $C$, while by the affine case $C \cap U$ has a generic point $p$ (considered as a subset of $U$) in $U$. Try to show that the closure of $p$ in $X$ is $C$.
Uniqueness: Suppose $p$ and $q$ has the same closure $C$. We want to show that $p = q$.
Take an affine open subset $U$ that contains $p$, and try to show that $p$ is the same as the generic point of $C \cap U$ in $U$.
Now take an affine open subset $V$ that contains $q$. Irreducibility of $C$ forces $U \cap V$ to be nonempty. The last paragraph then shows that both $p$ and $q$ are the generic point of $C \cap U \cap V$ in $U \cap V$, which means that they are the same.
-
I have just understood your answer! Thank you very much. – Tom Nov 23 '12 at 11:39
This is the whole point of scheme theory. Hilbert's Nullstellensatz only gives a bijection between radical ideals in $k[x_1,\cdots,x_n]$ and closed subsets of $\mathbb{A}^n$, for $k$ algebraically closed.
Now for any scheme, there is 1-1 correspondence between quasi-coherent ideal sheaves (subsheaves of the structure sheaf) and closed subschemes of X. (this is the content of proposition 5.9 in Harthorne)
The correspondence is given as follows: If $Y$ is a closed subscheme of $X$, then the inclusion morphism $i:Y \to X$ gives a morphism of sheaves: $i^\#:\mathcal{O}_X \to i_*\mathcal{O}_Y$. The ideal sheaf is the kernel of this map.
Conversely, given a scheme $X$ and a quasi-coherent shraf of ideals $\mathcal{J}$, let $Y$ be the support of the quotient sheaf $\mathcal{O}_X/\mathcal{J}$. Then $Y$ is a closed subscheme with structure sheaf $\mathcal{O}_X/\mathcal{J}$.
-
Thanks. There are several versions of Nullstellensatz. One of which says that any (not-necessarily-alg.closed)ring $A$ has a bijection between the irreducible closed sets of Spec $A$ with Zariski topology and the prime ideals of $A$. Is this also true for schemes? – Tom Nov 22 '12 at 12:32
Yes, the correspondence I answered above is the natural generalization of the Nullstellensatz, because sheaves are the "global" version of rings. – Fredrik Meyer Nov 22 '12 at 12:41
Thank you. But I haven't yet learned the words coherent and closed-subscheme. Probably I will be able to read your answer two months later. – Tom Nov 22 '12 at 23:24
This answer actually does not capture the point. An irreducible closed SUBSET does not capture any information of functions (which means it has nothing to do with sheaf), and is something purely topological. To read more about these spaces, see en.wikipedia.org/wiki/Sober_space – user27126 Nov 23 '12 at 7:27
Dear @Sanchez, your comment is unnecessarily harsh: Frederik's answer is an excellent answer to Tom's question and goes even further than just answering it, precisely because scheme theory takes not purely topological structures into account. If you (wrongly) insist on pure topology, just restrict Frederik's perfect 1-1 correspondence to reduced subschemes on one hand and to radical quasi-coherent ideals ($\mathcal I=\sqrt {\mathcal I}$) on the other (And, by the way, I know what a sober topological space is since I happen to be aware of the existence of [both versions of] EGA I ) – Georges Elencwajg Nov 23 '12 at 8:33
|
2014-10-22 00:38:12
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9276686310768127, "perplexity": 270.7839555426286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507445159.36/warc/CC-MAIN-20141017005725-00003-ip-10-16-133-185.ec2.internal.warc.gz"}
|
https://www.physicsforums.com/threads/need-help-interpreting-the-wronskian.851060/
|
# Need help interpreting the Wronskian
Tags:
1. Jan 6, 2016
### kostoglotov
I'm given bases for a solution space $\left \{ x,xe^x,x^2e^x \right \}$. Clearly these form a basis (are linearly independent).
But, unless I've made a mistake, doing the Wronskian on this yields $W(x) = x^3e^x$.
Isn't this Wronskian equal to zero at x = 0? Isn't that a problem for dependence/independence?
note: a DE to which this solution space applies has not been provided in the exercise.
2. Jan 6, 2016
### Staff: Mentor
No. The three functions are linearly independent on any interval that doesn't include 0. I'm assuming that you correctly evaluated the Wronskian.
|
2018-03-18 23:36:47
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7033210396766663, "perplexity": 943.822373086611}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646178.24/warc/CC-MAIN-20180318224057-20180319004057-00704.warc.gz"}
|
https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-8-coordinate-geometry-and-linear-systems-chapter-8-test-page-394/6
|
## Elementary Algebra
In order to solve this problem, we use the equation $m =\frac{y_2-y_1}{x_2-x_1}$, where m is the slope.
In order to solve this problem, we use the equation $m =\frac{y_2-y_1}{x_2-x_1}$, where m is the slope.
|
2019-01-20 23:40:56
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9752277135848999, "perplexity": 107.45374672058948}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583743003.91/warc/CC-MAIN-20190120224955-20190121010955-00576.warc.gz"}
|
https://www.structuralbasics.com/statically-determinate-structures/
|
# Statically Determinate & Indeterminate Structures
Last updated: November 14th, 2022
Calculating internal forces by hand is one of the first things Civil engineering students learn at university.
But internal forces can only be calculated in the simple way with the 3 equilibrium equations if the structure is Determinate.
If a structure is statically Indeterminate, then more complicated methods need to be used to calculate Moments, reaction, shear and axial forces.
So in this article, we’ll show, what statically determinate and indeterminate structures are and how to calculate the degree of indeterminacy for different structures.
But now, let’s get started.
## 🙋♂️ What’s the difference between Internal and External Determinate Structures?
Before we explain what statically determinate structures are, we first have to mention that when we talk about determinacy & indeterminacy in this post, then we mean Internal Determinacy, instead of External.
#### Explanation
External (In)determinacy:
The reaction/support forces in an externally statically determinate structure can be calculated by the 3 Equilibrium equations. If the reaction components can’t be calculated, then the structure is externally statically indeterminate.
Internal (In)determinacy:
Compared to External determinacy, the internal forces (Moment, Shear & Normal force) can be calculated by the 3 Equilibrium equations additionally to the reaction/support forces in an Internally Statically Determinate Structure. If the internal forces and reaction components can’t be calculated, then the structure is Internally Indeterminate.
#### So what’s the Difference?
While in Externally & Internally Determinate structures the reaction forces can be calculated by the 3 Equilibrium equations, the Internal forces can only be calculated in Internally Determinate structures.
When we talk about statically determinate structures in this post, then we mean Internally determinate structures.
## ❔ What is a statically determinate structure?
Statically determinate structures are structures in which the reaction forces and the internal forces can be calculated by the 3 Equilibrium equations.
Vertical equilibrium: $\sum V = 0$
Horizontal equilibrium: $\sum H = 0$
Moment equilibrium: $\sum M = 0$
### Examples of statically determinate structures are:
• Simply supported beam
• Cantilever beam
• Column (roller + pin support)
• 3-hinge arch
• Truss (Not all trusses)
## 🤔 What is a statically indeterminate structure?
Statically Indeterminate Structures are structures in which the reaction forces and the internal forces CAN NOT be calculated by the 3 Equilibrium equations.
When trying to solve the 3 Equilibrium equations for an indeterminate structure, you will experience that you have 4 or more Unknowns (Reaction & Internal forces) for 3 equations.
### Examples of statically indeterminate structures are:
• Continuous beams
• Frames
• Some Trusses
## 🧮 Determinacy Equations
#### Beams & Frames [1]:
The degree of indeterminacy D for beams and frames is calculated as
$$D = 3n + r – 3j – c$$
Where
• n = amount of members
• r = external restraints (number of support reactions)
• j = number of joints
• c = number of releases introduced (internal hinges)
Let’s have a look at some examples.
#### 3 span continuous beam
$$D = 3 \cdot 3 + 5 – 3 \cdot 4 – 0 = 9 + 5 – 12 = 2$$
D = 2 means that the structure is statically indeterminate to the 2nd degree. The reaction & internal forces CAN NOT be calculated by the 3 Equilibrium equations.
#### 3 span continuous beam with hinge
$$D = 3 \cdot 4 + 5 – 3 \cdot 5 – 1 = 12 + 5 – 15 – 1 = 1$$
D = 1 means that the structure is statically indeterminate to the 1st degree. The reaction & internal forces CAN NOT be calculated by the 3 Equilibrium equations.
### Trusses [1]:
The degree of indeterminacy D for trusses is calculated as
$$D = n + r – 2j$$
Where
• n = amount of members
• r = external restraints (number of support reactions)
• j = number of joints
Let’s have a look at some examples.
#### Warren Truss
$$D = 11 + 3 – 2 \cdot 7 = 0$$
D = 0 means that the structure is statically determinate. The reaction & internal forces can be calculated by the 3 Equilibrium equations.
#### Howe Truss
$$D = 21 + 3 – 2 \cdot 12 = 0$$
D = 0 means that the structure is statically determinate. The reaction & internal forces can be calculated by the 3 Equilibrium equations.
If you are new to structural design, then check out our design tutorials where you can learn how to use the calculated bending moments and shear forces to design structural elements such as
But now I would like to know from you, have you understood the concept of Bending moment, shear and normal force? Because I remember, it took me almost my entire 1st semester to really understand how to calculate moments. So let us know in the comments✍️, if you want more detailed posts and how you learned the concept of Moments.
## 📃 References
[1]: Williams A. Ph.D., S.E., C.ENG. (2009) Structural Analysis
|
2023-03-30 12:26:28
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7669356465339661, "perplexity": 2025.918813193666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949181.44/warc/CC-MAIN-20230330101355-20230330131355-00366.warc.gz"}
|
https://itprospt.com/num/884707/4-marks-let-f1-denote-the-real-vector-space-of-polynomials
|
5
# (4 marks) Let F1 denote the real vector space of polynomials of degree not greater than with the inner product{p, 9}1, pl)ql) &xfor p,q € P_ Show that the...
## Question
###### (4 marks) Let F1 denote the real vector space of polynomials of degree not greater than with the inner product{p, 9}1, pl)ql) &xfor p,q € P_ Show that the two polynomialsPi(z) = 1 P(T) =1-rbasis for Pi_ Use the Gram-Schmidt process thonormal hasis for Pe from the hasis (P1, Pz) .consttucn
(4 marks) Let F1 denote the real vector space of polynomials of degree not greater than with the inner product {p, 9} 1, pl)ql) &x for p,q € P_ Show that the two polynomials Pi(z) = 1 P(T) =1-r basis for Pi_ Use the Gram-Schmidt process thonormal hasis for Pe from the hasis (P1, Pz) . consttucn
#### Similar Solved Questions
##### Question (45 points): Determine the point group of the following molecules_coCH; Si "CH; Hyc- CH;C=c"HaN- HgN NH;H3C-""CH? CH;
Question (45 points): Determine the point group of the following molecules_ co CH; Si "CH; Hyc- CH; C=c" HaN- HgN NH; H3C- ""CH? CH;...
##### Student set about the conversion of compound an compound Question 5. (5 marks) but used result; they obtained mixture both and a5 well 45 much of the required reagent compounds and _ (compound results from the reaction of unused with product 3).OHOH6"Because the crude product was mixture; the student set about separating these four compounds: First; they dissolved the mixture in dichloromethane; and extracted with aqueous dilute hydrochloric acid, giving an organic phase (X) and an aqueous
student set about the conversion of compound an compound Question 5. (5 marks) but used result; they obtained mixture both and a5 well 45 much of the required reagent compounds and _ (compound results from the reaction of unused with product 3). OH OH 6" Because the crude product was mixture; t...
##### During lightning flash_ there exists potential ditcrenccVcloud Varaund 2.6 109 betwcen clauoroundresuil; charge oftrunsierred from the ground to the cloud_(a) How much work Moround -clcudthe charge bY the electric force?ClLi-SaaciesIf the work done by the electric lorce were useducccicrtc1100-kg automobile from rest; what would be its final speed?Delec_(c) If the work done bY the electric force were converted Into heat, how many kilograms of water at 0"C could be heated 100"C? Wground
During lightning flash_ there exists potential ditcrencc Vcloud Varaund 2.6 109 betwcen clauo round resuil; charge of trunsierred from the ground to the cloud_ (a) How much work Moround -clcud the charge bY the electric force? ClLi- Saacies If the work done by the electric lorce were used ucccicrtc ...
##### GIvenfunctions ((x)-2 6x and g(*)=6xFind the composition two functions:You can watch the video: https: / / wivm youtube cOm/ watch?v= 4z9EITz4inQafeature-youtu bef(9(x))=F((*))9((*))
GIven functions ((x)-2 6x and g(*)=6x Find the composition two functions: You can watch the video: https: / / wivm youtube cOm/ watch?v= 4z9EITz4inQafeature-youtu be f(9(x))= F((*)) 9((*))...
##### Uu shouta ue aole to answer thts question after studying Unit 12 (a) Solve the equationGive the solutions in polar form, and sketch them in thc complex plane:Let ~0,21,22,23,21,76 be the soltions that You found in part (a). Use the factorisation+1 =(t0 detormine tho complex Hher that is ohtained by multiplying together all tho solutious of the equationQuestion MAKS You shontd bc ablc to ausut[ this question "fter studying Unit 12 fwula to Iiud the Cutesian form ol the complex Wuber Alaivte
uu shouta ue aole to answer thts question after studying Unit 12 (a) Solve the equation Give the solutions in polar form, and sketch them in thc complex plane: Let ~0,21,22,23,21,76 be the soltions that You found in part (a). Use the factorisation +1 = ( t0 detormine tho complex Hher that is ohtaine...
##### Space vehicle of mass 000 kg (including empty of fuel lakes On 97.CCs9 of fuel at It Is ciew) wncn space station_ of 2 mls and throw released from the station with an initial speed rockets vehicle Icach out the gas at speed of s00mls when turned on 0) Can the speed of 4,500 mls will take b) If the answer is Yes then how much fuel needs to be t0 reach this speed? If the answer is No then what is the minimum speed the (uel ejected at for the rocket to be able to reach speed of 4,500 mis amount of
space vehicle of mass 000 kg (including empty of fuel lakes On 97.CCs9 of fuel at It Is ciew) wncn space station_ of 2 mls and throw released from the station with an initial speed rockets vehicle Icach out the gas at speed of s00mls when turned on 0) Can the speed of 4,500 mls will take b) If the a...
##### ExonGUAAGGene A5'ExonCUAAGmutGene A5'
Exon GU A AG Gene A 5' Exon CU A AG mutGene A 5'...
##### 84p83sa the avcage yaany aalary 0f an indiidual whose Fnal dac ce master' s [4 536 Lhousand 2ss Ihor bice Ihat of an Indivkdunl whose inpl degree I5 a enelots Comblnad, two people with each ol Lhese educatlonal amalnments earn 5114 thousand_ Find the avoraga yearly salary of an Individual with vach Iue9ito8 Iasa(nverge yeally enlury for Indmioual #hose Iinal degre# MEte HhnusandJacneioi & [Ihousand and Iha averaga yoarly salary fot Individual whon Ilnal deprae
84p83sa the avcage yaany aalary 0f an indiidual whose Fnal dac ce master' s [4 536 Lhousand 2ss Ihor bice Ihat of an Indivkdunl whose inpl degree I5 a enelots Comblnad, two people with each ol Lhese educatlonal amalnments earn 5114 thousand_ Find the avoraga yearly salary of an Individual with ...
##### Find the best approximation to z by Vectors of (he form € | ICzVzi3362 J2Zm33The best approximation to z is (Simplify yourianswer )
Find the best approximation to z by Vectors of (he form € | ICzVzi 3 3 6 2 J2 Zm 3 3 The best approximation to z is (Simplify yourianswer )...
##### Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point $P$.
Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point $P$....
##### 3. Cousider the integralK' [ &1dydc Sketch the region of integration_ Reverse the order of integration and compute the resulting integral.
3. Cousider the integral K' [ &1dydc Sketch the region of integration_ Reverse the order of integration and compute the resulting integral....
##### Which of the following visualizations best represents the distribution of $\mathrm{O}_{2}$ and $\mathrm{SO}_{2}$ molecules near an orifice some time after effusion occurs in the direction indicated by the arrows? The initial condition was one of equal numbers of $\mathrm{O}_{2}$ molecules $(\bullet)$ and $\mathrm{SO}_{2}$ molecules ( $\bullet$ ) on the left side of the orifice. Explain.
Which of the following visualizations best represents the distribution of $\mathrm{O}_{2}$ and $\mathrm{SO}_{2}$ molecules near an orifice some time after effusion occurs in the direction indicated by the arrows? The initial condition was one of equal numbers of $\mathrm{O}_{2}$ molecules \$(\bullet)...
##### Solve the following congruence equations. If there are nosolutions, explain how you know.1. 21𑥠≡ 7(ð‘šð‘œð‘‘35)2. 5𑥠≡ 4(ð‘šð‘œð‘‘9)
Solve the following congruence equations. If there are no solutions, explain how you know. 1. 21𑥠≡ 7(ð‘šð‘œð‘‘35) 2. 5𑥠≡ 4(ð‘šð‘œð‘‘9)...
##### The function f(x)= 1/ln(x^2) is guaranteed to have an absolute maximum and minimum on the interval [-5,-1]True or False?
The function f(x)= 1/ln(x^2) is guaranteed to have an absolute maximum and minimum on the interval [-5,-1] True or False?...
##### ProbAnalyze the graph the function f (Xi=x" 12x" 48X' 64x identifying all relative extrema and inflection points. (f(i=xX and f"(x) = 4(x - IX-412 * and f"(*1=126-4)(x-2)) (Wk 13, Sec. 3.6, Prob 1)f(i 1 (X)"(X) Characteristics of graph
Prob Analyze the graph the function f (Xi=x" 12x" 48X' 64x identifying all relative extrema and inflection points. (f(i=xX and f"(x) = 4(x - IX-412 * and f"(*1=126-4)(x-2)) (Wk 13, Sec. 3.6, Prob 1) f(i 1 (X) "(X) Characteristics of graph...
##### MM 1 1 0339 1 WW 1 1 1 U 1 1 1 1 1 1 1 1 1 L 1 1 1 1 1 1 #
MM 1 1 0339 1 WW 1 1 1 U 1 1 1 1 1 1 1 1 1 L 1 1 1 1 1 1 #...
|
2022-08-08 16:42:19
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7481368184089661, "perplexity": 7164.1747939012475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570868.47/warc/CC-MAIN-20220808152744-20220808182744-00150.warc.gz"}
|
https://www.rocketryforum.com/threads/featherweight-raven3-accel-data.140400/
|
# Featherweight Raven3 accel data?
### Help Support The Rocketry Forum:
#### Buckeye
##### Well-Known Member
TRF Supporter
I sent this inquiry to AdrianA, but I will post the question here, too. I launched my Raven3 for the first time. Fairly vertical flight, and the baro data is as expected. However, the acceleration data went bonkers. Attached are the fipa and some plots showing the issue.
Bottom line: The accel computed velocity< 0 well past the true apogee, and it kept merrily integrating positive altitude for another 12 seconds. As a result, the accel apogee is 5000 ft, while the true baro apogee was only 1700 ft. The #3 charge used for velocity-based apogee backup was pretty worthless, as the rocket was already half way to the ground. Good thing the backup was not needed.
What would cause the accelerometer to think it was still climbing, even though the rocket experienced the jolt of ejection and was falling under drogue for 12 seconds? I know that accelerometers really don't know their direction, but the accel data started off very wrong from liftoff. The first few seconds of accel data are supposed to be the most accurate, right?
I checked the real time data before the flight, after the flight, and after calibration. The readings didn't change much. Axial accel was between 0.8 and 1.2 as recommended.
Thanks.
View attachment firestick.i245.2017.04.23.FIPa
#### mikec
##### Well-Known Member
Looks to me like the usual issue of the accelerometer having a big accelerometer scale error, which has plagued the later production runs of the Raven 3. The Raven operates its accelerometer at voltage lower than the datasheet recommended value and some parts don't behave as well as others, though this one seems unusually far off. You likely won't be able to use accelerometer apogee detect.
Note that accelerometer altitude is never very accurate, but most Ravens do better than this on velocity.
#### OverTheTop
##### Well-Known Member
TRF Supporter
Have you run a calibration on the acclerometers? Maybe that might improve the situation.
#### Buckeye
##### Well-Known Member
TRF Supporter
Looks to me like the usual issue of the accelerometer having a big accelerometer scale error, which has plagued the later production runs of the Raven 3. The Raven operates its accelerometer at voltage lower than the datasheet recommended value and some parts don't behave as well as others, though this one seems unusually far off. You likely won't be able to use accelerometer apogee detect.
Note that accelerometer altitude is never very accurate, but most Ravens do better than this on velocity.
mikec, thanks for the input, even though it sounds pretty grim. I have studied many fipa files posted on this forum, and the accel altitude is often very close to the baro altitude and with good velocity/apogee detect. My goal is to use accel and velocity data to attempt to back out drag coefficient in the coast phase of more extreme flights than this one. I am not hopeful at this point.
I will wait for Adrian's response, and give it a couple more flights, but I am not gonna be happy if I plopped down $160 for a unit known to be "plagued" with "big accelerometer scale errors." Yes, as I mentioned in post #1, I re-calibrated the accel, but the real time output looks no different than before calibration, so I am not sure if anything really improved. #### OverTheTop ##### Well-Known Member TRF Supporter Yes, as I mentioned in post #1, I re-calibrated the accel, Oops. Missed that! #### SpaceManMat ##### Space Nut I wasn't aware of a plauge of problems with the Raven. its a bit hard to tell from the graph, can you confirm the accel values from before and after the flight? #### Buckeye ##### Well-Known Member TRF Supporter I wasn't aware of a plauge of problems with the Raven. its a bit hard to tell from the graph, can you confirm the accel values from before and after the flight? Wow, lots of feedback from Down Under! Thanks guys. The before/after accel data I am referring to are the setup/config tests performed when the unit is connected to the computer. The "real time" read out of axial G's fluctuates between 0.80 and 1.2, which the documentation says is OK. The "filtered" value holds pretty steady at 0.99 during the test. #### manixFan ##### Not a rocket scientist I don't quite understand your voltage plot. It looks like the voltage never recovers after apogee and then very quickly drops. What kind of battery were you using? The voltage looks like it drops to 1.4 volts which is obviously well under operating voltage. I would plot it with the main battery voltage instead of the pyro voltage. There have been cases where the payload bay is under under drogue and spinning in a big circle. That can produce input to the accelerometer that mimics flight. So that might explain the upward graph after apogee. It's also possible you just have a bad unit. I have several Ravens and have flown them on a variety of extreme flights with no issues. Adrian has been very good the couple of times I needed to have a unit fixed due to rough handling. If there is an issue with your unit I'm sure he'll make it right. I use barometric apogee detection whenever possible though. Just a lot more reliable than accelerometer based, regardless of altimeter. Tony Last edited: #### mikec ##### Well-Known Member I am not gonna be happy if I plopped down$160 for a unit known to be "plagued" with "big accelerometer scale errors."
Obviously I don't speak for Featherweight but if the unit's this far off I think there's a good chance it will be replaced. The errors Adrian was talking about (you can find discussions here if you search enough) were large enough that he stopped recommending the use of accelerometer apogee mode, but they were typically only off a few seconds, and your case seems worse than that.
The error only manifests itself during acceleration so it can't be calibrated out at 1g and the calibration process won't help.
#### SpaceManMat
##### Space Nut
Obviously I don't speak for Featherweight but if the unit's this far off I think there's a good chance it will be replaced. The errors Adrian was talking about (you can find discussions here if you search enough) were large enough that he stopped recommending the use of accelerometer apogee mode, but they were typically only off a few seconds, and your case seems worse than that.
The error only manifests itself during acceleration so it can't be calibrated out at 1g and the calibration process won't help.
All accelormeters suffer from the same errors not a particular issue with the Raven, it is however highly flexibable and if you play with the configuration easy enough to stuff up.
This one does however have something wrong, pretty sure this is somehow not callebrated right. Which is why I'm interested in what the accelerometer was reading immediately prior to launch.
#### UhClem
##### Well-Known Member
All accelormeters suffer from the same errors not a particular issue with the Raven, it is however highly flexibable and if you play with the configuration easy enough to stuff up.
This one does however have something wrong, pretty sure this is somehow not callebrated right. Which is why I'm interested in what the accelerometer was reading immediately prior to launch.
The Raven suffers from problems because it runs the sensor at 3.3V rather than its specified 5V. The data sheet says it will work at 3.3V but its performance is only specified at 5V. The specifications for the ADC are the worst it has ever been my displeasure to read.
The data file shows that the prelaunch acceleration was 1G but that isn't surprising as it is tracking the 1G offset. What is more to the point is that at motor burnout the acceleration barely goes negative. Then when it should be approaching zero while coasting to apogee, it passes that and reaches 0.3G. Not unreasonable for a helium filled Estes Dude but otherwise completely wrong. Since the acceleration due to drag was so badly off, the integrated velocity didn't decrease as fast as it should.
Apogee detection is immune to scale errors because you start at zero and end at zero. Offset errors are a problem but since the data shows 1G prelaunch, that isn't the problem here.
#### Buckeye
##### Well-Known Member
TRF Supporter
I don't quite understand your voltage plot. It looks like the voltage never recovers after apogee and then very quickly drops. What kind of battery were you using? The voltage looks like it drops to 1.4 volts which is obviously well under operating voltage. I would plot it with the main battery voltage instead of the pyro voltage.
There have been cases where the payload bay is under under drogue and spinning in a big circle. That can produce input to the accelerometer that mimics flight. So that might explain the upward graph after apogee.
It's also possible you just have a bad unit. I have several Ravens and have flown them on a variety of extreme flights with no issues. Adrian has been very good the couple of times I needed to have a unit fixed due to rough handling. If there is an issue with your unit I'm sure he'll make it right.
I use barometric apogee detection whenever possible though. Just a lot more reliable than accelerometer based, regardless of altimeter.
Tony
Thanks, manixFan. I plotted the pyro voltages just to show the deployment events during the flight. Below is the main battery voltage. It looks rock solid to me, at a near-constant 4.15 volts. The battery is the 1S Lipo that is partnered with the PowerPerch.
#### Buckeye
##### Well-Known Member
TRF Supporter
Obviously I don't speak for Featherweight but if the unit's this far off I think there's a good chance it will be replaced. The errors Adrian was talking about (you can find discussions here if you search enough) were large enough that he stopped recommending the use of accelerometer apogee mode,
Well, the default setting for apogee backup is still accel velocity, and there are no cautionary notes in the documentation. Interestingly, I also previously used a Marsa54L, and it recommended accel velocity as primary apogee mode! Those results were not good either (not as bad as this Raven example), so I reverted back to baro apogee after suffering a couple very early apogee events. I won't be using accel velocity for any apogee event from now on.
#### Buckeye
##### Well-Known Member
TRF Supporter
All accelormeters suffer from the same errors not a particular issue with the Raven, it is however highly flexibable and if you play with the configuration easy enough to stuff up.
This one does however have something wrong, pretty sure this is somehow not callebrated right. Which is why I'm interested in what the accelerometer was reading immediately prior to launch.
Well, I guess I can't answer that as the altimeter was buttoned-up in the rocket immediately before launch! Regardless, calibration error is now ruled-out as the root cause.
I may have stuffed up the settings, but I don't think so. I carefully went over this logic, and all 4 events worked as prescribed.
edit: oh, you mean the pre-launch accel from the flight data, not the calibration procedure. Duh. The fipa file is attached in the first post, but that looks ok.
#### jderimig
Interestingly, I also previously used a Marsa54L, and it recommended accel velocity as primary apogee mode!
Marsa recommends Baro OR Accel (which ever is detected first) as the primary apogee detection mode. But there is nothing wrong with accel based apogee detection on the Marsa unless you go way off vertical (then the Baro will back you up).
If you have very early apogee accel events you should have contacted me to troubleshoot, there may have been a local problem with the board.
#### mikec
##### Well-Known Member
Well, the default setting for apogee backup is still accel velocity...
True. It used to be the other way around (accel for primary, baro for backup.) You're right that the manual doesn't say anything specifically about the scale problem and it ought to.
I would really try to get this unit replaced.
#### manixFan
##### Not a rocket scientist
Here's some comparison data from several of my units, all Raven 2's. But it does show that the accelerometer error is a lot bigger with longer, higher altitude flights:
Code:
L265:
[Altitude (Accel-Ft)] = Min: 0 Max: 30588
[Altitude (Baro-Ft-AGL)] = Min: -1 Max: 19403
935:
[Altitude (Accel-Ft)] = Min: 0 Max: 36355
[Altitude (Baro-Ft-AGL)] = Min: -13 Max: 23589
K627:
[Altitude (Accel-Ft)] = Min: 0 Max: 18734
[Altitude (Baro-Ft-AGL)] = Min: -2 Max: 15466
I55:
[Altitude (Accel-Ft)] = Min: 0 Max: 7259
[Altitude (Baro-Ft-AGL)] = Min: 0 Max: 7826
Research N motor (BALLS)
[Altitude (Accel-Ft)] = Min: 0 Max: 15638
[Altitude (Baro-Ft-AGL)] = Min: -9258 Max: 13144
[Altitude (Accel-Ft)] = Min: 0 Max: 14420
[Altitude (Baro-Ft-AGL)] = Min: -3 Max: 13137
Just as a point of reference. All flew with a redundant altimeter (generally a Stratalogger CF or an RDAS Compact) that matched the baro altitude of the Ravens within typical margin of error.
Tony
Last edited:
#### Buckeye
##### Well-Known Member
TRF Supporter
The Raven suffers from problems because it runs the sensor at 3.3V rather than its specified 5V. The data sheet says it will work at 3.3V but its performance is only specified at 5V. The specifications for the ADC are the worst it has ever been my displeasure to read..
You are the second person to mention this. This is troubling. The Raven is using parts out of their performance range?
The data file shows that the prelaunch acceleration was 1G but that isn't surprising as it is tracking the 1G offset. What is more to the point is that at motor burnout the acceleration barely goes negative. Then when it should be approaching zero while coasting to apogee, it passes that and reaches 0.3G. Not unreasonable for a helium filled Estes Dude but otherwise completely wrong. Since the acceleration due to drag was so badly off, the integrated velocity didn't decrease as fast as it should.
Bingo. This is the analysis I am looking for. I compare the accel output to a simulation to see what the altimeter should be doing. You are correct, the accel barely goes negative and does not asymptotically approach zero at apogee. Since the accel is completely wrong, so is the resulting velocity and altitude.
The consensus seems to be that I am due a replacement altimeter. Waiting for Adrian to respond (either on the forum or to the email I sent several days ago.) I am on a bad luck streak. The last 3 rocketry electronics I purchased all required immediate replacement - altimeter, USB interface, and now another altimeter.
#### mikec
##### Well-Known Member
You are the second person to mention this. This is troubling. The Raven is using parts out of their performance range?
IMHO as a long-time user, the Raven has the best price-performance of anything comparable on the market, I haven't had any problems with any of the ones I've bought, and I would buy more without reservation. There does appear to be an issue with newer batches of devices; it's presumed this is due to the use of the accelerometer ( http://www.analog.com/en/products/mems/accelerometers/adxl278.html ) outside the recommended voltage range, but within the "functional" voltage range. In a perfect world this wouldn't be the case. The first several generations worked fine with the same accel.
The ADXL278 is in last-time-buy status so either the design will be revised to use a different accel or the Raven will eventually become unavailable depending on Featherweight's stock of parts on hand.
#### UhClem
##### Well-Known Member
The ADXL278 is in last-time-buy status so either the design will be revised to use a different accel or the Raven will eventually become unavailable depending on Featherweight's stock of parts on hand.
I am a little surprised that there isn't a Raven4 yet. Adrian sent me an email four years ago saying he was starting on a redesign using a LPC micro-controller. Perhaps other projects got in the way.
#### OverTheTop
##### Well-Known Member
TRF Supporter
IMHO as a long-time user, the Raven has the best price-performance of anything comparable on the market, I haven't had any problems with any of the ones I've bought, and I would buy more without reservation.
+1. I have seven of them. Very reliable based on my usage.
#### Buckeye
##### Well-Known Member
TRF Supporter
IMHO as a long-time user, the Raven has the best price-performance of anything comparable on the market, I haven't had any problems with any of the ones I've bought, and I would buy more without reservation. There does appear to be an issue with newer batches of devices;
As I mentioned earlier, my whole reason for using the accelerometer is to get data for drag analysis. I thought (naively, I guess) that accels were robust and will easily give the feature-rich info I need. Plus, they are much more expensive than baro altimeters, so they have to be good, right? :wink: So far, my accel experience has been less than stellar.
I like all the data generated in the Featherweight FIPA, it is easy to export, and it carries enough resolution and significant digits for my subsequent calculations. I just need the accel to act reasonably during coast drag!
Telemega is $400 and has 6 pyro channels, 70cm Ham band for telemetry downlink with onboard GPS/ http://altusmetrum.org/TeleMega/ #### Buckeye ##### Well-Known Member TRF Supporter Sorry,$300 EasyMega. I don't need the Tele stuff, just interested in what the accelerometer can do.
I sent this inquiry to AdrianA, but I will post the question here, too. I launched my Raven3 for the first time. Fairly vertical flight, and the baro data is as expected. However, the acceleration data went bonkers. Attached are the fipa and some plots showing the issue.
Bottom line: The accel computed velocity< 0 well past the true apogee, and it kept merrily integrating positive altitude for another 12 seconds. As a result, the accel apogee is 5000 ft, while the true baro apogee was only 1700 ft. The #3 charge used for velocity-based apogee backup was pretty worthless, as the rocket was already half way to the ground. Good thing the backup was not needed.
What would cause the accelerometer to think it was still climbing, even though the rocket experienced the jolt of ejection and was falling under drogue for 12 seconds? I know that accelerometers really don't know their direction, but the accel data started off very wrong from liftoff. The first few seconds of accel data are supposed to be the most accurate, right?
I checked the real time data before the flight, after the flight, and after calibration. The readings didn't change much. Axial accel was between 0.8 and 1.2 as recommended.
Thanks.
Sorry your acceleration data was off for your flight. Looking closely at your data file, I think part of the error could have been avoided with a manual re-calibration before the flight, but not all of it.
The pre-launch accel average was about 1.1 Gs, which we would expect to be 1.0 Gs after a re-calibration. But 0.1 G error is 3.2 feet/second per second, so in the 10 seconds to apogee, that could account for about 32 feet/second velocity error if it were a constant offset.
However, the recorded velocity was 200 feet/second at apogee, so there is another source of error. Some Raven units have a nonlinearity in the response of the hardware that makes the scale factor measured in the +/- 1 G calibration different than the scale factor when it's measuring larger accelerations during the boost phase. That's probably the case here. When the rocket was at apogee and the drag would be near zero, your data shows +0.3 Gs measured when it should be slightly negative. If the zero-accel reading is that far off when the +1G and -1G readings are close to what they should be, then that's an indicator of nonlinearity in the hardware. I'll exchange your unit for you.
Looks to me like the usual issue of the accelerometer having a big accelerometer scale error, which has plagued the later production runs of the Raven 3. The Raven operates its accelerometer at voltage lower than the datasheet recommended value
Based on measurements I have made on problem units, the issue of nonlinearity is not from the accelerometer, but from the analog/digital converter in the Zilog 2480 microcontroller, which can have a few counts of nonlinearity error in a certain range of its output. If that range lines up with one of the +/- 1G calibration points, then a relatively small error can make a big difference when the accel is operating 20x (or 70x) outside of the calibrated range. Most units don't have a significant problem with this, but for the few that have a problem, like the one in this thread, I'll replace the units.
Edited to delete info that's redundant with the next post
IMHO as a long-time user, the Raven has the best price-performance of anything comparable on the market, I haven't had any problems with any of the ones I've bought, and I would buy more without reservation.
Thanks, Mike
There does appear to be an issue with newer batches of devices; it's presumed this is due to the use of the accelerometer ( http://www.analog.com/en/products/mems/accelerometers/adxl278.html ) outside the recommended voltage range, but within the "functional" voltage range. In a perfect world this wouldn't be the case. The first several generations worked fine with the same accel.
The accel or its operating voltage range is a reasonable hypothesis, but testing of problem units doesn't bear that out. The analog/digital converter sometimes has a nonlinear response over part of its range that can cause significant calibration errors when the nonlinearity lines up with one of the 2 calibration points. This has been an occasional issue since the Ravens were developed in 2010. I haven't noticed any uptick in the frequency of the problem recently.
The ADXL278 is in last-time-buy status so either the design will be revised to use a different accel or the Raven will eventually become unavailable depending on Featherweight's stock of parts on hand.
Very true. I got the very last production run of Raven3 altimeters fabricated a few weeks ago.
I am a little surprised that there isn't a Raven4 yet. Adrian sent me an email four years ago saying he was starting on a redesign using a LPC micro-controller. Perhaps other projects got in the way.
Yes, it's mostly been because of my day job and travel. I find I can only really focus on one design project at a time, and so there have been several times I have gotten started on an altimeter redesign but had to put it aside for long enough that the parts I picked out are no longer the best available when I'm ready to get started again.
In the last few months I have been pouring time and money into a new Featherweight product, but it's not an altimeter. I'll announce it when I get a prototype done that I'm happy with. I'm on my 6th iteration. After that I'll work on a Raven replacement. There will likely be a gap between the last Raven3 sold and the next Featherweight Altimeter.
#### Buckeye
##### Well-Known Member
TRF Supporter
.. I'll exchange your unit for you.
OK, fair enough. Thanks for the feedback. You have my email from 4/29/17. Please let me know offline how to proceed with the exchange.
#### plugger
##### Well-Known Member
In the last few months I have been pouring time and money into a new Featherweight product, but it's not an altimeter. I'll announce it when I get a prototype done that I'm happy with. I'm on my 6th iteration. After that I'll work on a Raven replacement. There will likely be a gap between the last Raven3 sold and the next Featherweight Altimeter.
I look forward to new Featherweight products Adrian. In my opinion they're the go-to for larger and more aggressive HPR flights. I was actually browsing your photobucket account just last week and got quite excited when I saw this with the filename of RavenPlus. Having an integrated mag switch would be beneficial to the computer imo. It would also be nice to supersede the need for a common rail.
I have 5 ravens currently. One V1, two V2 (single and dual axis accel), two V3 (single and dual axis accel). I've buried a few more, like last year when I had two in a 54mm to 38mm MD staging stack that I've never seen again.
Keep making them and I'll keep buying them...
|
2021-02-26 02:12:58
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47700801491737366, "perplexity": 2129.24236020241}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178355944.41/warc/CC-MAIN-20210226001221-20210226031221-00638.warc.gz"}
|
http://math.stackexchange.com/questions/423764/galois-group-of-mathbbq-sqrt32-omega-sqrt-1-over-mathbbq
|
# Galois group of $\mathbb{Q}(\sqrt[3]{2},\omega,\sqrt{-1})$ over $\mathbb{Q}$
How to find the Galois group $Gal(E|Q)$, where $E=\mathbb{Q}(\sqrt[3]{2},\omega,\sqrt{-1})$? I know that $\text{Gal}(\mathbb{Q}(\sqrt[3]{2},\omega)|\mathbb{Q})=D_3$, where $D_3$ is the dihedral group, $\omega^3=1$. Does it implies that $$\text{Gal}(\mathbb{Q}(\sqrt[3]{2},\omega,\sqrt{-1})|\mathbb{Q})=D_3\times \mathbb{Z}_2 \quad \mbox{?}$$ Thanks for your attention!
-
Yes in this case, but no in general. What you know is $\text{Gal}(\mathbb{Q}(\sqrt[3]{2},\omega,\sqrt{-1})|\mathbb{Q})$ has $D_3$ as a subgroup of index two. If $G$ is a group which has a subgroup $H$ of index two, it is not in general the case that $G$ is isomorphic to $H\times \mathbb{Z}_2$.
However, it is the case that the only group of order 12 having $D_3$ as a subgroup of index two is $D_3\times\mathbb{Z}_2$. Thus the Galois group in this case must be isomorphic to $D_3\times\mathbb{Z}_2$ (or equivalently $D_6$).
|
2016-05-24 12:20:00
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9635044932365417, "perplexity": 40.03908618105337}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049270555.40/warc/CC-MAIN-20160524002110-00081-ip-10-185-217-139.ec2.internal.warc.gz"}
|
http://www.transtutors.com/questions/a-set-up-an-amortization-schedule-for-a-25-000-loan-to-be-repaid-in-equal-installmen-595433.htm
|
+1.617.933.5480
# Q: A)Set up an amortization schedule for a $25,000 loan to be repaid in equal installments at the... A)Set up an amortization schedule for a$25,000 loan to be repaid in equal installments at the end of each of the next 3 years. The interest rate is 10% compounded annually. B)What percentage of the
Connect with a tutor & get this question answered
Related Questions in Time Value of Money
## Ask a New Question
Copy and paste your question here...
Have Files to Attach?
Similar question? edit & resubmit »
## Transtutors Study Membership
• Unlimited Access to 600,000+ Classroom Assignments
• 24/7 availability of experts.
• Plans start from \$12.49
Top Corporate Finance experts
|
2016-05-01 21:13:12
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25633299350738525, "perplexity": 8997.70472983648}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860116929.30/warc/CC-MAIN-20160428161516-00017-ip-10-239-7-51.ec2.internal.warc.gz"}
|
https://chemistry.stackexchange.com/questions/43258/spontaneous-non-spontaneous-reactions-and-reversible-reactions/55696
|
Spontaneous/Non-Spontaneous Reactions and Reversible Reactions
My chemistry textbook states "Reversible reactions constitute a limiting case between spontaneous and non-spontaneous processes."
Does this mean that some of the reversible reactions are spontaneous and others are not? Or that the reversible reactions are sort of intermediary between said two types of reactions? Or something else?
• Your "non-spontaneous" in this context probably means with lowering of entropy of universe - there's no such process, reversible with constant entropy also doesn't really exist and spontaneous with raising entropy of univ. - all processes, so generally this sentence is stupid. – Mithoron Jan 4 '16 at 14:34
• – Mithoron Jan 4 '16 at 14:36
• Also I have a feeling you'd better get better textbook... – Mithoron Jan 4 '16 at 14:38
• cant its sort of a standard. – Batwayne Jan 4 '16 at 14:42
"Reversible reactions constitute a limiting case between spontaneous and non-spontaneous processes." So what does this mean?
To me this sentence is meaningless gobbledygook and should be ignored. That is, this sentence is unhelpful and trying to understand it will just make you more confused and less able to master chemistry. Here is a short summary version of the points I make in the "Advanced discussion" below:
• All reactions can be viewed as reversible from a mathematical standpoint, if the reacting system is "big enough". Reactions that are highly spontaneous in the forward direction mean that at equilibrium, the number of "reactant" molecules will be very very small (but not zero!).
• Many times, "big enough" would mean astronomically big, such as bigger than the Earth. In these cases, reactions can be regarded as "irreversible", although there is no strict, universally agreed upon boundary between "reversible" and "irreversible".
• Whether a reaction is spontaneous isn't that much related to whether it is "reversible". Don't worry about understanding the connection between these concepts until you have understood each concept independently.
The meaning of spontaneous
Spontaneous processes have negative Gibbs free energy changes ($dG < 0$) and also result in positive entropy changes in the universe ($dS_{univ} > 0$). However, $dG$ is a function of state.
For chemical reactions, this means that $dG$ depends on the concentration of the reactants and products, i.e.
$$dG = dG^\circ + RT \ln Q$$
where $Q$ is the reaction quotient.
Thus, if we start off with all "product" and no reactant, then the "reverse" direction of the reaction will be spontaneous. But if we start off with all reactants and no product, then the forward direction is spontaneous.
The meaning of reversible
The short answer is that for chemical reactions, "reversible" does not have a precise thermodynamic definition.
$$dG = dG^\circ + RT \ln Q = -RT \ln K + RT \ln Q = RT \ln \frac{Q}{K}$$
where $K$ is the equilibrium constant. People will usually call reactions with a "large" equilibrium constant irreversible and those with a "small" equilibrium constant reversible. But the exact definition of "large" and "small" isn't well-defined. Many people might say $\frac{Q}{K} \leq .01$ represents an "irreversible" reaction. For chemical reactions with very large equilibrium constants, the size of the system required to ensure that an equilibrium can be reached can get very large, as explained here.
Your textbook has it backwards. Reversible reactions are not a limiting case of spontaneous reactions and non-spontaneous reactions. Spontaneous reactions and non-spontaneous reactions are limiting cases of reversible reactions. As several responders have pointed out, if a reaction only proceeds a little before reaching equilibrium, it approaches the case where no reaction occurs (aka non-spontaneous reaction). If the reaction proceeds to nearly completion before reaching equilibrium, it approaches the case of complete conversion (aka spontaneous reaction).
I agree with other answers and comments that your textbook does not have things stated correctly so I have explained below in words only what I see as the difference between Irreversible and Reversible processes. (You will find spontaneous reactions hidden in these statements)
Every system left to itself will change, rapidly or slowly, in such a way as to reach a state of rest defined in a statistical way and this is also called the state of equilibrium. The system will only move away from its state of equilibrium through the influence of some external events. We are familiar with many processes that reach equilibrium, diffusion of a concentrated solution into a dilute one leading to uniform concentration, transfer of heat from a hot to a cold body leading to uniform temperature, oxidation of substances by the atmosphere, self demagnetisation of magnets are all examples of spontaneous events in nature.
These processes and all other natural processes are similar in one respect, that they all bring the system to equilibrium, and we may think of these systems as loosing some measure of their capacity for spontaneous change.
A system far from equilibrium is one which we would choose to harness for doing useful work, for example the combustion of coal in air to cause a steam engine to operate. However, the second law shows us that it is not the loss of energy that is important but rather the availability of the energy for external purposes.
The essential content of the second law can be given by the statement that when any actual process occurs it is impossible to invent a means of restoring every system concerned to its original condition. Therefore, in a technical sense, any actual process is said to be irreversible.
The ideal or reversible process
We now distinguish between an actual system, which is always irreversible, and an ideal one, which although never occurring in nature is nonetheless imaginable. Such an ideal process is called reversible. In such a process each stage is conducted so that an infinitesimal change in the external conditions would cause a change in the direction of the process. In this sense such an imaginary system is called reversible.
An example is a system of water and water vapour inside a cylinder with a frictionless moveable piston. (In practice, by careful engineering, we can make the friction so small that it is negligible). Outside the piston is gas at some pressure. At constant temperature the system comes to equilibrium with respect to external conditions (pressure , temperature). If now the external pressure is increased, by the piston moving in by an infinitesimal amount, water vapour condenses. If the pressure is now reduced by an infinitesimal amount, some water evaporates. Thus the work required to vaporise 1 mole of water and to condense 1 mole of vapour differs only by an infinitesimal amount.
Another example is provided by an electrochemical cell where the cell potential can be measured extremely accurately with a voltmeter. The cell can be balanced so finely against an external emf that the current that can be made to flow in one direction or the other is only microamps.
A similar situation applies to thermal processes, since if two bodies differ in temperature by only an infinitesimal amount, the transfer of heat is likewise a reversible process for it would be possible to restore the system to its original condition with only an infinitesimal change in the external system.
(for a fuller description see Lewis & Randall 'Thermodynamics')
Reversible reactions constitute a limiting case between spontaneous and non-spontaneous processes [?]
A reversible process is a hypothetical process where the entropy of the system and its surrounding is constant. This is hypothetical because nothing happens unless the entropy increase at least a tiny bit. In other words, if the system is at equilibrium, the entropy does not increase, but nothing happens either.
Colloquially, a reversible reaction is one where forward and reverse reaction happen, i.e. one that would attain equilibrium at some point (if "left alone").
What I think the textbook is trying to say is that the Gibbs energy is negative for a spontaneous process, is positive for a non-spontaneous process, and is zero for a process that is at equilibrium. (This would be at constant pressure in the absence of non-PV work). So if you have an axis with the Gibbs energy for a process, there is a point where the system is at equilibrium. On one side of it are the spontaneous and on the other side are the non-spontaneous processes.
I'm not sure how that statement helps to understand anything, though. I also don't think it is the correct way of using the term "limiting case". Wikipedia gives the following definition:
In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values.
So maybe one could say a reaction that goes to completion is the limiting case of a reaction with a high equilibrium constant. In the statement in question, however, there is talk about a "limiting case between" two cases, not the most extreme value of either of them.
|
2021-04-15 03:35:23
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6420928239822388, "perplexity": 530.0094640576996}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038082988.39/warc/CC-MAIN-20210415005811-20210415035811-00245.warc.gz"}
|
https://plaintifftriallawyertips.com/category/argument
|
### Browsed byCategory: Argument
EMPOWERING THE JURY TO ACT AS THE CONSCIENCE OF THE COMMUNITY
## EMPOWERING THE JURY TO ACT AS THE CONSCIENCE OF THE COMMUNITY
INTRODUCTION We know research has shown the majority of jurors want to feel their verdict is a “meaningful verdict.” That means a verdict which they will be proud of when they go home. They also want to do “the right thing” and be involved in a trial that has importance, so their time spent was not wasted. We should address these motivations in argument by making the case more important than simply resolving the issues involving the two sides in the trial….
GERRY SPENCE DAMAGE ARGUMENT IN A BIRTH INJURY CASE
## GERRY SPENCE DAMAGE ARGUMENT IN A BIRTH INJURY CASE
I’ve previously quoted from a jury argument Gerry Spence made in the trial of Hunter vs Lewis which took place in Utah in 1982. https://plaintifftriallawyertips.com/excerpts-from-gerry-spence-argument-in-hunter-v-lewis-malpractice-case The case involved a birth injury to a child. Here are some additional excerpts of his argument relating to money: I haven’t made your job easy. I’ve asked for $40 million dollars. People have said, “how could you ask for$40 million?” Some people are aghast, some even outraged, some have tried to shame me,…
EXCERPTS FROM GERRY SPENCE ARGUMENT IN HUNTER v LEWIS MALPRACTICE CASE
## EXCERPTS FROM GERRY SPENCE ARGUMENT IN HUNTER v LEWIS MALPRACTICE CASE
In 1982 Gerry Spence tried a case in Provo Utah, Hunter v. Lewis. The transcript of his opening summation has examples of persuasive ideas worth reviewing. Here are a few of them: “Now, in a little while the case of Joshua Hunter is going to be in your hands. And there’s something, however, that I want to say to you about that that’s important for you to understand; and that is: that each one of us are human beings, just…
|
2021-05-15 20:41:16
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5296099781990051, "perplexity": 3601.071306842531}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991378.52/warc/CC-MAIN-20210515192444-20210515222444-00629.warc.gz"}
|
https://khsm.be/calcium+metal+hydrochloric+acid+in+bulgaria+19760.html
|
# calcium metal hydrochloric acid in bulgaria
#### What''s the balanced equation for magnesium and
Apr 23, 2014· The balanced chemical equation is: Mg_((s))+ 2HCl_((aq))rarrMgCl_(2(aq)) + H_(2(g) The reaction between magnesium and hydrochloric acid coine to form a salt of magnesium chloride and release hydrogen gas. This single replacement reaction is a classic example of a metal reacting in an acid to release hydrogen gas. I hope this was helpful.
#### Answered: Aqueous hydrochloric acid reacts with… | bartleby
Aqueous hydrochloric acid reacts with solid calcium metal to form a solution of calcium chloride and hydrogen gas. The reaction is highly spontaneous and proceeds to completion. A chemist reacts 65.30 g calcium with excess hydrochloric acid at STP. You may assume the …
#### OQEMA Chemical Industry & Synthesis
Bulgaria. Czech Republic. Denmark. France. Germany. Great Britain. Greece. Hungary. Ireland. Italy. Lithuania. Netherlands. Poland. Calcium chloride Hydogen peroxide Sodium hydroxide solution 1N Hydrochloric acid 1N Sulphuric acid 95-97% Specialities Adipic acid
#### Difference Between Hydrochloric Acid and Sulfuric Acid
Jul 03, 2017· Difference Between Hydrochloric Acid and Sulfuric Acid Definition. Hydrochloric Acid: Hydrochloric acid is a strong acid composed of hydrogen and chlorine atoms. Sulfuric Acid: Sulfuric acid is a strong acid composed of hydrogen, sulfur and oxygen atoms. Molar Mass. Hydrochloric Acid: The molar mass of hydrochloric acid is about 36.5 g/mol.
#### Is Hydrochloric Acid or Phosphoric Acid Better for Scale
Phosphate ions can coine with calcium ions to form calcium phosphate, a highly insoluble compound. Because it can increase phosphate concentration and is a weaker acid, phosphoric acid is a less effective scale-removing agent than hydrochloric acid. Hydrochloric acid or sulfuric acid are more commonly used for industrial scale removal.
#### Reactions of Group 2 Elements with Acids - Chemistry
Aug 15, 2020· Reactions with dilute hydrochloric acid. Each metal reacts with dilute hydrochloric acid, producing bubbles of hydrogen gas and a colorless solution of the metal chloride: $X + 2HCl \rightarrow XCl_2 + H_2$ These reactions become more vigorous down the group.
#### Hydrochloric Acid Suppliers, CAS No. 7647-01-0
Hydrochloric acid is a clear, colorless to slightly yellow, highly pungent solution of hydrogen chloride (HCl) in water. It is a highly corrosive acid with many industrial uses. It is a monoprotic acid and is least likely to undergo an interfering oxidation-reduction reaction compared to other industrial acids.
#### What happens if calcium carbonate reacts with hydrochloric
18 12.0 Appendices Figure 1: Calcium Carbonate Figure 2: Hydrochloric Acid Gas Bubbles Calcium (Carbon Carbonate Dioxide) Calcium Carbonate: Powder Hydrochloric Acid: Liquid When they reacts, gas bubbles comes out Hydrochloric Acid Figure 3: Reaction of Calcium Carbonate and Hydrochloric Acid 19 13.0 Bibliography Authority, Q. S. (2014, 3).
#### Calcium Carbonate And Hydrochloric Acid Concentration
Calcium Carbonate And Hydrochloric Acid Concentration Experiment. Hypothesis: In a reaction between calcium carbonate and hydrochloric acid, the products calcium chloride, carbon dioxide and water are formed. I predict that the higher temperature of HCl acid, the higher the reaction rate will be, this is because at a higher temperature there will more fast-moving hydrochloric acid molecules
#### Hydrochloric acid | National Pollutant Inventory
Hydrochloric acid is a solution of hydrogen chloride in water. Hydrogen chloride occurs as either a colourless liquid with a an irritating, pungent odour, or a colourless to slightly yellow gas which can be shipped as a liquefied compressed gas; highly soluble in water.
#### UNdata | record view | Trade of goods , US$, HS 1992, 28 Calcium Strontium and barium Rare-earth metals, scandium and yttrium Mercury Hydrogen chloride (hydrochloric acid) Chlorosulphuric acid Sulphuric acid, oleum Nitric acid, sulphonitric acids Diphosphorus pentaoxide Phosphoric acid and polyphosphoric acids Oxides of boron, boric acids Hydrogen fluoride (hydrofluoric acid) Inorganic acids nes #### reactions between metals and acids Calcium. It is safe to carry out the reaction between calcium and hydrochloric acid as long as the acid is very dilute. The next piece of video talks about the acid being "0.5 molar". Molarity is a measure of concentration. Most dilute hydrochloric acid found in school labs will be either 1 molar or 2 molar. #### Hydrochloric Acid | เทียนนำเคมีเคิล อินดัสเทรียลเทรด ขาย ไฮโดรคลอริค เอซิด 35% โดย เทียนนำเคมีเคิล อันดัสเทรียลเทรด ผู้นำเข้าและจัดจำหน่ายเคมีภัณฑ์สำหรับอุตสาหกรรม มีประสบการณ์ดำเนินงานมากว่า 60 #### CALCIUM SILIE gradually hydrochloric acid until no effervescence is observed, then add 10 ml more of the acid, and evaporate the mixture on a steam bath to dryness. Cool, add 20 ml of water, boil and filter the mixture through an ash-free filter paper. An insoluble residue of silica remains. (Note. Retain the filtrate for the test for calcium). #### Chapter 11 reactivity of Metals - Q.docx - 1 2 3 4 Which 4 (a) Predict whether lithium carbonate will be decomposed on heating. Explain briefly. (2 marks) (b) Given a sample of lead(II) oxide. Suggest TWO methods to extract lead from lead(II) oxide. (2 marks) (c) Predict the observations of the following reactions: (i) A piece of copper is put into dilute hydrochloric acid. (1 mark) (ii) A piece of lead is put into silver sulphate solution. #### Calcium Carbonate and Hydrochloric Acid Reaction | CaCO3 + HCl Metal carbonate compounds react with dilute acids and emit carbon dioxide gas. Balanced chemical equation of CaCO 3 and HCl reaction with physical states CaCO 3(s) + 2HCl (aq) → CaCl 2(aq) + CO 2(g) + H 2 O (l). Calcium carbonate is not soluble in water and exists as white precipitate in the water. When aqueous hydrochloric acid is added, calcium chloride, carbon dioxide and water are formed. #### Mineral Primer - The Weston A. Price Foundation Nov 17, 2020· Minerals may “compete” for receptor sites. Excess calcium may impede the absorption of manganese, for example. Lack of hydrochloric acid in the stomach, an over-alkaline environment in the upper intestine or deficiencies in certain enzymes, vitamin C and other nutrients may prevent chelates from releasing their minerals. #### How to Balance: Ca + HCl = CaCl2 + H2| Breslyn Word equation: Calcium + Hydrochloric acid → Calcium chloride + Hydrogen gas. Type of Chemical Reaction: For this reaction we have a single displacement reaction. Balancing Strategies: In this reaction Calcium (Ca) metal is reacting with Hydrochloric acid (HCl).the Ca replaces the H in HCl and we end up with CaCl2 and H2. Overall it is a fairly straightforward equation to balance. #### Magnesium and Hydrochloric Acid | Chemdemos Magnesium reacts with hydrochloric acid according to the equation: Mg(s) + 2 HCl(aq) --> MgCl 2 (aq) + H 2 (g) This demonstration can be used to illustrate the characteristic reaction of metals with acid, a single replacement reaction, or to demonstrate the generation of hydrogen gas.The flammability of hydrogen gas can be demonstrated by carefully holding a match or fireplace lighter up to #### Hydrochloric acid - Wikipedia Hydrochloric acid, also known as muriatic acid, is an aqueous solution of hydrogen chloride.It is a colorless solution with a distinctive pungent smell. It is classified as a strong acid.It is a component of the gastric acid in the digestive systems of most animal species, including humans. Hydrochloric acid … #### Solved: Calcium Metal Reacts With Hydrochloric Acid (HCl Question: Calcium Metal Reacts With Hydrochloric Acid (HCl) To Form Aq Calcium Chloride And Hydrogen Gas.Ca(s)+2HCl(aq) ? CaCl2(aq)+H2(g)0.401 G Of Calcium Metal Is Reacted With 0.350L Of 0.0400M Hydrochloric Acid.(a)write The Complete Ionic Equation Of The Reaction.(b)Calculate The Moles Of Calcium And Hydrochloric Acid.(c)identify The Limiting Reagent.(d)Assuming #### UNdata | record view | Trade of goods , US$, HS 1992, 28
Calcium Strontium and barium Rare-earth metals, scandium and yttrium Mercury Hydrogen chloride (hydrochloric acid) Chlorosulphuric acid Sulphuric acid, oleum Nitric acid, sulphonitric acids Diphosphorus pentaoxide Phosphoric acid and polyphosphoric acids Oxides of boron, boric acids Hydrogen fluoride (hydrofluoric acid) Inorganic acids nes
#### Why does calcium carbonate dissolve in hydrochloric acid
I’m not sure I would use the term “dissolve.” I’d go for “react.” Calcium carbonate undergoes a chemical reaction with hydrochloric acid. The reaction results in the formation of carbon dioxide gas and leaves calcium ions and chloride ions in solu
#### reactions between metals and acids
Calcium. It is safe to carry out the reaction between calcium and hydrochloric acid as long as the acid is very dilute. The next piece of video talks about the acid being "0.5 molar". Molarity is a measure of concentration. Most dilute hydrochloric acid found in school labs will be either 1 molar or 2 molar.
#### Hydrochloric Acid, TraceGrade | | H1122 | Spectrum Chemical
Hydrochloric Acid, TraceGrade is a strong, highly corrosive mineral acid with extremely low metal content (over 50 with levels less than 1 PPB). This grade is primarily used as an analytical reagent in elemental analysis determinations using ICP and AA techniques, digestion of water samples and as a doping agent for organic semiconductors.
#### (Get Answer) - Calcium metal reacts with hydrochloric acid
Feb 24, 2021· Calcium metal reacts with hydrochloric acid (HCl) to form aq calcium chloride and hydrogen gas. Ca(s)+2HCl(aq) ? CaCl2(aq)+H2(g) 0.401 g of calcium metal is reacted with 0.350L of 0.0400M hydrochloric acid. (a)write the complete ionic equation of …
#### Hydrochloric Acid - an overview | ScienceDirect Topics
Sumit Chakraborty, Byung Wan Jo, in Carbon Dioxide Sequestration in Cementitious Construction Materials, 2018. 3.5.2.1.1 Hydrochloric acid extraction route. Hydrochloric acid (HCl) can be used to activate the Mg and Ca silie-based minerals (Lackner et al., 1995, 1997b; Haywood et al., 2001).This process is basically used to increase the availability of calcium or Mg ions from mineral
|
2021-09-23 03:34:55
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5655361413955688, "perplexity": 12969.572280948067}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057416.67/warc/CC-MAIN-20210923013955-20210923043955-00637.warc.gz"}
|
https://www.physicsforums.com/threads/what-to-learn-this-summer.796200/
|
What to learn this summer?
Hi, I study physics with computer instead of labs, and this summer I will only be taking one course (the first prog course). I will have free time to study other things, and I want to learn things that will not be covered in my uni program. I already know c++ basics from Accelerated c++.
I thought of Qt and opengl or an opensource engine like ogre.
Are these good ideas? Do you have suggestions on what could be interesting for my future studies and personal projects? Thanks
DEvens
Gold Member
First, congrats on learning C++ from Accelerated C++. This is one of the most highly recommended books on the subject.
I have kind of a curve-ball suggestion. Instead of learning a new language or two, or maybe in addition to learning them, learn to program well. Get the book _Code Complete_ by Steve McConnell. Get the Effective C++ books by Scott Meyers. Sample the other books about coding style, reducing bug count, and making your code easy to read, easy to test, easy to maintain, etc.
Many is the time I have had to follow behind somebody who learned algorithm and language features, but never the "ethical" way to apply them. It can often be very painful.
harborsparrow, Geranimo, Greg Bernhardt and 1 other person
D H
Staff Emeritus
Plus one on DEvens suggestion on reading Code Complete.
Some other suggestions:
• Learn about algorithms. The most important class a non-computer science major can take beyond the basic "can has programming?" class is "algorithms and data structures". Read "Introduction to Algorithms" by Cormen, Leiserson, Rivest, and Stein, or "Algorithms in C++" by Sedgewick.
• Learn about version control and configuration management. Much as I dislike it (the words "hate" and "loathe" aren't strong enough), I strongly suggest you learn how to use git.
• Learn the old-style tools of the trade of scientific programming. That would be BLAS (basic linear algebra subprograms) and the various packages such as LAPACK that are wrappers around BLAS.
• Learn some new-style tools of the trade of scientific programming. For example, Eigen.
• Learn a very different (but practical) language such as lisp or haskell. Functional programming will give you a new perspective on programming. The newest version of C++ (C++ 2014) introduced a number of functional programming concepts to the language.
• Learn a very, very different language such as brainf*ck (substitute the asterisk with the appropriate vowel), which is one of many Turing tarpit languages. Here's "Hello, World!" in that language:
Code:
++++++++[>++++[>++>+++>+++>+<<<<-]>+>+>->>+[<]<-]>>.>---.+++++++..+++.>>.<-.<.+++.------.--------.>>+.>++.
• Learn a very, very, very different language. Or more than one. It's a bit fun. This is LOLCODE:
Code:
HAI
CAN HAS STDIO?
PLZ OPEN FILE "LOLCATS.TXT"?
AWSUM THX
VISIBLE FILE
O NOES
INVISIBLE "ERROR!"
KTHXBYE
Last edited:
Geranimo and fluidistic
Thanks for your suggestions! My uni program already has algorithm in it so I think i'll focus on something else. Also, these strange languages are just for fun right? Nobody uses them seriously?
jtbell
Mentor
Physics Beard, Geranimo and DEvens
Thanks for your suggestions! My uni program already has algorithm in it so I think i'll focus on something else. Also, these strange languages are just for fun right? Nobody uses them seriously?
"Esoteric languages" are a bit of fun, but they are turing complete. So library support aside, you can write anything in them that you could do in any other turing complete language such as C++.
I can't really recommend something specific as I don't know your intentions but I will suggest that you learn the tools used by software developers. That means stuff like version control (i.e. github), shell scripting, how to talk to a database, and possibly some kind of dynamic language (Python?) as they're really useful for doing quick jobs.
Why?
I contribute to an advocacy group that teaches developer skills to domain programmers (http://software-carpentry.org/). For example I once met a biologist who was part of a group that shared the results of their software by emailing each other a spreadsheet which they updated and emailed to the next guy. Not only is this inefficient, it also breaks when someone misses an update. We taught them how to write the code that connects to a database, and some basic SQL (the language most databases use for queries), and enough bash (linux shell script) to automate the system, and they were much happier after that.
Anyway my #1 suggestion is that if you don't know how to use a VCS like git (github's backend), learn this NOW.
D H and Geranimo
|
2022-05-20 03:47:41
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21968138217926025, "perplexity": 2367.747544888432}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662531352.50/warc/CC-MAIN-20220520030533-20220520060533-00799.warc.gz"}
|
http://electricbook.works/typography/text/01-06.html
|
Contents
## Boxes
You should be able to throw a box around any block-level element (paragraphs, lists, blockquotes and more) by giving it a box class. Using some sample text from Gertrude Chandler Warner’s The Box-Car Children, here is a selection of elements with box classes, interspersed with text and other elements to see how they interact.
### The Flight
About seven o’clock one hot summer evening a strange family moved into the little village of Middlesex. Nobody knew where they came from, or who they were. But the neighbors soon made up their minds what they thought of the strangers, for the father was very drunk. He could hardly walk up the rickety front steps of the old tumble-down house, and his thirteen-year-old son had to help him. Toward eight o’clock a pretty, capable-looking girl of twelve came out of the house and bought a loaf of bread at the baker’s. And that was all the villagers learned about the newcomers that night.
“There are four children,” said the bakeshop woman to her husband the next day, “and their mother is dead. They must have some money, for the girl paid for the bread with a dollar bill.”
“Make them pay for everything they get,” growled the baker, who was a hard man. “The father is nearly dead with drink now, and soon they will be only beggars.”
This happened sooner than he thought. The next day the oldest boy and girl came to ask the bakeshop woman to come over. Their father was dead.
She went over willingly enough, for someone had to go. But it was clear that she did not expect to be bothered with four strange children, with the bakery on her hands and two children of her own.
“Haven’t you any other folks?” she asked the children.
“We have a grandfather in Greenfield,” spoke up the youngest child before his sister could clap her hand over his mouth.
• “Hush, Benny,” she said anxiously.
• “He doesn’t like us,” replied the oldest boy reluctantly. “He didn’t want my father to marry my mother, and if he found us he would treat us cruelly.”
• “Did you ever see him?”
• “Jess has. Once she saw him.”
“Well, did he treat you cruelly?” asked the woman, turning upon Jess.
“Oh, he didn’t see me,” replied Jess. “He was just passing through our—where we used to live—and my father pointed him out to me.”
• “Where did you use to live?” went on the questioner. But none of the children could be made to tell.
• “We will get along all right alone, won’t we, Henry?” declared Jess.
• “Indeed we will!” said Henry.
• “I will stay in the house with you tonight,” said the woman at last, “and tomorrow we will see what can be done.”
The four children went to bed in the kitchen, and gave the visitor the only other bed in the house. They knew that she did not at once go to bed, but sat by the window in the dark. Suddenly they heard her talking to her husband through the open window.
• “They must go to their grandfather, that’s certain,” Jess heard her say.
• “Of course,” agreed her husband. “Tomorrow we will make them tell us what his name is.”
• Soon after that Jess and Henry heard her snoring heavily. They sat up in the dark.
• “Mustn’t we surely run away?” whispered Jess in Henry’s ear.
“Yes!” whispered Henry. “Take only what we need most. We must be far off before morning, or they will catch us.”
Jess sat still for a moment, thinking, for every motion she made must count.
This is a blockquote in a box, by the way. The next three boxes are also blockquotes in boxes with multiple paragraphs. First singly separated with body text, then consecutively.—Ed.
“I will take both loaves of bread,” she thought, “and Violet’s little workbag. Henry has his knife. And all Father’s money is in my pocket.” She drew it out and counted it in the dark, squinting her eyes in the faint light of the moon. It amounted to nearly four dollars.
“You’ll have to carry Benny until he gets waked up,” whispered Jess. “If we wake him up here, he might cry.”
She touched Violet as she spoke.
“Sh! Violet! Come! We’re going to run away,” she whispered.
The little girl made no sound. She sat up obediently and tried to make out the dim shadow of her sister.
“What shall I do?” she said, light as a breath.
“Carry this,” said Jess, handing her the workbag and a box of matches.
Jess tiptoed over to the tin box on the table, drew out the two loaves of bread, and slipped them into the laundry bag. She peered around the room for the last time, and then dropped two small clean towels and a cake of soap into the bag.
“All right. Pick him up,” she said to Henry.
Henry bent over the sleeping child and lifted him carefully. Jess took the laundry bag, turned the doorknob ever so softly, opened the door ever so slowly, and they tiptoed out in a ghostly procession.
Jess shut the door with as much care as she had opened it, listened to the bakeshop woman’s heavy snoring for a moment, and then they turned and picked their way without a sound to the country road.
“She may wake up before morning, you know,” whispered Henry. “We must do our fastest walking before then. If we can only get to another town before they find out we’re gone, they won’t know which way to go.”
Jess agreed, and they all walked briskly along in the faint moonlight.
1. “How far can you carry Benny?” asked Violet.
2. “Oh, at least a mile,” said Henry confidently, although his arms were beginning to ache. Benny was five years old, and he was a fat, healthy boy as well.
1. “I think we could all walk faster if we woke him up,” said Jess decidedly. “We could each take his hand and almost carry him along.”
2. Henry knelt by the roadside and set the little fellow against his knee.
3. “Come, Benny, you must wake up now and walk!” said Jess coaxingly.
4. “Go away!” Benny mumbled with his eyes shut, trying to lie down again.
1. “Let me try,” Violet offered softly.
1. “Say, Benny, you know little Cinnamon Bear ran away to find a nice warm bed for the winter? Now, you play you’re Cinnamon, and Henry and Jess will help you along, and we’ll find a bed.”
2. Violet’s little plan worked. Benny was never too cross to listen to the wonderful stories his sister Violet could tell about Cinnamon Bear. He stood up bravely and marched along, yawning, while his big brother and sister almost swung him between them.
3. Not a soul passed them on the country road. All the houses they saw were dark and still. And when the first faint streaks of morning light showed in the sky, all four children were almost staggering with sleep.
5. “I must go to sleep, Henry,” murmured Jess at last. Little Benny was asleep already, and Henry was carrying him again.
6. “The first place we come to, then,” panted Henry.
Violet said nothing, but she kept her eyes open.
Finally she caught Henry’s sleeve. “Couldn’t we make that haystack do?” she asked, pointing across a newly mown field.
1. “Indeed we could,” said Henry thankfully. “What a big, enormous one it is! I was too sleepy to see it, I guess.”
2. “And see how far away from the farmhouse and barn it is, too!” echoed Jess.
1. The sight gave them new courage. They climbed over two stone walls, got across a brook somehow with the heavy child, and arrived at the haystack.
2. Henry laid his brother down and stretched his aching arms, while Jess began to burrow into the haystack. Violet, after a moment of watching her, did the same.
1. “Here’s his nest,” said Jess sleepily, taking her head out of the deep round hole she had made. Henry lifted the child into the opening and was pleased to see that he curled up instantly, smiling in his sleep.
2. Jess pulled wisps of hay over the opening so that it was absolutely invisible, and then proceeded to dig out a similar burrow for herself.
3. “We can stay here just—as long—as we like, can’t we, Henry?” she murmured, digging with her eyes shut.
3. “We sure can,” replied Henry. “You’re an old brick, Jess. Get in, and I’ll pull the hay over the hole.”
4. Violet was already curled up in her nest, which was hidden so completely that Henry spoke to her to see if she were there. Then he wriggled himself backward into the haycock without stopping to hollow it out, pulled a handful of hay over his head, and laid his head on his arm.
Just as he did so he heard a heavy voice say, “Now, then, lass, git along!” Then he heard the rumble of a milk wagon coming down a near-by lane, and he realized thankfully that they had hidden themselves just before the first farmer in the neighborhood had set off toward Middlesex with his milk cans.
“He will say he didn’t meet us coming this way,” thought Henry, “so they will hunt for us the other way. And that will give us time to cover a lot more ground.”
He dropped asleep just as the roosters all over the valley began to answer each other.
|
2017-06-23 10:28:56
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19566462934017181, "perplexity": 7854.190568362176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320049.84/warc/CC-MAIN-20170623100455-20170623120455-00189.warc.gz"}
|
https://math.stackexchange.com/questions/2819211/basic-probability-with-random-number
|
Basic Probability with random number
The question I have on hand is as follows :
We draw at random a number in interval [0,1] such that each number is "equally likely". Suppose we do the experiment two times (independently), giving us two numbers in [0,1]. What is the probability that the sum of these numbers is greater than 1/2?
My understanding is that since the experiments are independent, I am able to multiply the probability of each experiment with each other directly.
My attempt at this was to calculate probability of each experiment where x (the random number) is less than 1/4, thus giving me the probability of 1/16 when I multiply them. This would imply that there is a 15/16 chance my sum is greater than 1/2. However the answer is wrong since it is supposed to be 7/8.
Choosing two numbers randomly (uniformly, independently) in the unit interval $[0,1]$ is the same as choosing a single point uniformly in the unit square $[0, 1]\times [0,1]$, and looking at its first and second coordinate.
Now, take a look at that square (you can even draw it, if you want). See if you can tell which points are such that their two coordinates add up to more than $\frac12$. (The line $x+y = \frac12$ is very relevant here, because it consists of the points where the two coordinates add up to exactly $\frac12$. That is what $x + y = \frac12$ really means, after all. You can draw that too to help you.) What's the area of that region?
As an extra exercise, you tried looking at the region where both the variables were smaller than $\frac14$. Can you draw that into the square? Can you see why your answer was wrong?
|
2019-04-22 04:53:07
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9147115349769592, "perplexity": 137.43726066663984}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578534596.13/warc/CC-MAIN-20190422035654-20190422061654-00167.warc.gz"}
|
https://socratic.org/questions/if-it-takes-54-ml-of-0-100-m-naoh-to-neutralize-125-ml-of-an-hcl-solution-what-i
|
# If it takes 54 mL of 0.100 M NaOH to neutralize 125 mL of an HCl solution, what is the concentration of the HCl?
Apr 8, 2018
$c = 0.0432 m o l {\mathrm{dm}}^{-} 3$
#### Explanation:
The first step would be to find the molar ratio in the reaction. Now generally, one can simplify strong acid-strong base reaction by saying:
Acid+Base ->Salt+ Water
Hence:
$H C l \left(a q\right) + N a O H \left(a q\right) \to N a C l \left(a q\right) + {H}_{2} O \left(l\right)$
So our acid and base are in a 1:1 molar ratio in this case- so an equal amount of $N a O H$ must have reacted with $H C l$ for the solution to neutralize.
Using the concentration formula:
$c = \frac{n}{v}$
$c$=concentration in $m o l {\mathrm{dm}}^{-} 3$
$n$=number of moles of substance dissolved in solution volume $\left(v\right)$
$v$=volume of the solution in liters - ${\mathrm{dm}}^{3}$
We were given concentration and volume of $N a O H$, so we can find its number of moles:
$0.1 = \frac{n}{0.054}$
$n = 0.0054$ mol
Hence, this must be the number of moles of $H C l$ found in the 125-milliliter solution, as we established that they reacted in a 1:1 ratio.
So:
$\frac{0.0054}{0.125} = c$
$c = 0.0432 m o l {\mathrm{dm}}^{-} 3$
|
2019-09-21 17:19:04
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 17, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8461039662361145, "perplexity": 1557.181648679491}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574588.96/warc/CC-MAIN-20190921170434-20190921192434-00063.warc.gz"}
|
https://physics.aps.org/articles/v3/s43
|
Synopsis
# Drying out in 3D
Physics 3, s43
As aqueous emulsions containing colloidal particles dry, two very different behaviors are observed.
Mixtures of immiscible fluids with colloids can be very complex but they are technologically important for industries such as paints and protective coatings, especially when such materials undergo drying. Emulsions containing colloidal particles are particularly interesting as controllable test cases of such systems, but they are difficult to image because these mixtures typically scatter light strongly. Lei Xu at The Chinese University of Hong Kong and colleagues in the US, France, Switzerland, UK, and Japan now report in Physical Review Letters their ability to create a full 3D picture of what happens when these emulsions dry out.
The authors mixed a suspension of $1μm$ polymethylmethacrylate spheres (dyed green) in decahydronaphthalene with an aqueous emulsion of water and glycerol, plus a surfactant to stabilize the water droplets (dyed red). Pictures of this concoction were obtained with a confocal microscope, which captures very thin slices of the sample that can be built up into high-resolution 3D images. As the mixture dries on a microscope slide, two different behaviors emerge: large droplets evacuate quickly, whereas small droplets undergo shape changes yet remain essentially intact. A simple model allows the authors to calculate the threshold radius for evaporation, and with this technique they have been able to create a new class of hierarchical materials. – David Voss
## Related Articles
Soft Matter
### Record Lifetime for a Bubble
Researchers created a gas bubble that lived for 465 days, a world record for this type of object. Read More »
Fluid Dynamics
### Predicting the Shape of Pointy-Rock Forests
The shape and curvature evolution of dissolving rocks can be predicted using a new theory. Read More »
Soft Matter
### Particles Make Their Own Movie
Active particles organize into mesmerizing patterns in response to a time-varying electric field. Read More »
|
2022-01-24 17:14:26
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3663770258426666, "perplexity": 3239.5895503253664}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304572.73/warc/CC-MAIN-20220124155118-20220124185118-00278.warc.gz"}
|
https://www.physicsforums.com/threads/circular-motion-problem.210375/
|
# Circular Motion Problem
1. Jan 22, 2008
### rabar789
[SOLVED] Circular Motion Problem
1. The problem statement, all variables and given/known data
A coin is placed 0.11 meters from the center of a rotating turntable. The speed of the turntable is slowly increased; the coin remains fixed on the turntable until 36 rpm is reached and the coin slides off. What is the coefficient of the static friction between the coin and the turntable?
2. Relevant equations
T= (2*pi*r)/v
T= tau, which I believe is revolutions per second
(Fnormal)(coefficient of static friction) = (Ffriction)
Ac = v^2/r
Ac = centripetal acceleration
3. The attempt at a solution
First I divided the rpm by 60 to get the revolutions per second, or 0.6 rps. I put that as T in the tau equation and solved for v: 1.15 m/s. Then, because I was unsure of where to go next because of a lack of a mass value, I did something sort of stupid where I solved for Ffriction using the wrong equation or something (I'm reviewing an old test, not sure what my rationale was):
F = (coefficient)(Fnormal)
except for Fnormal part I did mass times centripetal acceleration
F = (coefficient)(m)(v^2/r)
and got a coefficient of 0.8123, which was wrong. At least I'm getting close; I believe coefficients of static friction must be less than 1.
Can anyone please give me a hand?
2. Jan 22, 2008
### awvvu
Your answer should end up independent of mass, as friction problems usually are.
T is the period, which is seconds per revolution, not revolutions per second (that's frequency).
You're on the right track using the centripetal acceleration though. However, you don't simply plug that as the normal force. The normal force is simply mg.
Try writing out newton's 2nd law for the coin.
Last edited: Jan 22, 2008
3. Jan 22, 2008
### rabar789
OK so this is what I tried:
Ffriction = Fc
(coefficient)(Fnormal mg) = (mass)(v^2/r)
I cancel out the masses and solve for the coefficient and I get 1.226, which I believe is impossible because it's greater than one. I follow your logic, but maybe I did something wrong in the math...?
4. Jan 22, 2008
### awvvu
Think about how you determined v.
$$v = \frac{2 \pi r} {T}$$
You plugged in T = 0.6 revolutions/second, which makes no sense in this equation. Check the units on T.
5. Jan 22, 2008
### rabar789
Wait, now I'm really confused. How do I convert 36 revolutions per minute to "X" seconds per revolution?
6. Jan 22, 2008
### awvvu
Simple, it's just T = 1/f, where f = 0.6 rev/s. You'll get units of [s/rev] or just .
7. Jan 22, 2008
### rabar789
Ah! Thanks! I took that answer, plugged it into all my other equations and solved for the coefficient of static friction, getting 0.15976. It seems right, but I have no way of checking. I appreciate the help!
|
2017-01-17 21:38:06
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.606630802154541, "perplexity": 1161.1261516995244}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280086.25/warc/CC-MAIN-20170116095120-00379-ip-10-171-10-70.ec2.internal.warc.gz"}
|
https://mathoverflow.net/questions/360540/decay-of-fourier-coefficients-of-real-analytic-functions
|
Decay of Fourier coefficients of real analytic functions
I would like to have any suggestion/reference to the following question. I have a differential operator $$\mathcal{L}$$ with discrete spectrum defined on a a suitable Sobolev space on a domain $$\Omega$$, generating an orthonormal basis of eigenfunctions $$\varphi_k$$ in $$L^2(\Omega)$$. Given a function $$f\in C^{0}(\overline{\Omega})$$ which is real-analytic inside $$\Omega$$, what can be said in general about the decay of the Fourier coefficients $$f_k=(f,\varphi_k)_{L^2}$$ of $$f$$ with respect the basis $$\varphi_k$$? Thanks a lot!
If the domain $$\Omega$$ were a closed analytic manifold and $$\mathcal{L}$$ were elliptic of order $$m$$ with analytic coefficients, the relevant result would be due to
Theorem. Denoting by $$\lambda_k$$ the eigenvalue of $$\varphi_k$$, $$f$$ is analytic iff $$\sup_k s^{\sqrt[m]{|\lambda_k|}} |f_k| < \infty$$ for some $$s>1$$.
I suppose that a similar result should apply for a domain $$\Omega \subset \mathbb{R}^n$$, once the boundary conditions and the self-adjointness of $$\mathcal{L}$$ are taken care of. But you should check that Seeley's argument continues to apply in your case.
• Thank you very much! An exponential decay is indeed something which I expected. I will check Seeley's argument but as far as I see from the last page the criterion is appliable on any (self adjoint) elliptic operator $\mathcal{L}$ of any order. May 18 '20 at 11:24
|
2022-01-25 07:37:32
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 19, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9614362120628357, "perplexity": 112.00820463623292}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304798.1/warc/CC-MAIN-20220125070039-20220125100039-00518.warc.gz"}
|
http://www.makelinux.net/books/GNU-Linux-Tools-Summary/general-shell-tips
|
# 4.1. General Shell Tips
Automatic Command Completion
Use the TAB key and bash will attempt to complete the command for you automatically. You can use it to complete command (tool) names. You can also use it when working with the file-system, when changing directories, copying files et cetera.
There are also other lesser known ways to use automatic command completion (for example completing user names):[1]
ESC-Y (Y: special character)
testing autoindexing Will attempt to complete the command name for you. If it fails it will either list the possible completions (if they exist). If there are none it will simply beep (and/or) flash the screen.
CTRL-X-Y (Y: special character)
Lists the possible completions (it won't attempt to complete it for you) or beep if there are no possible completions.
Special-characters:
Use the following special characters combined with either ESC-Y or CTRL-X-Y , where Y is some special characters. For example ESC-$or CTRL-X-$ to complete an environment variable name.
• ~ (tilde) complete a user name
• @ (at sign) complete a machine name
• \$ (dollars sign) complete an environment variable name
• ! (exclamation mark) a magic character for completing a command name or a file name. The ! special character has the same function as the TAB key. It works in some other situations; for example when completing man page names.
alias
The alias command will list your current aliases. You can use unalias to remove the alias (to disable it just for one command add a “\” (back-slash) before the command)...
An alias allows one command to be substituted for another. This is used to make a command do something else or to automatically add certain options. This can be either be done during one session using the alias command (see below) or the information can be added to the .bashrc file (found in the users home directory).
Below is an example of what an alias section (within your .bashrc file) might look like:
# my personal aliases alias cp='cp -vi' #to prompt when copying if you want to overwrite and will tell you where information is going alias rm='rm -i' #Prompts you if you really want to remove it. alias mv='mv -i' #Prompts you if you are going to overwrite something
On any Mandriva GNU/Linux system the global aliases (for all users) are all in /etc/profile.d/alias.sh. The above listed commands already have aliases, as well as several other commonly used commands.
set -x
set is one of bash's inbuilt commands, try looking in the bash manual for its many usage options.
Using set with the -x option will make bash print out each command it is going to run before it runs it.
This can be useful to find out what is happening with certain commands such as things being quoted that contain wildcards or special symbols that could cause problems, or complex aliases. Use set +x to turn this back off.
Examples
After using set -x you can run the command:
ls
The output printed before the command runs (for example):
+ ls -F --color=auto
Which means that the command is really an alias to run ls with the -F and --color=auto options. Use a “\” (backslash) before the command to run it without the alias.
\ (backslash)
The backslash escape character can be used before a shell command to override any aliases.
For example if rm was made into an alias for rm -i then typing “rm” would actually run rm -i.
However, typing \rm lets the shell ignore the alias and just run rm (its runs exactly what you type), this way it won't confirm if you want to delete things.
Using rm Please note that the alias for the remove command is there for a reason. Using it incorrectly could remove files which you don't want removed.Only use \rm if you know exactly what you are doing (recovering files is not easy, rm does not send things to a recycle bin).
The “\” character can be used before special characters (such as a space or a wildcard), to stop bash from trying to expand them. You can make a directory name with a space in it using a backslash before the space. For example you could type cd My\ Directory\ With\ Spaces which normally wouldn't work.
The “\” character can also be used to stop bash from expanding certain symbols (as an alternative you could use single quotation marks, although you may need to use both).
The TAB Key Please note that using the TAB key (automatic-command-completion) will automatically use escapes for spaces (so you don't have to type them manually).
script
The “script” command creates a typescript, or "capture log" of a shell session - it writes a copy of your session to a file, including commands you type and their output.
~ (tilde character)
The tilde character is used as an alias to a users home directory.
For example, if your user-name was “fred”, instead of typing cd /home/fred you could simply type cd ~. Or to get to fred's tmp directory (under his home directory) you could type cd ~/tmp.
Home directory shortcut ~ (tilde) can also be used as a shortcut to other users home directories, simply type: ~user_name and it will take you to the users home directory. Note that you need to spell the username exactly correct, no wildcards.
set bell-style none
This particular set command will turn off the system bell from the command-line (use xset -b for X windows). If you want the bell to stay off pernamently (no audible bell) then you can add this command to your “.bashrc” or “.bash_profile” (just add it to the same one you have your alises in...).
reset
The reset command re-initializes your current terminal. This can be useful when the text from your terminal becomes garbled, simply type “reset” and this will fix your terminal.
exit
Closes your current terminal (with x-terminals) or logs-out. Also try CTRL-D .
logout
Logs out of a terminal, also try CTRL-D .
echo
A little command that repeats anything you type.
Example:
echo “hello world”
Simply displays “ hello world”.
Example:
echo rm -R *
This will output what will be passed to the rm command (and therefore what would be deleted), putting echo before a command renders it harmless (it just expands wildcards so you know what it will do).
Also try using the -e option with echo. This will allow you to use the escape character sequences to format the output of a line. Such as '\t' for tab, '\n' for newline etc.
Using echo to prevent accidents Typing: echo command(s) could save you the trouble of accidentally doing something you didn't expect. Using echo allows you to expand the wildcards to understand what will happen before you actually run the command.
### Notes
[1] This information was adopted (with editing) from Mandrakesoft's Command Line Manual, see [7] in the Bibliography for further information.
|
2014-03-10 02:44:32
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47843486070632935, "perplexity": 3153.277496673606}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010557037/warc/CC-MAIN-20140305090917-00076-ip-10-183-142-35.ec2.internal.warc.gz"}
|
https://byjus.com/maths/numerator/
|
# Numerator
In mathematics, numerator and denominator play an essential role while dealing with fractions. As we know, that fraction represents a numerical value, which defines the parts of a whole. Suppose a number has to be divided into four parts, then it is described as p/5. So the fraction here, p/5, defines 1/5th of number p. If the line part of the fraction is at a slant, then the numerator will be on the left.
## Numerator meaning
A numerator is the part of a fraction above the line, which signifies the number to be divided by another number below the line. In the example given below, the number that lies above the line is the numerator, i.e. in the fraction 1/8, 1 represents the numerator, and 8 represents the denominator.
### Numerator and Denominator
Every fraction possesses two parts, namely numerator and denominator. The upper part of the horizontal line denotes the numerator, whereas the lower part is the denominator of that fraction. The below table helps in better understanding of the numerator and denominator of a fraction.
Fraction Numerator Denominator 7/12 7 12 (2 + 9)/ 15 (2 + 9) 15 5q/2c 5q 2c 9/(19 – 4) 9 (19 – 4) 4/3 4 3
### Numerator of a Fraction
Numerator of fraction represents the number of parts selected or removed from the total. For example, if a circle is cut into eight parts and four parts as shown in the below figure, then the selected parts of the circle, i.e. 3 over a part of the total number of parts can be written as 3/8 and 3/4, respectively.
Where 3 is the numerator of the fractions 3/8 and 3/4. This number is equivalent to the shaded parts of circles given. Below are the important points about the numerator of a fraction.
• If the numerator is equal to 0, then the entire fraction becomes zero irrespective of the denominator’s value. For example, 0⁄50 is 0, 0⁄3 is 0, and so on.
• If the numerator’s value is equal to the denominator, then the fraction’s value will be equal to 1. For example, 16/16 = 1, since numerator = 16 = denominator.
### Numerator Greater Than Denominator
Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.
Example:
Here, 9 is greater than 5, that means the denominator is less than the numerator.
## Numerator Examples
Example 1:
Geetha took 3 roses from a basket of 10 roses. Represent this in the form of a fraction and identify the denominator.
Solution:
Total number of roses = 10
Number of roses taken by Geetha = 3
Thus, Geetha took 3/10th of the roses from the basket.
Here, 3 is the numerator of the fraction 3/10.
Example 2:
Arun bought 20 mangoes. He gave 4 mangoes to his brother. What fraction of the mangoes was he left with? Also, find the numerator of the obtained fraction.
Solution:
Total number of mangoes = 20
Number of mangoes given to his brother = 4
Remaining mangoes = 20 – 4 = 16
The fraction of mangoes Arun was left with = 16/20 = 4/5
Thus, Arun was left with four-fifth of the mangoes.
Here, 4 represents the numerator.
## Frequently Asked Questions on Numerator
### What is a numerator and a denominator?
As we know, a fraction is the part of a whole thing. The general form of a fraction can be written as a/b, where a is called the numerator and b is called the denominator.
### What is the numerator in Division?
In division of numbers, the dividend, i.e. the number to be divided represents the numerator. For example, in the division of a number 56 by 7, i.e. 56/7, the number 56 is called the numerator
### How do you remember the numerator and denominator?
The simple way to remember the numerator and denominator is, when a fraction is given the upper part denotes the numerator, whereas the lower part denotes the denominator. For example, in the fraction 6/17, numerator = 6, denominator = 17.
### Is the numerator bigger than the denominator?
Yes, in some fractions the numerator will be bigger than the denominator, such fractions are called improper fractions. However, not in all the fractions, numerators are greater than denominators.
### Do you divide the numerator by denominator?
To divide the numerator by denominator, we need to express these parts as a multiplication of their factors. When we represent them in terms of factors, we can cancel out the common factors to get the reduced form.
|
2021-06-14 03:46:30
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9826850295066833, "perplexity": 539.072024166572}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487611320.18/warc/CC-MAIN-20210614013350-20210614043350-00261.warc.gz"}
|
https://www.intechopen.com/books/new-perspectives-in-forest-science/alternative-forest-restoration-techniques
|
Open access peer-reviewed chapter
# Alternative Forest Restoration Techniques
By Sebastião Venâncio Martins
Submitted: April 18th 2017Reviewed: December 5th 2017Published: December 21st 2017
DOI: 10.5772/intechopen.72908
## Abstract
This chapter seeks to describe the need to adapt the forest restoration to the different regional environmental filters and the different ecological opportunities of the landscapes, through the adoption of techniques not conventional or alternative restoration. When starting this text, it should be made clear that all restoration models and techniques have their environmental and socioeconomic importance, since they contribute to the return of forest ecosystems to a non-degraded state, with direct or indirect impacts on the recovery and conservation of hydrological and nutrient cycles, biodiversity, agricultural production, and the minimization of climate change. Therefore, there is no pretension here to present a set of models and techniques that are “superior and unique” and that should be standardized and followed throughout the country. To be clear in this text, there are innumerable possibilities and alternatives for forest restoration in Brazil, given its continental dimensions, with remarkable climatic, edaphic, cultural, and socioeconomic diversity. Therefore, there is no single restoration model or technique that can be applied widely and on a large scale; what is important is to take advantage of the remaining potential for ecosystem regeneration by adapting more appropriate techniques for each situation.
### Keywords
• ecological restoration
• natural regeneration
• nucleation
• direct seeding
• topsoil transposition
## 1. Introduction
As we started this text about what is being called “alternative forest restoration techniques,” it should be made clear that all restoration models and techniques have their environmental and socioeconomic importance since they contribute to the return of forest ecosystems to a non-degraded state, with direct or indirect impacts on the recovery and conservation of hydrological and nutrient cycles, biodiversity, agricultural production, minimization of climate change, and the well-being and quality of life of human populations.
Therefore, it is not our claim to present a set of models and techniques that are “superior and unique” and that should be standardized and followed all over the country. Indeed, standardization and the attempt to create rigid norms for restoration projects are strong features of the more conservative and traditional forest restoration, as it is well illustrated in the text by [1].
Forest restoration’s record in Brazil and in all the world, well documented by [2, 3, 4, 5, 6], reveals that innumerous initiatives of restoration have begun in a more empirical way, based on practical knowledge and without following preestablished norms, even because the “Ecology of Restoration” as the Science that guides the foundations of restoration (see [7]) did not even exist at that time. However, it cannot be denied that these first initiatives of ecological restoration of the forests, although without much scientific criteria, have resulted, in many cases, in forests with good quality of restoration, within the context of total or partial return of biodiversity and environmental or ecosystem services.
Over this trajectory of forest restoration in the world, one can see from the last two decades a great advance in the number of projects and area in restoration, with important initiatives of large-scale restoration and mainly focused on the riparian forests (areas of permanent preservation), which have been intensified with the demands arising from the 21st Session of the Conference of the Parties to the United Nations Framework Convention on Climate Change (COP 21, Paris, France), reinforced in the COP 22 (Marrakech, Morocco) and COP 23 (Bonn, Germany). In this new trend of restoration, an attempt is also made to standardize or dictate very strict rules for forest restoration, which often fails to consider the differences and specificities of each region, which presents a set of filters that rule the structural and functional organization and biodiversity of natural ecosystems and, of course, of ecosystems to be restored as well.
Thus, the objective of this chapter is to explain the need to adapt forest restoration to the different regional environmental filters and to the different ecological opportunities of the landscapes, translated here as the potential for self-recovery—or resilience—of ecosystems through the adoption of unconventional or alternative techniques of restoration, either alone or combined with traditional techniques.
## 2. The traditional forest restoration
Although it is sometimes difficult to establish a strict dividing line between what is traditional or conventional and what is alternative in the forest restoration, it is possible to consider as traditional the reforestation in a total area with fixed spacing between the planted seedlings and, as an alternative, all initiatives that escape this pattern of restoration.
It is important to emphasize that the ecological succession responsible for the regeneration process of forest ecosystems is initiated by the seeds present in the soil bank or from the seed rain and by the growth of stalks and root buds of various forms of life, usually forming regeneration nuclei; then why do we seek to restore forests only by planting tree seedlings, following alignments and predefined spacings?
The answer is not simple; it has a bias in the use of silvicultural and agronomic techniques, in the state of local degradation and landscape, in the differences between seed and seedling offerings, and in the costs of restoration in the different regions [6, 8].
The heterogeneous reforestation with seedlings of native species has its origin and mirror, the forestry, that is, this type of traditional forest restoration follows exactly the silvicultural techniques applied in the reforestation with Eucalyptus and Pinus to produce wood for cellulose, charcoal, etc., exchanging species, only.
To make it clear, this approach does not seek to criticize or diminish the socioeconomic and even environmental importance of Eucalyptus or Pinus forestry for timber production, which generates thousands of jobs, strengthens the country’s economy, and helps to reduce pressure on forests and to protect soils from erosive processes, among many other benefits [9].
When, for example, a forest restoration project is implemented with seedling planting following an alignment and spacing of 3 × 3 m between seedlings, with fertilization of 200 g of NPK 6-30-6 per pit, nothing else is being done than to follow exactly the spacing and fertilization used in many reforestations with Eucalyptus in soils with low levels of phosphorus. Although the defenders of this restoration model may refute by claiming that restoration uses a high diversity of native species, in some cases from 80 to 120, following functional groups with pioneer and non-pioneer lines or fill and diversity lines.
Once more, with the artificial organization that tries to impose the forest to be restored, the classic paradigm of ecology and succession [10] is present as never when defining functional groups, spacing, number of species, and, worse, strict parameters and criteria for monitoring such forests in restoration, based on control of mature forests. It is important to highlight that a diversity similar to that of the original ecosystem can be achieved over time, even with the planting of a single or few species, provided that the landscape is resilient, as verified, for example, in the Forest Garden of Campos do Jordão, State of São Paulo, Brazil, where the planting of Araucaria angustifolia alone served as a catalytic regenerating forest of the other regional native species [11].
It must be made clear that native forests have the diversity and arrangement of species controlled by ecological processes such as dispersal, predation, competition, nutrient cycling, and physiographic factors such as altitude and terrain slopes, among others, and that besides tree species, various other life forms compose the forest ecosystem, such as epiphytes, creepers, understory plants, and associated fauna. So, it is not uncommon to find forests considered as “restored” that even after two or more decades of traditional reforestation still maintains planting alignment and a virtually empty understory with extremely low density of regenerant shrub-trees.
Nevertheless, it cannot be disregarded that in certain situations, it is necessary to plant native tree species, for example, in the case of highly anthropic landscapes where resilience has been lost or is very low.
In addition, in the context of wood production of native species (“e.g., see [12]”), which is more like a rehabilitation of degraded areas, and not actually restoration, reforestation is more recommended, actually, since it allows the combination of groups of species of wood of different uses and characteristics in the planting lines, since a production control is necessary. Moreover, in relation to implantation of agroforestry or agroforestry systems—rehabilitation models—the planting of predefined lines of native trees and agricultural crop lines seems to be the most appropriate. It is worth noting that these rehabilitation models for the production of timber and non-timber products, when temporary, can be converted into restoration models, although they maintain the characteristics of the productive system for a long time [13].
In the context of forest restoration, interpreted as an ecological restoration of forest ecosystems, what is also essential to make clear is that planting of seedlings does not always need to be in the total area, nor does it always have to have a predefined, narrowed spacing, regardless of region, landscape, climate, etc. Therefore, it is not possible to accept for forest restoration a generalization of reforestations with predefined spacings, usually 3 × 3 m or even 2 × 2 m, and many species, which neglect the potential for forest regeneration, which could be stimulated through alternative techniques, with sensible reductions in restoration costs and the formation of forests through a more natural and sustainable process in the long term.
It is not possible to adopt in a generalized way for the different Brazilian regions, with their different ecological peculiarities, public policies of forest restoration based only on the reforestation through the planting of seedlings in total area, which ends up being more unfeasible than contributing to the advance of the restoration.
A good example of this paradigm shift has been occurring in the State of São Paulo, Brazil, where a set of legal norms, through resolutions issued by the Secretariat for the Environment (SMA), was initially launched to improve project quality and to speed restoration. These first resolutions, although well intentioned, unfortunately complicated and made it difficult rather than facilitating or stimulating restoration in the State and, after a long debate between the scientific community of São Paulo and of other states, which resulted in at least three publications of great impact [1, 14, 15], ultimately have become appropriate and have accepted different restoration models and techniques, provided that the final result is successful. In this context, the following are some alternatives for forest restoration, which, in general terms, pursue the formation of restored forests in a more ecological and sustainable way and with lower costs than traditional reforestation.
It is possible and feasible to make a reforestation with less traditional and less conservative. To do so, it is necessary to innovate and to create new alternatives of planting arrangements in the field, and this is configured as an open field for avant-garde studies.
Changing planting spacings according to the reality of each landscape or region means allowing the intensification of planting of seedlings to the regions or farms that really need this type of intervention. Thus, changing spacing may represent a reduction of 1100 seedlings per hectare (at 3 × 3 m spacing) to half or even a third of that, which at first may seem a reduction in the demand for seedlings, but when it is considered that using fewer seedlings per hectare can restore more hectares, all in all, the production and commercialization of seedlings may be little impacted or not impacted at all.
It is very common in reforestation to clean the area to be planted first. Such cleaning often eliminates everything; nothing is left after cutting followed by application of herbicide in a dirty pasture. In this cleaning of the area, it is common for many seedlings that were starting a process of succession to be eliminated, to give place to the planted seedlings, some that do not always occur in the region.
One of the first assumptions to make reforestation more ecologic and alternative is the use of regenerants, for example, if spots or nuclei of natural regeneration occur in an area of a few hectares, they must be maintained and the planting spacing altered. As a rule, in the vicinity of forest fragments, natural regeneration is more abundant, and it is reduced as it moves away from the remnant; this is a pattern of forest succession [16] in abandoned pastures [17, 18, 19], for example, and for these cases, the planting of seedling in broader spacings, such as 4 × 4 to 6 × 6 m in the parts with more regeneration, or even no planting of seedlings if regeneration is already very intense (Figures 1 and 2) is an alternative.
Another important aspect to be considered in traditional reforestation in total area is the uniformity, represented by the more or less standardized height of the seedlings. Although certain pioneer species show very rapid growth, for example, Schizolobium parahyba, as a rule, most native species grow slowly in height, and thus in the first years of planting, the area becomes a uniform carpet of seedlings of short height. Such an environment is unattractive for seed dispersal birds to move from isolated forest fragments in the landscape.
An alternative to make the planted area more attractive to birds is the installation of artificial perches made of bamboo, Eucalyptus sticks, and other materials [3, 20]. From these perches, installed at intervals of 20–50 m, birds can move and disperse fruit seeds that they used in forest fragments still existing in the landscape. With the installation of perches in the reforestation, larger spacings can be adopted inasmuch as nuclei of natural regeneration tend to be formed around the perches.
There may be also natural perches by planting fast-growing species, including exotic species, since some have much higher growth rates than most native species, provided they are not invasive. In this sense, the planting of isolated trees of fast-growing species, at 50-m intervals within the wide space of the reforestation with native ones, can be a good alternative. When these isolated trees reach a height of about 10 m, they can be killed with herbicide application on the stem and become dry perches for some years.
Another way to make reforestation less conventional and more ecological is by neither adopting planting alignments nor spacing between seedlings, that is, to carry out planting at random. Thus, in the development of the planted forest, the planting lines will not be maintained, as in traditional reforestation, making the restored forest more similar to a native forest. As the planting of the seedlings becomes more flexible, it is possible to increase the seedlings in worse stretches, for example, in exposed and compacted or eroded soils, and to increase the distance between seedlings in stretches that already present arboreal regenerants or colonization by ruderal shrubs.
## 4. Natural regeneration
Natural regeneration, understood as the process by which an ecosystem impacted by natural or anthropic disturbances recovers its total or partial biodiversity, its structure and functioning, through the successional sequence over time, is undoubtedly the most ecological and cheapest manner of restoring forests.
Several studies have been published and proved the viability of natural regeneration as an alternative to forest restoration in abandoned pastures [17, 18, 19, 20], in mined areas [16, 21] and in large-scale restoration [8, 22].
The study of [19] in Puerto Rico demonstrated that one restoration strategy for tropical forest in abandoned pastures is simply to protect the areas from fire and allow natural regeneration to produce secondary forest. In accord with the authors, this strategy will be most effective if remnant forest (i.e., seed sources) still exists in the landscape and soils have not been highly degraded.
Probably the study of [8] about “Natural regeneration potential of native forests in the different regions of the State of Espírito Santo, Brazil,” is the strongest evidence of the role of natural regeneration as an alternative to enable large-scale forest restoration in Brazil. This study, the result of a major project that analyzed natural regeneration on farms throughout the state of Espírito Santo, revealed that in a 33-year period, 18,979 forest fragments were naturally regenerated in lands in Espírito Santo, occupying an area of 106,554.87 ha. The study also showed that in the State of Espírito Santo, 60.88% of its total area, equivalent to 2,804,431 ha, has a high potential for natural regeneration of forests and in most of such areas, planting of seedlings for forest restoration was not necessary.
Despite all this potential of natural regeneration detected in Espírito Santo, which is probably repeated in other States, and it should be even greater in the region covered by the Amazon Rainforest, the study by [8] also revealed that there are areas of that state with low regeneration potential, notably the far North, where only the abandonment of the areas does not guarantee the regeneration of the forest and restoration interventions are necessary.
The findings of this study in Espírito Santo are very relevant because they indicate that large-scale forest restoration cannot follow a single model or a standardization. The five defining elements of ecological restoration—ecological, economic, social, cultural, and political—described in [23, 24] also move toward it, from this alternative approach.
By considering only the economic element, it is necessary to reflect on the main bottleneck to enable forest restoration through reforestation in a total area, which is its high cost, which varies greatly from one region to another, but which is hardly less than R$7000.00 per hectare, not being rare examples exceeding R$ 20,000.00 per ha, and being suggested an average of R\$ 10,000.00 per ha [2].
Through natural regeneration, this cost is substantially reduced to one-third or even zero, since it basically comes down to the cost of fencing and to construct fire breaks of areas under regeneration, for the isolation of livestock and fire, costs that also occur in traditional reforestation. Figure 3 shows a ciliary forest restored through the natural regeneration process, where the only intervention was the enclosure of the APP range, to prevent entry of cattle.
But as it was evident in that study in Espírito Santo, where most of the state’s territory has a high potential for natural regeneration, there are areas that the forest may not regenerate naturally, and thus even natural regeneration cannot be indicated as exclusive restoration technique for all regions, landscapes and situations of environmental degradation. As regeneration depends on three basic ecological mechanisms—seed rain, soil seed bank, and regrowth of vines and roots—in very anthropic landscapes, with a long history of intensive use only for agriculture or livestock and with forest remnants absent or very isolated and degraded, this process may not occur or be extremely slow.
In conclusion, before recommending natural regeneration as an exclusive restoration technique for a particular area, it is essential to make a diagnosis of its regeneration potential. The diagnosis should consider the landscape in which a particular area to be restored is inserted, the distance of forest fragments remaining in the landscape, the presence of regenerants and their abundance, and, if possible, the soil seed bank [25, 26]. In this aspect, [27] point that the natural regeneration techniques, however, are not innately superior or always more appropriate for restoring forest ecosystems than artificial techniques and the intervention must be based on management objectives, informed by evaluation and interpretation of site conditions, and incorporate silvicultural knowledge and skills. Where management objectives are best served by controlling the timing of restoration and the species composition of the restored forest, active intervention at the regeneration stage is critical [27].
In regenerated forests dominated by one or a few species, enrichment management can be recommended, but costs still tend to be much lower than total area planting. A study developed by [28] about polydominant spruce-broadleaved forest long-term economic use in Moscow, Russia, found good results with two management techniques: group-selective cutting aimed at imitating the treefall gaps’ natural mosaic structure of uneven-aged forests and combining gap falling with planting of species that occupied dominant position in preagricultural forest.
## 5. Nucleation techniques
For situations in which only the abandonment of a particular area has not resulted in progress of the natural regeneration process, by the factors already related, it is possible to stimulate and accelerate the process through the adoption of alternative techniques, such as nucleation, exclusively or combined with the reforestation.
The development and successful application of nucleation techniques as alternatives to improve—in terms of cost reduction and sustainability of restored ecosystems—has been widely documented [3, 29, 30, 31, 32, 33, 34, 35, 36, 37].
In a review of nucleation researches in several countries, [38] concluded that the results of experimental tests of applied nucleation indicate that the density and diversity of colonists is higher in planted nuclei than in areas where no planting takes place (e.g., passive restoration) and that these studies suggest that the applied nucleation strategy has the potential to restore deforested habitats into heterogeneous canopies with a diverse community composition while being cheaper than projects that rely on plantation designs.
### 5.1. Seedling nuclei
In abandoned areas, largely isolated in agricultural and pasture landscapes, the emergence over time of sparse, or even dense, coverage of ruderal herbs and shrub nuclei and even pioneer tree species, often forming monodominant communities, where one or a few species are established is common, but succession does not advance in terms of species diversity and biomass. As the main factor hindering the progress of forest regeneration in these situations is the lack of seedlings input, since the sources are very distant and the soil is degraded in terms of seed richness, the output is to potentiate regeneration through artificial introduction of propagules, either seedlings or seeds or both.
The planting of seedling nucleus in areas in slow regeneration process is an excellent alternative to make forest restoration possible in a more ecological way and at a low cost in comparison with the reforestation in a total area.
The ecological principle of seedling planting in nuclei is the realization that in many situations of degradation of terrestrial ecosystems, succession does not begin simultaneously, covering all the abandoned area, a pasture, for example, but generally small nuclei of pioneer facilitating species of succession are formed, which expand over time (Figure 4). In their study [39], on primary succession in the Canadian Rockies, pointed out that in looking for plants that might serve such nuclei for colonization during primary succession, plants that fix nitrogen should be considered.
There are several types of nuclei, in terms of number of species and distances between seedlings, but certainly Anderson’s Groups are still the most used. In this model, five cross-shaped seedlings with four peripheral seedlings and one central seedling were planted at 0.5 m between the central and peripheral seedlings [35].
Alternatively, seedling nuclei can be formed by planting four seedlings at the ends of a 1-m-side square, with a central seedling, preferably the four peripheral seedlings of pioneer species (each of a species) and the central non-pioneer species (late secondary or climax) that requires greater shading.
Among the advantages of this technique, in ecological terms, is the fact that the pioneer seedlings (Figure 5), when growing faster, provide the necessary shading for the late species planted in the center of the nuclei, in addition, formation of nuclei, with seedlings closer than in the conventional plantations, form clusters more resistant to the weather and to the attack of herbivores and pests. The nuclei must be distanced according to the potential of natural regeneration of the area, which allows a reduction in the total of seedlings per hectare, from 1100 to 1666 seedlings from traditional reforestation to about 200–400 seedlings with the nuclei, which, ultimately, dramatically reduces the costs of restoration.
The planting in nuclei also allows a single crowning for the nucleus as a whole, that is, for the five seedlings, which represents a strong reduction in the costs of implanting and maintaining restoration projects, since the crowning around the seedlings in many regions where herbicide application is not accepted by environmental agencies is the only way to avoid competition with aggressive exotic grasses.
Experimental reforestations were carried by [40] in the Sierra Nevada Protected Area (southeast Spain) with the aim of comparing the survival and growth of seedlings planted in open areas (reforestation) with seedlings planted under the canopy of preexisting shrub species. Their results showed that nurse shrubs had a stronger facilitative effect on seedling survival and growth at low altitudes and sunny, drier slopes and that pioneer shrubs facilitate the establishment of woody, late-successional Mediterranean species and thus can positively affect reforestation success in many different ecological settings.
The study of [41] in the Trevenque area, Sierra Nevada, Spain, tested the hypothesis that the use of shrubs as nurse plants is an alternative technique of reforestation with greater success than traditional techniques, in which preexisting vegetation generally considered a source of competition. They compared the traditional planting of Quercus pyrenaica seedlings in open areas with the planting of seedling nuclei in the canopy of a pioneer shrub Salvia lavandulifolia. The results showed that Quercus survival was 6.3× higher when planted under individuals of the pioneer shrub than open areas and, therefore, the use of shrubs as nurse plants for Q. pyrenaica reforestation is a viable technique to increase establishment success [41].
### 5.2. Plant residue and soil transposition
In areas with soil degradation, such as compaction and erosion, common in degraded pastures and mined areas, planting of seedlings may not be sufficient to provide forest restoration. In these situations, planted seedlings may present good initial growth, whether they find nutrients, organic matter, and free soil in the pits, but this growth can be slowed down as the root system depletes the resources of the planting pits and starts to explore the compacted or very poor soils around them. The final result ends up being the formation of an environment with small isolated trees, type bonsais, with soil exposed between them and without understory formation. Obviously, a vegetation with such characteristics tends to perish.
To enhance forest restoration in these highly degraded environments, the transposition of soil/litter and vegetal residues such as antlers and bark is an ecological and low-cost alternative. The surface soil, or topsoil, and the litter layer that covers it, when taken from native forests, contain, in addition to nutrients and organic matter, a rich seed bank, formed not only by pioneer tree species but also by herbaceous, shrub, epiphyte species. Therefore, the top soil/litter set is a rich and diversified component of the forests, and its transposition in nuclei or islands to degraded areas produces the necessary stimulus for the triggering of natural regeneration [29, 30, 31, 33, 34, 35]. However, it should be remembered that topsoil and native forest litter must be removed from areas where environmental licensing has authorized the suppression of vegetation for mining activities, impoundment of watercourses, among others.
In this sense, a study carried out by [42] in a secondary forest on the campus of the Federal University of Viçosa, in Viçosa, State of Minas Gerais, showed that the removal of layers of soil only 5 m in depth and litter, in ranges of 1 × 2 to 1 × 8 m, spaced at about 5 m, did not have a significant impact on forest regeneration, with retreatment sites naturally recovered after 1 year. Despite the need for new tests to evaluate the impact of topsoil and litter removal in other forests, these first results indicate the possibility of applying this technique from forests in legal reserve areas, through a project to be analyzed by the qualified environmental agency.
The plant residues that have been most used in forest restoration in degraded soils are the semi-composite bark of Eucalyptus, a very abundant material in pulp and charcoal production companies, and the branches resulting from legal suppression of vegetation or tree pruning. These residues provide nutrients and organic matter, which are essential for enhancing the chemical and physical properties of degraded soils, as well as to provide shelter and food source for insects, rodents, and reptiles, stimulating food chains [3, 30].
Although the application of these nucleation techniques is more common in areas with soil degradation, nothing prevents soil/litter nuclei and residues from being used also in areas with traditional reforestation. As with the installations of perches, the deposition of residues and top soil in the narrow bands or islands within the reforestation is a way to increase biodiversity and stimulate ecological processes, as well as to enable a reduction in the number of seedlings planted.
### 5.3. Direct seeding
One of the main factors that prevent or hinder the progress of the natural regeneration process in highly anthropized landscapes is the lack of seed rain with species diversity. Some ruderal and pioneer species with wide anemochory dispersion can reach in some situations great distances and colonize certain areas forming monodominant vegetation, since other species with more restricted zoocoric dispersion do not achieve the same success.
As the regeneration process does not advance in these areas due to the distance from the seed sources and/or the low supply of dispersers, the artificial dispersion through direct seeding becomes a promising alternative.
The seeding direct was recommended by [43] as technical for restoration of degraded Norway spruce forest in the Forstamt Weissenhorn, Bavarian region of southern Germany. The authors appoint that the direct seeding seemed a promising and cost-effective alternative to planting.
Despite being an alternative technique of restoration that shows good results, it also presents some limitations so it should not be recommended for every situation [37, 44, 45, 46]. In very degraded soils, such as mined areas and old pastures with exposed soils, the simple sowing of native species may not be sufficient to trigger the regeneration process. The previous prepare of soil by scarification in the case of compacted soils and the provision of a source of nutrients and organic matter is often necessary.
Also, one cannot expect much from direct seeding in brachiaria (Urochloa decumbens Stapf) pastures, where the main factor of inhibition of regeneration tends to be precisely the aggressiveness of the exotic grass and its previous control through herbicide application and cutting, among others, becomes necessary.
However, direct seeding has great potential for use in the enrichment of swiddens and pastures, where a regeneration process has already begun but at a very slow pace and with very low diversity. Thus, through sowing, species that have regional occurrence can be introduced into areas in regeneration, but cannot reach via dispersion.
A detailed study on the viability of direct seeding as a forest restoration technique is found in [46]. In it, the authors discuss very satisfactory results of the application of a new mechanized direct seeding methodology adopted in a large scale in the state of Mato Grosso, Brazil, in which seeding agricultural machines were adapted for seed sowing of native species. In addition, they present a review with excellent results of experiments of direct seeding of different species in the Brazilian biomes.
An option to reduce the costs and the use of agrochemicals in restoration areas is the direct seeding of green manures described by [47] and implemented in restoration projects coordinated by the Forest Restoration Laboratory of the Federal University of Viçosa (www.larf.ufv.br). In this technique, seeds of herbaceous and shrub species of the family Fabaceae (formerly Leguminosae), with symbiotic association with Rhizobium and fixation of atmospheric nitrogen, present rapid growth in poor and degraded soils and, therefore, can be sown together with seeds of arboreal native species or together with the seedlings planted in larger spaces or in nuclei. Several species of green manure have been used in direct seeding to cover the soil fast and reduce competition with grasses such as brachiaria, and it is worth mentioning Cajanus cajan (L.) Millsp. that in addition to enhancing soil, it rapidly leaves the system and releases space for growing seedlings (Figure 6).
## 6. Final considerations
The progress of forest restoration in the world is undeniable, which has gained strength in recent years from the 21st Session of the Conference of the Parties to the United Nations Framework Convention on Climate Change (COP21) and the recent water crisis that has increased the perception of society about the importance of preservation and restoration of riparian forests.
In this scenario, all forest restoration initiatives already carried out or under way are very important, although some have not achieved the expected results and others have presented very high costs. All over the world, there had been a great demand for studies and forest restoration services, mainly by mining, power generation, and pulp production companies, which are being increasingly encouraged to restore their Permanent Preservation Areas and Legal Reserves, not only in compliance with environmental legislation but also to certify their activities and export their products.
As it was pointed out in this text, there are innumerable possibilities and alternatives for forest restoration, with remarkable climatic, edaphic, cultural, and socioeconomic diversity between the countries and the different types of impacts to which its ecosystems are subjected. Therefore, there is no ready-made recipe, a single restoration model or technique that can be applied widely and on a large scale. The important thing is to take advantage of the remaining potential for ecosystem regeneration by adapting more appropriate techniques for each situation.
## Acknowledgments
I thank the National Council for Scientific and Technological Development (CNPq) for the research productivity grant and the Forest Research Society (SIF-UFV) linked to the Federal University of Viçosa by the feasibility of LARF-UFV projects with pulp and paper, hydroelectric, and mining companies.
## How to cite and reference
### Cite this chapter Copy to clipboard
Sebastião Venâncio Martins (December 21st 2017). Alternative Forest Restoration Techniques, New Perspectives in Forest Science, Helder Filipe dos Santos Viana and Francisco Antonio García Morote, IntechOpen, DOI: 10.5772/intechopen.72908. Available from:
### Related Content
#### New Perspectives in Forest Science
Edited by Helder Viana
Next chapter
By Foo Chee Hung
#### Global Perspectives on Sustainable Forest Management
Edited by Dr. Clement A. Okia
First chapter
#### Deforestation: Causes, Effects and Control Strategies
By Sumit Chakravarty, S. K. Ghosh, C. P. Suresh, A. N. Dey and Gopal Shukla
We are IntechOpen, the world's leading publisher of Open Access books. Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. We share our knowledge and peer-reveiwed research papers with libraries, scientific and engineering societies, and also work with corporate R&D departments and government entities.
View all Books
|
2020-01-23 21:49:55
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45131757855415344, "perplexity": 3103.2840248711595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250613416.54/warc/CC-MAIN-20200123191130-20200123220130-00123.warc.gz"}
|
https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-8-polynomials-and-factoring-8-6-factoring-ax-squared-bx-c-practice-and-problem-solving-exercises-page-509/15
|
# Chapter 8 - Polynomials and Factoring - 8-6 Factoring ax(squared) + bx + c - Practice and Problem-Solving Exercises - Page 509: 15
(2k+3)(k-8)
#### Work Step by Step
Given the polynomial $2k^{2}$ -13k - 24 *** We break of the middle term into two factors that add to give -13 and multiply to give -48. The two numbers are -16 and +3. $2k^{2}$ -16k +3k - 24 We take the GCD of the first two and the GCD of the last two terms. 2k(k-8) +3(k-8) We take (k-8) and factor it out which gives us. (2k+3)(k-8)
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
|
2020-05-29 07:15:18
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40448176860809326, "perplexity": 1556.2931096048626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347402457.55/warc/CC-MAIN-20200529054758-20200529084758-00400.warc.gz"}
|
https://molwiki.vishnevskiy.group/wiki/Qassandra
|
# Qassandra
## General information
Qassandra (QuAntum corrections to claSSical pArameters for gas electroN DiffRAction) is an open-source software for processing results from molecular dynamics (MD) and path-integral molecular dynamics (PIMD) simulations. In contrast to the available program MDVibCor by A. Zakharov, Qassandra additionally implements a method for calculation of quantum corrections for vibrational molecular parameters obtained using classical MD and MC simulations.<bib id="VishnevskiyTCA2016" />
## Usage
Qassandra is a command-line application. It is executed by the following command:
<PATH TO THE EXECUTABLE FILE> [OPTIONS] [OPTIONS+INPUT FILES] [OPTIONS+VALUES] > [OUTPUT FILE] .
Main results are printed to stdout and should normally be redirected (> [OUTPUT FILE]) to a file. Additional information, like interatomic distances for each frame of simulation or values of selected coordinates during the simulation, are dumped into a file with name [name of trajectory file]_atpairs.dat.
## Options
#### Options that require input files
-p - MD simulation trajectory file in XYZ format (path).
-e - file containing equilibrium geometries for all desired conformers.
-l - file containing description of internal coordinates for large amplitude motions (LAM).
-P - PIMD simulation trajectory files in XYZ format.
-V - MC simulation trajectory file in modified XYZ format (Viva Las Vegas!).
If the equilibrium geometry file is not presented the first configuration of MD trajectory will be considered to be equilibrium. In this case the algorithm for quantum correction for MD won't work since atomic masses were not specified. For the PIMD simulations this file should always be given.
#### Options that set the values
-D - a threshold value (in Å) for the distance of interatomic atomic pairs to be considered equal. Default = 0.00001 Å.
-t - a time step (in fs) for the MD simulation. Default = 1 fs.
-T - a MD simulation temperature (in K). Default = 300 K.
-m - a number of steps to be ignored from the start of the MD or PIMD simulation (minimal). Default = 2000.
-M - a maximal number of steps in trajectory to be used. Default = 10000.
-r - number of replicas of PIMD simulation. Default = 4.
The option "-m" deletes the part of the trajectory where the system is equilibrating. The "-t" and "-T" options are crucial for the quantum and thermal corrections calculations.
#### Options that trigger specific program behavior
-s - the parameters of interatomic terms for every conformer will be symmetrized.
-S - the parameters of interatomic terms of equal conformers will be symmetrized.
-h - calculate the amplitudes as $l = \langle (r - r_e)^2 \rangle^{1/2}$ (harmonic).
-H - force asymmetry parameters values (κ) to be 0 (harmonic).
-u - turns off algorithm that sorts interatomic terms by their $r_e$ value in the output (unsorted).
-U - print asymmetry parameters in UNEX style for "SMSModel=1" (6.0*κ).
-g - print $r_e - r_g$ corrections instead of $r_e - r_a$.
-R - include rotation-vibration interaction effects during MC simulations processing;
-b - print plain bibliography for this program.
-J - "Just do it!".
## Input files
In this section the lines that should be in file start with the ">" in the line beginning. Note! The maximal length of each line that Qassandra reads is 100 symbols.
### Equilibrium geometry files ("-e" option)
> <Nconf> <- number of conformers
----------------------------------- <- this section should be given Nconf times
> <Nat> <- number of atoms
> 17:28, 10 November 2015 (CET)~ <- comment line (it is skipped during the file processing)
*********************************** <- this section should be given Nat times
> <Atom Name> <AtomMass> <X> <Y> <Z>
format: [1 or 2 letters] [float number] [float number] [float number] [float number]
or(equivalently as a regexp):
'^ +[A-Z][a-z]? +[0-9]+\.[0-9]+ +-?[0-9]+\.[0-9]+ +-?[0-9]+\.[0-9]+ +-?[0-9]+\.[0-9]+'
***********************************
> <- blank line
-----------------------------------
Atomic mass should be in atomic mass units (a.m.u.), and the Cartesian coordinates in Å.
### MD or PIMD trajectory files ("-p" or "-P" option)
The format is basically XYZ file format. It is the default for output of CPMD or CP2K programs, for example.
----------------------------------- <- this section should be given as many times as the trajectory length is
> <Nat> <- number of atoms
> 17:28, 10 November 2015 (CET)~ <- comment line (it is skipped during the file processing)
*********************************** <- this section should be given Nat times
> <Atom Name> <X> <Y> <Z>
format: [word] [float number] [float number] [float number]
or(equivalently as a regexp):
'^ +[a-zA-Z]+ +-?[0-9]+\.[0-9]+ +-?[0-9]+\.[0-9]+ +-?[0-9]+\.[0-9]+'
***********************************
-----------------------------------
### MC trajectory files ("-V" option)
The format is basically slightly modified XYZ file format.
----------------------------------- <- this section should be given as many times as the trajectory length is
> <Nat> <- number of atoms
> <Energy of the conformation> [<additional weight of the configuration>] <- second number should be given if option "-W" is used
format: [float number] [float number]
or(equivalently as a regexp):
'^ -?[0-9]+\.[0-9]+ [0-9]+\.[0-9]'
*********************************** <- this section should be given Nat times
> <Atom Name> <X> <Y> <Z>
format: [word] [float number] [float number] [float number]
or(equivalently as a regexp):
'^ +[a-zA-Z]+ +-?[0-9]+\.[0-9]+ +-?[0-9]+\.[0-9]+ +-?[0-9]+\.[0-9]+'
***********************************
-----------------------------------
### LAM description file ("-l" option)
> <Nlam> <- number of torsion angles (currently Qassandra supports only this type of coordinates)
----------------------------------- <- this section should be given Nlam times
> <atom1> <atom2> <atom3> <atom4> <- four atoms making the torsion angle
format: [integer number] [integer number] [integer number] [integer number]
or(equivalently as a regexp):
'^ [0-9]+ +[0-9]+ +[0-9]+ +[0-9]+'
*********************************** <- this section should be given Nconf times (see equilibrium geometry file)
> <min_value> <max_value> <- minimal and maximum values possible for the corresponding conformer's torsion angle
format: [float number] [float number]
or(equivalently as a regexp):
'^ +-?[0-9]+\.[0-9]+ +-?[0-9]+\.[0-9]+'
***********************************
-----------------------------------
## Algorithm for quantum and thermal corrections of GED parameters obtained with MD simulations
### General considerations
The MD simulations are classical, while atoms in molecules are moving according to quantum mechanics. The lighter the atom the larger is its de Broglie wavelength $\lambda = \frac{h}{m v}$, the stronger its' quantum behavior. Therefore it was noticed that for the terms containing light elements (such as the ones in the 1st and 2nd row of Periodic table) the GED parameters are badly described by the MD.
MD simulations can also be affected by the "flying ice cube effect". It is the energy drain from high energy degrees of freedom to the low energy ones, such as translations, rotations and LAM. Because of it the high energy motions, such as bond stretch, become frozen leading to even worse agreement with the quantum behavior. This effect appears as a results of some thermostats imperfections.
In order to obtain better description of the GED parameters obtained from MD simulations quantum - thermal corrections should be applied to them.
An illustration of quantum - thermal correction for pair distribution function (C-H term of ethane).
|
2023-04-01 08:15:46
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6382812261581421, "perplexity": 9358.067232714797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949701.56/warc/CC-MAIN-20230401063607-20230401093607-00538.warc.gz"}
|
https://socratic.org/questions/what-is-the-vertex-of-y-3x-2-2x-4
|
# What is the vertex of y= -3x^2 + 2x − 4?
May 21, 2018
$v e r t e x \left(\frac{1}{3} , - \frac{11}{3}\right)$
#### Explanation:
${a}^{2} + b x + c$
y= -3x^2 + 2x − 4
a = -3
b=2
c=-4
vertex is $\left(h , k\right)$
$h = \frac{- b}{2 a}$
$k = f \left(h\right)$ i.e. put what you found for h back into your function as x and solve for y.
$h = \frac{- 2}{2 \cdot - 3} = \frac{1}{3}$
k = (-3*1/3)^2 + 2*1/3 − 4 = -11/3
$v e r t e x \left(\frac{1}{3} , \frac{1}{3}\right)$
May 21, 2018
$\text{vertex } = \left(\frac{1}{3} , - \frac{11}{3}\right)$
#### Explanation:
"given the equation in standard form ";y=ax^2+bx+c
$\text{then the x-coordinate of the vertex is}$
•color(white)(x)x_(color(red)"vertex")=-b/(2a)
$y = - 3 {x}^{2} + 2 x - 4 \text{ is in standard form}$
$\text{with "a=-3,b=2" and } c = - 4$
$\Rightarrow {x}_{\text{vertex}} = - \frac{2}{- 6} = \frac{1}{3}$
$\text{substitute this value into the equation for y}$
$y = - 3 {\left(\frac{1}{3}\right)}^{2} + \frac{2}{3} - 4$
$\textcolor{w h i t e}{y} = - \frac{1}{3} + \frac{2}{3} - \frac{12}{3} = - \frac{11}{3}$
$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(\frac{1}{3} , - \frac{11}{3}\right)$
|
2021-09-20 08:22:06
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 20, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9430801868438721, "perplexity": 3820.9070638030935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057033.33/warc/CC-MAIN-20210920070754-20210920100754-00390.warc.gz"}
|
http://allsoftwarereviews.com/circular-error/circular-error-probable-equation.php
|
Home > Circular Error > Circular Error Probable Equation
# Circular Error Probable Equation
## Contents
So there was a 50/50 chance of a V2 landing within 17 km of its target. This distribution is described in the Closed Form Precision section. Included in these methods are the plug-in approach of Blischke and Halpin (1966), the Bayesian approach of Spall and Maryak (1992), and the maximum likelihood approach of Winkler and Bickert (2012). Waging Nuclear Peace: The Technology and Politics of Nuclear Weapons. http://allsoftwarereviews.com/circular-error/circular-error-probability-equation.php
Grubbs, F. An approximation for the 50% and 90% quantile when there is systematic bias comes from Shultz (1963), later modified by Ager (2004). References ↑ GPS Accuracy: Lies, Damn Lies, and Statistics, Frank van Diggelen, GPS World, 1998 ↑ Update: GNSS Accuracy: Lies, Damn Lies, and Statistics, Frank van Diggelen, GPS World, 2007 ↑ For $$p < 0.5$$ with some distribution shapes, the approximation can diverge significantly from the true cumulative distribution function. https://en.wikipedia.org/wiki/Circular_error_probable
## Circular Error Probable Excel
It allows the x- and y-coordinates to be correlated and have different variances. The system returned: (22) Invalid argument The remote host or network may be down. p.342. ^ a b Frank van Diggelen, "GNSS Accuracy – Lies, Damn Lies and Statistics", GPS World, Vol 18 No. 1, January 2007. Several methods have been introduced to estimate CEP from shot data.
Rice: When the true center of the coordinates and the POA are not identical, the radial error around the POA in a bivariate uncorrelated normal random variable with equal variances follows It generalizes to three-dimensional data and can accommodate systematic accuracy bias, but it is limited to the 50% CEP. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Circular Error Excel The RAND-tables have also been fitted with a regression model to accommodate systematic accuracy bias in the 50% quantile (Pesapane & Irvine, 1977).
The Grubbs-Patnaik estimator (Grubbs, 1964) differs from the Grubbs-Pearson estimator insofar as it is based on the Patnaik two-moment central $$\chi^{2}$$-approximation (Patnaik, 1949) of the true cumulative distribution function of radial It is only available for $$p = 0.5$$. The resulting distribution reduces to the Hoyt distribution if the mean has no offset. http://www.dtic.mil/dtic/tr/fulltext/u2/a196504.pdf Your cache administrator is webmaster.
If systematic accuracy bias is taken into account, numerical integration of the multivariate normal distribution around an offset circle is required for an exact solution. Circular Error Pendulum The Krempasky (2003) estimate is based on a nearly correct closed-form solution for the 50% quantile of the Hoyt distribution. Cambridge, MA: MIT Press. What is the Lethal Radius?
## Circular Error Probable Gps
CEP is not a good measure of accuracy when this distribution behavior is not met. http://ballistipedia.com/index.php?title=Circular_Error_Probable Other old, and less relevant approximations to the 50% quantile of the Hoyt distribution include Bell (1973), Nicholson (1974) and Siouris (1993). Circular Error Probable Excel What is the SSPK? 1 – 0.5 (1.29/1.39)^2 = 0.4495 or 44.95% Calculating the Terminal Kill Probability (TKP) TKP = R * SSPK Where R = Probability of the Delivery System Circular Error Probable Calculator If the x- and y-coordinates of the shots follow a bivariate normal distribution, the radial error around the POA can follow one of several distributions, depending on the cirumstances (Beckmann 1962;
C. his comment is here That is, if CEP is n meters, 50% of rounds land within n meters of the target, 43% between n and 2n, and 7% between 2n and 3n meters, and the and Maryak, J. Lieber and Daryl G. Circular Error Probable Matlab
Y: 1.2(1/3) = 1.062659H: 10(1/3) = 2.154435 2.62 * (1.062659 / 2.154435) = 1.29 nautical miles Calculating the Single Shot Probability of Kill (SSPK) SSPK: 1 – 0.5 (LR/CEP)^2 Where: CEP: Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Your cache administrator is webmaster. http://allsoftwarereviews.com/circular-error/circular-error-probable-cep.php Please try the request again.
Converting from CEP (Circular Error Probable) to R95 The Circular Error Probable is actually the radius in which 50% of all weapons fired would land. Spherical Error Probable The smaller it is, the better the accuracy of the missile. Systematic Accuracy Bias Some approaches to estimating CEP conflate the question of precision with the question of accuracy, or "sighting in." The simpler case only tries to estimate precision, and computes
## Munitions with this distribution behavior tend to cluster around the aim point, with most reasonably close, progressively fewer and fewer further away, and very few at long distance.
Let's include some numerical values. and Maryak, J. Targeting smaller cities or even complexes was next to impossible with this accuracy, one could only aim for a general area in which it would land rather randomly. 2drms Sequel to previous article with similar title [1] [2] ^ Frank van Diggelen, "GPS Accuracy: Lies, Damn Lies, and Statistics", GPS World, Vol 9 No. 1, January 1998 Further reading Blischke,
The Hoyt distribution reduces to the Rayleigh distribution if the correlation is 0 and the variances are equal. ISBN978-0-262-13258-9. The cumulative distribution function of radial error is equal to the integral of the bivariate normal distribution over an offset disc. navigate here What is it's EMT? 30 x 0.552/3 = 20.14 Megatons of EMT ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL:
Applying the natural logarithm to both sides and solving for n results in: n = ln(0.1) / ln(0.944) = 40 So forty missiles with a CEP of 150 m are required It differs from them insofar as it is based on the recent Liu, Tang, and Zhang (2009) four-moment non-central $$\chi^{2}$$-approximation of the true cumulative distribution function of radial error. It assumes an uncorrelated bivariate normal process with equal variances and zero mean.
|
2018-02-23 00:28:09
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5956879258155823, "perplexity": 3035.7109611456876}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814300.52/warc/CC-MAIN-20180222235935-20180223015935-00222.warc.gz"}
|
https://www.oliviergibaru.org/courses/NA_LinearSystems2.html
|
# Numerical Solution of Linear Algebraic Equations with Iterative Methods
## Introduction
The most basic task in linear algebra, and perhaps in all of scientific computing, is to solve for the unknowns in a set of linear algebraic equations. Linear, algebraic equations occur in almost all branches of numerical analysis. But their most visible application in engineering is in the analysis of linear systems. Any system whose response is proportional to the input is deemed to be linear. Linear systems include structures, elastic solids, heat flow, seepage of fluids, electromagnetic fields and electric circuits. If the system is discrete, such as a truss or an electric circuit, then its analysis leads directly to linear algebraic equations.
In the case of a statically determinate truss, like the Eiffel tower which is a three-dimensional truss structure, the equations arise when the equilibrium conditions of the joints are written down. The unknowns $x_1, x_2,\ldots, x_n$ represent the forces in the members and the support reactions, and the constants $b_1, b_2,\ldots, b_n$ are the prescribed external loads. The behavior of continuous systems is described by differential equations, rather than algebraic equations. However, because numerical analysis can deal only with discrete variables, it is first necessary to approximate a differential equation with a system of algebraic equations. The well-known finite difference, finite element and boundary element methods of analysis work in this manner. They use different approximations to achieve the “discretization,” but in each case the final task is the same: solve a system (often a very large system) of linear, algebraic equations.
In summary, the modeling of linear systems invariably gives rise to equations of the form $\mathbf{A}.\mathbf{x} = \mathbf{b}$, where $\mathbf{b}$ is the input and $\mathbf{x}$ represents the response of the system. The coefficient matrix $\mathbf{A}$, which reflects the characteristics of the system, is independent of the input. In other words, if the input is changed, the equations have to be solved again with a different $\mathbf{b}$, but the same $\mathbf{A}$.
Therefore, it is desirable to have an equation solving algorithm that can handle any number of constant vectors with minimal computational effort. In general, a set of linear algebraic equations looks like this:
$\left\{ \begin{array} [c]{r}% a_{1,1}x_{1}+\ldots+a_{1,n}x_{n}=b_{1}\\ \vdots\\ a_{m,1}x_{1}+\ldots+a_{m,n}x_{n}=b_{m} \end{array} \right.$
The $n$ unknowns $x_j$ , $j=1,\ldots,n$ are related by $m$ equations. The coefficients $a_{i,j}$ with $i=1,\ldots,m$ and $j=1,\ldots,n$ are known numbers, as are the right-hand side quantities $b_i$ with $i=1,\ldots,m$. If $n=m$ then there are as many equations as unknowns, and there is a good chance of solving for a unique solution set of $x_j$’s. Otherwise, if $n\neq m$, things are even more interesting; we’ll have more to say about this below. If we write the coefficients $a_{i,j}$ as a matrix, and the right-hand sides $b_i$ as a column vector the previous system can be written in matrix form as $\mathbf{A}.\mathbf{x}=\mathbf{b}$ where $\mathbf{A}=\left[ \begin{array} [c]{cccc}% a_{1,1} & a_{1,2} & \cdots & a_{1,n}\\ a_{2,1} & a_{2,2} & \cdots & a_{2,n}\\ \vdots & \vdots & & \vdots\\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{array} \right].$ Throughout this page, we use a raised dot to denote matrix multiplication, or the multiplication of a matrix and a vector, or the dot product of two vectors.
With python, we will use the numpy library to deal with matrices. For instance, the following so called Wilson matrix $\mathbf{A}=\left[ \begin{array} [c]{cccc}% 10 & 7 & 8 & 7\\ 7 & 5 & 6 & 5\\ 8 & 6 & 10 & 9\\ 7 & 5 & 9 & 10 \end{array} \right]$ can be defined in python like this:
import numpy as np
from numpy import linalg as LA
""" Solve the linear system Ax=b """
A = np.array([[10, 7, 8, 7],[7, 5, 6, 5],[8, 6, 10, 9],[7, 5, 9, 10]])
b = np.array([1, 1, 1, 1])
x = LA.solve(A,b)
print("Error of the solution = ",b-np.dot(A,x))
The np.dot function allows to calculate the dot product of the matrix with the vector. We can also create a matrix by using some numpy functions
import numpy as np
A = np.zeros((3,3),type=Float)
A particularly useful representation of the equations for computational purposes is the augmented coefficient matrix obtained by adjoining the constant vector $\mathbf{b}$ to the coefficient matrix $\mathbf{A}$ in the following fashion: $$\left[\mathbf{A}|\mathbf{b}\right]= \left[ \begin{array}[c]{cccc} a_{1,1} & a_{1,2} & \cdots & a_{1,n}\\ a_{2,1} & a_{2,2} & \cdots & a_{2,n}\\ \vdots & \vdots & & \vdots\\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{array} \left| \begin{array}{c} b_1 \\ b_2 \\ \vdots \\ b_m \end{array}\right.\right]$$
For $m=n$, we can solve the unknows except when one or more of the $m$ equations is a linear combination of the others. We call this condition row degeneracy. When all equations contain certain variables only in exactly the same linear combination, we call this condition column degeneracy. It turns out that, for square matrices, row degeneracy implies column degeneracy, and vice versa. $\mathbf{A}$ set of equations that is degenerate is called singular.
What is a singular or noninvertible matrix?
There might be cases where the matrix is not invertible and then the system cannot be solved. Consider the following linear system of equations: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 1 & -2 & 3\\ 2 & -1 & 2 \end{array}\right],\qquad\mathbf{b}=\left[\begin{array}{c} 1\\ -2\\ 3 \end{array}\right]$$ where only the last element of $\mathbf{A}$ changed. Let us try to apply the Gauss-Jordan elimination here: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 1 & -2 & 3\\ 2 & -1 & 2 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{array}\right.\right]$$ Operations 2 and 3: Multiply row 1 by -1 and sum to row 2: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 0 & -3 & 4\\ 2 & -1 & 2 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ -1 & 1 & 0\\ 0 & 0 & 1 \end{array}\right.\right]$$ Operations 2 and 3: Multiply row 1 by -2 and sum to row 3: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 0 & -3 & 4\\ 0 & -3 & 4 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ -1 & 1 & 0\\ -2 & 0 & 1 \end{array}\right.\right]$$ Consequently two rows are equal on the left side... Multiply row 2 by -1 and sum to row 3: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 0 & -3 & 4\\ 0 & 0 & 0 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ -1 & 1 & 0\\ -1 & -1 & 1 \end{array}\right.\right]$$ We then lost one row. No matter the path we take, we will always have a zero-ed row in this case and cannot make the left side equal to the identity matrix. The reason for this is that any row in this matrix can be made by a linear combination of the other two (e.g. sum rows 1 and 2 of $\mathbf{A}$ and you get row 3). In other words, the system is really made from two equations and the other is generated by the original two rows. Then we have more variables than equations and the system cannot be solved. The fact that the matrix $\mathbf{A}$ cannot be inverted is a sign that the system is not solvable. In those situations, it is said the matrix is noninvertible or singular. We can also state that the rows of the matrix are linearly dependent, because we can make one by a linear combination of the others.
Now a piece of important trivia regarding matrix inversion:
• If a matrix is non-invertible, its transpose is non-invertible too
• From the previous, the columns of a non-invertible matrix are linearly dependent
• If the determinant of a matrix is zero, then the matrix is not invertible
• The rank of an invertible matrix of size $n\times n$ is $n$ (full rank)
• The eigenvalues of the an invertible matrix are all different from zero
Numerically, at least two additional things prevent us from getting a good solution:
• While not exact linear combinations of each other, some of the equations may be so close to linearly dependent that roundoff errors in the machine render them linearly dependent at some stage in the solution process. In this case your numerical procedure will fail, and it can tell you that it has failed.
• Accumulated roundoff errors in the solution process can swamp the true solution. This problem particularly emerges if $n$ is too large. The numerical procedure does not fail algorithmically. However, it returns a set of $x$’s that are wrong, as can be discovered by direct substitution back into the original equations. The closer a set of equations is to being singular, the more likely this is to happen, since increasingly close cancellations will occur during the solution. In fact, the preceding item can be viewed as the special case in which the loss of significance is unfortunately total.
Much of the sophistication of well-written linear equation-solving packages is devoted to the detection and/or correction of these two pathologies. It is difficult to give any firm guidelines for when such sophistication is needed, since there is no such thing as a “typical” linear problem. But here is a rough idea: Linear sets with $n$ no larger than $20$ or $50$ are routine if they are not close to singular; they rarely require more than the most straightforward methods, even in only single precision or float. With double precision, this number can readily be extended to $n$ as large as perhaps $1000$, after which point the limiting factor anyway soon becomes machine time, not accuracy. Even larger linear sets, $n$ in the thousands or millions, can be solved when the coefficients are sparse (that is, mostly zero), by methods that take advantage of the sparseness. Unfortunately, one seems just as often to encounter linear problems that, by their underlying nature, are close to singular. In this case, you might need to resort to sophisticated methods even for the case of $n=10$. Singular value decomposition is a technique that can sometimes turn singular problems into nonsingular ones, in which case additional sophistication becomes unnecessary.
There are many algorithms dedicated to the solution of large sets of equations, each one being tailored to a particular formof the coefficient matrix (symmetric, banded, sparse...). A well-known collection of these routines is LAPACK—Linear Algebra PACKage, originally written in Fortran77. The NumPy linear algebra functions rely on BLAS and LAPACK to provide efficient low level implementations of standard linear algebra algorithms. Those libraries may be provided by NumPy itself using C versions of a subset of their reference implementations but, when possible, highly optimized libraries that take advantage of specialized processor functionality are preferred (see numpy.linalg).
A system of $n$ linear equations in $n$ unknowns has a unique solution, provided that the determinant of the coefficient matrix is nonsingular; that is, $det(A)=0$. The rows and columns of a nonsingular matrix are linearly independent in the sense that no row (or column) is a linear combination of other rows (or columns). If the coefficient matrix is singular, the equations may have an infinite number of solutions, or no solutions at all, depending on the constant vector.
## Direct Methods
If matrix $\mathbf{A}$ is an upper triangular matrix (or lower triangular matrix) i.e. $\left\{ \begin{array} [c]{r}% a_{11}x_{1}+\ldots a_{1,n-1}x_{n-1}+a_{1n}x_{n}=b_{1}\\ \vdots\\ a_{n-1,n-1}x_{n-1}+a_{n-1,n}x_{n}=b_{n-1}\\ a_{nn}x_{n}=b_{n}% \end{array} \right.$ and $\det\left( A\right) =a_{11}a_{22}\ldots a_{nn}\neq0$ then the solution can be obtained in the following manner: $\left\{ \begin{array} [c]{l}% x_{n}=a_{nn}^{-1}b_{n}\\ x_{n-1}=a_{n-1,n-1}^{-1}\left( b_{n-1}-a_{n-1,n}x_{n}\right) \\ \vdots\\ x_{1}=a_{11}^{-1}\left( b_{1}-a_{12}x_{2}-\cdots-a_{1,n-1}x_{n-1}-a_{1n}% x_{n}\right) \end{array} \right.$ Consequently, to solve this system we need to do $\left\{ \begin{array} [c]{c}% 1+2+\cdots+\left( n-1\right) =\dfrac{n\left( n-1\right) }{2}\text{ additions}\\ 1+2+\cdots+\left( n-1\right) =\dfrac{n\left( n-1\right) }{2}\text{ multiplications}\\ n\text{ divisions.}% \end{array} \right.$
## Gauss-Jordan elimination method
The idea behind Gauss-Jordan elimination is to use elementary row operations on the system that replace a system with an equivalent but simpler sytem for which the answers to the questions about solutions are "obvious". The Gauss elimination method needs three steps:
1. algebraic operations by swapping rows for successively eliminating the unknows which is similar to define an invertible matrix $\mathbf{M}$ such that matrix $\mathbf{M}.\mathbf{A}$ becomes an upper triangular matrix
2. calculating vector $\mathbf{M}.\mathbf{b}$
3. solving the linear system $\mathbf{M}.\mathbf{A}.\mathbf{x}=\mathbf{M}.\mathbf{b}$ where $\mathbf{M}.\mathbf{A}$ is a upper triangular matrix
Let $\left\{ \begin{array} [c]{r} a_{11}x_{1}+a_{12}x_{2}+\ldots+a_{1n}x_{n}=b_{1}\;\;\;\left( L_{1}\right) \\ a_{21}x_{1}+a_{22}x_{2}+\ldots+a_{2n}x_{n}=b_{2}\;\;\;\left( L_{2}\right) \\ \vdots\\ a_{n1}x_{1}+a_{n2}x_{2}+\ldots+a_{nn}x_{n}=b_{n}\;\;\;\left( L_{n}\right) \end{array} \right.$ be a linear system of algebraic equations. If $a_{11}\neq0$ then $\left\{ \begin{array} [c]{c}% 1.x_{1}+a_{12}^{1}x_{2}+\ldots+a_{1n}^{1}x_{n}=b_{1}^{1}\;\;\;\left( L_{1}^{1}\leftarrow\dfrac{L_{1}}{a_{11}}\right) \\ \left. \begin{array} [c]{c}% 0.x_{1}+a_{22}^{1}x_{2}+\ldots+a_{2n}^{1}x_{n}=b_{2}^{1}\\ \vdots\\ 0.x_{1}+a_{n2}^{1}x_{2}+\ldots+a_{nn}^{1}x_{n}=b_{n}^{1}% \end{array} \right\} \begin{array} [c]{c}% \forall i\in\left[ 2,n\right] \\ \left( L_{i}^{1}\leftarrow L_{i}-a_{i1}L_{1}^{1}\right) \end{array} \end{array} \right.$ After applying $n$ time the previous method we finally obtain: $\left[ \begin{array} [c]{cccc}% 1 & a_{12}^{n} & \ldots & a_{1n}^{n}\\ 0 & 1 & & \\ \vdots & \ddots & \ddots & a_{n-1,n}^{n}\\ 0 & \cdots & 0 & 1 \end{array} \right] x=b^{\left[ n\right] }%$
Indeed case one pivot is null, we search in which column we have a non-null pivot and we swap these columns. If it is impossible then we have $det(A)=0$.
Example We assume that we have a computer with three significative digits. If we solve the following linear system $% \begin{array} [c]{r}% 10^{-4}x_{1}+x_{2}=1\\ x_{1}+x_{2}=2 \end{array}$ we obtain the 'true' solutions: $x_{1}=1,00010...\;\;,\;x_{2}=0,99990...$
By applying the Gauss elimination method, we obtain $% \begin{array} [c]{r}% x_{1}+10^{4}x_{2}=10^{4}\\ -9990x_{2}=-9990 \end{array}$ because $-10^{4}+1=-9999$ and $-10^{4}+2=-9998$ are roundoff to $-9990$. It yields $x_{1}\simeq0\text{ et }x_{2}\simeq1$ If we swap the two rows: $% \begin{array} [c]{r}% x_{1}+x_{2}=2\\ 10^{-4}x_{1}+x_{2}=1 \end{array}$ then we have: $% \begin{array} [c]{r}% x_{1}+x_{2}=2\\ 0,999x_{2}=0,999 \end{array}$ Indeed, $-10^{-4}+1=0,9999\simeq0,999$ and $-2.10^{-4}+1=0,9998\simeq 0,999.$ It yields the more accurate values $x_{1}\simeq1\text{ et }x_{2}\simeq1$
## Cramer's rule
We are now going to derive explicit formulas for the solution of $\mathbf{A}x=\mathbf{b}$. The matrix $\mathbf{A}$ of this linear system is a square matrix of order $n$, and we shall assume that is not singular. We set $x_{i}=\frac{\det\left( \mathbf{B}_{i}\right) }{\det\left( \mathbf{A}\right) }%$ where $\mathbf{B}_{i}=\left[ \begin{array} [c]{ccccccc}% a_{11} & \cdots & a_{1,i-1} & b_{1} & a_{1,i+1} & \cdots & a_{1n}\\ a_{21} & \cdots & a_{2,i-1} & b_{2} & a_{2,i+1} & \cdots & a_{2n}\\ \vdots & & \vdots & \vdots & \vdots & & \vdots\\ a_{n1} & \cdots & a_{n,i-1} & b_{n} & a_{n,i+1} & \cdots & a_{nn}% \end{array} \right]$ We then calculate $n+1$ determinants and $n$ divisions. For calculating one determinant, we must do $n!-1$ additions, $n!(n-1)$ multiplications. This yields to: \begin{align*} & \left( n+1\right) !\text{ additions,}\\ & \left( n+2\right) !\text{ multiplications,}\\ & \text{and } n\text{ divisions.} \end{align*} For $n=10$ we need to do \begin{align*} & 900\;\text{operations for the Gauss elimination}\\ & 400\;000\;000\;\text{operations for the Cramer method}\\ & \text{No comment ....}% \end{align*}
## Inverse of a matrix
What is the inverse of a matrix? Let's say we have the following system of linear equations: $$\begin{array}{ccccc} x_{1} & +x_{2} & -x_{3} & = & 1\\ x_{1} & -2x_{2} & +3x_{3} & = & -2\\ -x_{1} & 2x_{2} & -x_{2} & = & 3 \end{array}$$ This can be represented in matrix form as: $$\mathbf{Ax=b},$$ where $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 1 & -2 & 3\\ -1 & 2 & -1 \end{array}\right],\qquad\mathbf{x}=\left[\begin{array}{c} x_{1}\\ x_{2}\\ x_{3} \end{array}\right],\qquad\mathbf{b}=\left[\begin{array}{c} 1\\ -2\\ 3 \end{array}\right].$$ To find $\mathbf{x}$, one needs to do the equivalent to divide $\mathbf{b}$ by $\mathbf{A}$. Since $\mathbf{A}$ is a matrix, we cannot simply divide by it. Instead, we make use of the notion of inverse of a matrix. The inverse of a matrix $\mathbf{A}$ is a matrix such that, when one is multiplied by the other, the result is the identity matrix $\mathbf{I}$ (a special matrix with 1's in the diagonal and 0's everywhere else): $$\mathbf{A^{-1}A=AA^{-1}=I}$$ In our original problem, we can then premultiply each side of the equation by the inverse of $\mathbf{A}$ to get: $$\mathbf{A^{-1}Ax=x=A^{-1}b}$$ To find this inverse, we need to find each element in the matrix $\mathbf{A^{-1}}$ that, when multiplied by the matrix $\mathbf{A}$, will produce the identity matrix. To do that, we can use the widely known Gauss-Jordan elimination method. We will use a joint matrix $\left[\mathbf{A|I}\right]$ by concatenating the columns of $\mathbf{A}$ and $\mathbf{I}$. Then, we perform a set of operations that converts $\mathbf{A}$ into $\mathbf{I}$. In the process, $\mathbf{I}$ is converted into $\mathbf{A^{-1}}$, concluding the joint matrix $\left[\mathbf{I|A^{-1}}\right]$. For our example: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 1 & -2 & 3\\ -1 & 2 & -1 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{array}\right.\right]$$ We can do the following operations to the joint matrix:
1. Swap two rows
2. Multiply a row by a non-zero scalar
3. Sum two rows and replace one of them with the result
Now let us apply these operations to our joint matrix.
Operation 3: Sum rows 2 and 3 and store the result in row 3: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 1 & -2 & 3\\ 0 & 0 & 2 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 1 & 1 \end{array}\right.\right]$$ Operations 2 and 3: Multiply row 1 by -1, sum with row 2 and store result in 2: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 0 & -3 & 4\\ 0 & 0 & 2 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ -1 & 1 & 0\\ 0 & 1 & 1 \end{array}\right.\right]$$ Operations 2 and 3: Multiply row 3 by -2, sum with row 2 and store result in 2: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 0 & -3 & 0\\ 0 & 0 & 2 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ -1 & -1 & -2\\ 0 & 1 & 1 \end{array}\right.\right]$$ Operation 2: Multiply row 2 by -1/3 and row 3 by 1/2: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{array}\left|\begin{array}{ccc} 1 & 0 & 0\\ 1/3 & 1/3 & 2/3\\ 0 & 1/2 & 1/2 \end{array}\right.\right]$$ Operations 2 and 3: Mutiply row 2 by -1 and sum to row 1, then sum row 3 to row 1: $$\mathbf{A}=\left[\begin{array}{ccc} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{array}\left|\begin{array}{ccc} 2/3 & 1/6 & -1/6\\ 1/3 & 1/3 & 2/3\\ 0 & 1/2 & 1/2 \end{array}\right.\right]$$ We end with the inverse: $$\mathbf{A^{-1}}=\left[\begin{array}{ccc} 2/3 & 1/6 & -1/6\\ 1/3 & 1/3 & 2/3\\ 0 & 1/2 & 1/2 \end{array}\right]$$ Now we can solve the system of equations at the beginning by $\mathbf{x=A^{-1}b}$. We could have solved the original problem by joining $\mathbf{A}$ and $\mathbf{b}$, and solving with the same method $\left[\mathbf{A|b}\right]$ (we would end up with $\left[\mathbf{I|x}\right]$). One of the benefit of calculating the inverse of $\mathbf{A}$ is that, in case we change $\mathbf{b}$, we only need to apply again $\mathbf{x=A^{-1}b}$ to solve the new system of equations.
To solve the inverse of a matrix $A$, we know that $A.A^{-1}=I$ where $I$ is the identity matrix. If we set $e_{i}$ the vector with null coordinates except the $i$-coordinate which is equal to $1$ then we can find the inverse matrix of $A$ by solving the $n$ following linear systems \begin{align*} A.X_{i} & =e_{i} \end{align*} where $X_{i}$ is the $i$-column of $A^{-1}$. To solve iteratively this inverse problem, we can use the $L.U$ decomposition method.
Let $L$ be a lower triangular matrix with $1$ on its diagonal and $U$ be a upper triangular matrix then with some assumptions matrix $A$ can be written as $A=L.U$. Hence, \begin{align*} Ax & =b\\ LUx & =b \end{align*} where, $A=\left[ \begin{array} [c]{cccc}% 1 & 0 & \ldots & 0\\ \times & 1 & & \vdots\\ \vdots & \ddots & \ddots & 0\\ \times & \cdots & \times & 1 \end{array} \right] \left[ \begin{array} [c]{cccc}% \times & \times & \ldots & \times\\ 0 & \times & & \vdots\\ \vdots & \ddots & \ddots & \times\\ 0 & \cdots & 0 & \times \end{array} \right]$ If we set $y=U.x$ then we firstly solve $L.y=b$ by using a forward substitution methodology. Hence, as we know the vector $y$, we can solve $U.x=y$ by using a back substitution method. Consequently, we finally obtain the unknow vector $x$. The main interest of this method is that if we have many linear systems with the same matrix $A$ we can use iteratively solve the systems with this $L.U$ decomposition. It can be obtained by using the Gauss elimination.
## What is an ill-conditioned matrix?
Let us consider that the vector $\mathbf{b}$ is data collected by some sensors. This data comes with some error $\Delta\mathbf{b}$ attached to it. Our solution to the problem will be: $$\mathbf{x=A^{-1}(b+\Delta b)=A^{-1}b+A^{-1}\Delta b}=\mathbf{x^{\star}+A^{-1}\Delta b}$$ where $\mathbf{x^{\star}}$ is the true solution. The error of our solution caused by the error in the data is $$\mathbf{\Delta x=x-x^{\star}=A^{-1}\Delta b}$$ The error in $\mathbf{\Delta b}$ may get amplified by $\mathbf{A^{-1}}$ and produce a large error in $\mathbf{x}$. In those situations (where large error is a subjective criterion), we say the problem is ill-posed or ill-conditioned. Otherwise, the matrix is well-posed or well-conditioned. To make it simple, you can imagine $\mathbf{A}$ as a scalar $A$. If $\mathbf{A}$ is very small, then its inverse is very large. Then, even a small error in the data gets amplified by the large inverse of $\mathbf{A}$, producing a large deviation in the solution. For a pratical example: $$\mathbf{A}=\frac{1}{2}\left[\begin{array}{cc} 1 & 1\\ 1+10^{-10} & 1-10^{-10} \end{array}\right],\qquad\mathbf{A^{-1}}=\left[\begin{array}{cc} 1-10^{10} & 10^{10}\\ 1+10^{10} & -10^{10} \end{array}\right]$$ The problem with this matrix is that it is very close to being singular, although it is not. This is a condition of the problem and nothing can be done to solve it.
This condition is so important that a measure for it was defined, the so called condition number: low condition number means well-conditioned problems and high condition number means ill-conditioned problems. The condition number is the maximum ratio of the relative error in $\mathbf{x}$ by the relative error in $\mathbf{b}$: $$\kappa(\mathbf{A})=\sup\left({\frac{\left\Vert \mathbf{\Delta x}\right\Vert }{\left\Vert \mathbf{x}\right\Vert }}/{\frac{\left\Vert \mathbf{\Delta b}\right\Vert }{\left\Vert \mathbf{b}\right\Vert }}\right)=\sup\left(\frac{\left\Vert \mathbf{\Delta x}\right\Vert \left\Vert \mathbf{b}\right\Vert }{\left\Vert \mathbf{\Delta b}\right\Vert \left\Vert \mathbf{x}\right\Vert }\right)$$ Taking advantage of the fact that $\left\Vert \mathbf{\Delta x}\right\Vert =\left\Vert \mathbf{A^{-1}\Delta b}\right\Vert \le\left\Vert \mathbf{A^{-1}}\right\Vert \left\Vert \mathbf{\Delta b}\right\Vert$ and $\left\Vert \mathbf{b}\right\Vert =\left\Vert \mathbf{Ax}\right\Vert \le\left\Vert \mathbf{A}\right\Vert \left\Vert \mathbf{x}\right\Vert$, the above equation becomes: $$\kappa(\mathbf{A})=\sup\left(\frac{\left\Vert \mathbf{\Delta x}\right\Vert \left\Vert \mathbf{b}\right\Vert }{\left\Vert \mathbf{\Delta b}\right\Vert \left\Vert \mathbf{x}\right\Vert }\right)\le\frac{\left\Vert \mathbf{A^{-1}}\right\Vert \left\Vert \mathbf{\Delta b}\right\Vert \left\Vert \mathbf{A}\right\Vert \left\Vert \mathbf{x}\right\Vert }{\left\Vert \mathbf{\Delta b}\right\Vert \left\Vert \mathbf{x}\right\Vert }=\left\Vert \mathbf{A^{-1}}\right\Vert \left\Vert \mathbf{A}\right\Vert.$$ Now we have a very neat way of measuring the condition of the problem. The value, however, depends on the norm used. For the $\ell_{2}$-norm, the condition number amounts to: $$\kappa(\mathbf{A})=\frac{\sigma_{max}(\mathbf{A})}{\sigma_{min}(\mathbf{A})}$$ where $\sigma_{max}(\mathbf{A})$ and $\sigma_{min}(\mathbf{A})$ are the maximum and minimum singular values of $\mathbf{A}$.
## Exercice 1.
1) Define the Wilson matrix $\mathbf{A}$. For this, use the numpy and linalg python libraries.
import numpy as np
from numpy import linalg as LA
A=np.array([# To Do])
b=np.array([32,23,33,31])
c=np.array([32.1,22.9,33.1,30.9])
# Solve the linear system
x=LA.solve(A,b)
# solve the perturbated linear system
y=LA.solve(A,c)
print("Error : ",x-y)
2) Calculate the condition number of $\mathbf{A}$ for the $1$-norm and $2$-norm. For this, you need to create the following functions:
""" 1-Norm function """
def Norm1(A):
#TO DO
return
""" 2-Norm function """
def Norm2(A):
#TO DO
return value
For the $2$-norm you can use the eigenvals function of linalg.
## Exercice 2.
Define the Hilbert(n) function (see wikipedia for the definition of the Hilbert matrix) which allows to create the Hilbert matrix of dimension $n$. In this exercice, we want to show that this matrix is very ill-conditionned even for $n=5,10$ and $15$. We then solve the following linear system:
import numpy as np
from numpy import linalg as LA
""" Hilbert matrix function """
def Hilbert(n):
#TO DO
return value
n=5
H=Hilbert(n)
x=np.ones(n)
b=np.dot(H,x)
X=LA.solve(H,b)
print("Error = ",x-X)
## Exercice 3.
Define the iterative Jacobi and Gauss-Seidel functions in order to solve the following linear system: $Ax=\left[ \begin{array}{c} 1 \\ 1 \\ 1% \end{array}% \right]$ with $A=\left[ \begin{array}{ccc} 6 & 1 & -1 \\ 0 & -4 & 2 \\ 1 & 0 & 3% \end{array}% \right]$ For this, you can use the following link Jacobi method in wikipedia.
""" Iterative Jacobi function """
def Jacobi(A,b,nbiter):
#TO DO
return
""" Iterative Gauss-Seidel function """
def GS(A,b,nbiter):
#TO DO
return value
where $nbiter$ is the maximum iteration number of the method.
Define a python function to know if the iterative method converges or not. For this, you can define the spectral radius function of a matrix. In order to calculate this spectral radius, we will use the following result which enables to calculate the biggest eigenvalue in module of a matrix.
The calculation of eigenvalues and eigenvectors is essential in all branches of science, in particular for the solution of systems of linear differential equations, in theory of stability, for questions of convergence of iterative processes, and in physics and chemistry (mechanics, circuits, chemical kinetics, Schrodinger equation).
A simple algorithm to calculate the eigenvalues of a matrix $\mathbf{A}$ is based on the following iterations $$y_{k + 1} = \mathbf{A}.y_k$$ where $y_0$ is an arbitrary vector. In the following theorem, we show that $y_k = \mathbf{A}^k.y_0$ (method of the power) tends to an eigenvector of $\mathbf{A}$ and that the Rayleigh quotient $\dfrac{y^T_k.\mathbf{A}.y_k} {y^T_k.y_k}$ is an approximation of an eigenvalue of $\mathbf{A}$.
Theorem. Let $\mathbf{A}$ be a diagonalizable matrix of eigenvalues $\lambda_1,. . . ,\lambda_n$ and their associated eigenvectors $v_1,. . . , v_n$ such that each $v_i$ satisfies $\left\Vert v_i \right\Vert = 1$.
If $|\lambda_1| > |\lambda_2| ≥ |\lambda_3| ≥. . . ≥ |\lambda_n|$ then the $y_k$ vectors of the previous iteration algorithm satisfy $$y_k = \lambda^k_1 \left(a_1.v_1 + \mathcal{O} \left(\left| \dfrac{\lambda_2}{\lambda_1} \right|^k \right) \right)$$ where the scalar $a_1$ is obtained from the unknow decomposition $y_0 = \sum^n_{i=1} a_i.v_i$
If $a_1 \neq 0$ then the Rayleigh's quotient satisfies $$\dfrac{y^T_k.A.y_k}{y^T_k.y_k} = \lambda_1 + \mathcal{O} \left(\left|\dfrac{\lambda_2}{\lambda_1} \right|^k \right)$$
If $\mathbf{A}$ is a normal matrix (i.e. the eigenvectors are orthogonals) then the error becomes $\mathcal{O} \left(\left|\dfrac{\lambda_2} {\lambda_1} \right|^{2k}\right)$.
Remark. In practise, the componants of the vector $y_k$ grow exponentially with $k$. It is then recommended to normalize $y_k$ after each iteration, i.e. replace $y_k$ with $\dfrac{y_k}{\left\Vert y_k \right\Vert}$. Otherwise, one risks of an "overflow".
Implement this iterative power algorithm by defining the IterativePower function. Then, implement the SpectralRadius function in order to see if the Jacobi or Gauss-Seidel algorithms will converge or not.
""" Convergente test function """
def IterativePower(A, maxiter):
#TO DO
return value
#TO DO
return value
## Exercice [AL 1]
• Let $\left\Vert \mathbf{.}\right\Vert_p: \mathbb{R}^n \longrightarrow \mathbb{R}$ (with $p≥1$) be a function defined by $$\left\Vert \mathbf{x}\right\Vert_p = \left( \sum_{i=1}^{i=n} \left| x_i \right| \right)^\frac{1}{p}$$ Show that this application is a norm.
• Case p=1 is obvious.
• For $p>1$, we denote by $q>1$ the real value such that $$\frac{1}{p}+\frac{1}{q}=1$$
• ## References
1. P.G. Ciarlet (1982), Introduction à l’analyse numérique matricielle et à l’optimisation, Masson
2. J.J. Dongarra, C.B. Moler, J.R. Bunch & G.W. Stewart (1979), LINPACK Users’ Guide. SIAM.
3. D.K. Faddeev & V.N. Faddeeva (1963), Computational Methods of Linear Algebra. Freeman & Co.
4. G.H. Golub & C.F. Van Loan (1989), Matrix Computations. Second edition. John Hopkins Univ. Press.
5. N.J. Higham (1996), Accuracy and Stability of Numerical Algorithms. SIAM.
6. A.S. Householder (1964), The Theory of Matrices in Numerical Analysis. Blaisdell Publ. Comp.
7. G.W. Stewart (1973), Introduction to Matrix Computations. Academic Press.
8. L.N. Trefethen & D. Bau (1997), Numerical Linear Algebra. SIAM.
9. J.H. Wilkinson (1969), Rundungsfehler. Springer-Verlag.
10. J.H. Wilkinson & C. Reinsch (1971), Handbook for Automatic Computation, Volume II, Linear Algebra. Springer-Verlag.
|
2021-09-23 21:01:26
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9006995558738708, "perplexity": 274.21942504305423}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057447.52/warc/CC-MAIN-20210923195546-20210923225546-00337.warc.gz"}
|
https://physics.aps.org/articles/v7/s147
|
Synopsis
# How Oxygen Kindles Fireflies
Physics 7, s147
X-ray images of the light-emitting organs in fireflies clarify the mechanism by which oxygen controls the insects’ luminescence.
To communicate and find mates, fireflies produce light flashes through a luminescence process whose chemistry is well known: in the presence of oxygen, an enzyme acts on the compound luciferin (Latin for “light-bringer”), triggering an oxidation reaction that is accompanied by light emission. Determining the mechanism that regulates the oxygen supply has been difficult because the tracheal network that carries the gas to the light-emitting organs, known as photocites, has features as small as $100$ nanometers (nm), finer than the resolving power of most microscopes. Now, Yeukuang Hwu at the Academia Sinica and the National Cheng Kung University, Taiwan, and co-workers have used tomographic and microscopy techniques with 20-nm resolution to image the insects’ organs and derive oxygen flux estimates that support a specific supply mechanism.
The researchers designed their experiment to test two leading hypothesis for the oxygen supply mechanism. The first revolves around the firefly’s production of nitric oxide (NO) inside the photocites: before a flash, the gas soaks the mitochondria—organelles that, fed by oxygen, control energy production in cells— suppressing their activity and leaving extra oxygen available for bioluminescence. The second conjecture proposes that circulating fluid in the tracheal network rises or ebbs to control oxygen. The authors’ experiments, carried out at Taiwan’s synchrotron light source, provided evidence for the first theory: x-ray images of the tracheal system in live insects showed no fluid inside the tracheal system. By measuring the tracheal geometries with high resolution, the researchers were able to estimate how much gas could diffuse from the tracheal network to tissues, yielding values consistent with the NO hypothesis.
This research is published in Physical Review Letters.
–Matteo Rini
## Subject Areas
Biological Physics
## Related Articles
Geophysics
### A Jumpstart for Biochemistry
RNA can replicate in conditions that could be found on the early Earth, suggesting a possible step in the origin of life. Read More »
Complex Systems
### Resource Dynamics Dictate Diversity
A model that treats species and food sources as spins in a spin glass finds a surprising limit on species diversity for some types of ecosystems. Read More »
Biological Physics
### Speed Limit for Cell Growth
The composition of a cell’s protein-synthesis machinery is tuned to optimize the cell’s reproduction rate. Read More »
|
2020-08-11 10:47:30
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.492049902677536, "perplexity": 5696.269171262269}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738746.41/warc/CC-MAIN-20200811090050-20200811120050-00417.warc.gz"}
|
https://mmclassification.readthedocs.io/zh_CN/latest/api/generated/mmcls.models.LabelSmoothLoss.html
|
# mmcls.models.LabelSmoothLoss¶
class mmcls.models.LabelSmoothLoss(label_smooth_val, num_classes=None, mode='original', reduction='mean', loss_weight=1.0)[源代码]
Initializer for the label smoothed cross entropy loss.
This decreases gap between output scores and encourages generalization. Labels provided to forward can be one-hot like vectors (NxC) or class indices (Nx1). And this accepts linear combination of one-hot like labels from mixup or cutmix except multi-label task.
• label_smooth_val (float) – The degree of label smoothing.
• num_classes (int, optional) – Number of classes. Defaults to None.
• mode (str) – Refers to notes, Options are ‘original’, ‘classy_vision’, ‘multi_label’. Defaults to ‘original’
• reduction (str) – The method used to reduce the loss. Options are “none”, “mean” and “sum”. Defaults to ‘mean’.
• loss_weight (float) – Weight of the loss. Defaults to 1.0.
if the mode is “original”, this will use the same label smooth method as the original paper as:
$(1-\epsilon)\delta_{k, y} + \frac{\epsilon}{K}$
where epsilon is the label_smooth_val, K is the num_classes and delta(k,y) is Dirac delta, which equals 1 for k=y and 0 otherwise.
if the mode is “classy_vision”, this will use the same label smooth method as the facebookresearch/ClassyVision repo as:
$\frac{\delta_{k, y} + \epsilon/K}{1+\epsilon}$
if the mode is “multi_label”, this will accept labels from multi-label task and smoothing them as:
$(1-2\epsilon)\delta_{k, y} + \epsilon$
|
2022-12-07 03:37:11
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34454792737960815, "perplexity": 12711.477026825281}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711126.30/warc/CC-MAIN-20221207021130-20221207051130-00595.warc.gz"}
|
https://mathoverflow.net/questions/298061/h%C3%B6lder-continuity-of-weak-subsolutions-to-parabolic-equations
|
# Hölder continuity of weak subsolutions to parabolic equations
It is well known that a weak solution to linear parabolic equation $u_t - div(A(x)\nabla u) = 0$ with homogeneous Neumann boundary condition, is Holder continuous with $A(x)$ belongs only to $L^\infty(\Omega)$ and satisfies the uniform elliptic condition.
My question is that: can we say the same for a weak subsolution, i.e. $$\int_0^T\int_{\Omega}u_t\eta + A(x)\nabla u \nabla \eta \leq 0$$ for all non-negative test functions $\eta\geq 0$? Assume additionally that we have the subsolution is non-negative $u\geq 0$ and uniformly bounded $\|u\|_{L^\infty(\Omega\times (0,T))} \leq M$.
If it can not be true, how about the Laplacian case, i.e. when $A(x) = Id$.
|
2019-02-20 08:23:28
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.987484335899353, "perplexity": 149.69769534046884}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247494485.54/warc/CC-MAIN-20190220065052-20190220091052-00001.warc.gz"}
|
https://planetmath.org/digitalobject
|
# digital object
A digital object in a digital library is the textual or multimedia data and the metadata.
Formally, a digital object $DO$ is a quadruple $(h,SM,ST,SS)$ where
1. 1.
$h\in H$, where $H$ is a set of universally unique handles (labels);
2. 2.
$SM=\{sm_{1},sm_{2},...,sm_{n}\}$ is a set of streams;
3. 3.
$ST=\{st_{1},st_{2},...,st_{m}\}$ is a set of structural metadata specifications; and
4. 4.
$SS=\{stsm_{1},stsm_{2},...,stsm_{p}\}$ is a set of Structured Streams functions defined from the streams in $SM$ and from the structures in $ST$.
Title digital object DigitalObject 2013-03-22 15:30:38 2013-03-22 15:30:38 CWoo (3771) CWoo (3771) 11 CWoo (3771) Definition msc 00A20
|
2018-11-18 14:55:42
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 9, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2535329759120941, "perplexity": 5180.011400905229}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039744381.73/warc/CC-MAIN-20181118135147-20181118161147-00078.warc.gz"}
|
http://mymathforum.com/calculus/46985-about-diff-problem.html
|
My Math Forum About diff. problem
Calculus Calculus Math Forum
October 12th, 2014, 09:25 AM #1 Newbie Joined: Oct 2014 From: macau Posts: 4 Thanks: 0 About diff. problem I need your solution. ~please!! The question is: find all tangent lines through the origin to the graph of y=1+(x-1)^2 . Last edited by skipjack; October 13th, 2014 at 10:04 AM.
October 12th, 2014, 10:17 AM #2 Math Team Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677 a line tangent to the curve $\displaystyle y = 1+(x-1)^2$ will pass thru the points $\displaystyle (0,0)$ and $\displaystyle \left(x,1+(x-1)^2\right)$ ... slope of any such line is $\displaystyle \frac{\Delta y}{\Delta x} = \frac{1+(x-1)^2 - 0}{x-0} = \frac{1+(x-1)^2}{x}$ now ... what do you know about the slope of a tangent line from a calculus perspective? Thanks from topsquark and superzhong
October 12th, 2014, 03:31 PM #3 Global Moderator Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,974 Thanks: 1156 Math Focus: Elementary mathematics and beyond $\displaystyle y=kx$ $\displaystyle y=1+(x-1)^2$ $\displaystyle k=2x-2$ $\displaystyle (2x-2)x=1+(x-1)^2\Rightarrow x=\pm\sqrt2$ $\displaystyle y=2(\sqrt2-1)x$ $\displaystyle y=-2(\sqrt2+1)x$ Thanks from topsquark and superzhong
October 13th, 2014, 08:38 AM #4
Newbie
Joined: Oct 2014
From: macau
Posts: 4
Thanks: 0
Quote:
Originally Posted by greg1313 $\displaystyle y=kx$ $\displaystyle y=1+(x-1)^2$ $\displaystyle k=2x-2$ $\displaystyle (2x-2)x=1+(x-1)^2\Rightarrow x=\pm\sqrt2$ $\displaystyle y=2(\sqrt2-1)x$ $\displaystyle y=-2(\sqrt2+1)x$
thanks sensei !!! that is very helpful~~
Quote:
Originally Posted by skeeter a line tangent to the curve $\displaystyle y = 1+(x-1)^2$ will pass thru the points $\displaystyle (0,0)$ and $\displaystyle \left(x,1+(x-1)^2\right)$ ... slope of any such line is $\displaystyle \frac{\Delta y}{\Delta x} = \frac{1+(x-1)^2 - 0}{x-0} = \frac{1+(x-1)^2}{x}$ now ... what do you know about the slope of a tangent line from a calculus perspective?
Thanks, I almost get it. ~XD
Last edited by skipjack; October 13th, 2014 at 10:22 AM.
October 13th, 2014, 10:21 AM #5 Global Moderator Joined: Dec 2006 Posts: 21,110 Thanks: 2326 Each tangent line through the origin has equation y = kx. If y = kx = 1 + (x - 1)² = x² - 2x + 2, x² - (k + 2)x + 2 = 0. For the required tangents, that quadratic's discriminant must be 0, so k = -2 + 2√2 or -2 - 2√2. Thanks from topsquark
Tags diff, problem
Thread Tools Display Modes Linear Mode
Similar Threads Thread Thread Starter Forum Replies Last Post Niko Bellic Calculus 2 July 8th, 2013 11:01 AM zacmz Calculus 1 February 23rd, 2012 06:08 AM David_Lete Calculus 0 November 1st, 2009 10:11 AM thummel1 Calculus 2 September 1st, 2009 06:58 PM kien Geometry 1 April 12th, 2009 10:19 AM
Contact - Home - Forums - Cryptocurrency Forum - Top
|
2019-11-14 23:49:16
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6124540567398071, "perplexity": 3515.4198661789146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668544.32/warc/CC-MAIN-20191114232502-20191115020502-00084.warc.gz"}
|
https://socratic.org/questions/which-of-the-following-is-a-redox-reaction
|
# Which of the following is a redox reaction?
## $C {r}_{2} {O}_{7}^{2 -} + 2 O {H}^{-} \to 2 C r {O}_{4}^{2 -} + {H}_{2} O$ ${\left[C u {\left({H}_{2} O\right)}_{6}\right]}^{2 +} + 4 C {l}^{-} \to {\left[C u C {l}_{4}\right]}^{2 -} + 6 {H}_{2} O$ $4 O {H}^{-} + 4 M n {O}_{4}^{-} \to 4 M n {O}_{4}^{2 -} + 2 {H}_{2} O + {O}_{2}$ ${\left[F e {\left({H}_{2} O\right)}_{6}\right]}^{3 +} + 3 O {H}^{-} \to \left[F e {\left({H}_{2} O\right)}_{3} {\left(O H\right)}_{3}\right] + 3 {H}_{2} O$ Is there a way to work this out without going through every single oxidation state? The question is only worth one mark, although I'd like to understand the concept behind this. Thank you
Dec 9, 2017
You need to learn something early on in chemistry, maybe in life.
It's not about how little work you can do. If you work hard now, this will be easier in an exam setting. I worked hard at this and this is trivial to me, now—I can do this in my head. Moving on!
In reduction-oxidation reactions, one species is reduced and another is oxidized. Usually this is straightforward, having calculated the oxidation states, one must see which atom's increases, decreases, or neither.
In (A) the chromium cation is being reduced, however nothing is being oxidized.
In (B) no measurable oxidation or reduction are occurring.
In (C) the manganese ion is being reduced and the oxide ion is being oxidized to oxygen gas.
In (D) not much is measurably happening.
Hence, $\text{C}$ is the answer.
|
2020-05-27 09:26:04
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8330590724945068, "perplexity": 1017.8663908044848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347392142.20/warc/CC-MAIN-20200527075559-20200527105559-00280.warc.gz"}
|
https://socratic.org/questions/what-is-20-percent-of-80
|
# What is 20 percent of 80?
Nov 29, 2016
$16$
#### Explanation:
20%" " of " "80=?
$\text{ }$
$\frac{20}{100} \times 80$
$\text{ }$
$= \frac{1600}{100} = 16$
Aug 4, 2017
$16$
#### Explanation:
20% is the same as $\frac{20}{100}$ which is the fraction $\frac{1}{5}$
To find one fifth of a number is the same as dividing by $5$
$\frac{\cancel{20}}{\cancel{100}} ^ 5 \times 80$
$= \frac{1}{5} \times 80$
$= 16$
|
2018-12-15 01:49:31
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 15, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9719430208206177, "perplexity": 1501.33241006155}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826686.8/warc/CC-MAIN-20181215014028-20181215040028-00036.warc.gz"}
|
https://www.ideals.illinois.edu/handle/2142/50877
|
## Files in this item
FilesDescriptionFormat
application/vnd.openxmlformats-officedocument.presentationml.presentation
TF11_Presentation.pptx (7MB)
PresentationMicrosoft PowerPoint 2007
application/pdf
TF11_Abstract.pdf (17kB)
AbstractPDF
text/plain
TF11_Abstract.txt (2kB)
AbstractText file
## Description
Title: Molecular Spectral Lines In Filamentary Infrared Dark Clouds Author(s): Lu, Xing Contributor(s): Liu, Hauyu Baobab; Zhang, Qizhou Subject(s): Mini-symposium: Astronomical Molecular Spectroscopy in the Age of ALMA Abstract: Many infrared dark clouds (IRDCs) in our Galaxy have filamentary structures, and some of them present converging filaments to a central hub, known as hub-filament systems (HFSs). These filaments could play a crucial role in feeding gas to the star forming regions at the hub. We analyzed NH$_3$ (J,K)=(1,1) and (2,2) spectral lines data obtained with the Very Large Array (VLA) towards five filamentary IRDCs, and derived the gas temperature based on the line ratios. Furthermore, with the Submillimeter Array (SMA) in the compact and sub-compact configurations, we obtained dust emission and spectra lines at 1.3 mm towards these sources. We found filamentary structures in both dust continuum and spectral line emission, with a characteristic width of 0.1 pc and length of 1 pc. The dust emission is consistent with the infrared extinction features, indicating the existence of dense and cold gas, while massive dust cores are usually associated with the hubs. Complex organic molecules including CH$_3$OH are found towards the dust cores. In particular, optically-thin intermediate density gas tracers, such as C$^{18}$O, reveal a possible trend of gas infall along filaments towards hubs. This is consistent with the scenario that dense gas is accreted onto dense cores through filaments and form high-mass star clusters. Issue Date: 2014-06-17 Publisher: International Symposium on Molecular Spectroscopy Citation Info: Lu, X.; Liu, H.B.; Zhang, Q. MOLECULAR SPECTRAL LINES IN FILAMENTARY INFRARED DARK CLOUDS. Proceedings of the International Symposium on Molecular Spectroscopy, Urbana, IL, June 16-21, 2014. DOI: 10.15278/isms.2014.TF11 Genre: CONFERENCE PAPER/PRESENTATION Type: Text Language: English URI: http://hdl.handle.net/2142/50877 DOI: https://doi.org/10.15278/isms.2014.TF11 Rights Information: Copyright 2014 by the authors. Licensed under a Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/ Date Available in IDEALS: 2014-09-172015-04-14
|
2019-01-18 00:19:35
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4535036087036133, "perplexity": 10126.538545880085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583659417.14/warc/CC-MAIN-20190117224929-20190118010929-00095.warc.gz"}
|
https://crunchingnumbers.live/2017/09/08/iterative-methods-part-3/
|
# Iterative Methods: Part 3
Let’s look at one more way to solve the equation $A\vec{x} = \vec{b}$. We assume that $A \in \mathbb{R}^{n \times n}$ is nonsingular, and define the $k$-th Krylov subspace as follows:
$\mathscr{K}_{k} \,:=\, \mbox{span}\{\vec{b},\,A\vec{b},\,\cdots,\,A^{k - 1}\vec{b}\}$.
Krylov subspace methods are efficient and popular iterative methods for solving large, sparse linear systems. When $A$ is symmetric, positive definite (SPD), i.e.
$\left\{\begin{array}{l} A^{T} = A \\[12pt] \vec{x}^{T}A\vec{x} > 0,\,\,\,\forall\,\vec{x} \neq \vec{0}, \end{array}\right.$
we can use a Krylov subspace method called Conjugate Gradient (CG).
Today, let’s find out how CG works and use it to solve 2D Poisson’s equation.
## a. Creating iterates
Let $(\cdot,\,\cdot)$ be an inner product for $\mathbb{R}^{n}$, and $||\cdot|| := \sqrt{(\cdot,\,\cdot)}$ the norm associated with the inner product.
How Krylov subspace methods work is simple. We will approximate the exact solution $\vec{x} = A^{-1}\vec{b}$ with a sequence of iterates $\vec{x}_{k}$ that meet two conditions:
$\begin{array}{l} \mbox{1.}\,\,\,\vec{x}_{k} \in \mathscr{K}_{k} \\[12pt] \mbox{2.}\,\,\,||\vec{x}_{k} - \vec{x}|| = \min\limits_{\vec{y}\,\in\,\mathscr{K}_{k}}\,||\vec{y} - \vec{x}||.\end{array}$
In other words, when measured in the norm $||\cdot||$, $\vec{x}_{k}$ is the best approximation to $\vec{x}$ from the $k$-th Krylov subspace.
(For initialization, we will take $\vec{x}_{0} = \vec{0}$ and $\mathscr{K}_{0} = \{\vec{0}\}$.)
The optimality condition above is the same as the orthogonality condition $\vec{x}_{k} - \vec{x} \perp \mathscr{K}_{k}$ under the inner product $(\cdot,\,\cdot)$. Therefore, $\vec{x}_{k}$ satisfies the equation,
$(\vec{x}_{k} - \vec{x},\,\vec{y}) = 0,\,\,\,\forall\,\vec{y} \in \mathscr{K}_{k}$.
### Lemma 1.
The orthogonality condition and the fact that $\mathscr{K}_{k - 1} \subset \mathscr{K}_{k}$ imply two things. At every iteration $k \geq 1$,
$\begin{array}{l} \mbox{1.}\,\,\,\vec{x}_{k} - \vec{x}_{k - 1} \in \mathscr{K}_{k} \\[12pt] \mbox{2.}\,\,\,\vec{x}_{k} - \vec{x}_{k - 1} \perp \mathscr{K}_{k - 1}.\end{array}$
### Proof.
First, note that the vector
$\vec{x}_{k} - \vec{x}_{k - 1} \,\equiv\, (\vec{x}_{k} - \vec{x}) - (\vec{x}_{k - 1} - \vec{x})$
represents the decrease in error over 1 iteration.
Since $\vec{x}_{k} \in \mathscr{K}_{k}$ and $\vec{x}_{k - 1} \in \mathscr{K}_{k - 1} \subset \mathscr{K}_{k}$, we know that $\vec{x}_{k} - \vec{x}_{k - 1} \in \mathscr{K}_{k}$.
Furthermore, for any $\vec{y} \in \mathscr{K}_{k - 1}\,(\subset \mathscr{K}_{k})$,
$(\vec{x}_{k} - \vec{x}_{k - 1},\,\vec{y}) \,=\, \underbrace{(\vec{x}_{k} - \vec{x},\,\vec{y})}_{=\,0} \,-\, \underbrace{(\vec{x}_{k - 1} - \vec{x},\,\vec{y})}_{=\,0} \,=\, 0.$
## b. Creating residuals
Next, we select a vector $\vec{p}_{k} \neq \vec{0}$ that meets these conditions:
$\begin{array}{l} \mbox{1.}\,\,\,\vec{p}_{k} \in \mathscr{K}_{k} \\[12pt] \mbox{2.}\,\,\,\vec{p}_{k} \perp \mathscr{K}_{k - 1}.\end{array}$
(For initialization, we will take $\vec{p}_{1} = \vec{b}$.)
The vector $\vec{x}_{k} - \vec{x}_{k - 1}$ also satisfied these conditions, so the two are linearly dependent. There is some constant $\alpha_{k} \in \mathbb{R}\,\backslash\,\{0\}$ such that $\vec{x}_{k} - \vec{x}_{k - 1} = \alpha_{k}\vec{p}_{k}$.
We now have a way to compute the best approximation $\vec{x}_{k}$ from the previous one:
$\boxed{\vec{x}_{k} = \vec{x}_{k - 1} + \alpha_{k}\vec{p}_{k},\,\,\,\forall\,k \geq 1}$.
This holds, provided we have a search direction $\vec{p}_{k}$.
### Lemma 2.
The coefficient $\alpha_{k}$ is given by,
$\boxed{\displaystyle\alpha_{k} = -\frac{(\vec{x}_{k - 1} - \vec{x},\,\vec{p}_{k})}{(\vec{p}_{k},\,\vec{p}_{k})} = \frac{(A^{-1}\vec{r}_{k - 1},\,\vec{p}_{k})}{(\vec{p}_{k},\,\vec{p}_{k})},\,\,\,\forall\,k \geq 1}$,
where $\vec{r}_{k} := \vec{b} - A\vec{x}_{k}$ is the residual.
### Proof.
We have the equation,
$\vec{x}_{k} - \vec{x} = (\vec{x}_{k - 1} - \vec{x}) + \alpha_{k}\vec{p}_{k}$.
On each side, take the inner product with $\vec{p}_{k}$:
$(\vec{x}_{k} - \vec{x},\,\vec{p}_{k}) = (\vec{x}_{k - 1} - \vec{x},\,\vec{p}_{k}) + \alpha_{k}(\vec{p}_{k},\,\vec{p}_{k})$.
Since $\vec{x}_{k} - \vec{x} \perp \mathscr{K}_{k}$ and $\vec{p}_{k} \in \mathscr{K}_{k}$, the LHS is equal to 0. Hence,
$\displaystyle\alpha_{k} = -\frac{(\vec{x}_{k - 1} - \vec{x},\,\vec{p}_{k})}{(\vec{p}_{k},\,\vec{p}_{k})}$.
Note, $\vec{r}_{k - 1} = A(\vec{x} - \vec{x}_{k - 1})$.
### Lemma 3.
The residuals are related in the following manner:
$\boxed{\vec{r}_{k} = \vec{r}_{k - 1} - \alpha_{k}A\vec{p}_{k},\,\,\,\forall\,k \geq 1}$.
### Proof.
Apply $A$ to both sides of the equation:
$(\vec{x} - \vec{x}_{k}) = (\vec{x} - \vec{x}_{k - 1}) - \alpha_{k}\vec{p}_{k}$.
## c. Creating search directions
We will now construct the search direction $\vec{p}_{k + 1}$ so that we can continue the iteration. Along the way, we required the search directions to satisfy,
$\vec{p}_{i} \in \mathscr{K}_{i} \,\backslash\, \{\vec{0}\} \,\,\,\mbox{and}\,\,\,\vec{p}_{i} \perp \mathscr{K}_{i - 1},\,\,\,\forall\,i = 1,\,\cdots,\,k$.
Thus, if $\vec{p}_{k + 1}$ also meets these conditions, namely,
$\vec{p}_{k + 1} \in \mathscr{K}_{k + 1} \,\backslash\, \{\vec{0}\} \,\,\,\mbox{and}\,\,\,\vec{p}_{k + 1} \perp \mathscr{K}_{k}$,
then $\{\vec{p}_{1},\,\cdots,\,\vec{p}_{k + 1}\}$ will end up forming an orthogonal basis for $\mathscr{K}_{k + 1}$.
We can create such a sequence using Gram-Schmidt method! Specifically, $\vec{p}_{k + 1}$ will be the sum of a vector in $\mathscr{K}_{k}$ (which can be written as a linear combination of $\vec{p}_{1},\,\cdots,\,\vec{p}_{k}$) and an offshoot $\vec{w}_{k} \in \mathscr{K}_{k + 1} \,\backslash\, \mathscr{K}_{k}$:
$\boxed{\displaystyle\vec{p}_{k + 1} = \vec{w}_{k} + \sum_{i\,=\,1}^{k}\,\gamma_{i}\vec{p}_{i},\,\,\,\forall\,k \geq 1}$.
Then, we orthogonalize $\vec{p}_{k + 1}$ against $\vec{p}_{1},\,\cdots,\,\vec{p}_{k}$.
### Lemma 4.
In the $k$-th iteration, the coefficients $\gamma_{i}$ are given by,
$\boxed{\displaystyle\gamma_{i} = -\frac{(\vec{w}_{k},\,\vec{p}_{i})}{(\vec{p}_{i},\,\vec{p}_{i})},\,\,\,\forall\,i = 1,\,\cdots,\,k}$.
### Proof.
Given the equation,
$\displaystyle\vec{p}_{k + 1} = \vec{w}_{k} + \sum_{j\,=\,1}^{k}\,\gamma_{j}\vec{p}_{j}$,
we can take the inner product with $\vec{p}_{i}$:
$\displaystyle(\vec{p}_{k + 1},\,\vec{p}_{i}) = (\vec{w}_{k},\,\vec{p}_{i}) + \sum_{j\,=\,1}^{k}\,\gamma_{j}(\vec{p}_{j},\,\vec{p}_{i})$.
Since $\vec{p}_{k + 1} \perp \mathscr{K}_{i}$ and $\vec{p}_{i} \in \mathscr{K}_{i}$, the LHS is equal to 0. Furthermore, $\{\vec{p}_{1},\,\cdots,\,\vec{p}_{k}\}$ forms an orthogonal basis, so the summation on the RHS reduces to a single term:
$\displaystyle\sum_{j\,=\,1}^{k}\,\gamma_{j}(\vec{p}_{j},\,\vec{p}_{i}) = \gamma_{i}(\vec{p}_{i},\,\vec{p}_{i})$.
We can now solve for $\gamma_{i}$:
$\displaystyle\gamma_{i} = -\frac{(\vec{w}_{k},\,\vec{p}_{i})}{(\vec{p}_{i},\,\vec{p}_{i})}$.
Isn’t it cool to work backwards and see the motivations? We just need to figure out how to choose $\vec{w}_{k} \in \mathscr{K}_{k + 1} \,\backslash\, \mathscr{K}_{k}$.
## d. SPD
So far, we have not used the fact that $A$ is SPD. We do so now to obtain CG.
### Lemma 5.
If $A \in \mathbb{R}^{n \times n}$ is SPD, then
$(\vec{x},\,\vec{y})_{A} := \vec{x}^{T}A\vec{y}$
defines an inner product for $\mathbb{R}^{n}$. Then, $||\vec{x}||_{A} := \sqrt{(\vec{x},\,\vec{x})_{A}}$ gives us a norm, called the $A$-norm.
### Proof.
Let’s show that, for all vectors $\vec{x},\,\vec{y},\,\vec{z} \in \mathbb{R}^{n}$ and scalars $\alpha,\,\beta \in \mathbb{R}$, the $A$-inner product is symmetric, bilinear, and positive-definite:
#### Symmetric:
\begin{aligned} (\vec{x},\,\vec{y})_{A} &= \vec{x}^{T}A\vec{y} \\[12pt] &= \vec{x}^{T}A^{T}\vec{y} \\[12pt] &= (A\vec{x})^{T}\vec{y} \\[12pt] &= \vec{y}^{T}(A\vec{x}) \\[12pt] &= (\vec{y},\,\vec{x})_{A}. \end{aligned}
Notice how we used symmetry of the Euclidean inner product.
#### Bilinear:
\begin{aligned} (\alpha\vec{x} + \beta\vec{y},\,\vec{z})_{A} &= (\alpha\vec{x} + \beta\vec{y})^{T}A\vec{z} \\[12pt] &= \alpha(\vec{x}^{T}A\vec{z}) + \beta(\vec{y}^{T}A\vec{z}) \\[12pt] &= \alpha(\vec{x},\,\vec{z})_{A} + \beta(\vec{y},\,\vec{z})_{A}. \end{aligned}
Since the $A$-inner product is symmetric, we also have linearity in the second argument.
#### Positive-definite:
Because $A$ is positive definite,
$(\vec{x},\,\vec{x})_{A} = \vec{x}^{T}A\vec{x} > 0,\,\,\,\forall\,\vec{x} \neq \vec{0}$.
The $A$-inner product is equal to zero only when $\vec{x} = \vec{0}$.
The key thing to realize is that Sections 4a – 4c are valid for any nonsingular matrix $A$. We can create a Krylov subspace method even if $A$ is not positive definite, or even symmetric. We just need to define an inner product and select $\vec{w}_{k}$ appropriately.
Let’s summarize what we learned so far using the $A$-inner product.
We want to arrive at the solution $\vec{x}$ by a sequence of best approximations $\vec{x}_{k}$. Best approximations satisfy the orthogonality condition:
$(\vec{x}_{k} - \vec{x},\,\vec{y})_{A} = 0,\,\,\,\forall\,\vec{y} \in \mathscr{K}_{k}$.
By sheer luck (or well-planning), the residual $\vec{r}_{k}$ is orthogonal to the Krylov subspace $\mathscr{K}_{k}$ in the Euclidean inner product:
$(\vec{r}_{k},\,\vec{y})_{E} = (\vec{x} - \vec{x}_{k},\,\vec{y})_{A} = 0,\,\,\,\forall\,\vec{y} \in \mathscr{K}_{k}$.
In particular, this means the residuals are orthogonal to each other. Hence the name Conjugate Gradient (“orthogonal residuals” didn’t sound good).
Given a best approximation $\vec{x}_{k - 1} \in \mathscr{K}_{k - 1}$, we can find the next one $\vec{x}_{k} \in \mathscr{K}_{k}$:
$\vec{x}_{k} = \vec{x}_{k - 1} + \alpha_{k}\vec{p}_{k}$,
where,
$\displaystyle\alpha_{k} = \frac{(A^{-1}\vec{r}_{k - 1},\,\vec{p}_{k})_{A}}{(\vec{p}_{k},\,\vec{p}_{k})_{A}} = \frac{\vec{r}_{k - 1}^{T}\vec{p}_{k}}{\vec{p}_{k}^{T}A\vec{p}_{k}}$.
We can also find the residual:
$\vec{r}_{k} = \vec{r}_{k - 1} - \alpha_{k}A\vec{p}_{k}$.
Notice that $A\vec{p}_{k}$ appeared again. It’d be nice to implement a sparse matrix-vector multiplication and store this result.
To continue the iteration, we decide on a search direction for some $\vec{w}_{k}$:
$\displaystyle\vec{p}_{k + 1} = \vec{w}_{k} + \sum_{i\,=\,1}^{k}\,\gamma_{i}\vec{p}_{i}$,
where,
$\displaystyle\gamma_{i} = -\frac{(\vec{w}_{k},\,\vec{p}_{i})_{A}}{(\vec{p}_{i},\,\vec{p}_{i})_{A}} = -\frac{\vec{w}_{k}^{T}A\vec{p}_{i}}{\vec{p}_{i}^{T}A\vec{p}_{i}}$.
## e. Creating offshoots
There are a few candidates for $\vec{w}_{k} \in \mathscr{K}_{k + 1}\,\backslash\,\mathscr{K}_{k}$. We will select the residual,
$\boxed{\vec{w}_{k} = \vec{r}_{k}}$,
so that all but one of the coefficients $\gamma_{i}$ will be 0!
### Lemma 6.
When $\vec{w}_{k} = \vec{r}_{k}$,
$(\vec{w}_{k},\,\vec{p}_{i})_{A} = 0,\,\,\,\forall\,i = 1,\,\cdots,\,(k - 1)$.
### Proof.
First, let’s check that $\vec{r}_{k} \in \mathscr{K}_{k + 1} \,\backslash\, \mathscr{K}_{k}$.
We know that the residual $\vec{r}_{k}$ resides in $\mathscr{K}_{k + 1}$, because $\vec{b} \in \mathscr{K}_{k + 1}$ (by definition of the Krylov subspace) and $\vec{x}_{k} \in \mathscr{K}_{k}$ implies $A\vec{x}_{k} \in \mathscr{K}_{k + 1}$.
Moreover, $\vec{r}_{k}$ is orthogonal to $\mathscr{K}_{k}$ in the Euclidean inner product, so $\vec{r}_{k} \not\in \mathscr{K}_{k}$. By the same token,
$(\vec{r}_{k},\,\vec{p}_{i})_{A} = (\vec{r}_{k},\,A\vec{p}_{i})_{E} = 0,\,\,\,\forall\,i = 1,\,\cdots,\,(k - 1).$
### Lemma 7.
When $\vec{w}_{k} = \vec{r}_{k}$, we can simplify the formulas for $\alpha_{k}$, $\gamma_{k}$, and $\vec{p}_{k + 1}$:
$\begin{array}{c} \displaystyle\alpha_{k} = \frac{\vec{r}_{k - 1}^{T}\vec{r}_{k - 1}}{\vec{p}_{k}A\vec{p}_{k}} \\[20pt] \displaystyle\gamma_{k} = \frac{\vec{r}_{k}^{T}\vec{r}_{k}}{\vec{r}_{k - 1}^{T}\vec{r}_{k - 1}} \\[28pt] \vec{p}_{k + 1} = \vec{r}_{k} + \gamma_{k}\vec{p}_{k}. \end{array}$
### Proof.
The formula for $\vec{p}_{k + 1}$ comes from Lemma 6.
From Section 4d, we know that,
$\displaystyle\alpha_{k} = \frac{\vec{r}_{k - 1}^{T}\vec{p}_{k}}{\vec{p}_{k}^{T}A\vec{p}_{k}}, \,\,\,\,\,\,\gamma_{k} = -\frac{\vec{r}_{k}^{T}A\vec{p}_{k}}{\vec{p}_{k}^{T}A\vec{p}_{k}}, \,\,\,\,\,\,-A\vec{p}_{k} = \frac{\vec{r}_{k} - \vec{r}_{k - 1}}{\alpha_{k}}$.
By orthogonality, the numerator of $\alpha_{k}$ simplifies to:
$\vec{r}_{k - 1}^{T}\vec{p}_{k} \,=\, \vec{r}_{k - 1}^{T}\vec{r}_{k - 1} + \gamma_{k - 1}\underbrace{\vec{r}_{k - 1}^{T}\vec{p}_{k - 1}}_{=\,0} \,=\, \vec{r}_{k - 1}^{T}\vec{r}_{k - 1}.$
As for $\gamma_{k}$, note that,
$\displaystyle-\vec{r}_{k}^{T}A\vec{p}_{k} = \frac{\vec{r}_{k}^{T}\vec{r}_{k} - \vec{r}_{k}^{T}\vec{r}_{k - 1}}{\alpha_{k}} = \frac{\vec{r}_{k}^{T}\vec{r}_{k}}{\alpha_{k}}, \,\,\,\,\,\,\vec{p}_{k}^{T}A\vec{p}_{k} = \frac{\vec{r}_{k - 1}^{T}\vec{r}_{k - 1}}{\alpha_{k}}$.
## f. Summary
The pseudocode for CG looks like this:
% Initialize
x0 = zeros(n, 1), r0 = b, p1 = b;
for k = 1 : numIterations
% Sparse matrix-vector multiply
Ap1 = A * p1;
% Find alpha
alpha1 = (r0' * r0) / (p1' * Ap1);
% Find the iterate
x1 = x0 + alpha1 * p1;
% Find the residual
r1 = r0 - alpha1 * Ap1;
% Find gamma
gamma1 = (r1' * r1) / (r0' * r0);
% Find the search direction
p2 = r1 + gamma1 * p1;
% Update the iterates
x0 = x1;
r0 = r1;
p1 = p2;
end
Notice how we only need a sparse matrix-vector multiply, a vector-scalar multiply (axpy), and a dot product to solve a matrix equation. This is the power of iterative methods. We can make our code more efficient by reusing variables:
% Initialize
x = zeros(n, 1), r = b, p = b;
r_dot = r' * r;
for k = 1 : numIterations
% Sparse matrix-vector multiply
Ap = A * p;
% Find alpha and initialize gamma
alpha = r_dot / (p' * Ap);
gamma = r_dot;
% Find the iterate
x = x + alpha * p;
% Find the residual
r = r - alpha * Ap;
r_dot = r' * r;
% Find gamma
gamma = r_dot / gamma;
% Find the search direction
p = r + gamma * p;
end
# 5. Example
Let’s go back to 2D Poisson’s equation on a unit square domain, with homogeneous Dirichlet BC. Our RHS function is given by,
$f(x,\,y) = (a^{2} + b^{2})\pi^{2}\sin(a\pi x)\sin(b\pi y)$,
and we choose $a = 1$, $b = 9$, and $N = 200$ as before.
Stunningly, CG converges in 1 iteration! As far as iterative methods go, you can’t do better than that.
The question is how? The RHS function that I chose makes the Poisson’s equation an eigenfunction problem. Even at the discrete level, the RHS vector $\vec{f}$ happens to be an eigenvector of $K$:
$K\vec{f} = \lambda\vec{f}$.
As a result, in the first iteration,
$\begin{array}{l} \displaystyle\alpha_{1} \,=\, \frac{\vec{f}^{T}\vec{f}}{\vec{f}^{T}K\vec{f}} \,=\, \frac{1}{\lambda} \\[20pt] \displaystyle\vec{r}_{1} \,=\, \vec{f} - \alpha_{1}K\vec{f} \,=\, \vec{f} - \frac{1}{\lambda} \cdot \lambda\vec{f} \,=\, \vec{0}. \end{array}$
# Notes
A big thanks goes to Dr. Ye, one of my teachers at Kentucky. He instilled my passion for numerical linear algebra and applications thereof. To learn additional iterative methods, I recommend reading his paper linked below.
You can find the code in its entirety here:
|
2018-09-22 22:25:15
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 148, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9799115657806396, "perplexity": 846.7775017219242}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158766.53/warc/CC-MAIN-20180922221246-20180923001646-00089.warc.gz"}
|
https://stats.stackexchange.com/questions/329382/why-ignore-the-denominator-of-bayes-rule
|
# Why ignore the denominator of bayes rule? [duplicate]
I am a new beginner in stats. I have specifically diverted my attention towards this because, I wish to understand the concept of Deep Bayesian Learning, so I am starting with the basics. The question is:
The Bayes rule equation is given by
$P(X | Y)$ = $\cfrac{P(Y | X). P(X)}{P(Y)}$
But, I have noticed in some places, the denominator being ignored entirely and using just the numerator of the RHS of the equation. making it:
$P(X | Y)$ = $P(Y|X).P(X)$
Is there some special case where we can ignore the P(Y)? as in when P(Y) = 1? But, if that's the case, wouldn't all the things become very easy: P(Y | X) will become 1, and P(X | Y) will be just P(X) and done.
• A reference to "some places" might be helpful – Juho Kokkala Feb 19 '18 at 6:12
• Instead of $P(X|Y)=P(Y|X)P(X)$ did you intended to write $P(X|Y) \propto P(Y|X)P(X)$? The latter form is correct while the former is not, since it is not always a proper probability. – Sycorax says Reinstate Monica Feb 19 '18 at 6:15
• @JuhoKokkala , I was refering to this video -> youtube.com/watch?v=o2Tpws5C2Eg – Animesh Karnewar Feb 19 '18 at 6:20
• It's horrible video, I'm sorry, ridden with errors – Aksakal Feb 19 '18 at 7:01
• @AnimeshKarnewar Just want to second Aksakal. That video is garbage, and what he writes is just wrong. – Matthew Drury Feb 19 '18 at 7:10
Indeed, ignoring P(Y) is very common. This is not done since P(X) equals one. This is done when we are interested which value of X is more probable, like in classification.
For positive, $$P(X=Positive | Y)$$ = $$\cfrac{P(Y | X=Positive)* P(X=Positive)}{P(Y)}$$
For negative, $$P(X=Negative | Y)$$ = $$\cfrac{P(Y | X=Negative)* P(X=Positive)}{P(Y)}$$
If we want to know if $$P(X=Positive | Y) > P(X=Negative | Y)$$, we can omit $${P(Y)}$$ from both expressions. $${P(Y)}$$ is a probability and therefore it is a positive constant and can be removed.
Think of a medical example. A person Y goes into a physician office that would like to know if Y suffers from X. $${P(Y)}$$ is the probability the Y will step into the office. Y might be very common or rare but it doesn't matter, he is already in the office.
Add to that, that measuring $${P(Y)}$$ is no longer a medical question. The physician knowledge cannot help with that. Therefore we prefer avoiding coping with an unnecessary hard problem.
Note that if you would like to be precise, after omitting P(Y) you should write $$P(X=Positive | Y) \approx P(Y | X=Positive)* P(X=Positive)$$ and use approximation instead of equality.
• well, in your last equation, $P(Y)$ is not really omitted. Moreover, in your example, $P(Y)$ would be the probability of the characteristics/variables that predicts $X$, not the probability of going into the office. For example, if $X=\text{suffers from cancer}$, $P(Y)$ would be the probability that the blood test is positive (unless the probability of having cancer depends on you going into the doctor's office, which of course is absurd). Notice that you used $X$ for the dependent variable (has cancer?) and Y for the independent one – rtrtrt Apr 27 '19 at 9:33
• Thanks. I should have omit the P(Y) there. In that part I meant to say that if you omit you should say it is an approximation and not equality. I hope it is clearer now. As for the rest, it is just Bayes rule.See it as knowledge given event and not as causality. – DaL Apr 28 '19 at 5:49
|
2020-04-08 12:55:41
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7909161448478699, "perplexity": 591.7649007916675}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371813538.73/warc/CC-MAIN-20200408104113-20200408134613-00344.warc.gz"}
|
http://math.wikia.com/wiki/Function
|
# Function
1,016pages on
this wiki
A function (or more strictly, a well-defined function) is a rule that assigns to every element in a set $D$ exactly one element, called the image, from another set $C$ . The set $D$ is called the domain, while the set $C$ is called the codomain. The subset of the codomain which precisely contains the set of all values that are assigned to some value in the domain is called the range
## Definition
When defining a function $f$ with domain $D$ and codomain $C$ , it is common to denote it by $f:D\to C$ .
For example, the function $f:\R\to\R$ could be defined by the formula
$f(x)=x^2$
with domain D being the real numbers and the range R being the non-negative real numbers. This function assigns the value 4 in the range to the number −2 in the domain.
$f(-2)=4$
Formally, a relation $\mapsto$ from a set $D$ to set $C$ is said to be a function if it satisfies the following properties:
• Totality: for each $d\in D$ , there exists a $r\in C$ such that $d\mapsto r$ .
• Functionality: for each $d\in D$ and any $r,s\in C$ , if $d\mapsto r$ and $d\mapsto s$ , then $r=s$ .
The first condition asserts that every element in the domain has an image in the codomain, while the second states that such an image is unique. This definition, however, allows the following possibilities for a function:
• Two or more distinct elements in the domain may have the same image;
• One or more element in the codomain may not be the image of any element in the domain.
One may also speak of multi-valued functions, which only satisfy the totality property, and of partially-defined functions, which only satisfy the functional property.
With those possibilities in mind, we may define a function $f:D\rightarrow C$ to be one of these three types of functions:
• Injection, injective function, or one-to-one: for any $a,b\in D$ , if $f(a)=f(b)$ then $a=b$ ;
• Surjection, surjective function, or onto: for any $c\in C$ , there exists an $a\in D$ such that $f(a)=c$ ;
• one-to-one correspondence, bijection, bijective function, or invertible, if $f$ is both injective and surjective.
## Notation
As a function $f$ from a set $D$ to a set $C$ is formally a relation, which itself is a subset of the cartesian product $D\times C$ , the notations $x\,f\,y$ (viewing $f$ as a relation), and $(x,y)\in f$ are valid. However, whenever given an arbitrary $x\in D$ , it is cumbersome in writing to state that "there exists a unique $y\in C$ such that $x\,f\,y$". Therefore, we will define the preferred notation $f(x)$ to refer to the aforementioned unique $y\in C$ . Therefore, the following notations are equivalent:
• $(x,y)\in f$ , when viewing $f$ as a subset of the Cartesian product $D\times C$ ;
• $x\,f\,y$, when viewing $f$ as a relation from $D$ to $C$ ;
• $f(x)=y$
## Examples
In practice, a function is completely determined through a formula that assigns the variables. For example:
$y=f(x)=x^2+1$
$y$ is the depending variable and $x$ is the independent one.
|
2017-05-27 06:03:32
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 53, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9572272896766663, "perplexity": 168.9155291164767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608870.18/warc/CC-MAIN-20170527055922-20170527075922-00503.warc.gz"}
|
http://openstudy.com/updates/55a7c47ae4b045595078dd47
|
A community for students. Sign up today
Here's the question you clicked on:
anonymous one year ago I'm on problem set 6, question 3B-5. Why is the integrand in the solution sin(bx) as opposed to sin(x)?
• This Question is Closed
1. phi
Are you asking about this question (see attached file)
2. phi
The Riemann sum is computed by dividing the area under the curve into thin rectangles and adding up the area of these rectangles. say we have "n" rectangles |dw:1437134049812:dw|
3. phi
the height of the kth rectangle is f( x), or in this case sin( b x) where x = k * width of each rectangle. if we have n rectangles over the interval from x=0 to x=1, each rectangle has width 1/n, and the kth rectangle will have area $\sin(b⋅k⋅width)⋅width \\ \sin\left(b⋅k⋅\frac{1}{n}\right)⋅\frac{1}{n}$
4. phi
notice that we are working with sin(b x) Just sin(x) would mean the kth rectangle has area $\sin\left( k \cdot \frac{1}{n}\right) \cdot \frac{1}{n}$
5. anonymous
Thanks!
Ask your own question
Sign Up
Find more explanations on OpenStudy
Privacy Policy
|
2016-10-27 23:15:55
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8005502820014954, "perplexity": 1989.1639643260705}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721405.66/warc/CC-MAIN-20161020183841-00352-ip-10-171-6-4.ec2.internal.warc.gz"}
|
https://datacrayon.com/posts/plotapi/terminus/vertical-terminus-diagram/
|
## Plotapi, beautiful by default.
Let plotapi do the heavy lifting – enabling beautiful interactive visualisations with a single line of code (instead of hundreds).
# Vertical Terminus Diagram
Contents
You can create beautiful, interactive, and engaging visualisations like this one with Plotapi in any programming language.
## Preamble¶
In [ ]:
from plotapi import Terminus
Terminus.set_license("your username", "your license key")
## Introduction¶
Let's take a look at the vertical property of the Terminus diagram. Using it can give the impression that the particles are "falling" through the pipes.
As we can see, we have set our license details in the preamble with Terminus.set_license().
## Dataset¶
Terminus expects a list of dictionary items, these will define the flow of pixels between a source and a target.
In [ ]:
links = [
{"source":"England", "target":"Germany", "value": 1000},
{"source":"England", "target":"France", "value": 3000},
{"source":"England", "target":"Spain", "value": 5000},
{"source":"England", "target":"Italy", "value": 4000},
{"source":"England", "target":"Japan", "value": 800},
{"source":"Ireland", "target":"Germany", "value": 3500},
{"source":"Ireland", "target":"France", "value": 3750},
{"source":"Ireland", "target":"Spain", "value": 1750},
{"source":"Ireland", "target":"Italy", "value": 5000},
{"source":"Ireland", "target":"Japan", "value": 400},
]
We can add many source's and target's! As they increase, we may need to adjust Terminus layout properties to accomodate the diagram's size and throughput.
## Visualisation¶
To produce a vertical Terminus diagram, we simply set vertical=True.
A vertical Terminus diagram is more suited to a portrait container, so we'll also set our width and height to improve the presentation.
Here we're using .show() which outputs to a Jupyter Notebook cell, however, we may want to output to an HTML file with .to_html() instead. More on the different output methods later!
In [3]:
Terminus(links, vertical=True, width=400, height=600).show()
Plotapi - Terminus Diagram
You can do so much more than what's presented in this example, and this is covered in other sections. If you want to see the full list of growing features, check out the Plotapi API Documentation.
|
2021-09-24 09:19:36
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1992911994457245, "perplexity": 8647.71144280473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057508.83/warc/CC-MAIN-20210924080328-20210924110328-00645.warc.gz"}
|
https://testbook.com/question-answer/the-value-of-the-integral-mathop-smallint-lim--5f0d676f44470f0d1384df3c
|
# The value of the integral $$\mathop \smallint \limits_{ - \infty }^\infty \sin {c^2}\left( {5t} \right)dt$$ is ________
This question was previously asked in
GATE EC 2014 Official Paper: Shift 2
View all GATE EC Papers >
## Answer (Detailed Solution Below) 0.19 - 0.21
Free
CT 1: Ratio and Proportion
1784
10 Questions 16 Marks 30 Mins
## Detailed Solution
Concept:
The Fourier transform of a signal x(t) is defined as:
$$X\left( \omega \right) = \mathop \smallint \limits_{ - \infty }^\infty x\left( t \right){e^{ - j\omega t}}dt$$
Let ω = 0
$$X\left( 0 \right) = \mathop \smallint \limits_{ - \infty }^\infty x\left( t \right)dt$$
Analysis:
For x(t) = sin c2 (5t), we find it’s Fourier transform X(ω) and then find X(0) using the above concept.
Sinc function is defined as:
$$\sin ct = \frac{{\sin \pi t}}{{\pi t}}$$
Also, the Fourier transform of a sinc function is a rectangular pulse as shown:
$${x_1}\left( t \right) \cdot {x_2}\left( t \right) \leftrightarrow \frac{1}{{2\pi }}\left[ {\frac{1}{1}\left( \omega \right)*\frac{1}{2}\left( \omega \right)} \right]$$
Calculation:
x(t) = sin c25t = (sin c 5t) (sin c 5t)
$$x\left( t \right) = \left( {\frac{{\sin 5\pi t}}{{5\pi t}}} \right) \cdot \left( {\frac{{\sin 5\pi t}}{{5\pi t}}} \right)$$
$$\mathop \smallint \limits_{ - \infty }^\infty \sin {c^2}\left( {5t} \right)dt = X\left( 0 \right)$$
X(0) = 0.2
|
2021-09-20 00:03:48
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.89909428358078, "perplexity": 7154.026690076852}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056902.22/warc/CC-MAIN-20210919220343-20210920010343-00352.warc.gz"}
|
https://math.stackexchange.com/questions/597718/finding-the-recurrence-relation-of-a-known-series-frac12-frac124-fra
|
# Finding the recurrence relation of a known series $\frac{1}{2}+\frac{1}{24}+\frac{1}{720}+…$
If you have a series of numbers (where the first number corresponds to the index zero):
$$\frac{1}{2}+ \frac{1}{24}+ \frac{1}{720}+...$$
Is there a systematic way to work backwards and find a recurrence relation? Or in other words, something that would be easier for a computer to understand (let's say I wanted to write a program which can take a series of numbers and then compute the relation automatically) $a_n=...$
No, since there are infinitely many infinite series that have the same first three terms. It’s really a problem in pattern recognition: you’re being asked to spot the pattern that the person who posed the question had in mind, which will typically be some fairly simple, regular pattern. Here the expectation is that you will recognize the denominators as factorials, specifically, as $2!,4!$, and $6!$. If you do, it becomes clear that the $k$-th term is $\frac1{(2k+2)!}$. If $a_k$ is the $k$-th term, then
$$a_k=\frac{a_{k-1}}{(2k+1)(2k+2)}\;.$$
$2!$ $4!$ $6!$ Hmm, do I see a pattern?
• You've nailed it. I did not see this pattern. I wonder if there is another method besides 'recognizing'? Maybe something that would be more friendly for a computer to understand. – Bob Shannon Dec 8 '13 at 4:20
• If there were a positive answer to your question, many of us would be out of a job :( – Igor Rivin Dec 8 '13 at 4:22
Don't believe what they tell you, the real answer is $$a_n=\frac{1}{337n^2-989n+654}$$ ;-)
P.S. Actually, I can tell you how to write a computer program which will solve all these questions without having to guess anything. This is called Lagrange interpolation. But I doubt that it is the expected answer.
• Wow, look at that, it holds for all $n \ge 1$...nice. Will have to read up on that. Thank you. – Bob Shannon Dec 8 '13 at 4:42
If course the only valid answer is (2*p)! in the denominators, where p runs through the non-composite positive integers, p=1,2,3,5,7,11,13,... :-)
|
2019-12-11 08:57:01
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8401170372962952, "perplexity": 218.2589234538276}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540530452.95/warc/CC-MAIN-20191211074417-20191211102417-00376.warc.gz"}
|
http://tex.stackexchange.com/questions/36756/combine-two-items-in-an-enumerated-list
|
# Combine two items in an enumerated list
Is there an easy way to combine two items in an enumerated list? For example:
1. First bullet
2-3. Second bullet
4. Third bullet
My current plan involves screwing with \labelenumi and then manually incrementing \enumi, but that seems ugly
-
Don't know if it's true, but if you are in a situation in which you don't decide the numbers, or at least they're fixed and will never change (for example typing up answers to a problem set), then I would suggest that you do a custom label for every item (using enumitem perhaps), since that way you can see which number you're on in the code. Also, if you decide to split #2 and #3 up later on, it won't mess up the subsequent numbering. – JohnJamesSmith Dec 1 '11 at 4:29
@JohnJamesSmith That's exactly the situation; I'm answering two parts of a homework problem (a and b) at once. I normally just use comments above each \item to track the number, but enumitem looks interesting – Michael Mrozek Dec 1 '11 at 4:34
Haha, just checked. You can forget enumitem. See my answer. – JohnJamesSmith Dec 1 '11 at 4:41
Here's a more automated solution that saves you the trouble of numbering by hand. The basic idea is to define a new kind of \item called \combine which combines n items into one, where n can be specified as an optional argument (default 2).
In order to deal with enumerations with different label formats (alpha, roman etc.) I've also added a command to set the label format for the combined labels. This can be done before any particular list, or once in the document if all the lists will require combined elements will be of the same sort.
One caveat: don't try to use \label with the combined items.
\documentclass{article}
\usepackage{calc}
\makeatletter
\newcounter{tmp@cnt}
\newcommand*\@labelpunc{.}
% command to combine items: optional argument to specify the number to be combined
% \combine[<num>]<item>
%
\newcommand*\combine[1][2]{%
\refstepcounter{enumi}
\setcounter{tmp@cnt}{\value{enumi}}
\item[\thetmp@cnt--\theenumi\@labelpunc]}
% command to set the label format and punctuation
% \labeltype[<punc>]{<format>} where default punctuation is none; <format> is
% \alph \Alph \roman \Roman etc. Not needed for default enumerations
%
\makeatother
\usepackage{enumitem} % for demonstration purposes (not required for the above commands)
\begin{document}
\begin{enumerate}
\item An item
\item Another item
\combine Two items combined
\item Another one
\combine[4]Four items combined
\end{enumerate}
\labeltype{\Roman}
\begin{enumerate}[label=\Roman*]
\item An item
\combine Two items combined
\item The last item
\end{enumerate}
\end{document}
-
\item[1] Let $p$ be a number. What if it doesn't want to be a number? Then \dots
|
2014-04-20 04:19:18
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8491715788841248, "perplexity": 2092.7516679733612}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00162-ip-10-147-4-33.ec2.internal.warc.gz"}
|
http://codereview.stackexchange.com/questions/16468/circular-ringbuffer
|
# Circular RingBuffer
I am trying to get into C stuff, and I thought it would be a good idea to try and implement a circular buffer.
I have defined my struct like this:
typedef struct
{
int8_t* buffer;
int8_t* buffer_end;
int8_t* data_start;
int8_t* data_end;
int64_t count;
int64_t size;
} ring_buffer;
And the functions:
void RB_init(ring_buffer* rb, int64_t size)
{
rb->buffer = malloc(sizeof(int8_t) * size);
rb->buffer_end = rb->buffer + size;
rb->size = size;
rb->data_start = rb->buffer;
rb->data_end = rb->buffer;
rb->count = 0;
}
void RB_free(ring_buffer* rb)
{
free(rb->buffer);
}
bool RB_push(ring_buffer* rb, int8_t data)
{
if (rb == NULL || rb->buffer == NULL)
return false;
*rb->data_end = data;
rb->data_end++;
if (rb->data_end == rb->buffer_end)
rb->data_end = rb->buffer;
if (RB_full(rb)) {
if ((rb->data_start + 1) == rb->buffer_end)
rb->data_start = rb->buffer;
else
rb->data_start++;
} else {
rb->count++;
}
return true;
}
int8_t RB_pop(ring_buffer* rb)
{
if (rb == NULL || rb->buffer == NULL)
return false;
int8_t data = *rb->data_start;
rb->data_start++;
if (rb->data_start == rb->buffer_end)
rb->data_start = rb->buffer;
rb->count--;
return data;
}
bool RB_full(ring_buffer* rb)
{
return rb->count == rb->size;
}
I did some testing and it seems to work well. Can you suggest some improvements ?
-
RB_pop does not check for an empty buffer and has no way of indicating that the buffer is empty. – William Morris Oct 12 '12 at 14:24
I would consider it better style to use size_t instead of int64_t for all sizes and counts of in-memory objects. – Seg Fault Oct 27 '12 at 7:11
Looks nice, is very readable and is probably fast.
Sometimes ring buffer wrap is implemented by using the following kind of remainder stuff and offsets:
end_offset = (end_offset + 1) % size;
But I like your way to do it without offsets and without division.
Some minor findings:
1. NULL pointer checks in RB_pop prevents segfaults, but caller will get return value zero. So caller won't know is zero an error or success result.
int8_t RB_pop(ring_buffer* rb)
{
if (rb == NULL || rb->buffer == NULL)
return false;
2. RB_pop and RB_push both do the check: rb == NULL. Maybe other functions should do it too.
-
• I agree with @User1 about RB_pop() and would like to add on to it:
If you want to prevent the function from returning false as an unexpected return value, you can make the function void and have a second parameter for data that will update the argument passed into it. Also, by making it void, you can return early if the first condition is false.
void RB_pop(ring_buffer* rb, int8_t& data)
{
if (rb == NULL || rb->buffer == NULL)
return;
// update data parameter...
}
• RB_free() looks a little too simple, so free() can just be called inline. Both function names also read the same, so you don't need an extra one to specify the meaning.
-
|
2014-04-24 05:58:33
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17152626812458038, "perplexity": 9807.650307000724}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00085-ip-10-147-4-33.ec2.internal.warc.gz"}
|
https://www.physicsforums.com/threads/sum-function-matlab.511939/
|
Sum function (MATLAB)
1. Jul 5, 2011
Apudapa
Hey,
I'm new to MATLAB and was stuck on a problem which requires me to calculate the expectation value of a poisson distribution by summing the probability mass function *k ie P = k*lambda^k*exp(-lambda)/factorial(k) for k= 1 to infinity. I thought of using "for k1:1000 P =... " but then had no idea how to sum the individual results. Any help much appreciated. =)
edit: I think I've sorted it out now by having a sum term initialised before and included into the loop. However, Im finding that if I increase k to above a value of 400 or so, both the answer for the poisson process and the sum become NaN. Surely, the probability should just reach 0 and the expectation value just 5. Is there any way to avoid this?
Last edited: Jul 5, 2011
2. Jul 6, 2011
MATLABdude
Welcome to PhysicsForums! Can you post the code from your m-file? (Please put it between the [ code][/ code] tags without spaces inside the square brackets).
|
2017-11-17 22:06:21
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8731215000152588, "perplexity": 885.6869469623845}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934803944.17/warc/CC-MAIN-20171117204606-20171117224606-00743.warc.gz"}
|
https://math.stackexchange.com/questions/1814733/how-can-i-use-bessels-equation-to-solve-the-lengthening-pendulum-differential-e
|
# How can I use Bessel's equation to solve the Lengthening Pendulum differential equation?
Taking a small extract of this previous bounty question of mine:
It can be shown that the differential equation: $$\fbox{y^{\prime\prime}+\left(\frac{1-2a}{x}\right)y^{\prime}+\left[\left(bcx^{c-1}\right)^2+\frac{a^2-p^2c^2}{x^2}\right]y=0}\tag{1}$$ has the solution $$\fbox{y=x^aZ_p\left(bx^c\right)}\tag{2}$$ where $Z_p$ stands for $J_p$ or $N_p$ or any linear combination of them, and $a,b,c,p$ are constants.
To see how to use this, let us “solve” the differential equation: $$y^{\prime\prime}+9xy=0\tag{3}$$ If $(3)$ is of the type $(1)$, then we must have $$1-2a=0$$ $$2(c-1)=1$$ $$(bc)^2=9$$ $$a^2-p^2c^2=0$$ from these $4$ equations we find $$a=\dfrac12$$ $$c=\dfrac32$$ $$b=2$$ $$p=\dfrac{a}{c}=\dfrac13$$
Then the solution of $(3)$ is $$y=x^{1/2}Z_{1/3}\left(2x^{3/2}\right)$$ This means that the general solution of $(3)$ is $$y=x^{1/2}\left[AJ_{1/3}\left(2x^{3/2}\right)+BN_{1/3}\left(2x^{3/2}\right)\right]$$ where $A$ and $B$ are arbitrary constants.
The differential equation of a lengthening pendulum is $$l\dfrac{d^2\theta}{dl^2}+2\dfrac{d\theta}{dl}+\dfrac{g}{v^2}\theta=0\qquad\quad\tag{4}\longleftarrow\text{proved in this former question}$$
I have to solve this differential equation for $\theta$ by comparing $(4)$ with $(1)$ in the same manner as used to find the solution to $(3)$
So here is my attempt:
First I begin by writing $(1)$ in terms of the new variables $\theta$ and $l$ $$\frac{\mathrm{d}^2\theta}{\mathrm{d}l^2}+\left(\frac{1-2a}{l}\right)\frac{\mathrm{d}\theta}{\mathrm{d}l}+\left[\left(b\,c\,l^{c-1}\right)^2+\frac{a^2-p^2c^2}{l^2}\right]\theta=0\tag{5}$$ Now I compare $(4)$ with $(5)$ to obtain $$l=1$$ $$\frac{1-2a}{l}=2\implies a=-\frac12\qquad\text{since l=1}$$ $$\left(b\,c\,l^{c-1}\right)^2+\frac{a^2-p^2c^2}{l^2}=\frac{g}{v^2}\tag{6}$$ Substituting $a=\frac12$ and $l=1$ into $(6)$ $$\implies b^2c^2+\frac14 -p^2c^2=\frac{g}{v^2}\tag{7}$$
Now if $l=1$ we must have $$c=1$$ Substituting $c=1$ into $(7)$ $$\implies b^2+\frac14 -p^2=\frac{g}{v^2}\tag{8}$$ But I am unable to proceed from here and I have made a mistake anyway as I can tell you that the correct answer is $$\theta=l^{-1/2}Z_1\left(\frac{2{g}^{1/2}}{v}l^{1/2}\right)$$ Comparison with $$\fbox{y=x^aZ_p\left(bx^c\right)}\tag{2}$$
shows that $$a=-\frac12, \quad c=\frac12, \quad b=\frac{2{g}^{1/2}}{v},\quad p=1$$
Could someone please help me find the correct values of $a,b,c,p$?
Any hints or advice is well appreciated.
• Why are you drawing the conclusion that $c = 1$ at $(7)$? Doesn't the expression $6$ allow $c$ to be anything given that the $l$ is 1? Don't we have $4 c^2 (b^2 - p^2) = \dfrac{4g}{v^2} -1 \implies 4 c^2 (b+p)(b-p) = 1\left(\dfrac{2 g^{1/2}}{v}+1\right)\left(\dfrac{2 g^{1/2}}{v}-1\right)$? This gives$4 c^2 = 1 \implies c = \dfrac{1}{2}, b \ \dfrac{2 g^{1/2}}{v}, p = 1$. – Moo Jun 5 '16 at 17:05
• Oops, that is $b = \dfrac{2 g^{1/2}}{v}$. – Moo Jun 5 '16 at 17:13
Hint: In the pendulum example the variable $l$ plays the role of $x$ and $\theta$ the role of $y$.
• Excellent answer! I have just one further question: Can it be done without dividing the differential equation by $l$? If it can be done could you please show me? I ask this because it was the way I tried to solve it. Many thanks! :) – BLAZE Jun 6 '16 at 8:57
• @BLAZE: The division by $l$ was done just to make the relationship with (1) better visible. In (1) we have the term $\left(\frac{1-2a}{x}\right)y^\prime$. Since $x$ is in the denominator it seems quite natural to also divide by $l$ and put it in the denominator since $l$ plays the role of $x$. Of course you are free to do it in any other way as long as you perform equivalence transformations – Markus Scheuer Jun 6 '16 at 9:17
• @BLAZE: (cont.) . Your setting $l=1$ is not valid, since $l$ corresponds with $x$. Proposal: Transform the pendulum differential equation by exchanging $\theta$ with $y$ and by exchanging $l$ with $x$. Then you will better see what's going on. – Markus Scheuer Jun 6 '16 at 9:18
|
2020-05-25 12:06:33
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8744375705718994, "perplexity": 124.72049538891243}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347388427.15/warc/CC-MAIN-20200525095005-20200525125005-00438.warc.gz"}
|
https://blog.jordan.matelsky.com/365papers/293/
|
# 293 — The logic of single-cell projections from visual cortex
Unsurprising: Neural projections from V1 aren’t random after all. And we can statistically verify that, if you please: If the probability of an axon projecting to area A is random and independent from the probability of the same axon projecting to area B, then $P(A) \times P(B) = P(A\cap B)$. But this does not hold, based upon the MAPseq data. So that’s neat.
|
2022-05-22 20:19:54
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8925042748451233, "perplexity": 986.0006165213921}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662546071.13/warc/CC-MAIN-20220522190453-20220522220453-00525.warc.gz"}
|
https://stats.stackexchange.com/questions/475601/multivariate-linear-regressions-with-heterogeneous-covariance-matrices
|
Multivariate Linear Regressions with heterogeneous covariance matrices
Let $$\mathbf Y$$ be $$N\times K$$ response matrix and $$\mathbf X$$ be $$N\times (p+1)$$ design matrix (including the intercept), consider the multivariate linear regression,
$$\mathbf Y = \mathbf{XB+E}\,,$$
where $$\mathbf B$$ is the $$(p+1)\times K$$ matrix of parameters and $$\mathbf E$$ is the matrix of errors.
Suppose the covariance matrices $$\mathbf\Sigma_i$$ of the error are different for each observation, $$i=1,\ldots, N$$, then solve $$\mathbf B$$ by minimizing the multivariate weighted criterion,
$$\mathrm{RSS}(\mathbf{B};\mathbf{\Sigma})=\sum_{i=1}^N(y_i-\mathbf B^Tx_i)^T\mathbf{\Sigma}_i^{-1}(y_i-\mathbf B^Tx_i)\,,$$
where $$y_i$$ is the vector of $$K$$ responses for observation $$i$$, and $$x_i$$ is the $$i$$-th observation with $$p+1$$ elements (including the intercept).
I tried to differentiate it as follows,
$$\frac{\partial \mathrm{RSS}(\mathbf{B};\mathbf{\Sigma})}{\partial \mathbf B} = -2\sum_{i=1}^Nx_i(y_i-\mathbf B^Tx_i)^T\mathbf{\Sigma}_i^{-1} = -2\left(\sum_{i=1}^Nx_iy_i^T\mathbf{\Sigma}_i^{-1}-\sum_{i=1}^Nx_ix_i^T\mathbf B^T\mathbf{\Sigma}_i^{-1}\right)\,,\tag{*}$$
but I failed to continue since it seems that we cannot decouple the coefficient matrix with the covariance matrices.
I am wondering if there is an analytical solution for such a problem. If not, how can we get the numerical solution? I am also confused about which algorithm can be employed to solve such matrix multiplication equation $$(*)$$.
This question is adapted from Exercise 3.11 of The Elements of Statistical Learning.
• If you have a gradient, you can do gradient ascent on the log likelihood – Firebug Jul 5 at 14:18
• @Firebug, If B is a vector, I think I can use gradient descent or other similar methods to solve it, but here B is a matrix. I don't have a clear idea. – ya wei Jul 5 at 14:42
• It doesn't change anything actually. Even though it's easier to represent coefficients as a matrix, on the jacobian formulation you'll have them as a long vector. It's the same, for example, when using gradient methods on neural networks. – Firebug Jul 5 at 19:29
• @Firebug, I got your point, thanks for your hint! – ya wei Jul 6 at 0:56
|
2020-09-27 15:04:20
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 20, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9167091250419617, "perplexity": 312.9311560360066}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400279782.77/warc/CC-MAIN-20200927121105-20200927151105-00776.warc.gz"}
|
https://www.dealii.org/developer/doxygen/deal.II/classCellId.html
|
Reference documentation for deal.II version Git 500a7ed831 2022-01-17 20:04:17 -0700
CellId Class Reference
#include <deal.II/grid/cell_id.h>
Public Types
using binary_type = std::array< unsigned int, 4 >
Public Member Functions
CellId (const types::coarse_cell_id coarse_cell_id, const std::vector< std::uint8_t > &child_indices)
CellId (const types::coarse_cell_id coarse_cell_id, const unsigned int n_child_indices, const std::uint8_t *child_indices)
CellId (const binary_type &binary_representation)
CellId (const std::string &string_representation)
CellId ()
std::string to_string () const
template<int dim>
binary_type to_binary () const
template<int dim, int spacedim>
Triangulation< dim, spacedim >::cell_iterator to_cell (const Triangulation< dim, spacedim > &tria) const
bool operator== (const CellId &other) const
bool operator!= (const CellId &other) const
bool operator< (const CellId &other) const
bool is_parent_of (const CellId &other) const
bool is_ancestor_of (const CellId &other) const
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
types::coarse_cell_id get_coarse_cell_id () const
ArrayView< const std::uint8_t > get_child_indices () const
Private Attributes
types::coarse_cell_id coarse_cell_id
unsigned int n_child_indices
std::array< std::uint8_t, internal::p4est::functions< 2 >::max_level > child_indices
Friends
std::istream & operator>> (std::istream &is, CellId &cid)
std::ostream & operator<< (std::ostream &os, const CellId &cid)
Detailed Description
A class to represent a unique ID for a cell in a Triangulation. It is returned by cell->id() (i.e., CellAccessor::id()) where cell is assumed to be a cell iterator.
This class stores the index of the coarse cell from which a cell is descendant (or, more specifically, the entry on coarse cell IDs), together with information on how to reach the cell from that coarse cell (i.e., which child index to take on each level of the triangulation when moving from one cell to its children). The important point about this class is that an object of the current class uniquely identifies a cell in triangulation, and it even does so in the context of objects of type parallel::distributed::Triangulation where the local portion of a mesh may not store all cells. For example, the CellId computed for a ghost cell on one processor will be exactly the same as the CellId computed for the very same cell on the processor that actually owns the cell, although the level and index of the iterators pointing to that cell within the triangulation stored on each of the processors may (and in general will) be different. In other words, CellId provides the tool with which it is possible to globally and uniquely identify cells in a parallel triangulation, and consequently makes it possible to exchange, between processors, data tied to individual cells.
Note
How this data is internally represented is not of importance (and not exposed on purpose).
Definition at line 70 of file cell_id.h.
◆ binary_type
using CellId::binary_type = std::array
A type that is used to encode the CellId data in a compact and fast way (e.g. for MPI transfer to other processes). Note that it limits the number of children that can be transferred to 20 in 3D and 30 in 2D (using 2 times 32 bit for storage), a limitation that is identical to the one used by p4est.
Definition at line 80 of file cell_id.h.
◆ CellId() [1/5]
CellId::CellId ( const types::coarse_cell_id coarse_cell_id, const std::vector< std::uint8_t > & child_indices )
Construct a CellId object with a given coarse_cell_id and vector of child indices. child_indices is interpreted identical to the member variable with the same name, namely each entry denotes which child to pick from one refinement level to the next, starting with the coarse cell, until we get to the cell represented by the current object. Therefore, each entry should be a number between 0 and the number of children of a cell in the current space dimension (i.e., GeometryInfo<dim>::max_children_per_cell).
Definition at line 38 of file cell_id.cc.
◆ CellId() [2/5]
CellId::CellId ( const types::coarse_cell_id coarse_cell_id, const unsigned int n_child_indices, const std::uint8_t * child_indices )
Construct a CellId object with a given coarse_cell_id and array of child indices provided in child_indices. child_indices is interpreted identical to the member variable with the same name, namely each entry denotes which child to pick from one refinement level to the next, starting with the coarse cell, until we get to the cell represented by the current object. Therefore, each entry should be a number between 0 and the number of children of a cell in the current space dimension (i.e., GeometryInfo<dim>::max_children_per_cell). The array child_indices must have at least n_child_indices valid entries.
Definition at line 49 of file cell_id.cc.
◆ CellId() [3/5]
CellId::CellId ( const binary_type & binary_representation )
Construct a CellId object with a given binary representation that was previously constructed by CellId::to_binary.
Definition at line 61 of file cell_id.cc.
◆ CellId() [4/5]
CellId::CellId ( const std::string & string_representation )
explicit
Create a CellId from a string with the same format that is produced by to_string().
Definition at line 100 of file cell_id.cc.
◆ CellId() [5/5]
CellId::CellId ( )
Construct an invalid CellId.
Definition at line 24 of file cell_id.cc.
◆ to_string()
std::string CellId::to_string ( ) const
Return a human-readable string representation of this CellId.
The string returned by this function consists of only ASCII characters and will look, for example, like this: "0_3:006". It can be interpreted by humans as saying "This cell originates from the zeroth coarse mesh cell, lives on refinement level 3, and the path from the coarse mesh cell to its children and grand children is given by 006". But it is not meant to be interpreted in any meaningful way: It's just a way of representing the internal state of the current object using only ASCII characters in the printable range.
Definition at line 156 of file cell_id.cc.
◆ to_binary()
template<int dim>
CellId::binary_type CellId::to_binary ( ) const
Return a compact and fast binary representation of this CellId.
Definition at line 110 of file cell_id.cc.
◆ to_cell()
template<int dim, int spacedim>
Triangulation< dim, spacedim >::cell_iterator CellId::to_cell ( const Triangulation< dim, spacedim > & tria ) const
Return a cell_iterator to the cell represented by this CellId.
Deprecated:
Definition at line 167 of file cell_id.cc.
◆ operator==()
bool CellId::operator== ( const CellId & other ) const
inline
Compare two CellId objects for equality.
Definition at line 316 of file cell_id.h.
◆ operator!=()
bool CellId::operator!= ( const CellId & other ) const
inline
Compare two CellIds for inequality.
Definition at line 333 of file cell_id.h.
◆ operator<()
bool CellId::operator< ( const CellId & other ) const
inline
Compare two CellIds with regard to an ordering. The details of this ordering are unspecified except that the operation provides a total ordering among all cells.
Definition at line 341 of file cell_id.h.
◆ is_parent_of()
bool CellId::is_parent_of ( const CellId & other ) const
inline
Determine if this cell id is the direct parent of the input cell id.
Definition at line 366 of file cell_id.h.
◆ is_ancestor_of()
bool CellId::is_ancestor_of ( const CellId & other ) const
inline
Determine if this cell id is the ancestor of the input cell id.
Definition at line 384 of file cell_id.h.
◆ serialize()
template<class Archive >
void CellId::serialize ( Archive & ar, const unsigned int version )
Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
Serialization function
Definition at line 276 of file cell_id.h.
◆ get_coarse_cell_id()
types::coarse_cell_id CellId::get_coarse_cell_id ( ) const
inline
Return the id of the coarse cell.
Definition at line 402 of file cell_id.h.
◆ get_child_indices()
ArrayView< const std::uint8_t > CellId::get_child_indices ( ) const
inline
Return a read-only container of integers that denotes which child to pick from one refinement level to the next, starting with the coarse cell, until we get to the cell represented by the current object.
The number of elements in this container corresponds to (level-1) of the current cell.
Definition at line 410 of file cell_id.h.
◆ operator>>
std::istream& operator>> ( std::istream & is, CellId & cid )
friend
Read a CellId object from a stream.
Definition at line 287 of file cell_id.h.
◆ operator<<
std::ostream& operator<< ( std::ostream & os, const CellId & cid )
friend
Write a CellId object into a stream.
Definition at line 257 of file cell_id.h.
◆ coarse_cell_id
types::coarse_cell_id CellId::coarse_cell_id
private
The number of the coarse cell within whose tree the cell represented by the current object is located.
Definition at line 221 of file cell_id.h.
◆ n_child_indices
unsigned int CellId::n_child_indices
private
The number of child indices stored in the child_indices array. This is equivalent to (level-1) of the current cell.
Definition at line 227 of file cell_id.h.
◆ child_indices
std::array::max_level> CellId::child_indices
private
An array of integers that denotes which child to pick from one refinement level to the next, starting with the coarse cell, until we get to the cell represented by the current object. Only the first n_child_indices entries are used, but we use a statically allocated array instead of a vector of size n_child_indices to speed up creation of this object. If the given dimensions ever become a limitation the array can be extended.
Definition at line 240 of file cell_id.h.
The documentation for this class was generated from the following files:
|
2022-01-18 07:34:41
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3102263808250427, "perplexity": 3909.2272806156548}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300805.79/warc/CC-MAIN-20220118062411-20220118092411-00023.warc.gz"}
|
https://www.groundai.com/project/spontaneous-repulsion-in-the-abto0-reaction-on-coupled-networks/
|
Spontaneous repulsion in the A+B\to 0 reaction on coupled networks
Spontaneous repulsion in the $A+B\to0$ reaction on coupled networks
Abstract
We study the transient dynamics of an process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions of cross-couplings, the concentration of (or ) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time . By numerical and analytical arguments, we show that for symmetric and homogeneous structures where is the mean degree of both networks. Being this behavior in marked contrast with a purely diffusive process—where the mixing time would go simply like —we identify the logarithmic slowing down in to be the result of a novel spontaneous mechanism of repulsion between the reactants and due to the interactions taking place at the networks’ interface. We show numerically how this spontaneous repulsion effect depends on the topology of the underlying networks.
Reaction-diffusion, Self-repulsion, Complex Networks, Statistical Mechanics
pacs:
89.75.Hc, 05.40.-a, 82.20.-w
1
Nearly one hundred years ago, Marian von Smoluchowski introduced a mathematical model to describe coagulation phenomena in terms of diffusion-controlled reaction processes Smo917 (). Despite its apparent simplicity, the kinetics of this model was found to yield a wealth of intriguing phenomena, whose analysis have widely enriched our understanding of pattern formation in chemical compounds, biological systems Murray (); Kaneko () and elsewhere.
From the Statistical Mechanics perspective, reaction-diffusion (RD) processes represent a fertile groundwork where to analyze the emergence of spontaneous mechanism by starting from microscopic rules kampen1992 (). Most studies in this direction aimed to unveil the effect that dynamical correlations and geometrical (or topological) constraints of the underlying structures have on the spatiotemporal evolution of the reactants’ concentrations ShlomoBen ().
The process, in particular, is known to exhibit anomalous kinetics on low dimensional and fractal geometries, where density fluctuations yield the formation of self-segregation domains composed of particles of the same type OZ (); Wilczek (); Redner (); Front (). These phenomena result in a drastic slowing down in the rate of the reactions, forcing the system in a long-lived non-equilibrium state with a sub-linear decay in the density of the surviving particles. Since this type of process grasps the essential kinetics featured by the spreading of pathogen-antipathogen agents Castellano2009 (); Vespignani (), or underlying the pattern-formation of diverse chemical reaction Galfi (); Ovchinnikov (); Taitelbaum (), the appearance of sub-diffusive dynamics may become inefficient for practical applications, which typically aim in fast mixing regimes. With this goal, it was later proved that the adoption of Lévy processes indeed washes out segregation phenomena, leading to super-diffusive dynamics Levy1996 ().
After this “classical” period, the study of RD processes has experienced a relevant boost with the inception of network theory as a new field for characterizing the structures underlying real-world complex systems Newman (); Reuvenbook (). In fact, besides the focus on networks’ topological properties, a mainstream has been (and still is) to understand the interplay between their structure and the dynamics of processes taking place on them Sbrocca ().
Consistently with the scenario observed in other models Calda (); collective (), complex networks significantly influence the collective properties of RD processes pastorsatorras2015 (). Numerical gallos1 (); gallos2 () and theoretical catanzaro () results have showed that the small-world property of these substrates mitigates the local fluctuations in the particles’ density, facilitating their reactions. Notably, on scale-free (SF) networks (i.e. random graphs with connectivity distribution and ) the kinetics of the process exhibit jamming effects at early stages and then super-diffusive behaviors weber (), with the latter becoming stronger as the network heterogeneity increases. Homogeneous structures—like random regular (RR), Erdős-Rényi (ER) or scale-rich (SR, i.e. and ) networks—result instead in a linear decay of the density, in accordance with the mean-field predictions gallosRev (); catanzaroRev ().
Though the portrait of RD processes on isolated structures is nowadays clear, not much is known regarding their dynamical behaviors on multilayer networks gomez (); garas (). The influence that their mesoscopic organization has on the collective behaviors of processes acting on them is attracting significant interest havlin (); boccaletti (); Kivela (); ginestra (); garasbook (), and has already produced interesting results interdep1 (); interdep2 (); bornholdt17 (). Increasing evidence, in fact, is showing that the existence of multiple layers, joined with the possibility of modeling different types of cross-system interactions, results in novel collective behaviors whose analysis is still in its infancy charoSA (); arenas17 (); micha17 (). Following this mainstream, we study here the dynamics on a pair of randomly coupled networks with initially separated reactants, where we find a novel spontaneous dynamical phenomenon.
Our results show that, for sufficiently small fractions of the cross-couplings between the layers, the concentration of both reactants decays as for a long transient, and then crosses over to a second linear regime where (with ) at a mixing time . We interpret the initial transient () as the unmixed regime, where the reactions between and particles take place mainly at the boundaries between the networks (i.e. at the interconnected nodes). At larger times (), the reactants penetrate more and more the two layers and start to react everywhere in the system. After this fast mixing stage (, the remaining particles are uniformly distributed in the system and their dynamics is driven essentially by diffusion. We find that the mixing time depends on the ratio , where is the average degree of the networks, according to the formula
tx∝⟨k⟩qlog(⟨k⟩q), (1)
that we derive analytically for RR graphs and verified by extensive simulations on diverse synthetic networks. Since Eq. (1) is in marked contrast with a purely diffusive process, where would simply scale as , we interpret the logarithmic factor as the reflection of a spontaneous repulsion mechanism between reactants due to the reactions taking place at the boundary between the networks. We find that this mechanism becomes stronger with increasing heterogeneity of the underlying structures, in which case Eq. (1) holds only approximately.
The paper is organized as follows. We derive analytically Eq. (1) for RR graphs, that we verify against extensive simulations on uncorrelated configuration model (UCM) networks. After investigating the effects that the underlying topology has on and on the dynamical regimes observed, we give our conclusions.
I. Analytic approach.
We consider two configuration model networks Bollobas (), composed by the same number of nodes and same structural properties, a condition that we will refer hereafter as the “symmetry” of the interconnected network. Let us further assume the two layers are coupled by means of undirected interlinks, placed at random between a fraction of couples of nodes belonging to different layers (Fig. 1). Two populations of and reactants are then randomly distributed with initially separated concentrations, so that all the particles of the same type are placed on the same layer. For simplicity we assume that the initial concentrations of reactants are equal. To track the evolution of each populations, let us denote by and the concentration of particles in network 1 and 2, respectively; similarly, let and be the concentration of particles in network 1 and 2, respectively. Having assumed equal initial conditions, we have and . Moreover, by symmetry, and for all . It is worth to notice here that, whilst this symmetric condition certainly holds in the case of coupled layers with the same or mildly different topological features (say RR and ER layers, or two ER networks with different average degrees), it will in general require some adjustments for layers with different structures.
To further simplify the analysis, let us assume that the networks underlying the RD process have homogeneous topologies, so that the average degree of nodes is the only characteristic parameter of the structure. In this case, disregarding any dynamical effect due to the topological fluctuations, we assume that the overall behavior is captured by the average densities and . We can then describe the rate of change of the concentrations and which, by symmetry, is given by
˙ρ1 =−~qρ1+~qρ2−ρ1ρ2, (2) ˙ρ2 =−~qρ2+~qρ1−ρ1ρ2, (3)
where the first two terms in both lines are due to diffusion, and the last term is due to reaction. The effective diffusion rate is the probability at each node to move to the other network.
Subtracting Eq. (2) from Eq. (3), one obtains whose solution is . Inserting this expression into, say Eq. (2), leads to
˙ρ1=ρ0(ρ1−~q)e−2~qt−ρ21. (4)
which is a Riccati differential equation. Being the densities now decoupled, we can focus hereafter only on the solutions of one of them, dropping dumb labels. Solving numerically Eq. (4) will give us the theoretical predictions for the evolution of the reactants’ concentrations.
Let us now notice that Eq. (4) is characterized by two distinct regimes: a reaction-dominated regime, where with solution which can be understood as the asymptotic behavior of the system, and a diffusion-limited regime where the exponentially decaying terms are dominant over the reaction one. By comparing these two regimes, we obtain an equation for the quasi-stationary behavior, namely
ρ2≈ρ0|ρ−~q|e−2~qt. (5)
Eq. (5) can be adopted in order to define the mixing time , that is the characteristic time it takes for the and reactants to mix and react like in a single network. To this aim, we make the assumption that the second summand on the right hand side of Eq. (5) is dominant, i.e. comment (). In this approximation, we get
logρ≈−~qtxlog(~qρ0), (6)
which, in combination with the solution of the reaction-limited regime, gives to the leading order Eq. (1).
II. Simulations and results
To simulate the process on two randomly coupled networks, we have first generated two equal synthetic networks composed of nodes where the reactants will be initially distributed. Once the networks are prepared, we randomly place the cross-couplings between them with probability by quenching the labels of interconnected nodes. To avoid any dynamical effect due to degree-degree correlations, we have constructed two random networks according to the UCM. Each network is hence assigned with a specific degree sequence having the desired connectivity distribution for the structure, with lower and structural cut-off given by , where is the minimum degree of each node UCM ().
Two population of reacting ( and ) species are then randomly distributed on the interconnected network with initially separated concentrations, meaning that all particles are placed on nodes of one layer, and all particles on nodes of the other. Following our symmetric choice for the system, we fix the initial densities of reactants to be the same, so that .
Particles diffuse in the system by performing independent random walks, where hops are allowed only to nearest neighbor nodes. Being interested in studying an process, we further assume that reactants of the same species do not interact with each other once they occupy the same site simultaneously, i.e. we adopt a bosonic version of the dynamics bosonic1 (); bosonic3 (). A reaction occurs whenever an and a particle occupy the same site, in which case both reactants generate an inert species and are then removed from the system. We monitor the time evolution of the concentrations of and particles, where the total time advances at each step as , being the number of particles currently present in the system. Results are then averaged over a set of realizations, whose nominal cardinality is hereafter assumed to be , unless otherwise stated.
In Fig. 2 we present the inverse particle density as a function of time for decreasing values of in coupled RR (Fig. 2a), ER (Fig. 2b) and SF networks (Fig. 2c). In all the cases, we find that for small enough values of the fractions of interconnected nodes, three distinct dynamical regimes exist. One for short times (), where the particles diffuse inside their own layer and reactions occur mainly at the interface, one for intermediate times (), where particles start to cross and react in the opposite layer, and a third one for long times (), where eventually the survived reactants are well mixed and the coupled systems behave like a single network. As shown in the inset of Fig. 2b, this kinetic pattern strongly depends on the choice of an initial separation of the reactants, and eventually disappears when the particles concentrations are initially mixed. To demonstrate these results, we have compared in Fig. 2b the numerical solution obtained from the theory and given by Eq. (4) with the data collected from the simulation, in which case we observe an excellent agreement.
For homogeneous structures, we have also tested the effects that the average degree has on the mixing of the system. In Fig. 2d, it is depicted again the inverse particle density as a function of time for ER networks, only this time with a fixed fraction and increasing values of the mean degree. For these substrates, we find that the same repulsion mechanism is obtained by both increasing or decreasing , as one might expect since a particle hopping to a node which is cross-coupled to the other layer will diffuse to it with probability . Finally we tested the sensitivity of this dynamical scenario with respect to different choices of the initial concentrations . As shown in Fig. 2e,f, increasing values of slightly affect the dynamical behavior of the system for both ER and SF interconnected networks, mainly influencing the transients in which the system indulges before entering the first diffusive regime. In particular, higher values of the densities make the particles in the two systems to experience earlier the repulsive effects.
At this point, it worth to notice that the phenomenology described so far partially agrees with the results presented earlier in Ref. garas () by A. Garas, where the same system was investigated from the more general perspective of different strategies of cross-systems interactions. However, by contrast with the conclusions drown in Ref. garas (), here we have shown that in the limit of low enough fractions of interconnected nodes, an initial separation of reactants generally leads to a novel spontaneous mechanism of repulsion among the reactants which, at the best of our knowledge, has been so far overlooked.
Next, we investigate the effects that different values of the effective transmission probability has on the mixing properties of the system, so to verify the accuracy of the approximations adopted to derive the relation (1) for . To evaluate this quantity, we have plot the logarithmic derivative of the -axis in Fig. 2, and searched for the maxima of the corresponding curves (see Fig. 3). The time at which a maximum is reached defines the mixing time , sharply marking the dynamical crossover between the two regimes. As shown in Fig. 4a, we find that the time for the process on ER (and equivalently, though not shown, RR) networks depends on as predicted by Eq. (1). To further support this behavior, in the inset of Fig. 4a we have validated the logarithmic dependency of due to the repulsion mechanism by comparing the pattern observed with the constant behavior that one would have found in the case of a purely diffusive process.
By performing the same analysis on heterogeneous (SF and SR) networks, we find that the mixing time surprisingly follows the behavior predicted by the mean-field theory for homogeneous structures (Fig. 4b), though with slightly less accuracy. We trace the origin of this result to the fact that, in our model, low-degree nodes are indeed the most important ones for reactions to occur between the two populations, as they most likely carry the cross-connections. In fact, as percolation results would suggest SFperc1 (), the probability of picking at random a hub is very low in SF or SR networks, making even harder the chance of having hub-to-hub interconnections. In this respect, we expect that degree-based couplings among networks will likely tune the effects of the repulsion mechanism, leading to a faster mixing of the reactants for e.g. hub-to-hub couplings.
To complete the analysis of the model for this Rapid Communication, we have tested the response to the system to finite-size effects, by adopting networks with equal topologies, but different number of nodes. In particular, for ER networks the three dynamical regimes encountered in Fig.2b remain unaltered in their main stages (Fig. 5a), and only exhibit an extinction point at earlier times for networks of decreasing sizes. Finally in Fig. 5b we have repeated the test for SR networks, where we have found that the pattern observed in Fig. 2c is again mainly unchanged, except that the convergence of the mixing time to its thermodynamic value is monotonic in , enlightening the possible occurrence of finite-size effects in the case of power-law networks of small-size whose study will be performed elsewhere.
III. Summary and conclusions
In this work we have studied, both numerically and analytically, the dynamics of an process on a pair of randomly coupled networks, where reactants are initially separated. For small enough values of the fraction of interconnected nodes between the layers, we have found that the inverse particle density scales linearly at short times and then crosses over to a second linear regime at time . As the crossover determines the time at which the two population start to extensively mix, we have analyzed the dependence of the mixing time on the effective diffusion rate , unveiling a novel repulsive mechanism whose spontaneous emergence delays the mixing of the reactants. We gave numerical evidence that, on randomly coupled synthetic networks, this effect does not show a sensitive dependence on the heterogeneity of the underlying topology, but it is in fact dominated by nodes with low connectivity. Whether or not the same behavior will appear on networks with targeted (e.g. hub-to-hub, or non-hub-to-hub) interconnections Aguirre () or on more realistic structure having e.g. a spatial embedding or degree-degree correlations, remains an intriguing question calling for further investigations. Moreover, since the diffusion-controlled annihilation process adopted in this work can be considered as an archetypal model for reaction kinetics Redner2 (), we believe that these results will inspire the investigation of the effects that the initial distribution of reactants, together with the mesoscopic architecture of the interconnected network, will have on the pattern formation in more elaborated and realistic spreading models Castellano2009 (); agliari (), enlarging in this way our understanding of the interplay between structure and dynamics.
Acknowledgments
Results presented in this work have been produced using the European Grid Infrastructure (EGI) through the National Grid Infrastructures (HellasGrid) as part of the SEE Virtual Organisation. This research was supported by European Commission FP-FET project Multiplex # . S.H. acknowledges the ISF, ONR Global, the Israel-Italian collaborative project NECST, Japan Science Foundation, BSF-NSF, and DTRA (Grant # HDTRA-1-10-1-0014), together with the Israeli Ministry of Science, Technology and Space (MOST, grant #3-12072) for financial support.
Footnotes
1. thanks: F. L. and B. G. contributed equally to this paper.
References
1. M. V. Smoluchowski, Z. Phys. Chem. 92, 129 (1917).
2. J. D. Murray, Mathematical Biology, Inter. App. Math. 17 (Springer, 2004).
3. C. Furusawa & K. Kaneko, Science 338, 215 (2012).
4. N. G. Van Kampen, Stochastic processes in chemistry and physics (Amsterdam: North Holland, 1992).
5. D. Ben-Avraham & S. Havlin, Diffusion and reactions in fractals and disordered systems (Cambridge U.P., 2000).
6. A. A. Ovchinnikov & Ya. B. Zeldovich, Chem. Phys. 28, 215 (1978).
7. D. Toussaint & F. Wilczek, J. Chem. Phys. 78, 2642 (1983).
8. F. Leyvraz & S. Redner, Phys. Rev. Lett. 66, 2168 (1991).
9. M. Araujo, H. Larralde, S. Havlin & H. E. Stanley, Phys. Rev. Lett. 71, 3592 (1993).
10. C. Castellano, S. Fortunato, V. Loreto, Rev. Mod. Phys. 81(2), 591 (2009).
11. A. Vespignani, Nature Phys. 8(1), 32 (2012).
12. L. Gálfi, Z. Rácz, Phys. Rev. A, 38(6), 3151 (1988).
13. A. A. Ovchinnikov, S. F. Timashev, A. A. Belyĭ, Kinetics of Diffusion Controlled Chemical Processes (Nova Science Pub. Inc., 1989).
14. H. Taitelbaum, S. Havlin, J. E. Kiefer, B. Trus, G. H. Weiss, Jour. Stat. Phys. 65(5-6), 873 (1991).
15. G. Zumofen, J. Klafter & M. F. Shlesinger, Phys. Rev. Lett. 77, 2830 (1996).
16. M. Newman, Networks: an introduction (Oxford U. P., 2010).
17. R. Cohen & S. Havlin, Complex networks: structure, robustness and function (Cambridge U. P., 2010).
18. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, & D.-U. Hwang, Phys. Rep. 424, 175 (2006).
19. A. Barrat, M. Barthelemy & A. Vespignani, Dynamical Processes on Complex Networks (Cambridge U. P., 2008).
20. G. Caldarelli, Scale-free networks: complex webs in nature and technology (Oxford U. P., 2007).
21. S. N. Dorogovtsev, A. V. Goltsev & J. F. F. Mendes, Rev. Mod. Phys. 80, 1275 (2008).
22. R. Pastor-Satorras, C. Castellano, P. V. Mieghem & A. Vespignani, Rev. Mod. Phys. 87, 925 (2015).
23. L. K. Gallos & P. Argyrakis, Phys. Rev. Lett. 92, 138301 (2004).
24. L. K. Gallos & P. Argyrakis, Phys. Rev. E 72, 017101 (2005).
25. M. Catanzaro, M. Boguñá, & R. Pastor-Satorras, Phys. Rev. E 71, 056104 (2004).
26. S. Weber & M. Porto, Phys. Rev. E 74, 046108 (2006).
27. L. K. Gallos & P. Argyrakis, J. Phys.: Cond. Matt. 19, 065123 (2007).
28. M. Catanzaro, M. Boguñá, & R. Pastor-Satorras, Reaction-diffusion processes in scale-free networks in Handbook of Large-Scale Random Networks, 203 (2008).
29. S. Gómez, A. Díaz-Guilera, J. Gómez-Gardeñes, C. J. Pérez-Vicente, Y. Moreno & A. Arenas, Phys. Rev. Lett. 110, 028701 (2013).
30. A. Garas, Phys. Rev. E 92, 020801(R) (2015).
31. S. Havlin et al., Eur. Phys. J., Special Topics 214, 273 (2012).
32. S. Boccaletti, G. Bianconi, R. Criado, C. Del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang, & M. Zanin, Phys. Rep. 544, 1 (2014).
33. M. Kivelä, A. Arenas, M. Barthelemy, J. P. Gleeson, Y. Moreno & M. A. Porter, J. Compl. Net. 2, 203 (2014).
34. G. Bianconi, Eur. Phys. Lett. 111, 56001 (2015).
35. A. Garas, Ed. Interconnected networks (Springer, 2016).
36. S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley & S. Havlin, Nature 464, 1025 (2010).
37. J. Gao, S. V. Buldyrev, H. E. Stanley % S. Havlin, Nat. Phys. 8, 40 (2012).
38. D. F. Klosic, A. Grimbs, S. Bornholdt & M.-T. Hütt, Nat. Comm. 8:534 (2017).
39. C. del Genio, J. Gómez-Gardeñes, I. Bonamassa & S. Boccaletti, Sci. Adv. 2, e1601679 (2016).
40. V. Nicosia, P. S. Skardal, A. Arenas & V.Latora, Phys. Rev. Lett. 118, 138302 (2017).
41. M. M. Danziger, I. Bonamassa, S. Boccaletti & S.Havlin, arXiv:1705.00241 (2017).
42. B. Bollobás, Random graphs, in Modern graph theory (Springer, New York, NY, 1998).
43. M. Catanzaro, M. Boguñá & R. Pastor-Satorras, Phys. Rev. E 71, 027103 (2005).
44. After the crossover, the reactants become (so to say) oblivious of the “mesoscopic” structure of the interconnected network. This means that the fraction of interconnected nodes must be much larger then the density of the survived particles, which justifies the condition adopted in deriving Eq. (6).
45. V. Colizza, R. Pastor-Satorras & A. Vespignani, Nature Physics 3, 276 (2007).
46. A. Baronchelli, M. Catanzaro & R. Pastor-Satorras, Phys. Rev. E 78(1), 016111 (2008).
47. R. Cohen, K. Erez, D. ben-Avraham & S. Havlin, Phys. Rev. Lett. 85, 4626 (2000).
48. J. Aguirre, D. Papo, J. M. Buldú, Nature Physics, 9(4), 230 (2013).
49. P. L. Krapivsky, S. Redner, E. Ben-Naim, A kinetic view of statistical physics (Cambridge Uni. Press, 2010).
50. E. Agliari, R. Burioni, D. Cassi, F. Maria Neri, IMA Jour. Man. Math., 21(1), 67 (2009).
You are adding the first comment!
How to quickly get a good reply:
• Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
• Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
• Your comment should inspire ideas to flow and help the author improves the paper.
The better we are at sharing our knowledge with each other, the faster we move forward.
The feedback must be of minumum 40 characters
|
2019-03-24 10:48:17
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8404563069343567, "perplexity": 1122.9686123480533}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203438.69/warc/CC-MAIN-20190324103739-20190324125739-00202.warc.gz"}
|
https://www.greencarcongress.com/2015/06/20160616-joule.html
|
## Joule issued patent on production of medium chain-length alkanes from sunlight and CO2; diesel, jet fuel and gasoline
##### 16 June 2015
Joule, the developer of engineered photosynthetic bacteria as catalysts for the direct production of targeted fuel molecules in a continuous, single-step conversion process, announced the issuance of an additional patent, extending its ability to target the highest-value molecules of the petroleum distillation process and generate them on demand from sunlight and CO2.
US Patent Nº 9,034,629, issued on 19 May, covers both the cyanobacterium and the process for directly converting CO2 into medium chain-length alkanes (C7-11), which are in the diesel, jet fuel and gasoline ranges.
Examples from the patent document of pathways for the production of medium chain-length alkanes. The engineered cyanobacteria comprise recombinant genes encoding one or more enzymes which catalyze the production of medium chain-length alkanes. Click to enlarge.
This latest issuance complements Joule’s existing patents on the production of long-chain alkanes, ethanol and multiple chemicals, protecting the company’s capability to produce a full breadth of drop-in products without biomass feedstocks or complex refining. Because the process consumes waste CO2 emissions, the resulting fuels can enable carbon-neutral transportation by supplanting their petroleum-derived counterparts.
Free of feedstock constraints and complex processing, Joule’s process can achieve scalability, volumes and costs without the use of any agricultural land, fresh water or crops. Joule is privately held and has raised more than $200 million in funding to date, led by Flagship Ventures. The company operates from Bedford, Massachusetts and The Hague, The Netherlands with production operations in Hobbs, New Mexico. ### Comments Excellent. Now when the hell are we going to see retail products? I would happily pay$6 per gallon for carbon-neutral gasoline for my Prius.
Richard, would you pay them \$6 a gallon to top-off your 1975 AMC Pacer?
The comments to this entry are closed.
|
2022-11-26 15:51:33
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2573612332344055, "perplexity": 14563.363203551035}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446708010.98/warc/CC-MAIN-20221126144448-20221126174448-00743.warc.gz"}
|
https://proxies123.com/tag/calculation/
|
## Need Suggestion for Numerology Calculation Software or Script
Hi,
Need to know that for numerology calculation ….. personal software development is good or we should use any API???
According to me (I seen formula and other details) numerology calculation software or script is a bit expensive if we are thinking to create our own …. and also it will take a bit long time because there are very long and complex process. If any one is developed then please let me know ideas or time frame that about how many days it will take.
If i google for numerology software then getting many websites ….. as i see some good sites also like astrologyapi but think to see some more ….. So if any one can suggest us more website or software provider then it would be very helpful for me.
Looking for your suggestion for both.
Thanks
## calculus and analysis – Definite integral gets stuck in the calculation
$$f=frac{sinh ^{-1}left(e^{-2 k t} sinh (6 k)right)}{2 k}-2$$
for $$k=20$$ I have:
$$frac{df}{dt}=-frac{e^{-20 t} sinh (60)}{sqrt{e^{-40 t} sinh ^2(60)+1}}$$
``````f = -2 + ArcSinh(E^(-2 k t) Sinh(6 k))/(2 k)
Integrate(D(f, t), {t, 0, 10})
``````
And he just gets stuck and doesn’t move on. Then I tried to apply parallel computation, but got the error:
``````Needs("Parallel`Developer`")
f = -2 + ArcSinh(E^(-2 k t) Sinh(6 k))/(2 k)
Integrate(D(f, t), {t, 0, 10})
Parallelize::nopar1: !(*SubsuperscriptBox(((Integral)), (0), (10))(*SubscriptBox(((PartialD)), (t))f (DifferentialD)t)) cannot be parallelized; proceeding with sequential evaluation.
``````
I would be grateful for help in finding out the reason.
Processor AMD Ryzen 7 2700 Pro, 16 Gb RAM. When calculating this task, the processor is loaded by 8-10%.
## Prologue
Im quite new to data oriented programming and my goal is to implement a runescape stats & damage mechanic.
This is quite a pretty complex topic : [Runescape-Mechanics][1] and i havent found any ECS related sources on that topic yet.
In the following example we see a bunch of items which modify the weares stats based on a few conditions.
This happens in two different variants, either for the damage calculation only, or as a buff.
``````Brine sabre and Brackish blade increase damage against crabs.
or
Silverlight and Darklight increase ability damage by a scaling of 25-124% against most demons. The exact damage bonus is based on your base Attack and Strength, and the monster's base Defence.
``````
## The problem
Such a RPG system is very complex. There different damage types, different resistences and other stats.
Having a strong OOP background and no real experience in DOP, i cant find a suitable architecture to fill those needs.
In my current approach every stat is a component. Items and Buffs are structs. A item “buffs” its owner and the buff modifies his stats. This works so far, but i have no idea how i could realise the damage calculation, while still keeping it that flexible as it is in runescape.
This little example would just be able to buff the stats… not deal, receive or modify the damage itself.
``````
// The stats
public struct Health{
float max;
float value;
}
public struct MeeleDamage{
float base;
float value;
}
public struct MeeleResistence{
float base;
float value;
}
// Item & Buffs
public struct Item{
string name;
int amount;
bool equipable;
List<Buff> buffs;
}
public struct Buff{
string name;
float duration;
Condition applyable;
ToBuff stat;
float value;
}
``````
Its also important that an entity can also deal damage to multiple other entities in one frame.
How would you implement such an complex mechanic ? Any examples are appreciated !
## google sheets – GogleSheet Date and Time Calculation – Automation
I have a column that has 34 records of Week Day, Month/Day, and Times. I am looking for two formulas that I can use in a table that will give me the count of weekdays and the time duration per day. Eventually, I would like to just copy and past new dates into column A and have the table automatically calculate. Here is my google sheet example. Is there a way to do this without creating helper columns? If not, no big deal. Anything to help automate the process will be helpful.
## unity – Why does my in-game frame calculation not correlate with animation length?
I need to play an animation in such a way that each frame is for sure being played and not skipped.
To do that, I use a very slow animator speed like this:
``````_animator.speed = 0.01f;
``````
The Unity editor says this about the animation:
To make sure that each frame is really shown / played, I have implemented my own counter.
My counter however returns 43 frames and not 51 frames as the Inspector.
No matter how often I repeat this process, it always return 43 frames.
What am I missing?
Thank you!
``````private void LateUpdate()
{
float f = _animator.GetCurrentAnimatorClipInfo(0)(0).clip.length * (_animator.GetCurrentAnimatorStateInfo(0).normalizedTime % 1) * _animator.GetCurrentAnimatorClipInfo(0)(0).clip.frameRate;
int iCurrentFrameIDInAnimationFile = (int)f;
bool bIsNewFrame = (iCurrentFrameIDInAnimationFile != _iLastFrameIDInAnimationFile);
if (!bIsNewFrame)
{
return;
}
else if (bIsNewFrame)
{
_iFrameCount += 1;
}
_iLastFrameIDInAnimationFile = iCurrentFrameIDInAnimationFile;
if (_animator.GetCurrentAnimatorStateInfo(0).normalizedTime > 1 && !_animator.IsInTransition(0))
{
//animation has finished playing
Debug.Log("Frames: " + _iFrameCount); //this returns 43 frames. Why???
}
``````
## trigonometry – Use trigonometric output expression for calculation in a next step
Can’t use output sin[p] since Sin[p] is expected.
As a result of D[x, u] D[x, u] + D[y, u] D[y, u] + D[z, u] D[z, u] I’ve got a Mathematica output like u²+v²cos[p]² + v²sin[p]². As you see, cos and sin are given in lowercase letters, and Mathematica can’t use the expression for further simplifications since Cos and Sin are expected. What can I do to get the expected solution u²+v²?
## 8 – Cart order total summary vat calculation issue
When you have items in your cart and the shipping price is available, there is an issue with the order total summary:
Subtotal: 62,00 €
Shipping: 15,00 €
VAT: 10,76 €
Total: 77,00 €
The VAT is calculated on the ‘subtotal’. That is not clear, if the ‘shipping cost’ appears before the ‘VAT’. Or we need to switch both, or we need to calculate the VAT based on both ‘subtotal’ AND ‘shipping’.
This looks more logic to me:
Subtotal: 62,00 €
VAT (21%): 10,76 €
Shipping (incl. VAT 21%): 15,00 €
Total: 77,00 €
OR recalculate VAT:
Subtotal: 62,00 €
Shipping: 15,00 €
VAT (21%): 13,36 €
Total: 77,00 €
Solution?
I’ve tried to sort the adjustments in `commerce_shipping.commerce_adjustment_types.yml` but I don’t see any changes. Maybe because it only affects the adjustments in the admin UI orders?
Where do I need to store the yml file?
In the custom theme as: `mytheme.commerce_adjustment_types.yml`? That is not working.
I’m not sure if that will affect the values in `commerce-order-total-summary.html.twig` array.
If I can order the adjustments, that solution would be fine.
## focal length – Photogrammetry – use nodal point or entrance pupil for distance calculation?
I’m trying to accurately measure the size of objects via photogrammetry. The objects are 1 to 2 feet from the front of the camera lens, so where I start measuring from makes a difference.
I think the proper distance measurement is from either the “nodal point” or “entrance pupil” of the lens. Is that correct? I’m not even sure if there’s a difference between the two for a non-zoom lens.
Which is the proper measuring point? And how to figure out where that is on the lens?
## magento2 – Tax calculation and tax display issues
I would like to set all the products to show prices with tax included for
logged in users as well as guest users, but besides I tried all possible
combinations with tax settings, I didn’t managed to set this up,
as I’ve encounter all sorts of weird behaviors. In addition,
it seems there is separate issue with “Catalog New Product List” widget
Global settings:
• Magento version 2.4.1
• Shipping origin is set to Serbia.
• Product price is set to 100 din.
• Tax rate is set to 20%.
At “Tax settings” in admin panel, only change is:
• Stores > Configuration > Sales > Tax > Default Tax Destination Calculation > Default Country > Serbia
What is happening:
“Catalog New Product List” widget shows the product price of 100 din.
for guest user which is fine, but when I logged in with the registered user,
at first, the price is still hanging at 100 din, but after I refresh the page
the price changes to 83.33 din. which is amount with deducted tax percentage,
which is wrong.
When I click the same product and go to product page, the price
displayed is 100 din. which is the correct one.
When I click “View and Edit Cart” and go to `../checkout/cart` page,
the cart summary for logged in user is calculated as 100 din. + 20 din. (tax amount)
equal 120 din. in total and that’s OK, but with the guest user, cart summary is
calculated as 100 din. + 0 for tax amount which is wrong. So, I ended up
with one product price for guest user, another totally wrong calculated price
at “Catalog New Product List” widget for logged in user, then one total amount
of 100 din. for guest user and different total amount of 120 din. for logged in user.
registered user:
guest user:
Basically, I can’t set up the correct prices with tax amount for guest user, as
Magento keep deducting tax amount for guest user instead of adding it to price
value. I’ve managed to set up what I want, but just for logged in user.
For guest user I always end up with prices without tax amount (83.33 din)
instead of 120 din. which will be the right one. On top of that there is that widget
price odd behavior.
I can’t figure it out what is wrong here and how to handle it, but it seems to me
that something is really not right…
Any help will be highly appreciated.
## logic – Checking the logical coding calculation
Initial method of logical coding with constraints. The method I count is pigeon-hole based encoding. I tried to calculate formula 11 according to the formula.
Would anyone be able to check if this is correct?
Created sm helper variables according to constraints
``````>=5 x1 x2 x3 x4 x5 x6 x7
p11 p12 p13 p14 p15 p16 p17
p21 p22 p23 p24 p25 p26 p27
p31 p32 p33 p34 p35 p36 p37
p41 p42 p43 p44 p45 p46 p47
p51 p52 p53 p54 p55 p56 p57
``````
He then adjusted the variables according to the procedure
`````` p15 p16 p17
p24 p25 p26
p33 p34 p35
p42 p43 p44
``````
p51 p52 p53
And solved according to formula 11.
``````p51 v -p42
p42 v -p33
p33 v -p24
p24 v -p15
p51 v p52 v -p43
p42 v p43 v -p34
p33 v p34 v -p25
p24 v p25 v -p16
``````
I also enclose the whole article
https://pdfs.semanticscholar.org/5382/42c3aed93808a2312acfdde38285a19a2d1d.pdf
Is this the right procedure?
|
2021-04-22 11:57:04
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2429663985967636, "perplexity": 3901.366422250019}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00033.warc.gz"}
|
http://www.numerical-tours.com/matlab/sparsity_5_dictionary_learning_denoising/
|
Dictionary Learning for Denoising
# Dictionary Learning for Denoising
This tour follows the Dictionary Learning numerical tour. It uses a learned dictionary to perform image denoising.
## Installing toolboxes and setting up the path.
You need to download the following files: signal toolbox and general toolbox.
You need to unzip these toolboxes in your working directory, so that you have toolbox_signal and toolbox_general in your directory.
For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'.
Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab command you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands.
Execute this line only if you are using Matlab.
getd = @(p)path(p,path); % scilab users must *not* execute this
Then you can add the toolboxes to the path.
getd('toolbox_signal/');
getd('toolbox_general/');
## Learning the Dictionary
We aim at applying the dictionary learning method to denoising. We thus consider a noisy image obtained by adding Gaussian noise to a clean, unknown image $$f_0 \in \RR^N$$ where $$N=n_0 \times n_0$$.
Noise level $$\sigma$$.
sigma = .06;
Size of the image.
n0 = 256;
name = 'barb';
Display $$f_0$$.
clf;
imageplot(f0);
Noisy observations $$f=f_0+w$$ where $$w$$ is a realization of $$\Nn(0,\si^2\text{Id}_N)$$.
f = f0 + sigma*randn(n0);
Display $$f$$.
clf;
imageplot(f);
Perform the numerical tour on Dictionary Learning to obtain a dictionary $$D \in \RR^{n \times p}$$
if not(exist('D'))
sparsity_4_dictionary_learning;
end
Width $$w$$ of the patches.
w = sqrt(size(D,1));
Number $$p$$ of atoms.
p = size(D,2);
Dimension $$n= w \times w$$ of the data to be sparse coded.
n = w*w;
## Denoising by Sparse Coding
Here we apply sparse coding in the learned dictionary to the problem of image denoising, as detailed in:
M. Elad and M. Aharon, Image Denoising Via Sparse and Redundant representations over Learned Dictionaries, IEEE Trans. on Image Processing, Vol. 15, no. 12, pp. 3736-3745, December 2006.
The method first extract lots of patches from $$f$$, then perform sparse coding of each patch in $$D$$, and then average the overlapping patch to obtained the denoised image $$f_1$$.
We extract a large number $$m$$ of patches $$Y = (y_j)_{j=1}^m \in \RR^{n \times m}$$ from the noisy image $$f$$.
To extract the patche, we use $y_j(t) = f( a_j + t )$ where $$a_j$$ is the location of patch indexed by $$j$$.
In practice, splitting $$j=(j_1,j_2)$$ as a 2-D index, we use $$a_j = (j_1 q,j_2 q)$$ where $$q>0$$ is an overlap factor ( so that setting $$q=w$$ implies no overlap). Overlap is important to obtain good denoising performance (reduced blocking artifact).
q = 2;
Define regularly space positions for the extraction of patches.
[y,x] = meshgrid(1:q:n0-w/2, 1:q:n0-w/2);
m = size(x(:),1);
Xp = repmat(dX,[1 1 m]) + repmat( reshape(x(:),[1 1 m]), [w w 1]);
Yp = repmat(dY,[1 1 m]) + repmat( reshape(y(:),[1 1 m]), [w w 1]);
Ensure boundary conditions (reflexion).
Xp(Xp>n0) = 2*n0-Xp(Xp>n0);
Yp(Yp>n0) = 2*n0-Yp(Yp>n0);
Extract the $$m$$ patches $$Y$$.
Y = f(Xp+(Yp-1)*n0);
Y = reshape(Y, [n, m]);
Save the mean $$\theta_j$$ of each patch appart, and remove it.
theta = mean(Y);
Y = Y - repmat( theta, [n 1] );
Denoising of the patches is obtained by performing a sparse coding of each patch $$y_j$$ in $$D$$ $\umin{\norm{D x_j - y_j} \leq \epsilon} \norm{x_j}_1.$
The value of $$\epsilon>0$$ is set proportionaly to the noise level $$\sqrt{n}\sigma$$ that contaminates each patch. We denote $$\rho \approx 1$$ the proportionality factor, that is a parameter of the method.
rho = .95;
epsilon = rho*sqrt(n)*sigma;
The sparse coding problem can written equivalently in a way that is easier to deal using proximal splitting schemes. We introduce an auxiliary variable $$u=D x \in \RR^n$$ as follow $\umin{ z=(x,u) \in \RR^p \times \RR^n } F(z) + G(z)$ where for $$z=(x,u)$$, one defines $F(x,u) = \norm{x}_1 + \iota_{B_\epsilon(y)}(u) \qwhereq B_\epsilon(y) = \enscond{u}{ \norm{u-y} \leq \epsilon }$ and $G(x,u) = \iota_{\Cc}(x,u) \qwhereq \Cc = \enscond{(x,u)}{ u=D x }.$
Here we included the constraints using characteristic functions $\iota_{A}(z) = \choice{ 0 \qifq z \in A, \\ +\infty \quad \text{otherwise}. }$
## Douglas-Rachford Algorithm
To minimize the sparse coding problem, we make use of a proximal splitting scheme to minimize an energy of the form $$F(z)+G(z)$$. These schemes are adapted to solve structured non-smooth optimization problem.
They basically replace the traditional gradient-descent step (that is not available because neither $$F$$ nor $$G$$ are smooth functionals) by proximal mappings, defined as $\text{Prox}_{\gamma F}(z) = \uargmin{y} \frac{1}{2}\norm{z-y}^2 + \ga F(y)$ (the same definition applies also for $$G$$).
The Douglas-Rachford (DR) algorithm is an iterative scheme to minimize functionals of the form $\umin{z} F(z) + G(z)$ where $$F$$ and $$G$$ are convex functions for which one is able to comptue the proximal mappings $$\text{Prox}_{\gamma F}$$ and $$\text{Prox}_{\gamma G}$$.
The important point is that $$F$$ and $$G$$ do not need to be smooth. One onely needs then to be "proximable".
A DR iteration reads $\tilde z_{k+1} = \pa{1-\frac{\mu}{2}} \tilde z_k + \frac{\mu}{2} \text{rPox}_{\gamma G}( \text{rProx}_{\gamma F}(\tilde z_k) ) \qandq z_{k+1} = \text{Prox}_{\gamma F}(\tilde z_{k+1},)$
We have use the following shortcuts: $\text{rProx}_{\gamma F}(z) = 2\text{Prox}_{\gamma F}(z)-z$
It is of course possible to inter-change the roles of $$F$$ and $$G$$, which defines another set of iterations.
One can show that for any value of $$\gamma>0$$, any $$0 < \mu < 2$$, and any $$\tilde z_0$$, $$z_k \rightarrow z^\star$$ which is a minimizer of $$F+G$$.
Please note that it is actually $$z_k$$ that converges, and not $$\tilde z_k$$.
Proximal Splitting Methods in Signal Processing, Patrick L. Combettes and Jean-Christophe Pesquet, in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, New York: Springer-Verlag, 2010.
## Douglas-Rachford for Sparse Coding
In the special case of the constrained sparse coding problem, the proximal mapping of $$G$$ is the orthogonal projection on the convex set $$\Cc$$: $(\tilde x, \tilde u) = \text{Prox}_{\ga G}(x,u) = \text{Proj}_\Cc(x,u).$
It can be computed by solving a linear system of equations since $\tilde u = D \tilde x \qwhereq \tilde x = (\text{Id} + D^* D)^{-1}(f + D^* u).$
Define Proj$$_\Cc$$, by pre-compuring the inverse of $$\text{Id} + D^* D$$.
U = (eye(p) + D'*D)^(-1);
Replicate = @(z)deal(z, D*z);
ProjC = @(x,u)Replicate( U*( x + D'*u ) );
One has $$\text{Prox}_{\ga G} = \text{Proj}_{\Cc}$$, whatever the value of $$\ga$$.
ProxG = @(f,u,gamma)ProjC(f,u);
Function $$F(x,u)$$ is actully a separable sum of a function that only depends on $$x$$ and a function that depends only on $$u$$: $F(x,u) = \iota_{B_\epsilon(y)}(u) + \norm{x}_1.$ The proximal operator of $$F$$ reads $\text{Prox}_{\ga F}(x,u) = ( \text{Proj}_{B_\epsilon(y)}(u), \text{Prox}_{\ga \norm{\cdot}_1 }(x) ).$
In order to speed up the implementation, the DR algorithm will be performed in parallel on all the $$x_j$$. We thus define $$y=Y$$ to be the set of all the patches.
y = Y(:,1:m);
Define the projector $\text{Proj}_{B_\epsilon(y)}(u) = y + (u-y) \max\pa{1 , \frac{\epsilon}{\norm{u-y}} }$
amplitude = @(a)repmat( sqrt(sum(a.^2,1)), [n 1] );
ProjB = @(u)y + (u-y) .* min(1, epsilon./amplitude(u-y) );
The proximal operator of the $$\ell^1$$ norm $$\norm{\cdot}_1$$ is a soft thresholding: $\text{Prox}_{\ga \norm{\cdot}_1}(x)_i = \max\pa{ 0, \frac{\ga}{\abs{x_i}} } x_i.$
ProxL1 = @(x,gamma)max(0,1-gamma./max(1e-9, abs(x))) .* x;
Define the proximal operator of $$F$$.
ProxF = @(x,u,gamma)deal( ProxL1(x,gamma), ProjB(u) );
Set the value of $$\mu$$ and $$\gamma$$. You might consider using your own value to speed up the convergence.
mu = 1;
gamma = 1;
Number of iterations.
niter = 800;
Exercice 1: (check the solution) Implement the DR iterative algorithm on niter iterations. Keep track of the evolution of the minimized energy $$\norm{x}_1$$ during the iterations.
exo1;
## Patch Averaging
Once each $$x_j$$ is computed, one obtains the denoised patch $$\tilde y_j = D x_j$$. These denoised patches are then aggregated together to obtained the denoised image: $f_1(t) = \frac{1}{W_t} \sum_j \tilde y_j(t-a_j)$ where $$W_t$$ is the number of patches that overlap at a given pixel location $$t$$ (note that in this formula, we assumed $$\tilde y_j(t-a_j)=0$$ when $$t-a_j$$ falls outside the patch limits).
Approximated patches $$Y_1 = (\tilde y_j)_j = D X$$.
Y1 = reshape(D*x, [w w m]);
Insert back the mean.
Y1 = Y1 - repmat( mean(mean(Y1)), [w w] );
Y1 = Y1 + reshape(repmat( theta, [n 1] ), [w w m]);
To obtain the denoising, we average the value of the approximated patches $$Y_1$$ that overlap.
W = zeros(n0,n0);
f1 = zeros(n0,n0);
for i=1:m
x = Xp(:,:,i); y = Yp(:,:,i);
f1(x+(y-1)*n0) = f1(x+(y-1)*n0) + Y1(:,:,i);
W(x+(y-1)*n0) = W(x+(y-1)*n0) + 1;
end
f1 = f1 ./ W;
Display the result.
clf;
imageplot(clamp(f1), ['Denoised, SNR=' num2str(snr(f0,f1),4) 'dB']);
Exercice 2: (check the solution) Compare the obtained result with translation invariant wavelet hard thresholding.
exo2;
Exercice 3: (check the solution) Study the influence of the parameter $$\rho$$ on the quality of the denoising. Study the influence of the number $$p$$ of atoms.
exo3;
|
2022-05-28 01:19:22
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8275495767593384, "perplexity": 1824.512294130777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663011588.83/warc/CC-MAIN-20220528000300-20220528030300-00237.warc.gz"}
|
http://monolix.lixoft.com/data-and-models/mixturedistributions/
|
Select Page
# Mixture of distributions
Objectives: learn how to implement a mixture of distributions for the individual parameters.
Projects: PKgroup_project, PKmixt_project
## Introduction
Mixed effects models allow us to take into account between-subject variability. One complicating factor arises when data is obtained from a population with some underlying heterogeneity. If we assume that the population consists of several homogeneous subpopulations, a straightforward extension of mixed effects models is a finite mixture of mixed effects models, assuming, for instance, that the probability distribution of some individual parameters vary from one subpopulation to another one. The introduction of a categorical covariate (e.g., sex, genotype, treatment, status, etc.) into such a model already supposes that the whole population can be decomposed into subpopulations. The covariate then serves as a \emph{label} for assigning each individual to a subpopulation.
In practice, the covariate can either be known or not. Mixture models usually refer to models for which the categorical covariate is unknown, but whichever the case, the model is the same. The difference appears when having to perform certain tasks and in the methods needed to implement them. For instance, model building is different depending on whether the labels are known or unknown: we have supervised learning if the labels are known and unsupervised otherwise. For the sake of simplicity, we will consider a basic model that involves individual parameters $(\psi_i,1\leq i \leq N)$ and observations $(y_{ij}, i \leq N, 1\leq j \leq n_i)$. Then, the easiest way to model a finite mixture model is to introduce a label sequence $(z_i , 1\leq i \leq N)$ that takes its values in $\{1,2,\ldots,M\}$ such that $z_i=m$ if subject i belongs to subpopulation m.
In some situations, the label sequence $(z_i , 1\leq i \leq N)$ is known and can be used as a categorical covariate in the model. If $(z_i)$ is unknown, it can modeled as a set of independent random variables taking its values in $\{1,2,\ldots,M\}$ where for $i=1,2,\ldots, N$, $P(z_i = m)$ is the probability that individual belongs to group m. We will assume furthermore that the $(z_i)$ are identically distributed, i.e., $P(z_i = m)$ does not depend on i for $m=1,\ldots,M$.
## Mixture of distributions – supervised learning
• PKgroup_project (data = ‘PKmixt_data.txt’, model = ‘lib:oral1_1cpt_kaVCl.txt’)
The sequence of labels is known as GROUP in this project and is therefore defined as a categorical covariate:
We can then assume, for instance different population values for the volume in the 2 groups:
and estimate the population parameters using this covariate model
Then, this covariate GROUP can be used as a stratification variable.
## Mixture of distributions – unsupervised learning
• PKmixt_project (data = ‘PKmixt_data.txt’, model = ‘lib:oral1_1cpt_kaVCl.txt’)
We will use the same data with this project but ignoring the column GROUP (which is equivalent to assume that the label is unknown)
If we suspect some heterogeneity in the population, we can introduce a “latent covariate” and select the number of categories for this latent covariate.
Remark: several latent covariates can be introduced in the model, with different number of categories.
We can then use this latent covariate lcat as any observed categorical covariate. We can assume again different population values for the volume in the 2 groups:
and estimate the population parameters using this covariate model. Proportions of each group are also estimated:
Once the population parameters are estimated, the sequence of latent covariates $(ZM_i)$, i.e. the group to which belongs each subject, can be estimated together with the individual parameters, as the modes of the conditional distributions.
The sequence of estimated latent covariates $(ZM_i)$ can be used as a stratification variable:
We can for example display the VPC in the 2 groups:
By plotting the distribution of the individual parameters, we see that $V_i$ has a bimodal distribution
This distribution can be decomposed into 2 distributions by ticking the box By group:
|
2017-04-23 07:58:16
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 16, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7726314067840576, "perplexity": 722.4511903757277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118310.2/warc/CC-MAIN-20170423031158-00219-ip-10-145-167-34.ec2.internal.warc.gz"}
|
https://people.maths.bris.ac.uk/~matyd/GroupNames/320i1/C2xD20.2C4.html
|
Copied to
clipboard
G = C2×D20.2C4order 320 = 26·5
Direct product of C2 and D20.2C4
Series: Derived Chief Lower central Upper central
Derived series C1 — C10 — C2×D20.2C4
Chief series C1 — C5 — C10 — C20 — C4×D5 — C2×C4×D5 — C2×C4○D20 — C2×D20.2C4
Lower central C5 — C10 — C2×D20.2C4
Upper central C1 — C2×C4 — C2×M4(2)
Generators and relations for C2×D20.2C4
G = < a,b,c,d | a2=b20=c2=1, d4=b10, ab=ba, ac=ca, ad=da, cbc=b-1, dbd-1=b11, dcd-1=b10c >
Subgroups: 718 in 266 conjugacy classes, 151 normal (27 characteristic)
C1, C2, C2 [×2], C2 [×6], C4 [×2], C4 [×2], C4 [×4], C22, C22 [×2], C22 [×10], C5, C8 [×4], C8 [×4], C2×C4 [×2], C2×C4 [×4], C2×C4 [×10], D4 [×12], Q8 [×4], C23, C23 [×2], D5 [×4], C10, C10 [×2], C10 [×2], C2×C8 [×2], C2×C8 [×14], M4(2) [×4], M4(2) [×8], C22×C4, C22×C4 [×2], C2×D4 [×3], C2×Q8, C4○D4 [×8], Dic5 [×4], C20 [×2], C20 [×2], D10 [×4], D10 [×4], C2×C10, C2×C10 [×2], C2×C10 [×2], C22×C8 [×3], C2×M4(2), C2×M4(2) [×2], C8○D4 [×8], C2×C4○D4, C52C8 [×4], C40 [×4], Dic10 [×4], C4×D5 [×8], D20 [×4], C2×Dic5 [×2], C5⋊D4 [×8], C2×C20 [×2], C2×C20 [×4], C22×D5 [×2], C22×C10, C2×C8○D4, C8×D5 [×8], C8⋊D5 [×8], C2×C52C8 [×2], C2×C52C8 [×4], C2×C40 [×2], C5×M4(2) [×4], C2×Dic10, C2×C4×D5 [×2], C2×D20, C4○D20 [×8], C2×C5⋊D4 [×2], C22×C20, D5×C2×C8 [×2], C2×C8⋊D5 [×2], D20.2C4 [×8], C22×C52C8, C10×M4(2), C2×C4○D20, C2×D20.2C4
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], D5, C22×C4 [×14], C24, D10 [×7], C8○D4 [×2], C23×C4, C4×D5 [×4], C22×D5 [×7], C2×C8○D4, C2×C4×D5 [×6], C23×D5, D20.2C4 [×2], D5×C22×C4, C2×D20.2C4
Smallest permutation representation of C2×D20.2C4
On 160 points
Generators in S160
(1 94)(2 95)(3 96)(4 97)(5 98)(6 99)(7 100)(8 81)(9 82)(10 83)(11 84)(12 85)(13 86)(14 87)(15 88)(16 89)(17 90)(18 91)(19 92)(20 93)(21 64)(22 65)(23 66)(24 67)(25 68)(26 69)(27 70)(28 71)(29 72)(30 73)(31 74)(32 75)(33 76)(34 77)(35 78)(36 79)(37 80)(38 61)(39 62)(40 63)(41 147)(42 148)(43 149)(44 150)(45 151)(46 152)(47 153)(48 154)(49 155)(50 156)(51 157)(52 158)(53 159)(54 160)(55 141)(56 142)(57 143)(58 144)(59 145)(60 146)(101 139)(102 140)(103 121)(104 122)(105 123)(106 124)(107 125)(108 126)(109 127)(110 128)(111 129)(112 130)(113 131)(114 132)(115 133)(116 134)(117 135)(118 136)(119 137)(120 138)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)(21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60)(61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100)(101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)
(1 98)(2 97)(3 96)(4 95)(5 94)(6 93)(7 92)(8 91)(9 90)(10 89)(11 88)(12 87)(13 86)(14 85)(15 84)(16 83)(17 82)(18 81)(19 100)(20 99)(21 62)(22 61)(23 80)(24 79)(25 78)(26 77)(27 76)(28 75)(29 74)(30 73)(31 72)(32 71)(33 70)(34 69)(35 68)(36 67)(37 66)(38 65)(39 64)(40 63)(41 145)(42 144)(43 143)(44 142)(45 141)(46 160)(47 159)(48 158)(49 157)(50 156)(51 155)(52 154)(53 153)(54 152)(55 151)(56 150)(57 149)(58 148)(59 147)(60 146)(101 123)(102 122)(103 121)(104 140)(105 139)(106 138)(107 137)(108 136)(109 135)(110 134)(111 133)(112 132)(113 131)(114 130)(115 129)(116 128)(117 127)(118 126)(119 125)(120 124)
(1 116 58 66 11 106 48 76)(2 107 59 77 12 117 49 67)(3 118 60 68 13 108 50 78)(4 109 41 79 14 119 51 69)(5 120 42 70 15 110 52 80)(6 111 43 61 16 101 53 71)(7 102 44 72 17 112 54 62)(8 113 45 63 18 103 55 73)(9 104 46 74 19 114 56 64)(10 115 47 65 20 105 57 75)(21 82 122 152 31 92 132 142)(22 93 123 143 32 83 133 153)(23 84 124 154 33 94 134 144)(24 95 125 145 34 85 135 155)(25 86 126 156 35 96 136 146)(26 97 127 147 36 87 137 157)(27 88 128 158 37 98 138 148)(28 99 129 149 38 89 139 159)(29 90 130 160 39 100 140 150)(30 81 131 151 40 91 121 141)
G:=sub<Sym(160)| (1,94)(2,95)(3,96)(4,97)(5,98)(6,99)(7,100)(8,81)(9,82)(10,83)(11,84)(12,85)(13,86)(14,87)(15,88)(16,89)(17,90)(18,91)(19,92)(20,93)(21,64)(22,65)(23,66)(24,67)(25,68)(26,69)(27,70)(28,71)(29,72)(30,73)(31,74)(32,75)(33,76)(34,77)(35,78)(36,79)(37,80)(38,61)(39,62)(40,63)(41,147)(42,148)(43,149)(44,150)(45,151)(46,152)(47,153)(48,154)(49,155)(50,156)(51,157)(52,158)(53,159)(54,160)(55,141)(56,142)(57,143)(58,144)(59,145)(60,146)(101,139)(102,140)(103,121)(104,122)(105,123)(106,124)(107,125)(108,126)(109,127)(110,128)(111,129)(112,130)(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,98)(2,97)(3,96)(4,95)(5,94)(6,93)(7,92)(8,91)(9,90)(10,89)(11,88)(12,87)(13,86)(14,85)(15,84)(16,83)(17,82)(18,81)(19,100)(20,99)(21,62)(22,61)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,145)(42,144)(43,143)(44,142)(45,141)(46,160)(47,159)(48,158)(49,157)(50,156)(51,155)(52,154)(53,153)(54,152)(55,151)(56,150)(57,149)(58,148)(59,147)(60,146)(101,123)(102,122)(103,121)(104,140)(105,139)(106,138)(107,137)(108,136)(109,135)(110,134)(111,133)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124), (1,116,58,66,11,106,48,76)(2,107,59,77,12,117,49,67)(3,118,60,68,13,108,50,78)(4,109,41,79,14,119,51,69)(5,120,42,70,15,110,52,80)(6,111,43,61,16,101,53,71)(7,102,44,72,17,112,54,62)(8,113,45,63,18,103,55,73)(9,104,46,74,19,114,56,64)(10,115,47,65,20,105,57,75)(21,82,122,152,31,92,132,142)(22,93,123,143,32,83,133,153)(23,84,124,154,33,94,134,144)(24,95,125,145,34,85,135,155)(25,86,126,156,35,96,136,146)(26,97,127,147,36,87,137,157)(27,88,128,158,37,98,138,148)(28,99,129,149,38,89,139,159)(29,90,130,160,39,100,140,150)(30,81,131,151,40,91,121,141)>;
G:=Group( (1,94)(2,95)(3,96)(4,97)(5,98)(6,99)(7,100)(8,81)(9,82)(10,83)(11,84)(12,85)(13,86)(14,87)(15,88)(16,89)(17,90)(18,91)(19,92)(20,93)(21,64)(22,65)(23,66)(24,67)(25,68)(26,69)(27,70)(28,71)(29,72)(30,73)(31,74)(32,75)(33,76)(34,77)(35,78)(36,79)(37,80)(38,61)(39,62)(40,63)(41,147)(42,148)(43,149)(44,150)(45,151)(46,152)(47,153)(48,154)(49,155)(50,156)(51,157)(52,158)(53,159)(54,160)(55,141)(56,142)(57,143)(58,144)(59,145)(60,146)(101,139)(102,140)(103,121)(104,122)(105,123)(106,124)(107,125)(108,126)(109,127)(110,128)(111,129)(112,130)(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,98)(2,97)(3,96)(4,95)(5,94)(6,93)(7,92)(8,91)(9,90)(10,89)(11,88)(12,87)(13,86)(14,85)(15,84)(16,83)(17,82)(18,81)(19,100)(20,99)(21,62)(22,61)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,145)(42,144)(43,143)(44,142)(45,141)(46,160)(47,159)(48,158)(49,157)(50,156)(51,155)(52,154)(53,153)(54,152)(55,151)(56,150)(57,149)(58,148)(59,147)(60,146)(101,123)(102,122)(103,121)(104,140)(105,139)(106,138)(107,137)(108,136)(109,135)(110,134)(111,133)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124), (1,116,58,66,11,106,48,76)(2,107,59,77,12,117,49,67)(3,118,60,68,13,108,50,78)(4,109,41,79,14,119,51,69)(5,120,42,70,15,110,52,80)(6,111,43,61,16,101,53,71)(7,102,44,72,17,112,54,62)(8,113,45,63,18,103,55,73)(9,104,46,74,19,114,56,64)(10,115,47,65,20,105,57,75)(21,82,122,152,31,92,132,142)(22,93,123,143,32,83,133,153)(23,84,124,154,33,94,134,144)(24,95,125,145,34,85,135,155)(25,86,126,156,35,96,136,146)(26,97,127,147,36,87,137,157)(27,88,128,158,37,98,138,148)(28,99,129,149,38,89,139,159)(29,90,130,160,39,100,140,150)(30,81,131,151,40,91,121,141) );
G=PermutationGroup([(1,94),(2,95),(3,96),(4,97),(5,98),(6,99),(7,100),(8,81),(9,82),(10,83),(11,84),(12,85),(13,86),(14,87),(15,88),(16,89),(17,90),(18,91),(19,92),(20,93),(21,64),(22,65),(23,66),(24,67),(25,68),(26,69),(27,70),(28,71),(29,72),(30,73),(31,74),(32,75),(33,76),(34,77),(35,78),(36,79),(37,80),(38,61),(39,62),(40,63),(41,147),(42,148),(43,149),(44,150),(45,151),(46,152),(47,153),(48,154),(49,155),(50,156),(51,157),(52,158),(53,159),(54,160),(55,141),(56,142),(57,143),(58,144),(59,145),(60,146),(101,139),(102,140),(103,121),(104,122),(105,123),(106,124),(107,125),(108,126),(109,127),(110,128),(111,129),(112,130),(113,131),(114,132),(115,133),(116,134),(117,135),(118,136),(119,137),(120,138)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60),(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100),(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)], [(1,98),(2,97),(3,96),(4,95),(5,94),(6,93),(7,92),(8,91),(9,90),(10,89),(11,88),(12,87),(13,86),(14,85),(15,84),(16,83),(17,82),(18,81),(19,100),(20,99),(21,62),(22,61),(23,80),(24,79),(25,78),(26,77),(27,76),(28,75),(29,74),(30,73),(31,72),(32,71),(33,70),(34,69),(35,68),(36,67),(37,66),(38,65),(39,64),(40,63),(41,145),(42,144),(43,143),(44,142),(45,141),(46,160),(47,159),(48,158),(49,157),(50,156),(51,155),(52,154),(53,153),(54,152),(55,151),(56,150),(57,149),(58,148),(59,147),(60,146),(101,123),(102,122),(103,121),(104,140),(105,139),(106,138),(107,137),(108,136),(109,135),(110,134),(111,133),(112,132),(113,131),(114,130),(115,129),(116,128),(117,127),(118,126),(119,125),(120,124)], [(1,116,58,66,11,106,48,76),(2,107,59,77,12,117,49,67),(3,118,60,68,13,108,50,78),(4,109,41,79,14,119,51,69),(5,120,42,70,15,110,52,80),(6,111,43,61,16,101,53,71),(7,102,44,72,17,112,54,62),(8,113,45,63,18,103,55,73),(9,104,46,74,19,114,56,64),(10,115,47,65,20,105,57,75),(21,82,122,152,31,92,132,142),(22,93,123,143,32,83,133,153),(23,84,124,154,33,94,134,144),(24,95,125,145,34,85,135,155),(25,86,126,156,35,96,136,146),(26,97,127,147,36,87,137,157),(27,88,128,158,37,98,138,148),(28,99,129,149,38,89,139,159),(29,90,130,160,39,100,140,150),(30,81,131,151,40,91,121,141)])
80 conjugacy classes
class 1 2A 2B 2C 2D 2E 2F 2G 2H 2I 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 5A 5B 8A ··· 8H 8I ··· 8P 8Q 8R 8S 8T 10A ··· 10F 10G 10H 10I 10J 20A ··· 20H 20I 20J 20K 20L 40A ··· 40P order 1 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 5 5 8 ··· 8 8 ··· 8 8 8 8 8 10 ··· 10 10 10 10 10 20 ··· 20 20 20 20 20 40 ··· 40 size 1 1 1 1 2 2 10 10 10 10 1 1 1 1 2 2 10 10 10 10 2 2 2 ··· 2 5 ··· 5 10 10 10 10 2 ··· 2 4 4 4 4 2 ··· 2 4 4 4 4 4 ··· 4
80 irreducible representations
dim 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 type + + + + + + + + + + + image C1 C2 C2 C2 C2 C2 C2 C4 C4 C4 C4 D5 D10 D10 D10 C8○D4 C4×D5 C4×D5 D20.2C4 kernel C2×D20.2C4 D5×C2×C8 C2×C8⋊D5 D20.2C4 C22×C5⋊2C8 C10×M4(2) C2×C4○D20 C2×Dic10 C2×D20 C4○D20 C2×C5⋊D4 C2×M4(2) C2×C8 M4(2) C22×C4 C10 C2×C4 C23 C2 # reps 1 2 2 8 1 1 1 2 2 8 4 2 4 8 2 8 12 4 8
Matrix representation of C2×D20.2C4 in GL4(𝔽41) generated by
40 0 0 0 0 40 0 0 0 0 40 0 0 0 0 40
,
34 40 0 0 1 0 0 0 0 0 32 0 0 0 23 9
,
7 1 0 0 34 34 0 0 0 0 40 1 0 0 0 1
,
32 0 0 0 0 32 0 0 0 0 14 27 0 0 28 27
G:=sub<GL(4,GF(41))| [40,0,0,0,0,40,0,0,0,0,40,0,0,0,0,40],[34,1,0,0,40,0,0,0,0,0,32,23,0,0,0,9],[7,34,0,0,1,34,0,0,0,0,40,0,0,0,1,1],[32,0,0,0,0,32,0,0,0,0,14,28,0,0,27,27] >;
C2×D20.2C4 in GAP, Magma, Sage, TeX
C_2\times D_{20}._2C_4
% in TeX
G:=Group("C2xD20.2C4");
// GroupNames label
G:=SmallGroup(320,1416);
// by ID
G=gap.SmallGroup(320,1416);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,758,297,80,102,12550]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^20=c^2=1,d^4=b^10,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,d*b*d^-1=b^11,d*c*d^-1=b^10*c>;
// generators/relations
×
𝔽
|
2021-02-26 04:34:51
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9997087717056274, "perplexity": 2947.813539435972}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178356140.5/warc/CC-MAIN-20210226030728-20210226060728-00290.warc.gz"}
|
http://clay6.com/qa/27919/mixture-of-volatile-components-a-and-b-has-total-vapour-pressure-in-torr-p-
|
Browse Questions
# Mixture of volatile components A and B has total vapour pressure (in torr) P=$250-115X_A$ where $X_A$ is mol fraction of 'A' in mixture.Hence $P_A^0$ and $P_B^0$ respectively are (in torr)
$\begin{array}{1 1}(a)\;250,120\\(b)\;135,250\\(c)\;250,115\\(d)\;115,250\end{array}$
Total pressure $P=250-115X_A$
If $X_A=1$, then $P=P_A^0$
$\therefore P_A^0=250-115\times 1$
$\Rightarrow 135$
$P=250-115(1-X_B)$
$\;\;\;=250-115+115X_B$
If $X_B=1$,then $P=P_B^0$
$\therefore P_B^0=250-115+115\times 1$
$\Rightarrow 250$
Hence (b) is the correct answer.
|
2017-02-26 21:21:22
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9760797619819641, "perplexity": 2962.3024847665442}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172077.66/warc/CC-MAIN-20170219104612-00451-ip-10-171-10-108.ec2.internal.warc.gz"}
|