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Mon, 05 Dec 2022 12:02:09 +07009to5ScienceWhat are the inverses of $1,3,7,9$ in the group $(G,*_{10})$?
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Solution 1
There is no "division operation" in a group, it only signifies $a/b$=$ab^{-1}$ So you are right to say that $1/3$ is the inverse of 3, but a better notation would be $3^{-1}$. Now, to see that 3 and 7 are inverses in the group of units mod 10, we see that $3\cdot 7=21 \equiv 1\pmod{10}$ and 1 is the identity. We xan do the same to find the inverse of 9.
Solution 2
Let $(G, \cdot)$ be a group whose identity is $e$. By definition, for an element $a \in G$, any other $b \in G$ is calledMon, 05 Dec 2022 11:26:08 +0700
https://9to5science.com/what-are-the-inverses-of-1-3-7-9-in-the-group-g-_-10
https://9to5science.com/what-are-the-inverses-of-1-3-7-9-in-the-group-g-_-10If $x+y+z=5$ and $xy+yz+zx=3$,then least and largest value of $x$ are?
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Solution 1
Using $(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)$
So $x^2+y^2+z^2 = (x+y+z)^2-2(xy+yz+zx) = 5^2-2\cdot 3 = 19$
So $y^2+z^2 = 19-x^2$ and $y+z = 5-x$
Now Using $\bf{Cauchy\; Schwarz}$ Inequality
$$(y^2+z^2)(1^2+1^2)\geq (y+z)^2$$
So $$(19-x^2)\cdot 2 \geq (5-x)^2$$
So $$25+x^2-10x\leq 38-2x^2$$
So $$3x^2-10x-13\leq 0$$
So $$3x^2-13x+3x-13\leq0$$
So $$(x+1)(3x-13)\leq 0\Rightarrow -1 \leq x\leq \frac{13}{3}$$
Solution 2
$x(y+z) = 3 - yz \implies x(5-x) = 3 - yz \implies yz = x^2-5x+3\implies x^2-5x+3 \le \dfrac{(y+z)^2}{4}= \dfrac{(5-x)^2}{4}\implies 4x^2-20x + 12 \le 25-10x+x^2\implies 3x^2-10x-13 \le 0 \implies (x+1)(3x-13) \le 0 \implies -1 \le x \le \dfrac{13}{3} \implies x_{\text{max}} = \dfrac{13}{3}, x_{\text{min}} = -1.$
Mon, 05 Dec 2022 09:57:16 +0700
https://9to5science.com/if-x-y-z-5-and-xy-yz-zx-3-then-least-and-largest-value-of-x-are
https://9to5science.com/if-x-y-z-5-and-xy-yz-zx-3-then-least-and-largest-value-of-x-areHow can sulfate be nonpolar covalent if it is a polyatomic ion?
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Solution 1
These two species have bonds within them, and (non)polar covalency refers to those internal bonds. The species as a whole can be an ion, and yet not have net polarity on its bonds.
Sulfate is tetrahedral, so each individual dipole vector would be opposed and cancelled, making the overall molecule non-polar (in the same way that this question and answer about $\ce{CO2}$ details).
Sulfate has negative charges which could make a Lewis dot structure appear to have a net dipole, there is resonance that distributes that charge throughout the molecule, negating the net effect.
Sulfite, on the otherMon, 05 Dec 2022 07:31:04 +0700
https://9to5science.com/how-can-sulfate-be-nonpolar-covalent-if-it-is-a-polyatomic-ion
https://9to5science.com/how-can-sulfate-be-nonpolar-covalent-if-it-is-a-polyatomic-ionReduce space after title once
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As Werner said in his comment, \vspace{<len>} ( <len> negative) solves this problem.
Mon, 05 Dec 2022 07:23:54 +0700
https://9to5science.com/reduce-space-after-title-once
https://9to5science.com/reduce-space-after-title-onceWhat is the Minimum GPA for admission in a graduate school in a respectable science university in the US?
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(In the US) in Physics, some programs will weight things like the physics subject GRE and research experience, especially publications, ahead of the GPA. However, some schools do have a GPA cut-off around 3.0, so it's possible some schools wouldn't get far enough into your application to read it.
If you want to apply to prestigious or highly-selective programs right now, I think you would need:
To have scored very well on the general and physics-subject GREs.
Very good letters of recommendation that speak directly to your ability to succeed in a graduate program.
An "explanation" for your GPA inMon, 05 Dec 2022 05:52:10 +0700
https://9to5science.com/what-is-the-minimum-gpa-for-admission-in-a-graduate-school-in-a-respectable-science-university-in-the-us
https://9to5science.com/what-is-the-minimum-gpa-for-admission-in-a-graduate-school-in-a-respectable-science-university-in-the-usUnder what circumstances would a University revoke a student's degree?
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I'm not going to answer all of your questions, some being duplicates, too broad or opinion-based.
Is there any examples of degrees being revoked? If so, what types of academic misconduct would justify this?
There have been spectacular examples of falling from grace.
Pal Schmitt resigned as President of Hungary after his doctorate was stripped by Semmelweis University on findings of plagiarism.
Former German Defence Minister Karl-Theodor zu Guttenberg graduated summa cum laude from the University of Bayreuth in 2006 with a dissertation entitled "Constitution and Constitutional Treaty: Constitutional developments in the USA and EU." A finding of plagiarism ledMon, 05 Dec 2022 02:48:42 +0700
https://9to5science.com/under-what-circumstances-would-a-university-revoke-a-student-39-s-degree
https://9to5science.com/under-what-circumstances-would-a-university-revoke-a-student-39-s-degreeThe discrete metric on $\mathbb R $ is not induced by a norm
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Suppose it is possible, the norm of $1$ would have to be $1$ because $d(0,1)=1$ but then the norm of $2$ would have to be $2$ (since $||av||$ is equal to $|a|\cdot||v||$). This implies $d(0,2)=2$, a contradiction.
Mon, 05 Dec 2022 02:20:02 +0700
https://9to5science.com/the-discrete-metric-on-mathbb-r-is-not-induced-by-a-norm
https://9to5science.com/the-discrete-metric-on-mathbb-r-is-not-induced-by-a-normHyperref package causing error: You can't use a prefix with \begingroup
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As pointed out by egreg, \documentclass is missing a parameter. The line should be of the form:
\RequirePackage[l2tabu, orthodox]{nag}
\documentclass{article}
.....
Mon, 05 Dec 2022 01:54:14 +0700
https://9to5science.com/hyperref-package-causing-error-you-can-39-t-use-a-prefix-with-begingroup
https://9to5science.com/hyperref-package-causing-error-you-can-39-t-use-a-prefix-with-begingroupWhy is water considered a pure substance instead of a mixture?
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Solution 1
A mixture is when two or more substances combine physically together.
However, in water, two hydrogen atoms combine with one oxygen atom chemically, forming a new substance that has properties different from hydrogen alone or oxygen alone.
For example, if you combine iron powder and sulfur powder physically (just mixing them together without applying heat), you can find that the mixture retains the properties of the original components, i.e. you can still use a magnet to attract the iron inside the mixture.
However, if you heat it up, the iron and the sulfur would combine chemically, and aMon, 05 Dec 2022 01:16:58 +0700
https://9to5science.com/why-is-water-considered-a-pure-substance-instead-of-a-mixture
https://9to5science.com/why-is-water-considered-a-pure-substance-instead-of-a-mixturepirates treasure divide problem
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Solution 1
We can get below table for each pirate if assume total number as 1:
\begin{array} {|l|l|l|}
\hline N & Taken & Remaining \\ \hline
1 & \frac{1}{12} & \frac{11}{12} \\
\hline
2 & \frac{11}{12}\cdot \frac{2}{12} & \frac{11}{12}\cdot \frac{10}{12} \\
\hline
3 & \frac{11}{12}\cdot \frac{10}{12}\cdot \frac{3}{12} & \frac{11}{12}\cdot \frac{10}{12}\cdot \frac{9}{12} \\
\hline
4 & \frac{11}{12}\cdot \frac{10}{12}\cdot \frac{9}{12}\cdot \frac{4}{12} & \frac{11}{12}\cdot \frac{10}{12}\cdot \frac{9}{12}\cdot \frac{8}{12} \\
\hline
5 & \frac{11}{12}\cdot \frac{10}{12}\cdot \frac{9}{12}\cdot \frac{8}{12}\cdot \frac{5}{12} & \frac{11}{12}\cdot \frac{10}{12}\cdot \frac{9}{12}\cdot \frac{8}{12}\cdot \frac{7}{12} \\
\hline
6 & \frac{11}{12}\cdot \frac{10}{12}\cdot \frac{9}{12}\cdot \frac{8}{12}\cdot \frac{7}{12}\cdot \frac{6}{12} & \frac{11}{12}\cdot \frac{10}{12}\cdot \frac{9}{12}\cdot \frac{8}{12}\cdot \frac{7}{12}\cdot \frac{6}{12} \\
\hline
7 &Mon, 05 Dec 2022 00:49:44 +0700
https://9to5science.com/pirates-treasure-divide-problem
https://9to5science.com/pirates-treasure-divide-problemWhat does mol L−1 mean?
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The units are mole per liter. $\mathrm{mol \times L^{-1}}$ is more conveniently written $\mathrm{mol/L}$. This set of units is referred to as molarity, and is a common measure of concentration for a solute dissolved in a solvent. The solute may be a solid (ionic or covalent), a gas or a liquid, but is commonly a solid. The solvent may be a gas or liquid, but is commonly a liquid. Together, the solute and the solvent form a solution.
Specifically, molarity is defined as
$$\text{Molarity} = \frac{\text{mol of solute}}{\text{L of solution}}$$
Note that the volume is of the total solution, notMon, 05 Dec 2022 00:45:26 +0700
https://9to5science.com/what-does-mol-l-1-mean
https://9to5science.com/what-does-mol-l-1-meanCommon site for atherosclerosis
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I can give you some facts about atherosclerosis, but I should warn you that--judging by your question--you may be making a false equivalence between atherosclerosis thrombus/embolism. The two are often very interrelated, but there are times when an atherosclerotic plaque is significant without causing an embolism (e.g. stable angina) and there are times when a thromboembolism forms without the presence of a significant atherosclerotic plaque (e.g. atrial fibrillation). The likelihood of thrombus formation is dictated by Virchow's Triad: Endothelial Dysfunction, Blood stasis/turbulence, inherent coagulability of the blood (factor problems mostly).
Now to get to your main question: atherosclerosis. The currentMon, 05 Dec 2022 00:05:18 +0700
https://9to5science.com/common-site-for-atherosclerosis
https://9to5science.com/common-site-for-atherosclerosisResonance structures
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/222168/template_resonance-structures20221205-1937004-y5x51d.jpg
Personally, I would recommend drawing the resonance process this way (first line):
Please note the difference in arrows between forms; you have used the reversible equilibrium arrows instead of the double-headed resonance arrows. This may seem like merely a grammatical concern, but the processes of equilibrium and resonance are fundamentally different and indicating the wrong process is incorrect.
Assuming the substituent is indeed a methoxy group as you have drawn it, this compound is known as anisole (not phenol as mentioned elsewhere).
These resonance structures have significance in rationalizing and predicting experimental observations. They demonstrate the electron-donating nature of theMon, 05 Dec 2022 00:02:26 +0700
https://9to5science.com/resonance-structures
https://9to5science.com/resonance-structuresWhat are examples of penalties for "self-plagiarism"?
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It depends on many factors. Examples of those factors: Was it a first offense, was it an undergraduate or graduate student, was it faculty member, was it for an assignment or a publication? The list of penalties can range from using the incident as an "object-lesson", a failing grade for the paper or course, a formal sanction, expulsion, loss of funding and/or termination. Each university usually has an Academic Integrity Office, so you could always consult yours to see what the penalties are based on the seriousness of the charge.
Sun, 04 Dec 2022 22:23:32 +0700
https://9to5science.com/what-are-examples-of-penalties-for-quot-self-plagiarism-quot
https://9to5science.com/what-are-examples-of-penalties-for-quot-self-plagiarism-quotChemical Reaction ammonium hydroxide + aluminum chloride (3NH4OH + AlCl3 -> 3NH4Cl + Al(OH)3)
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/221923/template_chemical-reaction-ammonium-hydroxide-aluminum-chloride-3nh4oh-alcl3-gt-3nh4cl-al-oh-320221204-1937004-1sgnyif.jpg
I'm quite sure that it's white. Maalox is essentially an aluminum hydroxide solution and it's white. There is nothing structurally or electronically to suggest that it would be any other color.
Sun, 04 Dec 2022 18:05:32 +0700
https://9to5science.com/chemical-reaction-ammonium-hydroxide-aluminum-chloride-3nh4oh-alcl3-gt-3nh4cl-al-oh-3
https://9to5science.com/chemical-reaction-ammonium-hydroxide-aluminum-chloride-3nh4oh-alcl3-gt-3nh4cl-al-oh-3Reading vs studying?
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There is no difference.
If you wanted to use the word "reading", the proper usage would be "I am reading for a degree in X." This is not limited to social sciences; it would apply to any degree.
However, this has become something of an old-fashioned expression; it's far more common to say that you are "studying X" or "doing a degree in X".
Source: I am a student in the UK.
Sun, 04 Dec 2022 17:49:46 +0700
https://9to5science.com/reading-vs-studying
https://9to5science.com/reading-vs-studyingDifference between research gap and research question
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In short:
Research gap, I understand it as a field, subfield, mechanism, that has been under-researched and there is space for improvement.
For example, object detection using telepathy might be under-research, so there is a gap in the research of that specific field.
The research question seem to refer to a more specific hypothesis, which in cases, it can coincide with the gap. For example, can telepathy work to detect an object, or can telepathy work under these or those conditions. In my understanding the first could also be a gap, the latter is more of a question.
Then theSun, 04 Dec 2022 16:42:24 +0700
https://9to5science.com/difference-between-research-gap-and-research-question
https://9to5science.com/difference-between-research-gap-and-research-questionSource of blood glucose during starvation
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Solution 1
The (very) short answer is gluconeogenesis. When glucagon levels are high in response low glucose or low Insulin (perceived in the case of Insulin resistant DM Type II) key enzymes will be inhibited to prevent glycolysis and other enzymes will be activated to produce glucose from various substrates.
There are a few sources that can feed into the gluconeogensis machine. Two that are commonly used in short term fasting are lactate via the Cori Cycle and Alanine via the aptly named Alanine Cycle. Now when we get into long term fasting (i.e. starvation) things start to change aSun, 04 Dec 2022 15:10:40 +0700
https://9to5science.com/source-of-blood-glucose-during-starvation
https://9to5science.com/source-of-blood-glucose-during-starvationPDF not updating in TeXstudio
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I followed doncherry's advice here and downgraded to 2.10.8 and now it works.
Sun, 04 Dec 2022 12:33:00 +0700
https://9to5science.com/pdf-not-updating-in-texstudio
https://9to5science.com/pdf-not-updating-in-texstudioHow do i determine the direction of components of electric fields?
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since $q_2$ is negative, the direction of $E_2$ is always pointing at the charge $q_2$. obviously the $x$ component of $E_2$ is positive.
Sun, 04 Dec 2022 10:31:10 +0700
https://9to5science.com/how-do-i-determine-the-direction-of-components-of-electric-fields
https://9to5science.com/how-do-i-determine-the-direction-of-components-of-electric-fieldsProduct of two symmetric matrices is similar to a symmetric matrix
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Here is a counter-example of two symmetric matrices $A$, $B$ whose product, besides being non symmetrical, cannot be similar to a symmetric matrix.
Consider matrices
$$A=\pmatrix{1&2\\2&1} \ \ \ \text{and} \ \ \ B=\pmatrix{1&0\\0&-1}.$$
$AB=\pmatrix{1&-2\\2&-1}.$ which is non symmetric.
Moreover, the characteristic polynomial of $AB$ is $\lambda^2+3$: thus, the eigenvalues of $AB$ are $\pm i \sqrt{3}$. If it was similar to a symmetric matrix, it would have the same real eigenvalues.
Sun, 04 Dec 2022 09:26:40 +0700
https://9to5science.com/product-of-two-symmetric-matrices-is-similar-to-a-symmetric-matrix
https://9to5science.com/product-of-two-symmetric-matrices-is-similar-to-a-symmetric-matrixFind the smallest possible value and the largest possible value for the interquartile range.
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/221117/template_find-the-smallest-possible-value-and-the-largest-possible-value-for-the-interquartile-range20221204-1937004-17262bi.jpg
If we were to assume that each sausage has the minimum weight that entitles it to its bin then the $55$th and $56$th sausage would both have a weight of $40$ grams (and $Q_1$ would be $40$). If we were to assume that each sausage has the maximum weight that entitles it to a bin then these sausages would both have a weight of $45$ grams (treating the weight as continuous). Thus, without these assumptions, $40 < Q_1 < 45$.
Similarly, $50 < Q_3 < 60$.
The minimum value of the $IQR$, then must then be $50 - 45 =Sat, 03 Dec 2022 22:28:46 +0700
https://9to5science.com/find-the-smallest-possible-value-and-the-largest-possible-value-for-the-interquartile-range
https://9to5science.com/find-the-smallest-possible-value-and-the-largest-possible-value-for-the-interquartile-rangeFind PDF of $X-Y$
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This is how I solved it:
$$\begin{align}
f(x) = f(y) &= \begin{cases}1 & 0 \leq x \leq 1, 0 \leq y \leq 1\\0 & Otherwise \end{cases}
\\[2ex]f_{Z}(z)&=\int_{-\infty}^{\infty} f_{X}(y+z)f_{Y}(y)dy
\end{align}$$
Almost okay, but more correctly : $$\begin{align}
f_X(x) \cdot f_Y(y) &= \begin{cases}1 & 0 \leq x \leq 1, 0 \leq y \leq 1\\0 & \text{Otherwise} \end{cases}
\end{align}$$
now the integrated is $0$ unless $0 \leq y+z \leq 1 (i.e, -z \leq y \leq 1-z)$ and then it is $1$
but I don't know how I can find ranges for $Z$
You find it from the joint support. $0\leq z+y\leqSat, 03 Dec 2022 19:41:04 +0700
https://9to5science.com/find-pdf-of-x-y
https://9to5science.com/find-pdf-of-x-yIf G/N is cyclic, then G is abelian.
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/220939/template_if-g-n-is-cyclic-then-g-is-abelian20220723-4112153-1tgi712.jpg
This is false, let $G=S_3$, the symmetric group of order $6$ and let $N=A_3$ be the alternating group on three symbols. Then $S_3/A_3$ is of order $2$ hence cyclic, but $S_3$ is not abelian.
Sat, 03 Dec 2022 18:09:20 +0700
https://9to5science.com/if-g-n-is-cyclic-then-g-is-abelian
https://9to5science.com/if-g-n-is-cyclic-then-g-is-abelianSubmitted abstract accepted as Poster. How can I change it to an oral presentation?
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The choice among different presentations often depends on the program and planning of the congress and is in hands of the organising commitee. I don't consider fair to request this change. Take into account that you will have future opportunities to present your work on different ways. In addition, there are many conventions devoted mainly to poster sessions and these are very fruitful. Finally, the acceptance as a poster could have an other meaning (and I have such experience): "your work has little value, but, please, come in and discuss your paster with us!"
Sat, 03 Dec 2022 18:00:44 +0700
https://9to5science.com/submitted-abstract-accepted-as-poster-how-can-i-change-it-to-an-oral-presentation
https://9to5science.com/submitted-abstract-accepted-as-poster-how-can-i-change-it-to-an-oral-presentationIs glycine achiral?
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It is not chiral because If the amino group and the carboxylic acid group changed places, the "new" arrangement would be superimposable on the old arrangement.
Sat, 03 Dec 2022 16:03:12 +0700
https://9to5science.com/is-glycine-achiral
https://9to5science.com/is-glycine-achiralpage numbering (frontmatter and mainmatter) problem
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I solved it by myself. It is not about the latex script, but about the encode. I found only the introduction chapter caused the problem, therefore, I checked what kinds of encoding used, and compared to other latex files. the introduction latex file is UTF-8 Unicode (with BOM) text, while others are ASCII. therefore I first converted it to UTF-8 without BOM and it worked. I do not know what exactly difference between UTF-8 and UTF-8 with BOM, but it led the problem.
Sat, 03 Dec 2022 15:04:26 +0700
https://9to5science.com/page-numbering-frontmatter-and-mainmatter-problem
https://9to5science.com/page-numbering-frontmatter-and-mainmatter-problemHow to change font size of text in a latex table
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/220716/template_how-to-change-font-size-of-text-in-a-latex-table20221203-1937004-dg5o7j.jpg
If you try this MWE, you can see that both caption and table content have same fontsize. Change Large into small to get 9pt font.
\documentclass{article}
%\usepackage{ijcai17}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{verbatim}
\usepackage{booktabs}
\usepackage{adjustbox}
\usepackage{caption}
\begin{document}
\section{Test}
Test document
\begin{table}[h!]
\Large
\captionsetup{font=Large}
\centering
\caption{ AUC values for LR, LR-Regularized, RF-Default, RF-FS for 1s, 3s, 5s, 10s segment lengths and 2-class problems.}
\label{table:2}
%\resizebox{0.47\textwidth}{!}{%
\begin{tabular}{c||c|c|c|c}
\toprule
& 1s & 3s & 5s & 10s\\
\hline
LR & $0.9223$ & $0.9895$ & $0.9840$ & $0.9913$ \\ \hline
LR-Regularized & $0.9207$ & $0.9887$ & $0.9928$ & $0.9863$ \\ \hline
RF-Default & $0.9072$ & $0.9767$ &Sat, 03 Dec 2022 12:41:06 +0700
https://9to5science.com/how-to-change-font-size-of-text-in-a-latex-table
https://9to5science.com/how-to-change-font-size-of-text-in-a-latex-tableHarmonic Series Convergence
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/220713/template_harmonic-series-convergence20221203-1937004-1wlkqbd.jpg
Solution 1
This is a graphical explanation. The partial sums of the harmonic series is given by
$$
S_n=\sum_{k=1}^n\frac1k
$$
and they look like this
The partial sums of the alternating harmonic series is given by
$$
S_n=\sum_{k=1}^n\frac{(-1)^{k+1}}k
$$
and they look like this
These graphs might give us some idea that the first one probably diverges and the second probably converges (actually the limit of the alternating harmonic series is $\log2\approx0.6931$).
Solution 2
Alternating series converge "easier". If you consider the sums of the even and the odd terms separately, they will tend to the same limit (with anSat, 03 Dec 2022 12:36:48 +0700
https://9to5science.com/harmonic-series-convergence
https://9to5science.com/harmonic-series-convergenceWhat is the difference between project and thesis?
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/220412/template_what-is-the-difference-between-project-and-thesis20221203-1937004-deffs1.jpg
It differs by school. Technically, a thesis is a claim that can be proven or disproven, but, in practice, the term "thesis" is often used for a project (for undergraduate or Master's degrees). On the other hand, a PhD thesis is not just a project; it should advance the state of knowledge in a field in a way that can only be done by someone knowledgeable in the field.
My department is considering renaming our Master's thesis requirement to Master's project, to acknowledge that it need not be a research contribution.
Of course, even a project can entail publishable workSat, 03 Dec 2022 05:21:04 +0700
https://9to5science.com/what-is-the-difference-between-project-and-thesis
https://9to5science.com/what-is-the-difference-between-project-and-thesis