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Farmer John and his cows are planning to leave town for a long vacation, and so FJ wants to temporarily close down his farm to save money in the meantime.
The farm consists of $N$ barns connected with $M$ bidirectional paths between some pairs of barns ($1 \leq N, M \leq 3000$). To shut the farm down, FJ plans to close... | CommonCrawl |
Like many other mathematicians I use mathematical software like SAGE, GAP, Polymake, and of course $\LaTeX$ extensively. When I chat with colleagues about such software tools, very often someone has an idea of how to extend an existing tool, what (non-existent) tool would be useful, or which piece of documentation shou... | CommonCrawl |
Using the numbers $1, 2, 3, 4$ and $5$ once and only once, and the operations $\times$ and $ \div$ once and only once, what is the smallest whole number you can make?
Place value. Divisibility. Properties of numbers. Addition & subtraction. Working systematically. Factors and multiples. Multiplication & division. Inves... | CommonCrawl |
We obtain dimension free estimates for noncommutative Riesz transforms associated to conditionally negative length functions on group von Neumann algebras. This includes Poisson semigroups, beyond Bakry's results in the commutative setting. Our proof is inspired by Pisier's method and a new Khintchine inequality for cr... | CommonCrawl |
TL;DR What in the world is roughness remapping for?
In general, artists like working with a linear roughness value between 0 and 1 (similarly for all other material parameters), since this is easier to work with and to understand compared to directly using the parameters of certain BRDF components as presented in the l... | CommonCrawl |
In the building of Jewelry Art Gallery (JAG), there is a long corridor in the east-west direction. There is a window on the north side of the corridor, and $N$ windowpanes are attached to this window. The width of each windowpane is $W$, and the height is $H$. The $i$-th windowpane from the west covers the horizontal r... | CommonCrawl |
And then thine sharpened figure shall be rounded.
As other answerers have pointed out, the first six lines are from Shakespeare's sonnets, numbered 3, 60, 5, 5, 5, and 12. However, I believe that they have been misinterpreting the mathematics.
A decimal point must be placed somewhere near the start of those numbers. Wi... | CommonCrawl |
This book fills a real gap in the analytical literature. After many years and many results of analytic regularity for partial differential equations, the only access to the technique known as $(T^p)_\phi$ has remained embedded in the research papers themselves, making it difficult for a graduate student or a mature mat... | CommonCrawl |
One of the most prominent problems of ancient mathematics was the squaring of the circle: to construct the square with the same area as a given circle.
A related problem is linearizing the circle: to find a natural transition between a given line segment of length $L$ (having constant curvature $0 = 1/\infty$) and the ... | CommonCrawl |
1) find the value of the constant c.
"for x greater or equal to 1" means $\displaystyle 1 \leq x < + \infty$.
Exactly what i thought, from this would you find the continuous function, then use x=1?
Remember the properties of a probability density function..
Yes, and since it's an improper integral care must be taken in... | CommonCrawl |
Loco Mateo is crazy for tacos, so he decides to start a catering service which will feature his signature creation: Tacos el Fuego. Because he knows his tacos are so insanely delicious, he's absolutely certain that his new business is going to be a success. So, he needs to write up a business plan to make sure he's rea... | CommonCrawl |
are equivalent for discrete time systems.
I defined controllability as being able to get from an initial state $x_1$ to any other state $x_2$, reachability to get from the origin $0$ to any other state $x_2$ and null-controllability to get from an initial state $x_1$ to the origin $0$.
I see how being able to get from ... | CommonCrawl |
Tak has $N$ cards. On the $i$-th $(1≤i≤N)$ card is written an integer $x_i$. He is selecting one or more cards from these $N$ cards, so that the average of the integers written on the selected cards is exactly $A$. In how many ways can he make his selection?
$N, A, x_i$ are integers.
200 points will be awarded for pass... | CommonCrawl |
Now, I claim that both formulas are indeed valid.
The proofs are very similar so I'll focus on the first one. What I did is assuming by contradiction that the formula isn't valid, so it has the value $t\to f$. Then, it must be that there's an $a$ which satisfies $A$ but there isn't an $x$ which satisfies $B$.
We assume... | CommonCrawl |
Let $G$ be a complete DAG: It has vertices $v_1,\ldots,v_n$, and $v_iv_j$ is an edge if and only if $i<j$. Let $w(i,j)$ be the weight of the edge $v_iv_j$. The weight has the property that $w(i,j)<w(i,j+1)$ and $w(i+1,j)<w(i,j)$.
We are given an integer $k$. We are interested in finding the minimum $\lambda$, such that... | CommonCrawl |
Lemma 23.8.7. Let $A$ be a Noetherian ring. Then $A$ is a local complete intersection if and only if $A_\mathfrak m$ is a complete intersection for every maximal ideal $\mathfrak m$ of $A$.
In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the n... | CommonCrawl |
Lemma 9.8.4. Let $K/E/F$ be a tower of field extensions.
If $\alpha \in K$ is algebraic over $F$, then $\alpha $ is algebraic over $E$.
if $K$ is algebraic over $F$, then $K$ is algebraic over $E$.
In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling ... | CommonCrawl |
If there are multiple solutions, output the one with the smallest possible number of summands.
Each test case consists of one line containing an integer $N$ ($1 \leq N \leq 10^9$).
For each test case, output a single line containing the equation in the format $N = a + (a+1) + \ldots + b$ as in the example. If there is ... | CommonCrawl |
This article will review converting a simple algorithm, such as a least common multiple (LCM) algorithm, into a VHDL description. The data path of the algorithm will be discussed in this article. In the next article, we'll discuss the control path of the algorithm.
Traditional digital design splits a given problem into... | CommonCrawl |
Herbert Heyer, Satoshi Kawakami, Tatsuya Tsurii, Satoe Yamanaka, "Hypergroups Related to a Pair of Compact Hypergroups", SIGMA, 12 (2016), 111, 17 pp.
Abstract: The purpose of the present paper is to investigate a hypergroup associated with irreducible characters of a compact hypergroup $H$ and a closed subhypergroup $... | CommonCrawl |
Structure $\left<X,B\right>$ is an $n$-dimensional Euclidean incidence space iff $B$ is ternary betweenness relation associated with $n$-dimensional Euclidean geometry. That is, Euclidean incidence space is Euclidean geometry minus the notions of congruences.
$(*)$ There is a matroid $\left<X,\mathcal S\right>$ of rank... | CommonCrawl |
I found the following method to find one's age. It is working exactly for my case. I like to understand and solve this puzzle. If this is wrong forum, my sincere apologies. Please guide me solve this.
Now you will get 3 digit number. The first one is last digit of your mobile number, last two digits are your age.
This ... | CommonCrawl |
Why use $m_k$ to approximate $f_k$ in trust region method for optimization?
In the second algorithmic strategy, known as trust region, the information gathered about $f$ is used to construct a model function $m_k$ whose behavior near the current point $x_k$ is similar to that of the actual objective function $f$.
we fi... | CommonCrawl |
I know that animals can't make poly-unsaturated fatty acids (PUFA) and so require them from dietary sources. For eg.Omega -3 and Omega 6 fatty acids.
My questions : Can animals synthesize other unsaturated fatty acids from scratch? If not, does the unsaturated fatty acids in the phospholipids of plasma membrane of anim... | CommonCrawl |
This paper studies Newtonian Sobolev-Lorentz spaces. We prove that these spaces are Banach. We also study the global p,q- capacity and the $p,q$-modulus of families of rectifiable curves. Under some additional assumptions (that is, $X$ carries a doubling measure and a weak Poincar ́e inequality), we show that when $1 \... | CommonCrawl |
The short-rate tag has no usage guidance.
What's the difference between the short rate model projection and the 3M forward curve?
A term structure has a forward curve So what is it that the short rate model is projecting exactly? Why is it needed? How are they different?
why $f(t,u) \neq E_t^Q [r(u)]$ when $r$ is rando... | CommonCrawl |
We present some elementary ideas to prove the following Sylvester–Gallai type theorems involving incidences between points and lines in the planes over the complex numbers and quaternions. 1. Let $A$ and $B$ be finite sets of at least two complex numbers each. Then there exists a line $\ell$ in the complex affine plane... | CommonCrawl |
"New Contributions to Semipositive and Minimally Semipositive Matrices" by Projesh Nath Choudhury, Rajesh M. Kannan et al.
Semipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is semipo... | CommonCrawl |
Let G be a group and K a normal subgroup in G of finite index. Then the set X of all automorphisms phi of G that fix K (meaning phi(K)=K, so not necessarily pointwise) has finite index in Aut G.
Is this even true? I am trying to work out a larger problem and this would be the final step but I am not sure this is even c... | CommonCrawl |
The '-' in 'masons-days' is not a minus sign but a dash that should be interpreted as multiplication; yes, math is a language that, like any other language, sometimes has ambiguities.
So now we only need to memorize the tables of 3, 4, 5, 6, 7, and 8, from 2 to 8.. that is 6 x 6 = 36 products, instead of 110, which is ... | CommonCrawl |
Let $\mathcal L$ be a formal language used in the field of symbolic logic.
Then the well-formed formulas of $\mathcal L$ are often referred to as logical formulas.
They are symbolic representations of statements, and often of compound statements in particular.
In mathematics, the two most universal types of logical for... | CommonCrawl |
Abstract: The group-theoretical aspects of spontaneous breaking in linear $\Sigma$ models are discussed. General conditions are formulated which must be satisfied by a multiplet of the group $G$ (compact or noncompact) for the construction on it of a $\Sigma$ model with given stability subgroup $H$ of the vacuum. It is... | CommonCrawl |
has a finite number of solutions in integers $q$ ($\|\alpha\|$ is the distance from $\alpha$ to the nearest integer).
Mahler's problem was solved affirmatively in 1964 by V.G. Sprindzhuk . He also proved similar results for complex and $p$-adic numbers, and also for power series over finite fields.
The original paper o... | CommonCrawl |
I'm having trouble trying to make a $3\times3$ magic square with magic number $12$ and I can't figure it out.
all you need to do is come up with some 9-number sequence whose average is 4. Enter the sequence, in order, into the bottom cell, the top right cell, the left cell, the top left cell, the middle cell, the botto... | CommonCrawl |
We show that for a metric space with an even number of points there is a $1$-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic version of an unoriented Kantorovich duality. The study of the duality gives a version of global calibrations for $1$-chains with coefficients ... | CommonCrawl |
Ps or Pdf files of the following papers can been sent upon request, if there exists no link for the download.
The publications are sorted by type: Book, Journal papers, Conference papers, Book chapters and Industrial patents.
You can also consult Scholar Google, Mathscinet, or Hal CNRS.
F. Bribiesca Argomedo, E. Witran... | CommonCrawl |
The area of applied harmonic analysis provides a variety of multiscale systems such as wavelets, curvelets, shearlets, or ridgelets. A distinct property of each of those systems is the fact that it sparsely approximates a particular class of functions. Some of these systems even share similar approximation properties s... | CommonCrawl |
For a while now I've been looking for a Latex editor that allows real time preview. It's much more convenient and allows for a flexible and smooth workflow. So I wanted to give it a try. What I found was an Apple App called "Latexian" and I was a bit skeptical about it at the first place because its icon (a globe) look... | CommonCrawl |
Recent progress in the Langlands programm provides a significant step towards the understanding of the arithmetic of global fields. The geometric Langlands program provides a systematic way to construct l-adic sheaves (resp. D-modules) on algebraic curves which subsumes the construction of classical sheaves, like rigid... | CommonCrawl |
Rants about programming stuff, discussions about personal projects, or whatever else I feel like posting.
A bounding box generally refers to an axis-aligned rectangular region of space used as a first, coarse step of collision detection. Every object is given a bounding box which covers all space the object could possi... | CommonCrawl |
She was there every day, hour after hour."
a mischievious damsel, whose hair was a handful"
was in love with Rap-Punzel... as in love as can be.
when the prince could scale the tower with a short little climb."
"But he's tired of waiting, what a waste of days.
He should evaluate expressions but he doesn't know the way"... | CommonCrawl |
Takashi Takenouchi, Takafumi Kanamori; 18(56):1−26, 2017.
In this paper, we focus on parameters estimation of probabilistic models in discrete space. A naive calculation of the normalization constant of the probabilistic model on discrete space is often infeasible and statistical inference based on such probabilistic m... | CommonCrawl |
The Bézier points $\mathbf b_i \in \mathbb R^d$ form the control polygon.
input Bézier points $\mathbf b_i$ for $i = 0, \dots, n$, and parameter $t \in [0,1]$.
output The point $\mathbf b_0^n$ on the curve.
Visualisation of the steps of the De Casteljau's algorithm, $t=0.5$.
Animation of the De Casteljau's algorithm fo... | CommonCrawl |
One of the most fundamental structures in abstract algebra is called a magma. A magma is a pair $(M,\bullet )$, where $M$ is a nonempty set and $\bullet $ is a binary operation on $M$. This means that $\bullet $ maps each ordered pair of elements $(x,y)$ in $M$ to an element in $M$ (in other words, $\bullet $ is a func... | CommonCrawl |
You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter) exactly $4\times$ as fast as you can row, and he will always run towards the closest bit of shore to you. If you can to... | CommonCrawl |
The number of $n \times n$ matrices whose entries are either $-1$, $0$, or $1$, whose row- and column- sums are all $1$, and such that in every row and every column the non-zero entries alternate in sign, is proved to be $$[1!4! \dots (3n-2)!] \over [n!(n+1)! \dots (2n-1)!],$$ as conjectured by Mills, Robbins, and Rums... | CommonCrawl |
The lattice of a general crystal structure is determined by giving six lattice parameters, $a, b, c, \alpha, \beta,$ and $\gamma$. The first 3 parameters are connected with the length of the 3 primitive vectors of the crystal; the last 3 are the angles between the primitive vectors. The definition of the lattice parame... | CommonCrawl |
In this system, $a,b,c,d,e,f$ are constants and the sequences $x_n,y_n,z_n$ can run forever. Let's have $z_0 = x_0 = y_0 = 0$.
Given this setup, can we imagine what the plot of $(x,y)$ will look like?
To demonstrate this I've written a small app with canvas that does exactly this. You can draw the values of $a,b,c,d,e,... | CommonCrawl |
is there some analytical explanation of why this happens?
Browse other questions tagged frequency-spectrum power-spectral-density or ask your own question.
Does convolution done via the FFT _undo_ computational gains when signal has zeros every other sample?
What is meant by *sampling* in terms of the *sampling theorem... | CommonCrawl |
$\alpha_S(M_Z)$= 0.1210 +/- 0.0007(stat.) +/- 0.0021(expt.) +/- 0.0044(had.) +/- 0.0036(theo.) and with the NNLO+NLLA calculations the combined value is $\alpha_S$= 0.1172 +/- 0.0006(stat.) +/- 0.0020(expt.) +/- 0.0035(had.) +/- 0.0030(theo.) . The stability of the NNLO and NNLO+NLLA results with respect to missing hig... | CommonCrawl |
Volume 9, Number 3 (1996), 481-498.
A one-dimensional Sobolev-type inequality supplemented by a Prüfer transformation argument is used to derive upper and lower bounds for the eigenvalues of regular, self-adjoint second-order eigenvalue problems. These inequalities are shown to have applications to counting eigenvalues... | CommonCrawl |
with $8$ moves needed to swap the red and blue knights.
What is the minimum numbers of moves to swap the knights on a $4\times4$ grid?
All credit goes to @klm123 for demonstrating a good way to visualize this in a similar puzzle.
20 half moves, or 10 move pairs.
Not the answer you're looking for? Browse other questions... | CommonCrawl |
In NFU, is there a bijection between the set of all sets and the set of all one-element sets?
How can I minimize the real part of the roots of this function involving both $x$ and $e^x$ terms?
How many rounds are required in a "Swiss tournament sorting algorithm"?
What algorithm can I use to find this ellipse inscribed... | CommonCrawl |
To compute the minor M 2,3 and the cofactor C 2,3, we find the determinant of the above matrix with row 2 and column 3 removed. , = [ − ] = [−] = (− (−)) = So the cofactor of the (2,3) entry is , = (−) + (,) = − General definition. Let A be an m × n matrix and k an integer with 0 < k ≤ m, and k ≤ n. A k × k minor of A,... | CommonCrawl |
This may seem like a rather simple question, but I haven't been able to come up with an explanation myself or find one on the Internet.
but there seems to be something missing in the equation that I've given.
Would anybody be able to help me understand the derivation?
The textbook that I'm using is Introduction to Prob... | CommonCrawl |
Abstract: The large time asymptotics of the solutions of the sine-Gordon equation which tend to zero when $x\to\infty$ and tend to the finite-gap solution of this equation when $x\to-\infty$ are investigated. It is proved that at $t\to\infty$ these solutions split into infinite series of solitons with variable phases. ... | CommonCrawl |
Koyama, Y. , R. H. Coker, J. C. Denny, B. D Lacy, K. Jabbour, P. E. Williams, and D. H. Wasserman. 2001. Role of carotid bodies in control of the neuroendocrine response to exercise. American Journal of Physiology-Endocrinology And Metabolism 281:E742–E748.
Coker, R. H. , M. G. Krishna, B. D Lacy, E. J. Allen, and D. H... | CommonCrawl |
Vaidyanathan, VV and Sastry, PS and Ramasarma, T (1993) Regulation of the activity of glyceraldehyde 3-phosphate dehydrogenase by glutathione and $H_2O_2$. In: Molecular and Cellular Biochemistry, 129 (1). pp. 57-65.
The activity lost during storage of a solution of muscle glyceraldehyde 3-phosphate dehydrogenase was r... | CommonCrawl |
I am looking for Postdoc for machine learning research.
I have moved to University of Tokyo (Apr/2017).
I am interested in Statistics and Machine Learning, especially the following research topics.
Born in Japan, Oct, 1981.
Bachelor of Engineering from Mathematical Engineering Course, Department of Mathematical Enginee... | CommonCrawl |
Bessie likes downloading games to play on her cell phone, even though she does find the small touch screen rather cumbersome to use with her large hooves.
She is particularly intrigued by the current game she is playing. The game starts with a sequence of $N$ positive integers ($2 \leq N \leq 262,144$), each in the ran... | CommonCrawl |
Efficient way to solve equal sums $x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k$ with Mathematica?
P.S. The system $S_1$ leads to an $11$th degree identity, in case one is wondering why I am interested in it.
This isn't really an answer, but it's too big for a comment.
Here's some code to brute force solve the probl... | CommonCrawl |
Ned is trying to play music using a steel ruler extending beyond the table edge. When he strikes the ruler, a twang sound is produced.
If he wants to produce a higher frequency note, then what should he do?
A pen costs an integer number of cents. There are 100 cents in a dollar.
9 of these pens cost between $11 and $12... | CommonCrawl |
Single index linear models for binary response with random coefficients have been extensively employed in many settings under various parametric specifications of the distribution of the random coefficients. Nonparametric maximum likelihood estimation (NPMLE) as proposed by Kiefer and Wolfowitz (1956) in contrast, has ... | CommonCrawl |
Mr. K. I. has a very big movie collection. He has organized his collection in a big stack. Whenever he wants to watch one of the movies, he locates the movie in this stack and removes it carefully, ensuring that the stack doesn't fall over. After he finishes watching the movie, he places it at the top of the stack.
Sin... | CommonCrawl |
For those who are familiar with machine learning literatures would probably figure out that this is what most of machine learning problems deal with. In particular, if the output space '$Y$' is a real line '$R$', we call such problems as a regression problem and this is what this article will mainly deal with.
The seve... | CommonCrawl |
Abstract. We consider Sch\"odinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if $\Delta + V$ has no spectrum outside of the interval $[-2,2]$, then it has purel... | CommonCrawl |
The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Wein... | CommonCrawl |
Abstract: The highly radiopure $\simeq$ 250 kg NaI(Tl) DAMA/LIBRA set-up is running at the Gran Sasso National Laboratory of the I.N.F.N.. In this paper the first result obtained by exploiting the model independent annual modulation signature for Dark Matter (DM) particles is presented. It refers to an exposure of 0.53... | CommonCrawl |
The question is inspired by a short passage on the LMM in Mark Joshi's book.
The LMM cannot be truly Markovian in the underlying Brownian motions due to the presence of state-dependent drifts. Nevertheless, the drifts can be approximated 'in a Markovian way' by using predictor-corrector schemes to make the rates functi... | CommonCrawl |
Is it true "If $X \subset Y$ then $\Bbb I(Y) \subset \Bbb I(X)$"(proper inclusion)?
Is it true "If $X \subset Y$ then $\Bbb I(Y) \subset \Bbb I(X)$; here I am using proper inclusion. Couldn't prove it though. Trying for long time please help. Actually I saw here "https://people.maths.bris.ac.uk/~mp12500/teaching/Lectur... | CommonCrawl |
Specify the start of the range in which to interpolate.
Specify the end of the range in which to interpolate.
Specify the value to use to interpolate between x and y.
mix performs a linear interpolation between x and y using a to weight between them. The return value is computed as $x \times (1 - a) + y \times a$.
The ... | CommonCrawl |
A somewhat neglected model in the Data Science/Machine Learning community are Multivariate Adaptive Regression Splines (MARS). Despite being less popular than Neural Networks or Trees, I find the concept of MARS pretty interesting, especially because it comes as a fully linear model and thus can preserve model interpre... | CommonCrawl |
Abstract: A theory is constructed for attractors of all finite-energy solutions of conservative one-dimensional wave equations on the whole real line. The attractor of a non-degenerate (that is, generic) equation is the set of all stationary solutions. Each finite-energy solution converges as $t\to\pm\infty$ to this at... | CommonCrawl |
[astro-ph/9912499] RC J1148+0455 identification: gravitational lens or group of galaxies ?
Title:RC J1148+0455 identification: gravitational lens or group of galaxies ?
Abstract: The structure of the radio source RC B1146+052 of the ``Cold'' catalogue is investigated by data of the MIT-GB-VLA survey at 4850 MHz. This s... | CommonCrawl |
Abstract: We complete the study of static BPS, asymptotically AdS$_4$ black holes within N=2 FI-gauged supergravity and where the scalar manifold is a homogeneous very special Kahler manifold. We find the analytic form for the general solution to the BPS equations, the horizon appears as a double root of a particular q... | CommonCrawl |
In Ron Maimon's answer (linked below), he says that we should remove the "gadgets" at the top of the editor. I disagree that we should remove all the buttons, since this is a WYSIWYG editor, however, indeed some of them can go.
So I have set this thread up to discuss exactly which buttons we don't need, etc.
Also, I ha... | CommonCrawl |
How to find sets of polynomially bounded numbers whose subset sums are different?
No common terms between polynomials: an efficient check?
How can we prove Schwartz Zippel PIT is applicable to natural polynomials?
How to handle generator polynomial in CRC if given in (x+1) (x^3+ x^2 +1) form?
Is the following problem c... | CommonCrawl |
We assume that a base transmitter station (BTS) in a code division multiple access (CDMA) mobile network is equipped with a smart antenna. Each transmitting user is tracked by a beam of fixed width centered at the user. Mobiles are assumed to apply perfect power control such that each is received with the same unit pow... | CommonCrawl |
I'm trying to understand the advantages and disadvantages of using Direct Alpha versus Excess IRR for computing excess returns over a market index for private assets.
Wikipedia references a highly informative paper that compares the Direct Alpha against PME, PME+, mPME, and KS-PME and discusses the limitations of these... | CommonCrawl |
Paper summary davidstutz Schmidt et al. theoretically and experimentally show that training adversarially robust models requires a higher sample complexity compared to regular generalization. Theoretically, they analyze two very simple families of datasets, e.g., consisting of two Gaussian distributions corresponding t... | CommonCrawl |
I have been trying the build up my intuition on finding rotational symmetries of shapes and I have been looking at the dodecahedron from the platonic solids. I am convinced that I have the correct number of rotational symmetries, but I should only be finding $60$ rotational symmetries and $120$ if we include inversion ... | CommonCrawl |
Recently there has been a lot of interest in the mathematics of the popular game Sudoku. In a typical Sudoku puzzle, a number of initial clues are given, and the solver uses strategies to fill in the remaining clues to complete the board. A well-known open problem is, "How many initial clues are necessary for the puzzl... | CommonCrawl |
I think this is going to end up being a long one 1, and it possibly won't be the easiest post to follow; mostly because I will likely end up introducing a decent number of topics I haven't talked about here before. I guess we'll see how things turn out 2.
Historically, one topic of interest to number theorists has been... | CommonCrawl |
Lemma 15.42.8. Let $A \to B$ be a flat local homomorphism of Noetherian local rings such that $\mathfrak m_ A B = \mathfrak m_ B$ and $\kappa (\mathfrak m_ A) = \kappa (\mathfrak m_ B)$. Then $A \to B$ induces an isomorphism $A^\wedge \to B^\wedge $ of completions.
In order to prevent bots from posting comments, we wou... | CommonCrawl |
The exact subject matter of the seminar will be determined by the participants and their interests.
hypothesis, bicategories, higher Picard and Brauer groups...and beyond!
Participants should have some familiarity with the theory of $\infty$-categories.
Please consult the course website: http://nullplug.org/infty-semin... | CommonCrawl |
Many decades of work culminating in Perelman's proof of Thurston's geometrisation conjecture showed that a closed, connected, orientable, prime 3-dimensional manifold \(W\) is essentially determined by its fundamental group \(\pi_1(W)\). This group consists of classes of based loops in \( W\) and its multiplication cor... | CommonCrawl |
Mishka got a six-faced dice. It has integer numbers from $$$2$$$ to $$$7$$$ written on its faces (all numbers on faces are different, so this is an almost usual dice).
Mishka wants to get exactly $$$x$$$ points by rolling his dice. The number of points is just a sum of numbers written at the topmost face of the dice fo... | CommonCrawl |
Abstract: Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and scalability. Unfortunately, this 1-norm MKL is rarely observed to out... | CommonCrawl |
In this talk based on arXiv:1602.01674, we provide evidence for universality in the low-energy expansion of tree-level string interactions. More precisely, in the $\alpha'$-expansion of tree-level scattering amplitudes, we conjecture that the leading transcendental coefficient at each order in $\alpha'$ is universal fo... | CommonCrawl |
Let $\alpha_k(\lambda)$ denote the number of $k$-hooks in a partition $\lambda$ and let $b(n,k)$ be the maximum value of $\alpha_k(\lambda)$ among partitions of $n$. Amdeberhan posed a conjecture on the generating function of $b(n,1)$. We give a proof of this conjecture. In general, we obtain a formula that can be used... | CommonCrawl |
In the first research task of this theme we will build a new ultra-stable and low noise optical resonator. We will build a new optical cavity with 30-40 cm long spacer made of ULE glass and with passive thermal shielding to improve cavity temperature stability. Cavity will have a finesse greater than 200000, short ther... | CommonCrawl |
Neutrino Factory and Muon Collider R&DNov 05 2001European, Japanese, and US Neutrino Factory designs are presented. The main R&D issues and associated R&D programs, future prospects, and the additional issues that must be addressed to produce a viable Muon Collider design, are discussed.
A cubical model of homotopy typ... | CommonCrawl |
How to dock aggregated structures comprised of "elementary" protein units like LEGO pieces?
I was wondering how to use transformations such as: rotations, translation, replications to construct possible structures using 2 types of proteins.
Assume I found a binding site of the 2 proteins using Molecular Dynamics simula... | CommonCrawl |
If $n \in \mathbb N$ and $p$ is prime number solve equation $n^4+n^2+1=p$ i can write that like this $$n^4+2n^2-n^2+1=p$$ $$(n^2+1)^2-n^2=(n^2+1-n)(n^2+1+n)=p=1 \cdot p$$ Since $n^2+1+n>1$ then $n^2+1-n=1$ so $n=0$ or $n=1$ if I put $n=0$ then $p=1$ that is not true since one is not prime number, then $n=1$ and $p=3$, ... | CommonCrawl |
We show that every isoperimetric set in $\mathbb R^N$ with density is bounded if the density is continuous and bounded by above and below. This improves the previously known boundedness results, which basically needed a Lipschitz assumption; on the other hand, the present assumption is sharp, as we show with an explici... | CommonCrawl |
Current in a circuit is driven by voltage differences. Imagine you would disconnect the point Q from ground. Then it is clear that the battery drives a current $I = 0.5$ A from "+" to "-" through the resistors, and there is a voltage drop $\Delta U = R\times I$ across each resistor in the circuit. However, in this sett... | CommonCrawl |
specified, a tab-delimited table without lines is produced.
returns its results in e().
See the Introduction in the Examples section for an introduction on using estout.
See help estimates for general information about managing estimation results.
Furthermore, see help eststo for an alternative to the estimates store c... | CommonCrawl |
The independence number of a graph is the maximum number of vertices from the vertex set of the graph such that no two vertices are adjacent. We systematically examine a collection of upper bounds for the independence number to determine graphs for which each upper bound is better than any other upper bound considered.... | CommonCrawl |
Korosensei is fast, but can he do better?
Korosensei can move at Mach 20 and takes advantage of this fact to make frequent trips around the world. Obviously, in the interest of efficiency, he often takes the opportunity to make multiple stops per trip. But what is the most efficient way for him to do so?
We can think a... | CommonCrawl |
In the beginning mathematicians only used natural numbers: $1,2,3, \ldots$. Then, negative numbers were invented to represent things like debt. For example, $+5$ means a profit of $5$ units, while $-5$ means $5$ units of debt.
Multiplying a positive number with a negative number yields another negative number: $ -3 \ti... | CommonCrawl |
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