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Volume 9, Number 4 (1996), 761-778.
We are concerned with the asymptotic behavior of global solutions for a class of reaction-diffusion systems under homogeneous Neumann boundary conditions. An example of the system which we consider in this paper is what we call a diffusive epidemic model. After we show that every glo... | CommonCrawl |
A monoid is an algebraic structure with a single associative binary operation and an identity element.
Is (topology, union, empty set) with basis as generator a monoid?
Set - $\tau $ Generator - basis of $\tau $ Operator - $\cup $ Unit - empty set Is it a monoid?
What is the Krull dimension of the Burnside ring of $\ma... | CommonCrawl |
The paper is about squeezing the number of parameters in a convolutional neural network. The number of parameters in a convolutional layer is given by (number of input channels)$\times$(number of filters)$\times$(size of filter$\times$size of filter).
The paper proposes 2 strategies: (i) replace 3x3 filters with 1x1 fi... | CommonCrawl |
The following theorem tells us that the union of every finite collection of Lebesgue measurable sets is also Lebesgue measurable.
Theorem 1: The union of a finite collection of Lebesgue measurable sets is Lebesgue measurable.
So $(E_1 \cup E_2)$ is Lebesgue measurable.
Corollary 2: The set $\mathcal M$ of Lebesgue meas... | CommonCrawl |
Two people have to spend exactly 15 consecutive minutes in a bar on a given day, between 12:00 and 13:00. Assuming uniform arrival times, what is the probability they will meet?
but my methods felt a little ad hoc to me, and I would like to learn to make it more formal.
Also I'm curious whether people think the problem... | CommonCrawl |
Suppose that each person in a group of n people votes for exactly two people from a set of candidates to fill two positions on a committee. The top two finishers both win positions as long as each receives more than n/2 votes.
Describe a divide-and-conquer algorithm that determines the top two candidates and whether th... | CommonCrawl |
For spiked population model, we investigate the large dimension $N$ and large sample size $M$ asymptotic behavior of the Support Vector Machine (SVM) classification method in the limit of $N,M\rightarrow\infty$ at fixed $\alpha=M/N$. We focus on the generalization performance by analytically evaluating the angle betwee... | CommonCrawl |
Peptide Grafting to Aminated Cellulose and Related Aminated Condensation Polymers.
Natural and synthetic macroinitiators with primary amino substituents have been synthesized by one of the following techniques: (1) cyanoethylation of cellulose followed by diborane reduction to produce O-(3-aminopropyl)cellulose, (1), (... | CommonCrawl |
Abstract: In the work we consider a topological module $\mathcal P(a;b)$ of entire functions, which is the isomorphic image of the Schwarz space of distributions with compact supports in a finite or infinite interval $(a;b)\subset\mathbb R$ under the Fourier–Laplace transform. We prove that each weakly localizable modu... | CommonCrawl |
Several mechanical systems are modeled by the static momentum balance for the displacement $u$ coupled with a rate-independent flow rule for some internal variable $z$. We consider a class of abstract systems of ODEs which have the same structure, albeit in a finite-dimensional setting, and regularize both the static e... | CommonCrawl |
I will report on new joint work with Leandro Arosio (University of Rome, Tor Vergata). Complex manifolds can be thought of as laid out across a spectrum characterised by rigidity at one end and flexibility at the other. On the rigid side, Kobayashi-hyperbolic manifolds have at most a finite-dimensional group of symmetr... | CommonCrawl |
Starting at (0,0) top left, the objective is to find a dijikistra path to the bottom right.
We must go through each color exactly once, and once we go outside a color, we can't go back to the same one.
As per dikisjtra algorithm, we update the distance at once node if d[current] + weight(this_node, next_node) < d[next_... | CommonCrawl |
Suppose that $f(\theta)=g(\theta)/c$, where $g(\theta)$ is known but we cannot compute the integral $c=\int g(\theta)d\theta$. Given a sample $\theta_1,\ldots,\theta\sim f$, our interest is to estimate $c$?
is useless, which doesn't depend on the data.
This treatment acted as if we had a family of densities $f(\theta\m... | CommonCrawl |
Mariana P Torrente, Edward Chuang, Megan M Noll, Meredith E Jackrel, Michelle S Go and James Shorter.
Mechanistic Insights into Hsp104 Potentiation.. The Journal of biological chemistry 291(10):5101–15, March 2016.
Abstract Potentiated variants of Hsp104, a protein disaggregase from yeast, can dissolve protein aggregat... | CommonCrawl |
Abstract: We investigate dynamo action in global compressible solar-like convective dynamos in the framework of mean-field theory. We simulate a solar-type star in a wedge-shaped spherical shell, where the interplay between convection and rotation self-consistently drives a large-scale dynamo. To analyze the dynamo mec... | CommonCrawl |
Abstract: We consider the problem of morphing between two planar drawings of the same triangulated graph, maintaining straight-line planarity. A paper in SODA 2013 gave a morph that consists of $O(n^2)$ steps where each step is a linear morph that moves each of the $n$ vertices in a straight line at uniform speed. Howe... | CommonCrawl |
Deep Neural Networks have achieved extraordinary results on image classification tasks, but have been shown to be vulnerable to attacks with carefully crafted perturbations of the input data. Although most attacks usually change values of many image's pixels, it has been shown that deep networks are also vulnerable to ... | CommonCrawl |
Bandaru, Narasimha Murthy and Sampath, S and Jayaraman, Narayanaswamy (2005) Synthesis and Langmuir Studies of Bivalent and Monovalent $\alpha$-D-Mannopyranosides with Lectin Con A. In: Langmuir, 21 (21). pp. 9591-9596.
Highly avid interaction between carbohydrate ligands and lectin receptors nominally requires the lig... | CommonCrawl |
Cobalt stabilized gamma-chloroalkynones and alkynoates as gamma-carbonyl cation synthons.
$\gamma$-Cationic-$\alpha,\beta$-unsaturated carbonyl synthons have been prepared via hexacarbonyldicobalt complexed $\gamma$-chloroalkynoates and alkynones (100). Treatment of 100 with silver salts in the presence of silyl enol e... | CommonCrawl |
How does the topology of the graphs' Riemann surface relate to its knot representation?
Looking at the orientation of the edges around the vertices, it is obvious that left and right are oriented opposite.
where I stuck to the convention that I flipped every fat graph edge in the same direction. The resulting knot is a... | CommonCrawl |
While one can imagine, that a 3D surface could exist, that realizes all pairs of principal curvatures, because the set of all pairs of principal curvatures is, losely speaking, also 2D, it is counterintuitive that also a 3D curve could exists, that realizes all pairs of curvature $\kappa(s)$ and torsion $\tau(s)$ for $... | CommonCrawl |
Abstract: MDS matrices are important building blocks providing diffusion functionality for the design of many symmetric-key primitives. In recent years, continuous efforts are made on the construction of MDS matrices with small area footprints in the context of lightweight cryptography. Just recently, Duval and Leurent... | CommonCrawl |
Here is a interesting picture with two arrangements of four shapes.
How can they make a different area with the same shapes?
This is a famous physical puzzle that can be tied to the fibonacci series.
To answer the question as posed, the issue is that the two slopes are different ($\frac25$ vs $\frac38$). Note that all ... | CommonCrawl |
After applying the Goertzel algorithm, there will be 512 power spectrum values at $k=1,2,\ldots,512$. Looking at the results, it appears that in the upper half of the scale ($257 \leq k \leq 512$), the real (vs. imag) power spikes for frequencies 1/260 and 1/333 are negative. In addition, in the lower half of the range... | CommonCrawl |
I'm trying to implement metropolis light transport based on this paper, and I have the basic thing working. I run the algorithm multiple times with different starting points, add the results for each starting point together and multiply them by a scaling factor to approximate the real image.
In the resulting image, the... | CommonCrawl |
Hi, I am not sure on how to do questions 5.28 and 5.29, and I do not know how to finish 3.27 after putting the 6 red balls in place. Thanks!
For 5.28 try using complementary counting (proceed similar to example 5.8). To count how many ways are there to sum to $200$ with repeated digits consider cases: all numbers repea... | CommonCrawl |
As volatility goes to infinity, the delta of a call option goes to 1. The delta approximates the probability that the option expires in the money. So it seems that the probability of expiring in the money is very close to 1.
However, the price of the put option approaches the constant function at the strike price. This... | CommonCrawl |
We have a $5\times 5$ square table and $n$ different colours. We cut out $2\times 2$ squares from all vertex and remains $9$ unit squares. We will paint $9$ squares with $n$ colours. Some squares can be same colour. If the rotatings with respect to center of the table or the reftections of hortizonal symmetry axis, ver... | CommonCrawl |
Abstract: Bayesian inference is the workhorse of gravitational-wave astronomy, for example, determining the mass and spins of merging black holes, revealing the neutron star equation of state, and unveiling the population properties of compact binaries. The science enabled by these inferences comes with a computational... | CommonCrawl |
Previously, we saw how a regression line can help us describe our relationship between an input variable like a movie budget and an output variable like the expected revenue from a movie with that budget. Let's take a look at that line again.
We also showed how we can describe a line with the formula $y = mx + b $, whe... | CommonCrawl |
Just as circumference of circle will remain $\pi$ for unit diameter, no matter what standard unit we take, are the speeds of light and sound irrational or rational in nature ?
I'm talking about theoretical speeds and not empirical, which of course are rational numbers.
"Rational" and "irrational" are properties of numb... | CommonCrawl |
Abstract: These lecture notes form an expanded account of a course given at the Summer School on Topology and Field Theories held at the Center for Mathematics at the University of Notre Dame, Indiana during the Summer of 2012. A similar lecture series was given in Hamburg in January 2013. The lecture notes are divided... | CommonCrawl |
Abstract: The GT200 is a device that has been extensively used by the Mexican armed forces to remotely detect and identify substances such as drugs and explosives. A double blind experiment has been performed to test its effectivity. In seventeen out of twenty attempts, the GT200 failed in the hands of certified operat... | CommonCrawl |
Why did the cow cross the road? Well, one reason is that Farmer John's farm simply has a lot of roads, making it impossible for his cows to travel around without crossing many of them.
FJ's farm is arranged as an $N \times N$ square grid of fields ($3 \leq N \leq 100$), with a set of $N-1$ north-south roads and $N-1$ e... | CommonCrawl |
We give necessary and sufficient conditions on a presentable $\infty$-category $C$ so that families of objects of $C$ form an $\infty$-topos. In particular, we prove a conjecture of Joyal that this is the case whenever $C$ is stable.
Theory and Applications of Categories, Vol. 34, 2019, No. 9, pp 243-248. | CommonCrawl |
In the context of geometric quantisation, one starts with the data of a symplectic manifold together with a pre-quantum line bundle, and obtains a quantum Hilbert space by means of the auxiliary structure of a polarisation, i.e. typically a Lagrangian foliation or a Kähler structure. One common and widely studied probl... | CommonCrawl |
The tip calculator can be enhanced by asking the user the the meal cost and desired tip using input from the keyboard. You might want to review the input function from an earlier lesson. Here's the base code for doing the tip calculator with some interaction from the user (remember that $tip=per/100\times meal$ given t... | CommonCrawl |
Abstract: The Higgs field mass term, being superrenomalizable, has a unique status within the standard model. Through the opening it affords, $SU(3) \times SU(2) \times U(1)$ singlet fields can have renormalizable couplings to standard model fields. We present examples that are neither grotesque nor unnatural. A possib... | CommonCrawl |
The multiplicative identity property holds that $a\times1=a$, for some real number $a$. In other words, the property holds that the product of 1 and any real number $a$ will be equal to $a$. In this example, we can set $a\times 1=7\times 1$. Therefore, the other side of the equation will be $a=7$. | CommonCrawl |
This post is an overview of different optimization algorithms for neural networks.
In this post, we focus on two mainstreams of one-stage object detection methods: YOLO family and SSD family. Compared to two-stage methods (like R-CNN series), those models skip the region proposal stage and directly extract detection re... | CommonCrawl |
What happens when you cut a biconvex lens in half?
Specifically, does the focal length change? How can this be rationalized?
It might help to think about the symmetry of a sliced biconvex lens.
If the biconvex lens can focus light from point F1 to F2, both distance $f$ from the lens, then when you cut the lens in half,... | CommonCrawl |
Farmer John's $N$ cows, conveniently numbered $1 \ldots N$ ($2 \leq N \leq 10^5$), have a complex social structure revolving around "moo networks" --- smaller groups of cows that communicate within their group but not with other groups.
Each cow is situated at a distinct $(x,y)$ location on the 2D map of the farm, and ... | CommonCrawl |
Abstract. We consider a model of a leaky quantum wire with the Hamiltonian $-\Delta -\alpha \delta(x-\Gamma)$ in $L^2(\R^2)$, where $\Gamma$ is a compact deformation of a straight line. The existence of wave operators is proven and the S-matrix is found for the negative part of the spectrum. Moreover, we conjecture tha... | CommonCrawl |
Abstract. We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an $l \times l$ box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length $l$ in the boundary is bounde... | CommonCrawl |
Book — xxii, 300 pages : illustrations, maps ; 23 cm.
Chapter 18 : Local Adaptation to Climate Change: What Comes Next?
Don Albrecht and Paul Lachapelle.
The concept of community, in all its diverse definitions and manifestations, provides a unique approach to learn more about how groups of individuals and organization... | CommonCrawl |
In this paper, as elastic-plastic fracture toughness test under mixed mode loading was proposed using a single edge-cracked specimen subjected to bending moment(M), shearing force(F), and twisting moment(T). The J-integral of a crack in the specimen is expressed in the form J=$J_I$+ $J_II$$J_III$, where $J_I$, $J_II$ a... | CommonCrawl |
I've been using Google Earth Engine recently to scale up my remote sensing analyses, particularly by leveraging the full Landsat archive available on Google's servers. I've followed Earth Engine's development for years, and published results from the platform, but, before now, never had a compelling reason to use it. N... | CommonCrawl |
During germband retraction in the early embryonic development of fruit fly embryos, the epithelial cells of the amnioserosa (AS) undergo a dramatic change in cell shape. The average cell aspect ratio reduces from $\alpha $ $\sim $10 to $\sim $1 within three hours. We performed laser hole-drilling and confocal microscop... | CommonCrawl |
The parameters $a,b,c,d,e,f,g,h$ are known and $x_1,x_2,x_3,\dot x_1,\dot x_2,\dot x_3$ are known for $t = 0$ and $u$ are known $\forall t$. Also $u$ is constant $\forall t$.
So is there a way to to find $x_1,x_2,x_3$ by using linear algebra? I just got started with Armadillo and C++, then I realize that Armadillo does... | CommonCrawl |
We have been in the process of developing the ARICH detector for identifying charged $\pi $ and $K$ mesons in a super-B factory experiment (Belle II) to be performed at the High Energy Accelerator Research Organization (KEK), Japan. The ARICH detector is a ring-imaging Cherenkov counter that uses silica aerogel as a ra... | CommonCrawl |
Abstract: We study the simple hypothesis testing problem for the drift coefficient for stochastic fractional heat equation driven by additive noise. We introduce the notion of asymptotically the most powerful test, and find explicit forms of such tests in two asymptotic regimes: large time asymptotics, and increasing n... | CommonCrawl |
Implementation of <a href = "https://doi.org/10.1016/S0166-218X(96)00010-8"> Parberry's algorithm</a> for <a href = "https://en.wikipedia.org/wiki/Knight%27s_tour">closed knight's tour problem</a>. This algorithm was firstly introduced in "Discrete Applied Mathematics" Volume 73, Issue 3, 21 March 1997, Pages 251-260. ... | CommonCrawl |
This is the exercise 2.7.6 of the book Understanding analysis of Abbott, I want a check of my proof and if is needed additional information to complete it.
Your counter-example in the second part is good.
Not the answer you're looking for? Browse other questions tagged real-analysis sequences-and-series proof-verificat... | CommonCrawl |
(1) The class wi(ξ) ∈ Hi(B; \(\mathbb Z\)2), i ∈ \(\mathbb N\), with w0(ξ) = 1 and wi(ξ) = 0, for all i > n.
(2) (Naturality) If f : B → B' is covered by a map ξ → ξ', then wi(ξ) = f *wi(ξ').
wk(E ⊕ F) = ∑i=1k wi(E) ∪ wk – i(F) , or w(E ⊕ F) = w(E) ∪ w(F) .
(4) (They are not all trivial) The class w1(γ11) ≠ 0, where γ1... | CommonCrawl |
The tags on convexity are convex-geometry ($\times$560), convex-analysis ($\times$ 266), convexity ($\times$ 420). Here the number is the current (2019/02/23) number of uses and I ignore some more specific tags whose meaning is quite well-identified such as convex-polytopes or convex-optimization.
The tag convex-geomet... | CommonCrawl |
the J+K and by 90 days in the L+M bands. The IR echoes are sharp, while the H$\alpha$ echo is smeared. This together favours a bowl shaped toroidal geometry where the dust sublimation radius is defined by a bowl surface, which is virtually aligned with a single iso-delay surface, thus leading to the sharp IR echoes. Th... | CommonCrawl |
Abstract: The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms of interacting bosons (called spin waves or magnons) as an expansion in the inverse spin size. We calculate the first order interaction correction to the free energy, as an upper bound in the limit where the spin size $S \to \infty$ and... | CommonCrawl |
In another paper (Butterfield 2011), one of us argued that emergence and reduction are compatible, and presented four examples illustrating both. The main purpose of this paper is to develop this position for the example of phase transitions. We take it that emergence involves behaviour that is novel compared with what... | CommonCrawl |
I have heard of the puzzle with 100 or 10 dwarves wearing a hat of a color, either red or blue, and standing in a straight line, and having to guess the color of their own hat - it's quite easy.
The solution to save all dwarves or all dwarves minus the first one is fairly simple and relies on the fact that the number o... | CommonCrawl |
The angle between two circles at the point of intersection is the angle between the tangents to the circles at that point contained in the overlapping area or lune. Prove that, for any two circles, the angles at both points of intersection are equal.
Three circles intersect at the point $D$ and, in pairs, at the points... | CommonCrawl |
Sze-Bi Hsu, Hal L. Smith, Xiaoqiang Zhao. Special issue dedicated to the memory of Paul Waltman. Discrete & Continuous Dynamical Systems - B, 2016, 21(2): i-ii. doi: 10.3934\/dcdsb.2016.21.2i.
Ebraheem O. Alzahrani, Yang Kuang. Nutrient limitations as an explanation of Gompertzian tumor growth. Discrete & Continuous Dy... | CommonCrawl |
Abstract: Homotopy Type Theory may be seen as an internal language for the $\infty$-category of weak $\infty$-groupoids which in particular models the univalence axiom. Voevodsky proposes this language for weak $\infty$-groupoids as a new foundation for mathematics called the Univalent Foundations of Mathematics. It in... | CommonCrawl |
Y. Fu and N. C. Turgay Complete classification of biconservative hypersurfaces with diagonalizable shape operator in Minkowski 4-space (submitted).
N. C. Turgay Some classifications of Lorentzian surfaces with finite type Gauss map in the Minkowski 4-space (submitted).
E. Ö. Canfes, N. C. Turgay On the Gauss map of min... | CommonCrawl |
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-th... | CommonCrawl |
Exotic, neutron-rich proton-induced spallation products of 232Th and 238U obtained from the PS Booster ISOLDE facility have been investigated by $\gamma$-$\gamma$, $\alpha$-$\gamma$ coincidence and spectrum-multiscaling measurements. A new method for the reduction of isobaric contamination enabled to study the unknown ... | CommonCrawl |
This question is about estimating cut-off scores on a multi-dimensional screening questionnaire to predict a binary endpoint, in the presence of correlated scales.
I was asked about the interest of controlling for associated subscores when devising cut-off scores on each dimension of a measurement scale (personality tr... | CommonCrawl |
The mesophase structures of three novel mesomorphic porphyrin derivatives were examined using polarized optical microscopy and microfocus synchrotron X-ray diffraction at various temperatures using a beam with a 14 $\mu $m$\times $14$\mu $m cross-section at the bending magnet beamline of Sector 20 at the Advanced Photo... | CommonCrawl |
Abstract: Using the current precision electroweak data, we look for the minimal particle content which is necessary to add to the standard model in order to have a complete unification of gauge couplings and gravity at the weakly coupled heterotic string scale. We find that the addition of a vector-like fermion at an i... | CommonCrawl |
We present a new fast dynamo model for galactic magnetic fields, which is based on the Parker-shearing instability and magnetic reconnection, in the spirit of the model proposed by Parker (1992). We introduce a new scenario of flux tube interactions and estimate the dynamo transport coefficient basing on simple geometr... | CommonCrawl |
I understand that there are several characteristics of curly hair which differ from straight hair (such as an asymmetrical distribution of disulphide bonds in curly hair), but really am struggling to understand the root cause of inherent curl on the macroscopic level.
The most relevant part of the hair for our discussi... | CommonCrawl |
We know that $5\times~2=10$, but what about $-5\times~-2$? Or $5\times~-2$?
To learn how to multiply positive and negative numbers, we will make a table and look for patterns. We will also begin with simple problems that we definitely know the answer to. Starting with answers we know, we will follow the pattern to disc... | CommonCrawl |
Abstract: The paper is devoted to a certain class of doubly nonlinear higher-order anisotropic parabolic equations. Using Galerkin approximations it is proved that the first mixed problem with homogeneous Dirichlet boundary condition has a strong solution in the cylinder $D=(0,\infty)\times\Omega$, where $\Omega\subset... | CommonCrawl |
Just like equations, inequality problems can require multiple steps to calculate the answer. The steps to solve multi-step inequality problems start out the same as the steps to solve multi-step equations.
First, if parentheses are used in the problem, simplify those terms. Use the Distributive Property if needed. Next... | CommonCrawl |
Abstract: The wandering subspace problem for an analytic norm-increasing $m$-isometry $T$ on a Hilbert space $\mathcal H$ asks whether every $T$-invariant subspace of $\mathcal H$ can be generated by a wandering subspace. An affirmative solution to this problem for $m=1$ is ascribed to Beurling-Lax-Halmos, while that f... | CommonCrawl |
We have received many questions over the years about the meaning of multiplication. When we multiply \(2\times 3\), what are we really doing? This can confuse not only students and their parents, but also teachers. The next couple posts will deal with various aspects of this question.
Is the multiplier on the left or o... | CommonCrawl |
We study the convergence of volume-normalized Betti numbers in Benjamini-Schramm convergent sequences of non-positively curved manifolds with finite volume. In particular, we show that if $X$ is an irreducible symmetric space of noncompact type, $X \neq \mathbb H^3$, and $(M_n)$ is any Benjamini-Schramm convergent sequ... | CommonCrawl |
I'm doing some analysis on log returns and I notice that returns can exceed 100%. For example, if a security's close price \$1 today and \$10 yesterday, the log return is $ln(1) - ln(10) = -230\%$! Under arithmetic computation, returns for a long position cannot exceed 100% (i.e. the initial investment). So how would i... | CommonCrawl |
I debated whether to put this in SO or Mathematics but the problem I suspect is more a mathematical question rather than a programming one.
# consider x: same deal..
The reason it fails is due to the line search not returning a stepsize $\alpha$ through Wolfe condition search.
But I believe that a stepsize should exist... | CommonCrawl |
Algebras up to homotopy, or homotopy algebras, such as $A_\infty$, $C_\infty$, $E_\infty$ and $L_\infty$, play an increasingly important role in many areas of mathematics and physics, like topology, mathematical physics, and deformation theory. Let us mention a few examples of interest. Homotopy Lie algebras, also know... | CommonCrawl |
Format: MarkdownItexadded _[references on geometric BRST quantization](http://ncatlab.org/nlab/show/geometric+quantization#ReferencesBRST)_.
added references on geometric BRST quantization.
Format: MarkdownItexHey, I looked into your transparancies given at cafe. It is too hi level for my understanding yet, and certain... | CommonCrawl |
this is my first asking question here... forgive me if my question is not clear enough.
This is analogous to comparing coefficients of two parametric models (as in here and here). In parametric models, "test if two models behave in similar way" can be defined as test that coefficients of the models are statistically in... | CommonCrawl |
Abstract: Two triangle meshes are conformally equivalent if for any pair of incident triangles the absolute values of the corresponding cross-ratios of the four vertices agree. Such a pair can be considered as preimage and image of a discrete conformal map. In this article we study discrete conformal maps which are def... | CommonCrawl |
My solution: if $|x-1|=x-1$, then $x-1 \ge 0$, hence $x \ge 1$. For $x \ge 1$ your equations reads as follows: $x-1=x-1$.
Your answer is right, apart from the square bracket pointed out in @ElevenEleven's comment ($\infty$ can't be the upper end of a closed interval).
which gives you the answer without needing to consi... | CommonCrawl |
You would like to write a list of positive integers $1,2,3,\ldots$ using your computer. However, you can press each key $0$–$9$ at most $n$ times during the process.
What is the last number you can write?
The only input line contains the value of $n$.
Print the last number you can write.
Explanation: You can write the ... | CommonCrawl |
At some point you might come upon some operation that you wish it existed in Tensorflow or PyTorch, but no GPU implementation is available. In addition it might even be something that is easily parallelizable on GPU. So why not write your own CUDA kernel and integrate it in your main program? Let us start with the CUDA... | CommonCrawl |
Abstract: Subway shuffle is an addicting puzzle game created by Bob Hearn. It is played on a graph with colored edges that represent subway lines; colored tokens that represent subway cars are placed on the nodes of the graph. A token can be moved from its current node to an empty one, but only if the two nodes are con... | CommonCrawl |
Abstract: We study the full stable pair theory --- with descendents --- of the Calabi-Yau 3-fold $X=K_S$, where $S$ is a surface with a smooth canonical divisor $C$.
By both $\mathbb C^*$-localisation and cosection localisation we reduce to stable pairs supported on thickenings of $C$ indexed by partitions. We show tha... | CommonCrawl |
The suggestion that a number/sequence that does not terminate is the same as (in fact is) a number/sequence that terminates is very obviously untrue in general however you list them unless you have a proof to the contrary.
Zylo's process has no irrational numbers in it. It has few of the rationals in fact because every... | CommonCrawl |
Abstract: We model the Lights Out game on general simple graphs in the framework of linear algebra over the field $\mathbb F_2$. Based upon a version of the Fredholm alternative, we introduce a separating invariant of the game, i.e., an initial state can be transformed into a final state if and only if the invariant of... | CommonCrawl |
Abstract: We investigate the magnetic susceptibility $\chi(T)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic coupling as a function of their spatial decay exponent $\alpha$ and cutoff length $\xi$. The calculations are based on the strong disorder renormalization method which is u... | CommonCrawl |
Is M-theory just a M-yth?
Type I' String theory as M-theory compactified on a line segment?
I was considering the S-dual of the Type I' String theory (the solitonic Type I string theory).
That is the same as the S-dual of the T-Dual of Type I String theory. Then, that means both length scales and coupling constant are ... | CommonCrawl |
We consider partially observable discrete-time risk-sensitive control problems with path-dependent dynamics and costs. Using information state processes on past state trajectories, we reduce the problem to a completely observable stochastic control on time-varying infinite-dimensional state spaces. By the method of dyn... | CommonCrawl |
Abstract: This article presents an efficient hierarchical clustering algorithm that solves the problem of core community detection. It is a variant of the standard community detection problem in which we are particularly interested in the connected core of communities. To provide a solution to this problem, we question... | CommonCrawl |
How many distinct ways can a cube have $1$ green face, $2$ blue faces and $3$ red faces?
Note: Two ways are only distinct if one cube can't be rotated to look like the other.
Put the green anywhere. Now, consider all the ways to put the blue: 1. One opposite the green and the other anywhere else. 2. Two blue adjacent t... | CommonCrawl |
Abstract: The Korteweg–de Vries equation with a source given as a Fourier integral over eigenfunctions of the so-called generating operator is considered. It is shown that depending on the choice of a basis of eigenfunctions we have the following three possibilities: 1) evolution equations for the scattering data are n... | CommonCrawl |
Title: A Family of Godunov-type Solvers for the Pressureless Gas Dynamics and Related Models.
One of the fundamental results of Linear Algebra is the Cyclic Decomposition Theorem. Let $A:X o X$ be a linear operator on a finite dimensional vector space $X$ over a field $F$. The theorem states that $X$ is a direct sum of... | CommonCrawl |
Dawson, Clint. "Error Estimates for Godunov Mixed Methods for Nonlinear Parabolic Equations." (1988) https://hdl.handle.net/1911/101642.
Many computational fluids problems are described by nonlinear parabolic partial differential equations. These equations generally involve advection (transport) and a small diffusion t... | CommonCrawl |
Abstract: We show that Khovanov homology and Hochschild homology theories share common structure. In fact they overlap: Khovanov homology of a $(2,n)$-torus link can be interpreted as a Hochschild homology of the algebra underlining the Khovanov homology. In the classical case of Khovanov homology we prove the concrete... | CommonCrawl |
After numerous unfortunate freak fatalities and the lawsuits, settlements, protests, and boycotts that naturally followed, the beleaguered executives at ACME Clock Manufacturers have decided they need to finally fix their disastrous quality control issues. It has been known for years that the digital clocks they manufa... | CommonCrawl |
Consider a paging system with a page table stored in memory where memory reference takes 200 nanoseconds and all pages are in memory. What is the effective memory reference time if the hit ratio for the associative registers is 70%, the hitratio for memory is 20%, and 10% of the time we must go out to the disk to load ... | CommonCrawl |
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