For arbitrary w : R → [0, 1] the general form of the continuous linear functionals on the space C 0 w of all functions f continuous on the real line, lim |x|→+∞ w(x)f (x) = 0 , equipped with seminorm ||f || w := sup x∈R w(x)|f (x)| , is found. The weighted analog of the Weierstrass polynomial approximation theorem and a new version of M.G. Krein's theorem about partial fraction decomposition of...

The classical unique continuation theorem, which originates in the work of Carleman, in its simplest form is the following: Proposition: Assume that ∆u = V u in {|x| < 10}, with |u| ≤ C 0 and ||V || L ∞ ≤ M. If |u(x)| ≤ C N |x| N , for all N ≥ 0, then u ≡ 0. In order to establish this Proposition, Carleman developed a method, the " method of Carleman estimates " , which still permeates the subj...

Given complex numbers w1, . . . , wn, we define the weight w(X) of a set X of non-negative integer n-vectors as the sum of w1 1 · · ·w xn n over all vectors (x1, . . . , xn) in X. We present an algorithm, which for a set X of 0-1 vectors defined by a system of homogeneous linear equations with at most r variables per equation and at most c equations per variable, computes w(X) within a relative...

We study the difference analog of quotient differential operator from [Tarasov V., Uvarov F., Lett. Math. Phys. 110 (2020), 3375-3400, arXiv:1907.02117]. Starting with a space quasi-exponentials $W=\langle \alpha_{i}^{x}p_{ij}(x),\, i=1,\dots, n,\, j=1,\dots, n_{i}\rangle$, where $\alpha_{i}\in{\mathbb C}^{*}$ and $p_{ij}(x)$ are polynomials, we consider formal conjugate $\check{S}^{\dagger}_{W...

In an earlier work, we constructed the almost strict Morse n-category X which extends Cohen & Jones & Segal’s flow category. In this article, we define two other almost strict n-categories V and W where V is based on homomorphisms between real vector spaces and W consists of tuples of positive integers. The Morse index and the dimension of the Morse moduli spaces give rise to almost strict n-ca...

Expansions of multiple integrals w(aixi,.. .,anxn)g(xi,... ,x„)dxi ■ ■ -dxn, r°i r°n I " Ja\ J a„ where w is a function on R" which is (bk oj,)-periodic in the fcth variable, k = 1,... ,n, and g is smooth, are given in terms of negative powers of the integers o\,.. .,an. Estimates of the remainder term in the expansion are also given. Introduction. Let w be a function with integrable pth power ...

Introduction One of the best methods in the diagnosis and control of breast cancer is mammography. The importance of mammography is directly related to its value in the detection of breast cancer in the early stages, which leads to a more effective treatment. The purpose of this article was to calculate the X-ray spectrum in a mammography system with Monte Carlo codes, including MCNPX and MCNP5...

and Applied Analysis 3 W4 W̃ n, x ∇W n, x , x − pW n, x , lim |x|→∞ W̃ n, x ∞ uniformly for n ∈ Z, 1.7 and for any fixed 0 < c1 < c2 < ∞, inf n∈Z, c1≤|x|≤c2 W̃ n, x |x| > 0. 1.8 Then problem 1.1 has at least one nontrivial homoclinic solution. Remark 1.2. The function W n, x in this paper is asymptotically p-linear at infinity. The behavior of the gradient of W n, x at infinity is like that of a f...

Получены точные верхние и нижние грани для отношения $\operatorname{\mathbf E}w(\mathbf X-\mathbf v)/\operatorname{\mathbf X)$ центрированного гауссовского случайного вектора $\mathbf X$ в R^n$, а также оценки скорости изменения X-t\mathbf v)$ по отношению к $t$, где $w\colon\mathbf R^n\to[0,\infty)$ - произвольная одновершинная функция v$ произвольный вектор R^n$. В качестве следствия таких ре...

this study describes length-weight relationships of five species (platycephalus indicus, pseudorhombus elevates, plicofollis tenuispinis, grammoplites suppositus, pomadays stridens) collected from persian gulf (khuzestan province, iran) during december 2009 to november 2011. a total of 2065 specimen were examined for this study. the relationship between weight and total length were estimated: w...