Transformation Operators in the Problems of Controllability for the Degenerate Wave Equation with Variable Coefficients

Ukrainian Mathematical Journal - We study a control system $$ {w}_{tt}=\frac{1}{\rho }{\left(k{w}_x\right)}_x+\gamma w,w\left(0,t\right)=u(t),x\in \left(0,l\right),t\in \left(0,T\right), $$ in...     

MINIMAL SUBMANIFOLDS IN A RIEMANNIAN MANIFOLD OF QUASI CONSTANT CURVATURE

A Riemannian manifold V~m which admits isometric imbedding into two spaces V~(m+p)ofdifferent constant curvatures is called a manifold of quasi constant curvature.TheRiemannian curvature of V~m is expressible in the formand conversely.In this paper it is proved that if M~n is any compact minimal submanifoldwithout boundary in a Riemannian manifold V~(n+p)of quasi constant curvature,then∫_(M~u)(2-1/p)σ~2-[na+1/2(b-丨b丨)(n+1)]σ+n(n-1)b~2*丨≥0,where σ is the square of the norm of the second fundamental form of M~n When V~(n+p)is amanifold of constant curvature,b=0,the above inequality reduces to that of Simons.     

On p-adic valuations of certain m colored p-ary partition functions

The Ramanujan Journal - Let $$k\in \mathbb {N}_{\ge 2}$$ and for given $$m\in \mathbb {Z}{\setminus }\{0\}$$ consider the sequence $$(S_{k,m}(n))_{n\in \mathbb {N}}$$ defined by the power series...     

Homogenization of Nonstationary Maxwell System with Constant Magnetic Permeability

Functional Analysis and Its Applications - We study a nonstationary Maxwell system in $$\mathbb{R}^3$$ with dielectric permittivity $$\eta(\varepsilon^{-1}{\mathbf x})$$ and magnetic permeability...     

Note on the number of zeros of $$\zeta ^{(k)}(s)$$ ζ ( k ) ( s )

The Ramanujan Journal - Assuming the Riemann hypothesis, we prove that $$\begin{aligned} N_k(T) = \frac{T}{2\pi }\log \frac{T}{4\pi e} + O_k\bigg (\frac{\log T}{\log \log T}\bigg ), \end{aligned}$$...     

On the rate of convergence in the global central limit theorem for random sums of uniformly strong mixing random variables

Lithuanian Mathematical Journal - We present upper bounds of the integral $$ {\int}_{-\infty}^{\infty }{\left|x\right|}^l\left|\mathrm{P}\left\{{Z}_N0\left({S}_N{X}_1+\dots +{X}_N\right) $$ of...     

Local Marchenko–Pastur Law for Sparse Rectangular Random Matrices

Doklady Mathematics - We consider sparse sample covariance matrices with sparsity probability $${{p}_{n}} \geqslant {{c}_{0}}{{\log }^{{\frac{2}{\varkappa }}}}n{\text{/}}n$$ with $$\varkappa...     

An improved bound on the optimal paper Moebius band

Geometriae Dedicata - We show that a smooth embedded paper Moebius band must have aspect ratio at least $$\begin{aligned}\lambda _1= \frac{2 \sqrt{4-2 \sqrt{3}}+4}{\root 4 \of {3} \sqrt{2}+2...     

Asymptotics of Nahm sums at roots of unity

The Ramanujan Journal - We construct bases of the space of harmonic weak Maass forms of weight $$\kappa \in \frac{1}{2}{\mathbb {Z}}$$ . Using these bases, we obtain a Shintani lift from a positive...     

An asymptotic series for an integral

The Ramanujan Journal - Let $$f(z)=\sum _{n=0}^{\infty }a_{n}{\mathbf {e}}(nz),g(z)=\sum _{n=0}^{\infty }b_{n}{\mathbf {e}}(nz)\ ({\mathbf {e}}(z)=e^{2\pi \sqrt{-1}z})$$ be holomorphic modular...     

Non-simple blow-up solutions for the Neumann two-dimensional sinh-Gordon equation

For the Neumann sinh-Gordon equation on the unit ball

Boundedness of partial difference transforms for heat semigroups generated by discrete Laplacian

Semigroup Forum - We analyze the convergence of the following type of series $$\begin{aligned} T_N f(n)=\sum _{j=N_1}^{N_2} v_j\Big (e^{a_{j+1}{\varDelta }_d} f(n)-e^{a_{j}{\varDelta }_d} f(n)\Big...     

On the Range of the Aluthge Transform

Let be the algebra of all bounded linear operators on a complex separable Hilbert space For an operator let be the Aluthge transform of T and we define for all where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range of Δ. We prove that R(Δ) is neither closed nor dense in However R(Δ) is strongly dense if is infinite dimensional. An erratum to this article is available at .     

On the Fourier-Sine and Kontorovich–Lebedev Generalized Convolution Transforms and Their Applications

Ukrainian Mathematical Journal - We study generalized convolutions for the Fourier sine and Kontorovich–Lebedev transforms $$ \left(h\underset{F_s,K}{\ast }f\right)(x) $$ in a two-parameter...     

\mathcal{P}\mathcal{A}{\text{-isomorphisms}} of inverse semigroups

A partial automorphism of a semigroup S is any isomorphism between its subsemigroups, and the set all partial automorphisms of S with respect to composition is an inverse monoid called the partial automorphism monoid of S. Two semigroups are said to be if their partial automorphism monoids are isomorphic. A class of semigroups is called if it contains every semigroup to some semigroup from Although the class of all inverse semigroups is not we prove that the class of inverse semigroups, in which no maximal isolated subgroup is a direct product of an involution-free periodic group and the two-element cyclic group, is It follows that the class of all combinatorial inverse semigroups (those with no nontrivial subgroups) is A semigroup is called if it is isomorphic or antiisomorphic to any semigroup that is to it. We show that combinatorial inverse semigroups which are either shortly connected [5] or quasi-archimedean [10] are To Ralph McKenzieReceived April 15, 2004; accepted in final form October 7, 2004.     

The Terwilliger algebra of the halved folded 2n-cube from the viewpoint of its automorphism group action

Journal of Algebraic Combinatorics - Let $$\frac{1}{2}{\overline{H}}(2n,2)$$ denote the halved folded 2n-cube with vertex set X and let $$T{:}{=}T(x)$$ denote the Terwilliger algebra of...     

An iterated logarithm law related to decimal and continued fraction expansions

For an irrational number x and n ≥ 1, we denote by k _n (x) the exact number of partial quotients in the continued fraction expansion of x given by the first n decimals of x. G. Lochs proved that for almost all x, with respect to the Lebesgue measure In this paper, we prove that an iterated logarithm law for {k _n (x): n ≥ 1}, more precisely, for almost all x, for some constant σ > 0. Author’s address: Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China     

Existence of positive eigenfunctions to an anisotropic elliptic operator via the sub-supersolution method

Archiv der Mathematik - Using the sub-supersolution method, we study the existence of positive solutions for the anisotropic problem 0.1 $$\begin{aligned} -\sum _{i=1}^N\frac{\partial }{\partial...     

Positive Solutions of Nonuniformly Elliptic Equations with Weighted Convex-Concave Nonlinearity

Mathematical Notes - The paper contains the proof of the existence of two different positive solutions of the problem $$\frac{\partial}{\partial z_i}\biggl(a_{ij}(z) \frac{\partial u}{\partial...     

On a semilinear double fractional heat equation driven by fractional Brownian sheet

In this paper, we consider the stochastic heat equation of the form $$\frac{\partial u}{\partial t}=(\Delta_\alpha+\Delta_\beta)u+\frac{\partial f}{\partial x}(t,x,u)+\frac{\partial^2W}{\partial t\partial x},$$ where $1<\beta<\alpha< 2$, $W(t,x)$ is a fractional Brownian sheet, $\Delta_\theta:=-(-\Delta)^{\theta/2}$ denotes the fractional Lapalacian operator and $f:[0,T]\times \mathbb{R}\times \mathbb{R}\rightarrow\mathbb{R}$ is a nonlinear measurable function. We introduce the existence, uniqueness and H\"older regularity of the solution. As a related question, we consider also a large deviation principle associated with the above equation with a small perturbation via an equivalence relationship between Laplace principle and large deviation principle.