In this paper we find the necessary and sufficient conditionsfor the geometrical dimension of the real nerve of the modulispace of Riemann surfaces of odd genusg to be maximal.Furthermore, we prove some properties of Riemann surfaceswith extremal configuration of symmetries which lead to theconclusion that certain homology groups of the real nerveNgof the moduli space of Riemann surfaces of odd genusgare nontrivial.
We prove that a spherical tumor with free boundary furnished with an almost periodic nutrient supply has a twofold long term time evolution: either it vanishes or it tends towards a persistent tumor which oscillates almost periodically. This is determined by a relation of the mean of the nutrient supply and a threshold value meaning the minimal nutrient supply enabling the tumor to live. In each case, global stability is proved for the almost periodic solution(sigma star(t,x), P star(t,x)) of the corresponding reaction-diffusion equation.
Here we study the multivariate quantitative symmetrized approximation of complex valued continuous functions on a box by complex valued symmetrized and perturbed multivariate neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the used function's high order partial derivatives. The kind of our approximations are trigonometric and hyperbolic. Our multivariate symmetrized operators are defined by using a multivariate density function generated by a \(q\)-deformed and \(\lambda\)-parametrized hyperbolic tangent function. These enhanced approximations are pointwise and of the uniform norm. The related complex valued feed-forward neural networks are with one hidden layer.
In this paper we solve an open problem related to the calcu-lation of a quadratic series and we obtain that Also, we calculate the sum of the series involving the tail of ((2) and the square of the nth harmonic number: sum n=1 <^> infty H n <^> 2 n ( zeta(2) - 1 - 1/(2 <^> 2) -***- 1 n<^> 2 )-2 zeta(2) zeta(3). sum n=1 <^> infty H n <^> 2 ( zeta(2) - 1 - 1/(2 <^> 2) -***- 1 n<^> 2 )<^> 2 - 6zeta(3) - 19/2 * zeta(4) + 5/2 * zeta(5) + 2zeta(2) * zeta(3)
The article considers the Cauchy problem for a linear set-valued differential equation with the Hukuhara derivative and derives an analytical formula for its solution.
LetR be a commutative ring with identity andS a multi-plicative subset ofR. In this study, we introduce the con-cept of rings in which every ideal disjoint withS isS-almostprime. We investigate the possible transfer of the above ringproperty in the quotient rings, localizations, direct products,trivial ring extensions, and amalgamation algebra.
The aim of this paper is to study the symmetrized formassociated with a Hq-Laguerre-Hahn form, where Hqis theq-derivative operator. Given a Hq-Laguerre-Hahn form u ofclass s, it is shown that its symmetrized form w is H root q-Laguerre-Hahn of class s <= 2s + 3. We give the root q-Riccatiequation satisfied by the Stieltjes formal series S(w) as wellas a complete discussion of the class s.As an application of this work, we generate two examplesof symmetric H root q-Laguerre-Hahn orthogonal polynomials ofclass two and three.
Given a perfect Polish space X, a compact subset K subset of Xand a countable ordinal alpha < omega 1, we show that there exists acompact subsetbK subset of X such that <^>K(alpha)= K, where (boolean AND)K((alpha))denotes the alpha-th Cantor-Bendixson derivative of K-<^>. In other words, every compact subset of a perfect Pol-ish space admits an alpha-primitive with respect to the Cantor-Bendixson derivative. This extends to perfect Polish spacesa result previously known for countable compact subsets of the real line. The proof proceeds in three steps: first, we construct primitives for singletons; then, for countable com-pact subsets; and finally, for arbitrary compact subsets, using separability of Polish spaces.
This work investigates the existence and uniqueness of a solution to a discrete Robin boundary value problem involving the anisotropic (p) over right arrow -mean curvature operator. The existence result is established through variational methods, specifically by applying the Mountain Pass Theorem of Ambrosetti and Rabinowitz in combination with Ekeland's Variational Principle. Uniqueness is obtained under the assumption of Lipschitz continuity on the nonlinear term.
We introduce in this paper some new sequences that converge to the Euler-Mascheroni constant. These sequences have a higher convergence rate than the classical one. Further properties are given.
We provide new characterizations of the bicomplex harmonic and strongly bc-harmonic functions in terms of bcholomorphic functions. An extension to the bc-polyharmonic setting is investigated. We also derive similar bicomplex analog for strongly bc-polyharmonic functions of finite bi-order.
In this work, we consider the higher-order reaction-diffusion parabolic problem with time dependent coefficient. We prove the blow-up of solutions and obtain a lower and an upper bound for the blow-up time. Finally, we investigate the existence of a global weak solution to the problem.
The concept of metric dimension in graphs has the aim of finding a set of vertices in a graph with the smallest size that can be used as a reference to identify all vertices in the graph uniquely. Formally, let G be a connected graph, and let S = {s(1), ... , s(k)} subset of V (G) be an ordered set. For every v is an element of V (G), we define r(v vertical bar S) = (d(v, s(1)), ... , d(v, s(k))) where d is the distance function of G. We call S a resolving set if r(u vertical bar S) not equal r(v|S) for every u, v is an element of V(G), u not equal v. The metric dimension of G, denoted by dim(G), is the smallest integer k such that G has a resolving set of size k. Recently, the authors have initiated research on the relation between the metric dimension of a graph and its nullity (that is, the multiplicity of 0 in its adjacency spectrum), and we have obtained several results. In this paper, we present some new relationships between the metric dimension and the spectrum of graphs. In detail, we present an inequality involving the metric dimension and nullity of any bipartite or singular graph. Then, we give an infinite class of graphs having equal metric dimension and nullity using the rooted product of graphs. Finally, for any connected graph G other than a path, we show that a submatrix of the distance matrix of G, associated with a minimal resolving set of G, has the full-rank property.
In this paper, we study Kirchhoff equations with constraint conditions { - (a + b integral (3)(R) |del u1|(2) dx) triangle u(1) = lambda(1)u(1) + mu 1u(1|)(p1-2)u1 +beta r(1)|u(1)|r(1-2)u(1)|u(2)|(r2) in R-3, - a + b integral (3)(R) |del u(2)|(2) dx )triangle u(2) = lambda(2)u(2) + mu(2)|u(2)|p(2-2)u(2) + beta r(2)|u(1)|r(1) |u(2)|r(2-2)u(2) in R-3, integral(3)(R) |u(1)|(2) d(x) = c(1), integral(3)(R) |u(2)|2 dx = c(2), u1 is an element of H-1 (R-3) , u(2) is an element of H-1 (R-3) . (P) where a, b, beta, mu(i,) c(i) > 0, r(i) > 1, 2 < pi < 14/3 < r := r(1) + r(2) <= 2* for i = 1, 2, and lambda(1), lambda(2) is an element of R appear as Lagrange multipliers. The existence of normalized solutions for p1 and p2 within a specific range of (2, 14/3 ) has been considered both the Sobolev sub critical case (r < 2(*)) and the critical case (r = 2(*)) by the Minimax principle and variational methods. This paper provides a refinement and extension of the results for the normalized solutions to Kirchhoff equations.
The Aoki's function A(x) :=(1 + 1/x )(x) +(1-1/x)(-x )is sharply x x estimated for x >> 1. For example, we have the zero approximation given as 2e(1+1/4x(2)-1) = 29/14.
Among the class of generalized Fourier transformations, the linear canonical transform is of pivotal importance mainly due to its higher degrees of freedom in lieu of the conventional Fourier and fractional Fourier transforms. This article is a continuation of our recent work "Linear canonical deformed Hankel transform and the associated uncertainty principles, J. Pseudo-Differ. Oper. Appl.( 0 3), 14: 9". Building upon this, we formulate the generalized translation and convolution operators associated with this newly proposed transformation. Besides, the obtained results are invoked to examine and obtain an analytical solution of the generalized heat equation. Finally, we study the heat semi-group pertaining to the generalized heat equation.
This paper presents two inertial viscosity Mann-type extrapolated algorithms for finding a common solution to the variational inequality problem involving a monotone and Lipschitz continuous operator and the fixed-point problem for a demicontractive mapping in real Hilbert spaces. The proposed algorithms feature an adaptive step size strategy, computed iteratively, which circumvents the need for prior knowledge of the operator's Lipschitz constant. Under appropriate assumptions, we establish two strong convergence theorems guaranteeing the robustness of the methods. Furthermore, we provide a comparative performance analysis of the proposed algorithms against some existing strongly convergent schemes, supported by numerical experiments with MATLAB-based graphical illustrations.
In the present paper, we introduce the canonical SturmLiouville operator L-M := d(2)/d(x)(2) + (A '(x)/A(x) - 2i a/bx) d/(x) - (a(2)/b(2) x(2) + i a/bxA '(x)/A(x) + ia/b), satisfying certain conditions. We prove the boundedness of the canonical Sturm-Liouville Hausdorff operators on the space L-p(R+, A(x) dx), p is an element of [1, infinity). We investigate canonical Sturm-Liouville wavelet transform, and obtain some useful results. The relation between the canonical Sturm-Liouville operator is also established. The properties of the adjoint discussed. The harmonic analysis associated with the operator LM plays an important role in establishing the results of this paper.
In the following text we show if $X$ is an Alexandroff space, then $f:X\to Y$ has closed graph if and only if it has constant closed value on each connected component of $X$. Moreover, if $X$ an Alexandroff space and $f:X\to Y$ has closed graph, then $f:X\to Y$ is continuous. As a matter of fact, the number of maps which have closed graph from Alexandroff space $X$ to a topological space $Y$ depends just on the the number of connected components of $X$ and the number of closed points of $Y$.
Proponemos un m & eacute;todo algebraico para la clasificaci & oacute;n decubrientes de Galois ramificados de una curvaXcentr & aacute;ndonosen el estudio de las extensiones de Galois de anillos de suanillo de adeles geom & eacute;tricosAX. Como aplicaci & oacute;n, en el casode cubrientes c & iacute;clicos determinamos cu & aacute;ndo una extensi & oacute;nc & iacute;clica de anillos deAXproviene de un cubriente de curvasY -> X, situaci & oacute;n que evoca un problema de Grunwald-Wang, y tambi & eacute;n determinamos cu & aacute;ndo dos cubrientes danlugar a extensiones de anillos isomorfas, lo cual se conoce enla literatura como problema de equivalencia. Este m & eacute;todoalgebraico nos permite recuperar la ramificaci & oacute;n, ciertos datosanal & iacute;ticos como son los n & uacute;meros de rotaci & oacute;n y f & oacute;rmulas deenumeraci & oacute;n para cubrientes
