Results in Mathematics最新文献

In the paper we give new asymptotic evaluations for sequences of linear positive operators (V_{n}:C_{2pi }left( {{mathbb {R}}}right) rightarrow C_{2pi }left( {{mathbb {R}}}right) ). Our method of the proof is entirely different than those known in this area. As applications we complete and extend known asymptotic evaluations in this topic.

The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both the state and adjoint state equations. The article establishes the existence and uniqueness of solutions for both equations, with minimal assumptions made about the problem’s data. Next, the regularity of these solutions is studied in three frameworks: Hilbert–Sobolev spaces, Sobolev–Slobodeckiĭ spaces, and weighted Sobolev spaces. These regularity results enable a numerical analysis of the finite element approximation of both the state and adjoint state equations. The results cover both convex and non-convex domains and quasi-uniform and graded meshes. Finally, the optimal control problem is analyzed and discretized. Existence and uniqueness of the solution, first-order optimality conditions, and error estimates for the finite element approximation of the control are obtained. Numerical experiments confirming these results are included.

This article is a continuation of our investigations in the function space C(X) with respect to the topology (tau ^s_mathfrak {B}) of strong uniform convergence on (mathfrak {B}) in line of (Chandra et al. in Indag Math 31:43-63, 2020; Das et al. in Topol Appl 310:108005, 2022) using the idea of strong uniform convergence (Beer and Levi in J Math Anal Appl 350:568-589, 2009) on a bornology. First we focus on the notion of the tightness property of ((C(X),tau ^s_mathfrak {B})) and some of its variations such as the supertightness, the Id-fan tightness and the T-tightness. Certain situations are discussed when C(X) is a k-space with respect to the topology (tau ^s_mathfrak {B}). Next the notions of strong (mathfrak {B})-open game and (gamma _{mathfrak {B}^s})-open game on X are introduced and some of its consequences are investigated. Finally, we consider discretely selective property and related games. On ((C(X),tau ^s_mathfrak {B})) several interactions between topological games related to discretely selective property, the Gruenhage game on ((C(X),tau ^s_mathfrak {B})) and certain games on X are presented.

Projectively flat Finlser metrics on a convex domain U in (mathbb {R}^n) are regular solutions to Hilbert’s Fourth Problem. In this paper, we study projectively flat Finlser metrics on U. We find equations that characterize these metrics with weakly orthogonal invariance, refining a theorem due to Sol(acute{o})rzano-Le(acute{o})n. As its application, we obtain infinitely many new projectively flat Finlser metrics on (mathbb {S}^{n+1}) and determine their scalar flag curvature. These metrics contain Bryant’s projective spherically symmetric Finsler metric of constant flag curvature 1.

In this article, we reexamine properties of maximum log-likelihood parameter estimation for two-parameter Weibull distributions which have been applied in many different sciences. Finding reasons for this popularity is a key question. Our main contribution is a thorough existence and uniqueness proof for a global maximizer with respect to the parameter space. We first provide existence and uniqueness of local maximizers by Schauder’s first fixed point theorem, monotony arguments and local concavity of its Hessian matrix. Thus, we can prove our main result of existence and uniqueness of a global maximizer by considering all limiting cases with respect to the parameter space. We finally strengthen our theoretical findings on four data sets. On the one hand, two synthetic data sets underline our need for our data assumptions while, on the other hand, we choose two data sets from wind engineering and reliability engineering to demonstrate usefulness in real-world applications.

We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct partitions of the set of lattice points in the plane. Our object is to analyze these trajectories and to point out a few special arithmetic properties of the integers they represent. We also introduce and study the parabolic-taxicab distance, which measures the fast traveling on the steps of the stairs defined by points on the parabolic trajectories whose coordinates are based on triangular numbers.

We investigate the boundedness and compactness properties of integral operators, Volterra operators, and generalized Volterra operators between the Dales–Davie algebras. Additionally, we study the analogous properties of these operators when applied to the Lipschitz versions of Dales–Davie algebras.

In this paper, we are going to establish a reversed Hardy–Littlewood–Sobolev inequality on different dimensional space and prove the existence of extremal functions for the best constant. Furthermore, we investigate the regularity of extremal functions and provide a necessary conditions for the existence of solutions of the integral systems. Finally, we classify the extremal functions.

This paper focuses on the function estimation problem in nonparametric regression model based on biased samples under strong mixing. We propose a wavelet estimator by using wavelet kernel and investigate the consistency properties of the wavelet estimator. The mean consistency, strong consistency and convergence rate are obtained and the convergence rate is similar as that of wavelet estimator in the standard nonparametric model even although with the presence of bias and strong mixing dependence.

The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference–differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and another of mixed type Gevrey and q-Gevrey. These asymptotic phenomena are observed due to the modification of the norm established on the space of coefficients of the formal solution. The techniques used are based on the adequate path deformation of the difference of two analytic solutions, and the application of several versions of Ramis–Sibuya theorem.