Results in Mathematics最新文献

In this paper, we investigate the Lyapunov exponents of the generalized dynamically defined Szegő cocycle, corresponding to orthogonal polynomials on the circle with radius (lambda ). We give the upper and lower bounds of the top Lyapunov exponent in our setting by realification.

Let (mathscr {Z}(mathscr {R})') be the set of all non-unit and non-zero elements of ring (mathscr {R}), a commutative ring with identity (1ne 0). The cozero-divisor graph of (mathscr {R}), denoted by the notation ({Gamma '(mathscr {R})}), is an undirected graph with vertex set (mathscr {Z}(mathscr {R})'). Any two distinct vertices w and z are adjacent if and only if (wnotin zmathscr {R}) and (znotin wmathscr {R}), where (qmathscr {R}) is the ideal generated by the element q in (mathscr {R}). In this article, we evaluate the Sombor index of the graphs ({Gamma '(mathbb Z_n)}) for different values of n. Additionally, we compute ({Gamma '(mathbb Z_{n})}), the cozero-divisor graph Sombor spectrum.

In this paper, in view of the transformation formulas for basic hypergeometric series and the creative microscoping method introduced by Guo and Zudilin, we establish new q-analogues of Van Hamme’s (A.2) and (H.2) supercongruences with two parameters

The paper discusses a mass conserving Allen–Cahn equation with a small parameter (epsilon >0) perturbed by transport type noise involving the smeared noise ({dot{w}}^epsilon _i) (formally converging to white noise ({dot{w}}_i)), and investigate its sharp interface limit as (epsilon rightarrow 0). We restrict our discussion over the two-dimensional domain to construct the hypersurface driven by the stochastic term appearing due to the contribution from the transport term when (epsilon rightarrow 0). We make use of asymptotic expansion method to discuss the sharp interface limit.

In this paper, we focus on a problem with parameter dependence both in the leading term and in the reaction term. Such problem is driven by the sum of three anisotropic operators with distinct variable exponents and has in the reaction the combined effects of a singular term and of concave and convex nonlinearities. Under very general assumptions, we produce positive solutions for this problem as well as we establish the precise dependence of the set of such solutions on the parameter (lambda >0) (which appears in the reaction) as the latter varies. Our approach is based on the use of variational tools together with truncation and comparison techniques. We stress that here we also describe the asymptotic behavior of specific positive solutions as both parameters in the leading term and in the reaction term vary in an appropriate range.

A subgroup H of a finite group G is submodular in G if there is a subgroup chain (H=H_0le ldots le H_ile H_{i+1}le ldots le H_n=G) such that (H_i) is a modular subgroup of (H_{i+1}) for every i. We investigate finite factorised groups with submodular primary (cyclic primary) subgroups in factors. We indicate a general approach to the description of finite groups factorised by supersolvable submodular subgroups.

In this paper we study some curves of a trans-Sasakian manifold that generalize magnetic curves.

We extend the results about left-invariant Codazzi tensor fields on Lie groups equipped with left-invariant Riemannian metrics obtained by d’Atri in 1985 to the setting of reductive homogeneous spaces G/H, where the curvature of the canonical connection of second kind associated with the fixed reductive decomposition (mathfrak {g} = mathfrak {h}oplus mathfrak {m}) enters the picture. In particular, we show that invariant Codazzi tensor fields on a naturally reductive homogeneous space are parallel.

The article considers two properties of several metrics defined in the unit disk (Delta ) in ({mathbb {C}}). One is the Lipschitz constant of Möbius transformation preserving (Delta ), especially the t-metric case and the Hilbert metric case. In particular, we confirm a conjecture posed by Rainio and Vuorinen (Results Math 77:71–80, 2022) about t-metric, and disprove the conjecture posed by Rainio and Vuorinen (Stud Sci Math Hung 60:175–191, 2023) about Hilbert metric. Moreover, we show that the metric dimensions of metric spaces ((Delta , d)), where d includes hyperbolic metric, j-metric, Hilbert metric and t-metric, are 3. Thus, we solve the open question posed by Bau and Beardon (Comput Methods Funct Theory 13:295–305, 2013) about these metrics in the unit disk case.

We examine the problems associated with the Collatz map T from the point of view of functional analysis. We associate with T a certain linear operator (mathcal {T}) and show that cycles and (hypothetical) divergent trajectories (generated by T) correspond to certain classes of fixed points of the operator (mathcal {T}). We also show the relationship between the dynamic properties of the operator (mathcal {T}) and the map T. We prove that the absence of non-trivial cycles of T leads to hypercyclicity of the operator (mathcal {T}). In the second part, we show that the index of the operator (Id-mathcal {T}in mathcal {L}(H^2(D))) provides an upper estimate for the number of cycles of T. For the proof, we consider the adjoint operator (mathcal {F}=mathcal {T}^*)

which was first introduced by Berg, Meinardus in [3], and show that it has no non-trivial fixed points in (H^2(D)). Furthermore, we calculate the resolvent of the operator (mathcal {F}) and derive the equation for the characteristic function of the total stopping time (sigma _{infty }) as an application. In addition, we construct an invariant measure for (mathcal {T}) in a slightly different setup, and investigate how the operator (mathcal {T}) acts on generalized arithmetic progressions.