Earlier Related Results Research Articles

General Decay Rates of the Solution Energy in a Viscoelastic Wave Equation With Boundary Feedback and a Nonlinear Source

In a bounded domain, we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary and certain initial data. We establish an explicit and general decay rate result, using some properties of the convex functions. Our new results substantially improve several earlier related results in the literature. Keywords: General decay, nonlinear source, viscoelastic, wave equation, relaxation function.

Coneability of Anti-Fubini Functions and Other Lineability Properties

It is proved that the family of measurable real functions on the product measure space satisfying (or not) the conclusion of Fubini’s Theorem (along with a number of related families) is algebraically large, in the sense that it contains large convex cones or even large vector subspaces (except for zero) under rather general assumptions. Several earlier related results are improved, mainly regarding the cardinality of the generator set of the corresponding cones or subspaces.

Stability of viscoelastic wave equation with distributed delay and logarithmic nonlinearity

In this paper, we consider a quasilinear viscoelastic wave equation that features a distributed delay as well as logarithmic nonlinearity. We combine the potential well theory, Faedo‐Galerkin's approximation, and some energy estimates to construct the global existence of the solution. With weaker conditions on the relaxation function, we establish explicit and general decay rate results by using the multiplier method and some properties of convex functions. Our results improve and generalize several earlier related results in the literature.

New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

In this paper, we investigate the stability of the solutions of a viscoelastic plate equation with a logarithmic nonlinearity. We assume that the relaxation function g satisfies the minimal conditiong′(t)≤−ξ(t)G(g(t)),\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ g^{\\prime }(t)\\le -\\xi (t) G\\bigl(g(t)\\bigr), $$\\end{document} where ξ and G satisfy some properties. With this very general assumption on the behavior of g, we establish explicit and general energy decay results from which we can recover the exponential and polynomial rates when G(s) = s^{p} and p covers the full admissible range [1, 2). Our new results substantially improve and generalize several earlier related results in the literature such as Gorka (Acta Phys. Pol. 40:59–66, 2009), Hiramatsu et al. (J. Cosmol. Astropart. Phys. 2010(06):008, 2010), Han and Wang (Acta Appl. Math. 110(1):195–207, 2010), Messaoudi and Al-Khulaifi (Appl. Math. Lett. 66:16–22, 2017), Mustafa (Math. Methods Appl. Sci. 41(1):192–204, 2018), and Al-Gharabli et al. (Commun. Pure Appl. Anal. 18(1):159–180, 2019).

Asymptotic Stability for the Second Order Evolution Equation with Memory

In this paper, we consider an abstract viscoelastic equation. We use memory-type damping with a general assumption on the relaxation function and establish explicit energy decay result from which we can recover the optimal exponential and polynomial rates. Our result generalizes the earlier related results in the literature.

New $L^{p}$ -inequalities for hyperbolic weights concerning the operators with complex Gaussian kernels

In this article the authors present a systematic study of several new Lp-boundedness properties and Parseval-type relations concerning the operators with complex Gaussian kernels over the spaces Lp(R,cosh(αx)dx) and Lp(R,cosh(αx2)dx), 1≤p≤∞, α∈R. Relevant connections with various earlier related results are also pointed out.

The Schwarz lemma at the boundary of the symmetrized bidisc

The symmetrized bidisc G2 is defined byG2:={(z1+z2,z1z2)∈C2:|z1|<1,|z2|<1,z1,z2∈C}. It is a bounded inhomogeneous pseudoconvex domain without C1 boundary, and especially the symmetrized bidisc hasn't any strongly pseudoconvex boundary point and the boundary behavior of both Carathéodory and Kobayashi metrics over the symmetrized bidisc is hard to describe precisely. In this paper, we study the boundary Schwarz lemma for holomorphic self-mappings of the symmetrized bidisc G2, and our boundary Schwarz lemma in the paper differs greatly from the earlier related results.

Optimal decay rates for the viscoelastic wave equation

In this paper, we consider a viscoelastic equation with minimal conditions on the relaxation function g, namely, , where H is an increasing and convex function near the origin and ξ is a nonincreasing function. With only these very general assumptions on the behavior of gat infinity, we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial rates when H(s)=sp and p covers the full admissible range [1,2). We get the best decay rates expected under this level of generality, and our new results substantially improve several earlier related results in the literature.

General decay result for nonlinear viscoelastic equations

In this paper we consider a nonlinear viscoelastic equation with minimal conditions on the L1(0,∞) relaxation function g namely g′(t)≤−ξ(t)H(g(t)), where H is an increasing and convex function near the origin and ξ is a nonincreasing function. With only these very general assumptions on the behavior of g at infinity, we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial rates when H(s)=sp and p covers the full admissible range [1,2). We get the best decay rates expected under this level of generality and our new results substantially improve several earlier related results in the literature.

Admissibility Analysis and Control Synthesis for T–S Fuzzy Descriptor Systems

The problem of admissibility analysis and control synthesis for Takagi–Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Second, the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel distributed compensation controllers are designed, linear matrix inequalities conditions are given to construct the controllers. Finally, some examples are provided to illustrate the main results in this paper less conservative than some earlier related results.

New Lp-boundedness properties for the Kontorovich–Lebedev and Mehler–Fock transforms

ABSTRACTIn this paper, the authors present a systematic study of several new -boundedness properties for the Kontorovich–Lebedev transform and the Mehler–Fock transform on the spaces and . Relevant connections with various earlier related results are also pointed out.

Finite groups with an irreducible character of large degree

Let G be a finite group and d the degree of a complex irreducible character of G, then write |G| = d(d + e) where e is a nonnegative integer. We prove that |G| ≤ e 4−e 3 whenever e > 1. This bound is best possible and improves on several earlier related results.

Dissipativity Analysis of Descriptor Systems Using Image Space Characterization

In this paper, we analyze the dissipativity for descriptor systems with impulsive behavior based on image space analysis. First, a new image space is used to characterize state responses for descriptor systems. Based on such characterization and an integral property of delta function, a new necessary and sufficient condition for the dissipativity of descriptor systems is derived using the linear matrix inequality (LMI) approach. Also, some of the earlier related results on dissipativity for linear systems are investigated in the framework proposed in this paper. Finally, two examples are given to show the validity of the derived results.

Generalised Common Fixed Point Theorems of A-Compatible and S-Compatible Mappings

In this paper we prove a common fixed point theorem of four self mappings satisfying a generalized inequality using the concept of A-compatible and S-compatible mappings. Our result generalizes many earlier related results in the literature.

Norm inequalities for the absolute value of Hilbert space operators

We use norm inequalities for operators, such as Cauchy–Schwarz inequality and Minkowski inequality, to establish sharp norm inequalities for the absolute value of operators. Among other inequalities, it is shown that if A, B and X are operators on a Hilbert space, such that X is self-adjoint, and r ≥ 1, then This inequality generalizes some earlier related results. Other related inequalities are also discussed.

New Limit Formulas for the Convolution of a Function with a Measure and Their Applications

Asymptotic behavior of a convolution of a function with a measure is investigated. Our results give conditions which ensure that the exact rate of the convolution function can be determined using a positive weight function related to the given function and measure. Many earlier related results are included and generalized. Our new limit formulas are applicable to subexponential functions, to tail equivalent distributions, and to polynomial-type convolutions, among others.

Allocating work to a two-stage production system with interstage buffer

Consider a set of discrete tasks whose stochastic task times have specified means and variances, and these tasks have to be assigned to one of the two serial stations of a flow-type production system (e.g., an unpaced line) with an interstation buffer. Our purpose is to investigate: (i) what ideal combination of means and variances of station processing times will give the highest system utilization (U); and (ii) how serious it is to deviate from this ideal arrangement. A literature review shows that earlier related results are not applicable due to their modeling restrictions, and simplistic extension of earlier results leads to contradictory conclusions anyway. Numerous simulations were made for the system with different buffers sizes and different combinations of station-processing-times' means and variances. Conclusions from analyzing the extensive simulation results are: (i) U is maximized when the means and variances are both balanced, i.e., the two-station-processing times have the same mean and variance; (ii) variance imbalance has a surprisingly small effect on U, but this effect is greater under greater mean imbalance; (iii) for a given mean imbalance, a much larger counter variance-imbalance is needed to achieve a best possible U, but this counter variance-imbalance can never fully compensate for the ill effect of mean-imbalance on U, (iv) the ill effect of mean imbalance on U decreases substantially if the discrete tasks have more variable task times.