Mediterranean Journal of Mathematics最新文献

In this paper, we study the discrete nonlinear Schrödinger equation

where (Nge 3), V is a bounded periodic potential and 0 lies in a spectral gap of the Schrödinger operator (-Delta +V). The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite and the other is the lack of compactness of the Cerami sequence. We overcome these two major difficulties by the generalized linking theorem and Lions lemma. This enables us to establish the existence and asymptotic behavior of ground state solutions for small (rho ge 0).

The aim of this paper is to study the product of resolvents of a finite number of monotone vector fields on a Hadamard manifold to approximate both the singular points of their sum and a common singular point among them. For the sum of any finitely many maximal monotone vector fields, with some suitable assumptions, it is proved that the obtained sequence of the iterative method is convergent. The paper ends with some examples and applications.

Abstract

In this paper, a compact finite difference scheme with (O(tau ^{min {ralpha ,2}}+h^4)) convergence order for nonlinear Caputo–Hadamard fractional sub-differential equations is proposed, where (tau ) represents the maximum step size in temporal direction, h represents the step size in spatial direction, and (alpha ) is the order and r ( (rge 1) ) is an optional constant. First, we derive the implicit solution of the original equation using the modified Laplace transform and the finite Fourier sine transform. To obtain the regularity, an auxiliary function (t^{-kappa }) is applied to handle the nonlinear term, which is crucial to the analysis. Second, we approximate the Caputo–Hadamard fractional derivative with the (L_{log ,2-1_sigma }) formula on non-uniform grids. Furthermore, we adopt the Newton linearized method to handle the nonlinear term carefully. Based on the discrete fractional Gr (ddot{textrm{o}}) nwall inequality, the stability and convergence of the derived scheme are obtained by the energy method. Ultimately, three examples are presented to show the effectiveness of our method.

Abstract

Modeling dynamical systems with real-life data having time-dependent disturbances is better captured with time-varying systems. The qualitative properties of such a system in a fractional sense are hardly examined. Observability is one property where the system’s initial states are determined based on the output of some observation system. In this paper, we investigate the observability of time-varying fractional dynamical systems. A state-transition matrix represents the solution of the time-varying fractional dynamical systems. The observability results of linear and nonlinear systems are obtained using the Gramian matrix technique and the Banach contraction mapping theorem respectively. The obtained theoretical results for the observability of the time-varying fractional dynamical systems are compared with those of the time-invariant fractional dynamical system (FDS). Several numerical examples are provided to validate the theoretical results. Also, a numerical example to study the observability of a fractional spring–mass system is provided to verify the applicability of this study.

It is well known that the total torsion of a closed spherical curve is zero. Furthermore, if the total torsion of any closed curve on the surface is zero, then it is part of a plane or a sphere. In this paper, we examine the total torsion of a spherical curve during infinitesimal bending. We find the appropriate bending fields and show that the variation of the total torsion of a closed spherical curve is equal to zero. Some examples are considered both analytically and using our own software tool. For figures, we use colors to represent the value of torsion at different points of the curve, together with a colour-value scale.

Let G be a finite group and p be a prime. We define (N^{mathcal {N}_p*}(G)) to be the intersection of the normalizers of the p-nilpotent residuals of all two-generator subgroups of G whose p-nilpotent residuals are nilpotent. We show that (N^{mathcal {N}_p}(G)=N^{mathcal {N}_p*}(G)). Using the method in the present paper, we will be able to give an affirmative answer to an open problem in Shen et al. (Mediterr J Math 19:191, 2022), which also indicates that similar conclusions hold for many formations. It is also proved that (G=N^{mathcal {N}_p}(G)) if and only if every three-generator subgroup H of G satisfies (H=N^{mathcal {N}_p}(H)). To this end, we introduce and investigate the IO-(N^{mathcal {N}_p})-groups, i.e., the groups G such that (Gne N^{mathcal {N}_p}(G),) but each proper subgroup and each proper quotient of G equals its p-nilpotent norm. Moreover, new results in terms of the p-nilpotent norm and the p-nilpotent hypernorm (N^{mathcal {N}_p}_infty (G)) are given.

For positive integers n and k, with (n ge 4), let (F_{n}) be the free group of rank n and let (G_{n,k} = F_{n}/gamma _{3}(F^{prime }_{n})[F^{prime prime }_{n},~_{k}F_{n}]). We show that for sufficiently large n, the automorphism group ({textrm{Aut}}(G_{n,k})) of (G_{n,k}) is generated by the tame automorphisms and one more non-tame automorphism.

Abstract

In this article, we manifest the existence of a new class of (alpha ) -fractal functions without endpoint conditions in the space of continuous functions. Furthermore, we add the existence of the same class in numerous spaces such as the Hölder space, the convex Lipschitz space, and the oscillation space. We also estimate the fractal dimensions of the graphs of the newly constructed (alpha ) -fractal functions adopting some function spaces and covering methods.

We introduce a notion of good cohomology for multiple lines in ({mathbb {P}}^3) and we classify multiple lines with good cohomology up to multiplicity 4. In particular, we show that the family of space curves of degree d, not lying on a surface of degree (<d), and of maximal arithmetic genus is not irreducible already for (d=4) and (d=5).

Abstract

Let (L^{4}) be a 4-dimensional Lorentzian space with the sign (−,+,+,+). The aim of this study is to investigate the other missing algebraic forms of the constraint manifolds of 2C and 3C spatial open chains in (L^{4}) . For this purpose, firstly, we obtain the structure equations of a spatial open chain using the equations of open chains of the Lorentz plane and Lorentz sphere. After then, using these structure equations, we search the algebraic forms of the constraint manifolds of 2C and 3C spatial open chains in Lorentzian 3-space with respect to the causal characters of the first link and the axis of rotation of the joint.