Results in Mathematics最新文献

In this article, we introduce and study a natural version of the directional compactness, which can be viewed as one of the effective tools for constructing sufficient conditions in nonsmooth vector equilibrium problems. We also provide the generalized Hadamard directional derivative notion which is closely related to a version of contingent derivative. The relation among the first-order approximations/the Clarke generalized Jacobian and the generalized Hadamard directional differentiability is formulated. Using the tool of approximations, a new version of the constraint qualification of the (CQ) type is proposed for establishing KT-type necessary nonsmooth optimality conditions via the generalized Hadamard directional derivatives for the weak/and strict efficiency of constrained nonsmooth vector equilibrium problems. As applications, we study a nonsmooth vector equilibrium problem with set, cone constraints using approximations and the constraint qualification (CQ).

It is shown that any ring being a sum of two left T-nilpotent subrings is left T-nilpotent. The paper contains the description of all the semigroups S such that an S-graded ring (R=bigoplus _{sin S}A_s) has the property that the left T-nilpotency of all subrings among the subgroups (A_s) of the additive group of R implies the left T-nilpotency of R. Furthermore, this result is extended to rings R being S-sums.

Denote by (T_n^d(A)) an upper triangular operator matrix of dimension (nin mathbb {N}) whose diagonal entries (D_i, 1le ile n), are known, and (A=(A_{ij})_{1le i<jle n}) is an unknown tuple of operators. This article is aimed at investigation of defect spectrum (mathcal {D}^{sigma _*}=bigcup _{i=1}^nsigma _*(D_i){setminus }sigma _*(T_n^d(A))), where (sigma _*) is a spectrum corresponding to various types of invertibility: (left, right) invertibility, (left, right) Fredholm invertibility, left/right Weyl invertibility. We give characterizations for each of the previous types, and provide some sufficent conditions for the stability of certain spectrum (the case (mathcal {D}^{sigma _*}=emptyset )). The results are proved for all matrix dimensions (nge 2), and they hold in arbitrary Hilbert spaces without assuming separability, thus generalizing results from Wu and Huang (Ann Funct Anal 11(3):780–798, 2020; Acta Math Sin 36(7):783–796, 2020). We also retrieve a result from Bai et al. (J Math Anal Appl 434(2):1065–1076, 2016) in the case (n=2), and we provide a precise form of the well known ‘filling in holes’ result from Han et al. (Proc Am Math Soc 128(1):119–123, 2000).

The present study introduces an innovative link between integrable equations and the motion of timelike curves within a three-dimensional Minkowski space. This study aims to establish an anology between the modified generalizations of the Heisenberg spin chain model equation, a complex Korteweg–de Vries equation, and the Ablowitz–Kaup–Newell–Segur hierarchy systems of real type, respectively. This is accomplished through the application of specific functions, which are derived based on the curvatures and torsions of three distinct curves and their corresponding Frenet frames in a 3-dimensional Minkowski space. Making use of this method, the geometric derivation of the integrable equation has been demonstrated with success.

Given an open subset U of a complex Banach space E, a weight v on U and a complex Banach space F, let (H^infty _v(U,F)) denote the Banach space of all weighted holomorphic mappings from U into F, endowed with the weighted supremum norm. We introduce and study a version of the Bishop–Phelps–Bollobás property for (H^infty _v(U,F)) ((WH^infty )-BPB property, for short). A result of Lindenstrauss type with sufficient conditions for (H^infty _v(U,F)) to have the (WH^infty )-BPB property for every space F is stated. This is the case of (H^infty _{v_p}(mathbb {D},F)) with (pge 1), where (v_p) is the standard polynomial weight on (mathbb {D}). The study of the relations of the (WH^infty )-BPB property for the complex and vector-valued cases is also addressed as well as the extension of the cited property for mappings (fin H^infty _v(U,F)) such that vf has a relatively compact range in F.

In an earlier work (Castillo et al. in J Math Phys 61:103505, 2020), it was established, from a hypergeometric-type difference equation, tractable sufficient conditions for the monotonicity with respect to a real parameter of zeros of classical discrete orthogonal polynomials on linear, quadratic, q-linear, and q-quadratic grids. In this work, we continue with the study of zeros of these polynomials by giving a comparison theorem of Sturm type. As an application, we analyze in a simple way some relations between the zeros of certain classical discrete orthogonal polynomials.

In this paper, we study the no-flux boundary initial-boundary problem for a three-component reaction-diffusion system originating from the classical May-Nowak model for viral infection

in a smoothly bounded domain (Omega subset {mathbb {R}}^n), (nge 1). It is shown that for any (kappa >0), (mu >0) and sufficiently regular nonnegative initial data ((u_0,v_0,w_0)), the system possesses a unique nonnegative global bounded classical solution provided

Moreover, we show the large time behavior of the solution with respect to the size of (kappa ). More precisely, we prove that

• if (kappa <1+mu ), there exists (chi _1^*) such that if (|chi |le chi _1^*), then the solution satisfies

  $$begin{aligned} u(cdot , t)rightarrow u_*, v(cdot , t)rightarrow 0 text{ and } w(cdot , t)rightarrow 0quad text{ as } trightarrow infty end{aligned}$$

  in (L^{infty }(Omega )) exponentially, where (u_*) is the solution of algebraic equation

  $$begin{aligned} kappa -y-mu y^{alpha }=0; end{aligned}$$

• if (kappa >1+mu ), then there exists (chi _2^*) with the property that if (|chi |le chi _2^*), then the solution fulfills that

  $$begin{aligned} u(cdot , t)rightarrow 1, v(cdot , t)rightarrow kappa -1-mu text{ and } w(cdot , t)rightarrow kappa -1-mu quad text{ as } trightarrow infty end{aligned}$$

  in (L^{infty }(Omega )).

In this paper we introduce a new general multivariate fractal interpolation scheme using elements of the zipper methodology. Under the assumption that the corresponding Read-Bajraktarevic operator is well-defined, we enlarge the previous frameworks occurring in the literature, considering the constitutive functions of the iterated function system whose attractor is the graph of the interpolant to be just contractive in the last variable (so, in particular, they can be Banach contractions, Matkowski contractions, or Meir-Keeler contractions in the last variable). The main difficulty that should be overcome in this multivariate framework is the well definedness of the above mentioned operator. We provide three instances when it is guaranteed. We also display some examples that emphasize the generality of our scheme.

We consider two types of nonlinear eigenvalue problems involving Laplace and p-Laplace operators ((p>2)). The main result establishes the existence of at least two nontrivial weak solutions in the case of the perturbed equation and the existence of a continuous spectrum in the case of the (p, 2)-equation. In both cases, variational methods play a central role in our arguments.

We investigate the weighted approximation of functions in (L_p)-norm by Kantorovich modifications of the classical Szász-Mirakjan operator, with weights of type ((1+x)^{alpha }), (alpha in {mathbb {R}}). By using an appropriate K-functional we prove a strong converse inequality for the weighted error of approximation and characterize it exactly. We prove a Voronovskaya and Bernstein-type inequalities for the Szász-Mirakjan–Kantorovich operator.