Band 27, Heft 3

In this paper, the analysis of an HIV-1 epidemic model is presented by incorporating a distributed intracellular delay. The delay term represents the latent period between the time that the target cells are contacted by the virus and the time the virions penetrated into the cells. To understand the analysis of our proposed model, the Rouths–Hurwiz criterion and general theory of delay differential equations are used. It is shown that the infection free equilibrium and the chronic-infection equilibrium are locally as well as globally asymptotically stable, under some conditions on the basic reproductive number R0{R_{0}}. Furthermore, the obtained results show that the value of R0{R_{0}} can be decreased by increasing the delay. Therefore, any drugs that can prolong the latent period will help to control the HIV-1 infection.

Consider the first-order linear differential equation with several non-monotone retarded arguments x′⁢(t)+∑i=1mpi⁢(t)⁢x⁢(τi⁢(t))=0{x^{\prime}(t)+\sum_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0}, t≥t0{t\geq t_{0}}, where the functions pi,τi∈C⁢([t0,∞),ℝ+){p_{i},\tau_{i}\in C([t_{0},\infty),\mathbb{R}^{+})}, for every i=1,2,…,m{i=1,2,\ldots,m}, τi⁢(t)≤t{\tau_{i}(t)\leq t} for t≥t0{t\geq t_{0}} and limt→∞⁡τi⁢(t)=∞{\lim_{t\to\infty}\tau_{i}(t)=\infty}. New oscillation criteria which essentially improve the known results in the literature are established. An example illustrating the results is given.

We prove that if the transpose of every 2×2{2\times 2} idempotent matrix over a division ring D , different from the identity matrix, is not invertible, then D is commutative.

The aim of this paper is to study the algebraic aspects of the gluing procedure in the category of differential spaces. In particular, the Sikorski differential spaces are studied. The algebraic techniques are mainly based on the spectral approach. This paper is a continuation of some previous researches in differential spaces techniques.

Internal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. In this manuscript we generalize the concept of internal point in real vector spaces by introducing a type of points, called inner points, that allows us to provide an intrinsic characterization of linear manifolds, which was not possible by using internal points. We also characterize infinite dimensional real vector spaces by means of the inner points of convex sets. Finally, we prove that in convex sets containing internal points, the set of inner points coincides with the one of internal points.

The paper is devoted to the construction and study of the additive averaged semi-discrete scheme for one nonlinear multi-dimensional integro-differential equation of parabolic type. The studied equation is based on the well-known Maxwell’s system arising in mathematical simulation of electromagnetic field penetration into a substance.

The main goal of this article is to derive differential and associated integral equations for some 2-iterated and mixed type special polynomial families. By using the factorization method, the recurrence relations and differential equations are derived for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials. The Volterra integral equations for these polynomial families are also established. The graphical representation of these 2-iterated and mixed polynomials is presented. The zeros of these polynomials are investigated for certain values of the index n using numerical computation. The approximate solutions of the real zeros of these polynomials are also given.

We introduce and investigate the adjoint resolutions and adjoint dimensions of modules. As a consequence, we give some new characterizations of weak global dimensions of coherent rings in terms of adjoint resolutions and adjoint dimensions of modules.

In the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameter c . The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which preserves the test functions e0{e_{0}} and e1{e_{1}}. It is shown that these King type operators provide a better approximation order than some Baskakov–Durrmeyer operators for continuous functions defined on some closed intervals.

Let μ be a nonnegative Borel measure on the unit disk 𝔻{\mathbb{D}}. In this paper, we investigate measures μ such that the weighted BMOA{\mathrm{BMOA}} spaces are embedded boundedly or compactly into tent-type spaces 𝒯φ∞⁢(μ){\mathcal{T}_{\varphi}^{\infty}(\mu)}. As an application, we characterize the boundedness and compactness of Volterra integral operators on the weighted BMOA{\mathrm{BMOA}} space.

An interesting question about the perturbed sequences is: when do they inherit the properties of the original one? An elegant relation between frames (fusion frames) and their perturbations is the relation of their redundancies. In this paper, we investigate these relationships. Also, we express the redundancy of frames (fusion frames) in terms of the cosine angle between some subspaces.

The predual spaces of generalized grand Morrey spaces over non-doubling measure spaces are investigated. The case of the grand Lebesgue spaces is covered, which is also new. An example shows that the modification of Morrey spaces is essential.

We prove some trigonometric identities involving Chebyshev polynomials of the second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical stability of atomic form factor calculations for highly excited states.

In this paper we study the boundedness of localization operators associated with the Stockwell transform with symbol in Lp{L^{p}} acting on the Wiener amalgam space W⁢(Lp,Lq)⁢(ℝ){W(L^{p},L^{q})(\mathbb{R})}.

In the present paper we establish a general form of Voronovskaja’s theorem for functions defined on an unbounded interval and having exponential growth. The case of approximation by linear combinations is also considered. Applications are given for some Szász–Mirakyan and Baskakov-type operators.

We extend the quantitative Balian–Low theorem of Nitzan and Olsen to higher dimensions. We use Zak transform methods and dimension reduction. The characterization of the Gabor–Riesz bases by the Zak transform allows us to reduce the problem to the quasiperiodicity and the boundedness from below of the Zak transforms of the Gabor–Riesz basis generators, two properties for which dimension reduction is possible.

Given a matrix A such that AM=I{A^{M}=I} and 0≤α<n{0\leq\alpha<n}, for an exponent p satisfying p⁢(A⁢x)=p⁢(x){p(Ax)=p(x)} for a.e. x∈ℝn{x\in\mathbb{R}^{n}}, using extrapolation techniques, we obtain Lp⁢(⋅)→Lq⁢(⋅){L^{p(\,\cdot\,)}\rightarrow L^{q(\,\cdot\,)}} boundedness, 1q⁢(⋅)=1p⁢(⋅)-αn{\frac{1}{q(\,\cdot\,)}=\frac{1}{p(\,\cdot\,)}-\frac{\alpha}{n}}, and weak type estimates for integral operators of the form Tα⁢f⁢(x)=∫f⁢(y)|x-A1⁢y|α1⁢⋯⁢|x-Am⁢y|αm⁢𝑑y,T_{\alpha}f(x)=\int\frac{f(y)}{|x-A_{1}y|^{\alpha_{1}}\cdots|x-A_{m}y|^{\alpha% _{m}}}\,dy, where A1,…,Am{A_{1},\dots,A_{m}} are different powers of A such that Ai-Aj{A_{i}-A_{j}} is invertible for i≠j{i\neq j}, α1+⋯+αm=n-α{\alpha_{1}+\cdots+\alpha_{m}=n-\alpha}. We give some generalizations of these results.

In this study, we extend the concepts and fundamental results on statistical convergence from a single time scale to any product time scale. Various characterizations about these new notions are also obtained.