Exact values are obtained of the n-widths of 2π-periodic functions of the form f ( x ) = 1 2 π ∫ 0 2 π K ( x − t ) φ ( t ) d t = ( K ∗ φ ) ( x ) in space L2[0, 2π] and satisfy condition ( ∫ 0 h ω m p ( φ ; t ) sin γ nt d t ) 1 / p ≤ 1 , 0 < h ≤ π / n , γ > 0 , 0 < p ≤ 2 , where ω m (φ; t)−mth order modulus of continuity of function φ(x) ∈ L2[0, 2π]. Some further generalizations...

In this paper, we study the class of rings in which every flat ideal is finitely projective. We investigate the stability of this property under localizations and homomorphic images, and its transfer to various contexts of constructions such as direct products, amalgamation of rings \({A \bowtie^{f} J}\), and trivial ring extensions. Our results generate examples which enrich the...

Let k be an algebraically closed field of characteristic p ≠ 0 and \({X_{g} \subset A_{k}^{3}}\) be a normal surface defined by an equation of the form z p = g(x, y). The two original algorithms for calculating the group of Weil divisors of X g contain key errors. This paper presents an algorithm that corrects and improves upon the earlier attempts.

We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group. We show that the asymptotic properties of this function are closely connected to the Piltz divisor function. A generalization of Menon’s identity is also...

The present work investigates the effects of viscous dissipation and Ohmic heating on steady MHD convective flow due to a porous rotating disk taking into account the variable fluid properties (density (ρ) viscosity (μ) and thermal conductivity (κ)) in the presence of Hall current and thermal radiation. These properties are taken to be dependent on temperature. The partial...

Rings considered in this article are commutative with identity. A subring of a ring is assumed to contain the identity element of the ring. Let S be a multiplicatively closed subset of a ring R satisfying the following property (P): whenever \({ab \in S}\) with at least one of a, b is in S, then both of them are in S. The (P)-closure of any multiplicatively closed subset of R is...

Let A and B be two rings, let J be an ideal of B and let f : A → B be a ring homomorphism. In this paper, we study when the amalgamation of A with B along J with respect to f is a \({\phi}\)-ring. Hence, we study two different chain conditions over this structure. Namely, the nonnil-Noetherian condition and the Noetherian spectrum condition.

This paper is concerned with a quasilinear elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. The existence and multiplicity results of positive solutions are obtained by variational methods. Open image in new window

In this paper we investigate a maximax optimization problem related to a homogeneous Dirichlet problem in two classes of rearrangements. We prove existence and representation of the maximizers. Open image in new window

Let R be a Noetherian domain with quotient field K. Let A be an integral domain which contains R and whose elements are algebraic over K. We define \({{\rm Eass}_{R}(A/R)}\) to be the set of prime ideals \({\mathfrak{p}}\) ’s of R such that \({\mathfrak{p}}\) is a prime divisor of a generalized denominator ideal I[β] for some \({\beta \in A}\). Assume that \({A = R[\alpha_{1...

In this paper, we give existence and multiplicity results for the problem of prescribing the Webster scalar curvature on the three CR sphere of \(\mathbb{C}^{2}\) under mixed conditions: non-degenerancy and flatness. Open image in new window

Here we prove two upper bounds (one for bivariate polynomials, one for multivariate ones) for the symmetric tensor rank with respect to an infinite field with characteristic ≠ 2. Open image in new window

In the present paper, we introduce generalized Geraghty (Proc Am Math Soc 40:604–608, 1973) mappings on partial metric spaces and give a fixed point theorem which generalizes some recent results appearing in the literature. Open image in new window

Let R be a commutative ring. The unit graph of R, denoted by G(R), is a graph with all elements of R as vertices and two distinct vertices x, y ∈ R are adjacent if and only if x + y ∈ U(R) where U(R) denotes the set of all units of R. In this paper, we examine the preservation of the connectedness, diameter, girth, and some other properties, such as chromatic index, clique number...

In this paper, we introduce and study the essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving the definition and we investigate the characterization, the stability and some properties of these essential pseudospectra.

Using the Komatu integral operator, new subclasses of analytic functions are introduced. For these classes, several Fekete–Szegö type coefficient inequalities are derived.

We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a correspondence between vanishing ideals and toric ideals associated to numerical semigroups. This correspondence is shown to preserve the complete intersection property, and allows us to use some available...

In this paper, we consider a one-dimensional linear Timoshenko system of thermoelasticity type III and prove a polynomial stability result for the non-equal wave-propagation speed case.

In this paper, we shall give new examples on meromorphic functions that share one value with their first derivative and also give the solution for Riccati differential equation.

Let X be a uniformly convex and uniformly smooth real Banach space with dual X*. Let F : X → X* and K : X* → X be continuous monotone operators. Suppose that the Hammerstein equation u + KFu = 0 has a solution in X. It is proved that a hybrid-type approximation sequence converges strongly to u*, where u* is a solution of the equation u + KFu = 0. In our theorems, the operator...

In this paper, we prove that a principally generated C-lattice L is a Dedekind lattice if and only if L is a WI-lattice in which every invertible element is a finite meet of powers of prime elements.

In this paper, we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by an integral operator. Relevant connection of the results, which are presented in this paper with various known results are also considered.

In this paper, we introduce the notion of strongly \({\varphi_{h}}\) -convex functions with respect to c > 0 and present some properties and representation of such functions. We obtain a characterization of inner product spaces involving the notion of strongly \({\varphi_{h}}\) -convex functions. Finally, a version of Hermite–Hadamard-type inequalities for strongly \({\varphi_{h...

In this paper, we obtain a new characterization of p-nilpotent groups under the assumption that some maximal subgroups of Sylow subgroup are \({\mathcal{F}}\)-supplemented. As its applications, we generalize many known results.

In this paper, the exponential state estimation problem for impulsive neural networks with both leakage delay and time-varying delays is investigated. Several sufficient conditions which are given in terms of linear matrix inequalities (LMIs) are derived to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable by constructing...