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International Conference of Mathematical Sciences (ICMS) -- JUL 31-AUG 06, 2018 -- Maltepe Univ, Istanbul, TURKEY, WOS: 000472950300048, In this paper, we investigate the concept of Abel statistical delta quasi Cauchy sequences. A real function! is called Abel statistically delta ward continuous it preserves Abel statistical delta quasi Cauchy sequences, where a sequence (alpha(k)) of point in R is called Abel statistically delta quasi Cauchy if lim(x -> 1)- (1 - x) Sigma(k:vertical bar Delta 2 alpha k vertical bar >=epsilon) x(k) = 0 for every epsilon > 0, where Delta(2)alpha(k) = alpha(k+2) - 2 alpha(k+1) + alpha(k) for every k is an element of N. Some other types of continuities are also studied and interesting results are obtained.

In this paper, we obtain sufficient conditions for compactness of the commutator for the Riesz potential [b, Iα] in global Morrey-type spaces GMpθw .In this paper, we obtain sufficient conditions for compactness of the commutator for the Riesz potential [b, Iα] in global Morrey-type spaces GMpθw .

Let Ω ⊂ Rn be an open connected set such that if n = 2, it is assumed that Ω has a Green function. Let K be a compact subset of Ω. There are many equivalent ways to define the class H(K) of harmonic functions on K. In this note we present a new definition for the concept of harmonicity for a Borel measurable (not necessarily continuous) on K. We study this new class of functions and show that it coincides with the class of those quasi finely harmonic functions on the fine interior of K.

In this paper we give sufficient conditions for the precompactness of sets in general global Morrey-type spaces GMpθ,w(·)(ℝn). In the case θ = ∞, it follows the result for the generalized Morrey spaces Mpw(⋅), and for w(r) = r−λ, θ = ∞, 0≤λ≤np there follows the known result for the Morrey spaces Mpλ(ℝn). In the case λ = 0 this is the well-known Frechet-Kolmogorov theorem. The pre-compactness of sets in Morrey spaces was investigated in many works, and in generalized Morrey spaces Mpw(⋅)(ℝn) in our previous works. The aim of this paper is to generalize these results to the case of general global Morrey-type spaces GMpθ,w(·)(ℝn).

Recently, Shabir and Naz in [4] introduced the notion of Soft Topological Spaces (STS). They defined and studied about soft topology on the collection τ of soft sets over X. After the initiation of soft topological space many researcher developed its basic theory as like soft continuity, soft compactness and soft countability. Our main objective in this paper is to study the soft connectedness properties of soft topological space and also establish relations of soft connectedness with other properties of STS.

This paper has the necessary and additional conditions on weight functions for a weighted inequality of Hardy type to hold or the corresponding estimate for the norm of the embedding operator. The continuity and compactness of the embedding of weighted spaces are established. The criterion of embedding compactness is provided. We present some fundamental lemmas used in the proof of main theorems.

A new method for global optimization of Holder goal functions under compact sets given by inequalities is proposed. All functions are defined only algorithmically. The method is based on performing simple Monte Carlo trials and constructing the sequences of records and the sequence of their decrements. An estimating procedure of Holder constants is proposed. Probability estimation of exact global minimum neighborhood using Holder constants estimates is presented. Results on some analytical and algorithmic test problems illustrate the method’s performance.

Given a regular compact set E in the complex plane C, a unit measure µ supported by ∂E, a triangular point set β:={{βn,k}k=1n}n=1∞, β ⊂ ∂E and a function f, holomorphic on E, let πn,mβ,f be the associated multipoint β− Pade approximant of order (n, m). We show that if the sequence πn,mβ,f, n ∈ Λ, m− fixed, converges exact maximally to f relatively to the measure µ, then the points βn,k are uniformly distributed on ∂E with respect to µ as n ∈ Λ. Furthermore, a result about the zeros behavior of the exact maximally convergent sequence Λ is provided, under the condition that Λ is ”dense enough.”

In this paper, we present sufficient conditions for the pre-compactness of sets in the generalized Morrey spaces Mpw. From this theorem for the case of w(r) = r−λ follows the known result for the Morrey space Mpλ, and in the case of λ = 0 this is the well-known Frechet-Kolmogorov theorem.

Let H be a complex Banach space, T be the topological group of the unit circle with respect to the Euclidean topology, α be a strongly continuous isometric linear representation of T in H, {Fkα}k∈ℤ be the family of Fourier coefficients with respect to α, and {σkα}k∈ℤ be Cesaro means of the family {Fkα}k∈ℤ. In this work, we give some compactness tests for closed subsets of H.

The research is devoted to the solution of a convergence problem of a non-linear dynamic system to the target compact set in the n-dimensional Euclidean space at a fixed moment of time. A step-by-step method with respect to time is provided to construct an approximate resolving control. One of the main methods used to solve the convergence problem is the method of extreme attraction to the solvability set. The method described in the research differs from the method of extreme attraction by the choice of control for each step in the time, that provides maximal attraction of the dynamical system to the sections of the solvability set. The presented research describes the method of construction of the approximate resolving control and gives the estimates of the divergence of the generated control from the target set.

In this work a necessary and sufficient condition for the compactness of the resolvent of one second order degenerate differential operator in L2 is obtained. We also discuss the two-sided estimates for the radius of fredholmness of this operator.

The object of this paper is to study topological properties such as boundedness, compactness and geometric properties such as starlikeness and convexity for two fractional integral operators of Volterra-Type in the open unit disk. These operators are generalization of the Pommerenke integral operators. The boundedness and compactness are discussed in the space Blog.

In this paper, coarse soils are modeled by granular packings, because both of them have similar characteristics, such as: gaseousity, duality, dilatancy, fragility and hyperbolicity. By virtue of these properties, it is assumed that the contact force ensemble remains the same, while the packing changes because of its dual character, regarding the compactness of the soil. For the dense state, both assemblages coincide themselves, forming chains of contact forces; the transmission of stresses obeys the Trollope’s hypothesis of centroidal reactions; and the volumetric strain increases. For the loose state, the packing adopts a “passive” distribution, yielding a constant angle of internal friction at failure; so that, the strain is contractive and the stress transmission occurs fundamentally by shear, in a similar fashion to the Rowe’s mechanism. In the figures, the good correspondence between the results of the theory and the reported experimental data is shown.

We study the conditional expectations in the Lp-modules associated with a partition of unity of a Boolean algebra. Cyclic compactness criteria of the subsets of Lp found in terms of convergent nets of conditional expectations.

Let (X, ƒ) be a dynamical system, with X a compact metric space and ƒ:X→X a continuous map. For any xeX, let us consider the empirical measures En(x) = 1n ∑ i=1n−1δfi(x)⊂M(X), where δ is the Dirac point mass measure. The limit set of the sequence {En(x)} will be denoted by V(x) A particularly interesting case is when V(x) = {μ}, i.e. the points for which the time‐average along their orbits of any continuous potential ψ agrees with the average of ψ with respect to μ. This kind of points are called generic for the measure μ and let us denote Gμ = {x: V(x) = {μ}}. A measure μ is called a physical measure if there is a Lebesgue measure m such that m(Gμ)>0. In the case of considering C2 ‐maps ƒ :M→ M with a negative Lyapunov exponent, where M is a compact Riemannian manifold, the Sinai‐Ruelle‐Bowen measures (SRB‐measures) are physical measures. In the context of Lattice Statistical Mechanics the scheme is the following: the phase space X is a subset of the space {x: x = (xi)iezd,xieω = {1,2, …,k}}, i.e.a space...

The authors consider the notions of strong compactness, strong cocompactness, strong stability, strong costability and strong dicompactness in the setting of ditopological texture spaces.

We investigate torsional Alfven oscillations of relativistic stars with a global dipole magnetic field, via 2D numerical simulations. We find that a) there exist two families of quasi‐periodic oscillations (QPOs) with harmonics at integer multiples of the fundamental frequency, b) the QPOs are long‐lived, c) for the chosen form of dipolar magnetic field, the frequency ratio of the lower to upper fundamental QPOs is about 0.6, independent of the equilibrium model or of the strength of the magnetic field, and d) within a representative sample of EOS and of various magnetar masses, the Alfven QPO frequencies are given by accurate empirical relations that depend only on the compactness of the star and on the magnetic field strength. Compared to the observational frequencies, we also obtain an upper limit on the strength of magnetic field of SGR 1806‐20 (if is dominated by a dipolar component) between ∼3 and 7×1015 Gauss.

The aim of the present work is to introduce the notion of finite tightness and then to obtain some results of compactness in the lack of L1 — boundedness. We use these results in order to obtain information about the limit of the solutions for a sequence of one dimensional heat equations.

Let K be an algebraically closed field, complete for a non‐trivial ultrametric absolute value, and let A be a commutative normed K‐algebra with identity. We call multiplicative spectrum of A the set Mult(A, ‖ ⋅ ‖) of continuous multiplicative semi‐norms on A. We denote by Mult(K[x]) the set of multiplicative semi‐norms on the polynomial algebra K[x]. Both sets of semi‐norms are endowed with the topology of pointwise convergence. We also denote by X(A, K) the set of K‐algebra homomorphism from A onto K. Unlike in complex analysis, there might exist some maximal ideals in A which are not the kernel of elements of X(A, K). In A, we can define two kinds of Gelfand transform. GA and GMA. The first one, denoted by GA is similar to that in complex analysis, consisting of associating to each element f of A the mapping f from X(A, K) to K defined as f(χ) = χ(f), (χ ∈ X(A, K)). The second, denoted by GMA consists of associating to each element f of A the mapping f* from Mult(A, ‖ ⋅ ‖) to Mult(K[x]) defined as f*(φ)(P) = φ(P ∘ f). This transform allows us to interpret any element of A as a continuous function defined on a compact space (Mult(A, ‖ ⋅ ‖)) and with value in a locally compact space (Mult(K[x])). We study these transforms and particularly the injectivity of the second. We deduce some spectral properties of this injectivity. Given φ ∈ Mult(A, ‖ ⋅ ‖), we will denote by Zφ the mapping from A into Mult(K[x]) defined as Zφ(f) = f*(φ). We show that each function Zφ is continuous. Moreover we put a metric topology δ on (Mult(K[x])) such that the family of functions Zφ, φ ∈ Mult(A, ‖ ⋅ ‖) is equicontinuous.Let K be an algebraically closed field, complete for a non‐trivial ultrametric absolute value, and let A be a commutative normed K‐algebra with identity. We call multiplicative spectrum of A the set Mult(A, ‖ ⋅ ‖) of continuous multiplicative semi‐norms on A. We denote by Mult(K[x]) the set of multiplicative semi‐norms on the polynomial algebra K[x]. Both sets of semi‐norms are endowed with the topology of pointwise convergence. We also denote by X(A, K) the set of K‐algebra homomorphism from A onto K. Unlike in complex analysis, there might exist some maximal ideals in A which are not the kernel of elements of X(A, K). In A, we can define two kinds of Gelfand transform. GA and GMA. The first one, denoted by GA is similar to that in complex analysis, consisting of associating to each element f of A the mapping f from X(A, K) to K defined as f(χ) = χ(f), (χ ∈ X(A, K)). The second, denoted by GMA consists of associating to each element f of A the mapping f* from Mult(A, ‖ ⋅ ‖) to Mult(K[x]) defined as f*(...

In this work, Fredholm joint spectrum of noncommuting operator family which generates nilpotent Lie algebra is defined and investigated some properties of it. The joint spectrum of a is defined to be the set σF(a) of those λ ∈ Cn for which the complex Kos(a − λ, X) whose co‐homology spaces are not of finite dimension. It is proved that σF (a) is a compact set in Cn. Polynomial spectral mapping theorem with respect to polynomials in noncommuting variables is proved such that P(σF(a)) ⊂ σF(P(a)).

The possibility that the processes responsible for the Cosmic x‐ray Background (CXB) would also produce an e−−e+ annihilation feature is examined. Under the assumption that these processes are thermal, the absence of a strong e−=e+ annihilation feature places constraints on the compactness (L/R ratio) of these sources. Observations favor sources of small compactness ratio.