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In this paper, we investigate the problem of solving strongly monotone variational inequalities over the solution sets of split feasibility problems with multiple output sets in real Hilbert spaces. We present two new iterative algorithms when the involved subsets are given as the level sets of convex functions. In our algorithms, the projection to the half-space is replaced by the one to the intersection of two half-spaces. The algorithms are accelerated using the inertial technique and eliminate the need for calculating or estimating the norms of linear operators by employing self-adaptive step size criteria. We give convergence of the sequence generated by our algorithms under some suitable assumptions. Some applications to monotone variational inequalities over the solution set of the split feasibility problem are also reported. Finally, we present some numerical examples to illustrate the efficiency and implementation of our algorithms in comparison with existing algorithms in the literature. [ABSTRACT FROM AUTHOR]

This paper extends some results of Mattila (J. Fractal Geom. 66 (2021) 389–401 and Ann. Acad. Sci. Fenn. A Math. 42 (2017) 611–620), in particular, removing assumptions of positive lower density. We give conditions on a general family Pλ:Rn→Rm,λ∈Λ$P_{\lambda }:\mathbb {R}^n\rightarrow \mathbb {R}^m, \lambda \in \Lambda$, of orthogonal projections which guarantee that the Hausdorff dimension formula dimA∩Pλ−1{u}=s−m$\dim A\cap P_{\lambda }^{-1}\lbrace u\rbrace =s-m$ holds generically for measurable sets A⊂Rn$A\subset \mathbb {R}^{n}$ with positive and finite s$s$‐dimensional Hausdorff measure, s>m$s>m$. As an application we prove for Borel sets A,B⊂Rn$A,B\subset \mathbb {R}^{n}$ with positive s$s$‐ and t-dimensional$t{\text{-dimensional}}$ measures that if s+(n−1)t/n>n$s + (n-1)t/n > n$, then dimA∩(g(B)+z)⩾s+t−n$\dim A\cap (g(B)+z) \geqslant s+t - n$ for almost all rotations g$g$ and for positively many z∈Rn$z\in \mathbb {R}^{n}$. We shall also give an application to the estimates of the dimension of the set of exceptional rotations. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a version of the Feynman-Kac formula for the tempered fractional general diffusion equation$ \begin{align} \partial^{\beta, \eta}_{t} u(t,x) = \mathfrak{L}u(t,x) +b(t)u(t,x),\; \; x\in\mathcal{X},\; t\geq0, \end{align} $with initial value $ f $ belonging to a Banach space $ (\mathbb{B}, \|\cdot\|) $, where $ \partial^{\beta, \eta}_{t} $ denotes the Caputo tempered fractional derivative with order $ \beta\in(0,1) $ and tempered parameter $ \eta>0 $, $ b(t) $ is a bounded and continuous external potential on $ [0, \infty) $, $ \mathfrak{L} $ is the infinitesimal generator of a general time-homogeneous strong Markov process $ \{X_{t}\}_{t\geq0} $, and $ \mathcal{X} $ denotes a Lusin space that is a topological space being homeomorphic to a Borel subset of a compact metric space. By using the properties of the tempered $ \beta $-stable subordinator $ S_{\beta,\eta}(t) $ and the inverse tempered $ \beta $-stable subordinator $ D_{\beta,\eta}(t) $, and the stochastic calculus for the stochastic integral driven by $ D_{\beta,\eta}(t) $, we show that the Feynman-Kac representation $ u(t,x) $ defined by$ \begin{align} u(t,x) = {\mathbb{E}}^{x}\bigg[f(X_{D_{\beta,\eta}(t)}) e^{\int_{0}^{t}b(r)dD_{\beta,\eta}(r)}\bigg] \end{align} $is the unique mild and weak solutions to the tempered fractional general diffusion equation. From the Feynman-Kac formula, we further show the continuity of the solution with respect to time based on the integral properties of the Mittag-Leffler function and differential formula of covariance for $ D_{\beta,\eta}(t) $. By exploring the scaling property of $ D_{\beta,\eta}(t) $, the explicit order is also presented for the continuity of the solution with respect to tempered parameter $ \eta $. [ABSTRACT FROM AUTHOR]

Matching algorithms are commonly used to build comparable subsets (matchings) in observational studies. When a complete matching is not possible, some units must necessarily be excluded from the final matching. This may bias the final estimates comparing the two populations, and thus it is important to reduce the number of drops to avoid unsatisfactory results. Greedy matching algorithms may not reach the maximum matching size, thus dropping more units than necessary. Optimal matching algorithms do ensure a maximum matching size, but they implicitly assume that all units have the same matching priority. In this paper, we propose a matching strategy which is order optimal in the sense that it finds a maximum matching size which is consistent with a given matching priority. The strategy is based on an order-optimal matching algorithm originally proposed in connection with assignment problems by D. Gale. When a matching priority is given, the algorithm ensures that the discarded units have the lowest possible matching priority. We discuss the algorithm's complexity and its relation with classic optimal matching. We illustrate its use with a problem in a case study concerning a comparison of female and male executives and a simulation. [ABSTRACT FROM AUTHOR]

Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some covariates belong to general Borel conditioning subsets. We introduce several test statistics based on the equality of conditional Kendall's taus and derive their asymptotic distributions under the null hypothesis. In settings where such conditioning events are not fixed ex ante, we propose a data‐driven procedure to recursively build such relevant subsets. This procedure is based on decision trees that maximize the differences between the conditional Kendall's taus, which correspond to the leaves of the trees. Empirical results for such tests are illustrated in the Supplementary Material. Moreover, a study of the conditional dependence between financial stock returns is presented and highlights specific contagion effects of past returns. The last application deals with conditional dependence between coverage amounts in an insurance dataset. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce the notion of (α,β)-level sets with respect to intuitionistic fuzzy normed ideals. We extend the notion of intuitionistic fuzzy normed ideals to the (α,β)-level subsets where α and β are elements in the interval[0,1]. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR, NR' with a mapping NR', a relation between the intuitionistic fuzzy normed ideal I of NR and the intuitionistic fuzzy normed ideal f I) the image of I) of NR' will be obtained with the support of their (α,β)-level subsets. [ABSTRACT FROM AUTHOR]

Zero-variance control variates (ZV-CV) are a post-processing method to reduce the variance of Monte Carlo estimators of expectations using the derivatives of the log target. Once the derivatives are available, the only additional computational effort lies in solving a linear regression problem. Significant variance reductions have been achieved with this method in low dimensional examples, but the number of covariates in the regression rapidly increases with the dimension of the target. In this paper, we present compelling empirical evidence that the use of penalized regression techniques in the selection of high-dimensional control variates provides performance gains over the classical least squares method. Another type of regularization based on using subsets of derivatives, or a priori regularization as we refer to it in this paper, is also proposed to reduce computational and storage requirements. Several examples showing the utility and limitations of regularized ZV-CV for Bayesian inference are given. The methods proposed in this paper are accessible through the R package ZVCV. [ABSTRACT FROM AUTHOR]

Given a probability space (Ω , A , P) , a complete separable Banach space X with the σ -algebra B (X) of all its Borel subsets, an operator Λ : Ω → L (X , X) and ξ : Ω → X we consider the B (X) ⊗ A -measurable function f : X × Ω → X given by f (x , ω) = Λ (ω) x + ξ (ω) and investigate the continuous dependence of a weak limit π f of the sequence of iterates (f n (x , ·)) n ∈ N of f, defined by f 0 (x , ω) = x , f n + 1 (x , ω) = f (f n (x , ω) , ω n + 1) for x ∈ X and ω = (ω 1 , ω 2 , ⋯) . Moreover for X taken as a Hilbert space we characterize π f via the functional equation φ f (u) = ∫ Ω φ f (Λ (ω) u) φ ξ (u) P (d ω) with the aid of its characteristic function φ f . We also indicate the continuous dependence of a solution of that equation. [ABSTRACT FROM AUTHOR]

We characterize the completely determined Borel subsets of HYP as exactly the Δ 1 (L ω 1 c k ) subsets of HYP. As a result, HYP believes there is a Borel well-ordering of the reals, that the Borel Dual Ramsey Theorem fails, and that every Borel d-regular bipartite graph has a Borel perfect matching, among other examples. Therefore, the Borel Dual Ramsey Theorem and several theorems of descriptive combinatorics are not theories of hyperarithmetic analysis. In the case of the Borel Dual Ramsey Theorem, this answers a question of Astor, Dzhafarov, Montalbán, Solomon and the third author. [ABSTRACT FROM AUTHOR]

For any m distinct elements r1, r2, · · ·, rm in a ring R, the m-element centralizer of {r1, r2, · · ·, rm} in R is defined as CR({r1, r2, · · ·, rm}) = {s ∈ R | sr1 = r1s, sr2 = r2s, . . ., srm = rms}, where m ∈ N with m ≽ 2. We define the set of all distinct m-element centralizers in a ring R by m - Cent(R), where m ∈ N with m ≽ 2. Further, R is called (m, n)-centralizer ring if |m - Cent(R)| = n, where n ∈ N. In this paper, we characterize some of the (m, n)-centralizer finite rings for n ≼ 7. [ABSTRACT FROM AUTHOR]

We consider many-server queueing systems with heterogeneous exponential servers, for which the service rate of each server is a random variable drawn from a given distribution. We develop a framework for analyzing the heavy-traffic diffusion limits of these queues using measure-valued stochastic processes. We introduce the measure-valued fairness process, which denotes the proportion of cumulative idleness experienced by servers whose rates fall in a Borel subset of the support of the service rates. It can be shown that these processes do not converge in the usual Skorokhod-J1 topology. Hence, we introduce a new notion of convergence based on shifted versions of these processes. We also introduce some useful martingales to identify limiting fairness processes under different routing policies. To demonstrate the power of our framework, we show how it can be used to prove diffusion limits for parallel server systems with within-pool heterogeneity. [ABSTRACT FROM AUTHOR]

In this paper, we introduced and studied δ-small submodule over prime module. Two concepts are very important namely strongly prime submodule and completely prime submodule. Multiple results led to obtaining a δ-small submodule of a singular, divisible and Bezout module with R is local. Important terms that appeared in this article, together with some terms, produced the submodule that we were interested in. [ABSTRACT FROM AUTHOR]

Let A and B be Borel subsets of the Euclidean n-space with  dim A + dim B > n . This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections  A ∩ (g (B) + z)  for generic orthogonal transformations g and translations by z? [ABSTRACT FROM AUTHOR]

On our ordinary representations of space, space is composed of indivisible, dimensionless points; extended regions are understood as infinite sets of points. Region-based theories of space reverse this atomistic picture, by taking as primitive several relations on extended regions, and recovering points as higher-order abstractions from regions. Over the years, such theories have focused almost exclusively on the topological and geometric structure of space. We introduce to region-based theories of space a new primitive binary relation ('qualitative probability') that is tied to measure. It expresses that one region is smaller than or equal in size to another. Algebraic models of our theory are separationσ-algebras with qualitative probability: (B , ≪ , ≼) , where B is a Boolean σ-algebra, ≪ is a separation relation on B , and ≼ is a qualitative probability on B . We show that from algebraic models of this kind we can, in an interesting class of cases, recover a compact Hausdorff topology X, together with a countably additive measure μ on a σ-field of Borel subsets of that topology, and that (B , ≪ , ≼) is isomorphic to a 'standard model' arising out of the pair (X, μ). It follows from one of our main results that any closed ball in Euclidean space, ℝ n , together with Lebesgue measure arises in this way from a separation σ-algebra with qualitative probability. [ABSTRACT FROM AUTHOR]

Abstract. This paper studies a variant of ramifed/branched optimal transportation problems. Given the distributions of production capacities and market sizes, a frm looks for an allocation of productions over factories, a distribution of sales across markets, and a transport path that delivers the product to maximize its proft. Mathematically, given any two measures and a payof function h, the planner wants to minimize M(T) X hd(T) among all transport paths T from where M is the standard cost functional used in ramifed transportation. After proving the existence result, we provide a characterization of the boundary measures of the optimal solution. They turn out to be the original measures restricted on some Borel subsets up to a Delta mass on each connected component. Our analysis further fnds that as the boundary payof increases, the corresponding solution of the current problem converges to an optimal transport path, which is the solution of the standard ramifed transportation. [ABSTRACT FROM AUTHOR]

In this paper, given a function f: IxV → ℝm, where V is an open subset of ℝm, x0 ∈ V, and I = [0, T] is the interval of interest, we consider the Cauchy ordinary differential equation initial-value problem ...(f, x0) = f(t, x(t)), x(0) = x0. We first present a new quantitative stability result under a partial and/or global variation of the data of the problem by involving exact and/or approximate fixed points for which we apply Lim's Lemma either in its exact format or in its very recent approximate version. Our main result is then applied to parametric linear control systems. Finally, we demonstrate that our treatment is coherent with the management of perturbations generated in the classic one-step numerical method. A numerical example written in Scilab 6.1 illustrates the obtained stability. [ABSTRACT FROM AUTHOR]

We study analytic and Borel subsets defined similarly to the old example of analytic complete set given by Luzin. Luzin's example, which is essentially a subset of the Baire space, is based on the natural partial order on naturals, i.e. division. It consists of sequences which contain increasing subsequence in given order. We consider a variety of sets defined in a similar way. Some of them occurs to be Borel subsets of the Baire space, while others are analytic complete, hence not Borel. In particular, we show that an analogon of Luzin example based on the natural linear order on rationals is analytic complete. We also characterize all countable linear orders having such property. [ABSTRACT FROM AUTHOR]

Given a domain D in Cn and a compact subset K of D, the set AD/K of all restrictions of functions holomorphic on D the modulus of which is bounded by 1 is a compact subset of the Banach space C(K) of continuous functions on K. The sequence (dm(AD/K))m∈N of Kolmogorov m-widths of AD/K provides a measure of the degree of compactness of the set AD/K in C(K) and the study of its asymptotics has a long history, essentially going back to Kolmogorov's work on ϵ-entropy of compact sets in the 1950s. In the 1980s Zakharyuta showed that for suitable D and K the asymptotics where C(K,D) is the Bedford-Taylor relative capacity of K in D, is implied by a conjecture, now known as Zakharyuta's Conjecture, concerning the approximability of the regularised relative extremal function of K and D by certain pluricomplex Green functions. Zakharyuta's Conjecture was proved by Nivoche in 2004 thus settling (1) at the same time. We shall give a new proof of the asymptotics (1) for D strictly hyperconvex and K non-pluripolar which does not rely on Zakharyuta's Conjecture. Instead we proceed more directly by a two-pronged approach establishing sharp upper and lower bounds for the Kolmogorov widths. The lower bounds follow from concentration results of independent interest for the eigenvalues of a certain family of Toeplitz operators, while the upper bounds follow from an application of the Bergman-Weil formula together with an exhaustion procedure by special holomorphic polyhedra. [ABSTRACT FROM AUTHOR]

Conway's real closed field No of surreal numbers is a sweeping generalization of the real numbers and the ordinals to which a number of elementary functions such as log and exponentiation have been shown to extend. The problems of identifying significant classes of functions that can be so extended and of defining integration for them have proven to be formidable. In this paper we address this and related unresolved issues by showing that extensions to No , and thereby integrals, exist for most functions arising in practical applications. In particular, we show they exist for a large subclass of the resurgent functions , a subclass that contains the functions that at ∞ are semi-algebraic, semi-analytic, analytic, meromorphic, and Borel summable as well as solutions to nonresonant linear and nonlinear meromorphic systems of ODEs or of difference equations. By suitable changes of variables we deal with arbitrarily located singular points. We further establish a sufficient condition for the theory to carry over to ordered exponential subfields of No more generally and illustrate the result with structures familiar from the surreal literature. The extensions of functions and integrals that concern us are constructive in nature, which permits us to work in NBG less the Axiom of Choice (for both sets and proper classes). Following the completion of the positive portion of the paper, it is shown that the existence of such constructive extensions and integrals of substantially more general types of functions (e.g. smooth functions) is obstructed by considerations from the foundations of mathematics. [ABSTRACT FROM AUTHOR]

A set E in a Banach space X is compactivorous if for every compact set K in X there is a nonempty, (relatively) open subset of K which can be translated into E. In a separable Banach space, this is a sufficient condition which guarantees the Haar nonnegligibility of Borel subsets. We give some characterisations of this property in both separable and nonseparable Banach spaces and prove an extension of the main theorem to countable products of locally compact Polish groups. [ABSTRACT FROM AUTHOR]

In this paper we study hypergraphs definable in an algebraically closed field. Our goal is to show, in the spirit of the so-called transference principles in extremal combinatorics, that if a given algebraic hypergraph is "dense" in a certain sense, then a generic low-dimensional subset of its vertices induces a subhypergraph that is also "dense." (For technical reasons, we only consider low-dimensional subsets that are parameterized by rational functions.) Our proof approach is inspired by the hypergraph containers method, developed by Balogh, Morris, and Samotij and independently by Saxton and Thomason (although adapting this method to the algebraic setting presents some unique challenges that do not occur when working with finite hypergraphs). Along the way, we establish a natural generalization of the classical dimension of fibers theorem in algebraic geometry, which is interesting in its own right. [ABSTRACT FROM AUTHOR]

In this paper we will study the representations of isomorphisms between bases of topological spaces. It turns out that the perfect setting for this study is that of regular open subsets of complete metric spaces, but we have been able to show some results about arbitrary bases in complete metric spaces and also about regular open subsets in Hausdorff regular topological spaces. [ABSTRACT FROM AUTHOR]

Given two functions f , g : I → R and a probability measure μ on the Borel subsets of [0, 1], the two-variable mean M f , g ; μ : I 2 → I is defined by M f , g ; μ (x , y) : = (f g ) - 1 ∫ 0 1 f (t x + (1 - t) y) d μ (t) ∫ 0 1 g (t x + (1 - t) y) d μ (t) (x , y ∈ I). This class of means includes quasiarithmetic as well as Cauchy and Bajraktarević means. The aim of this paper is, for a fixed probability measure μ , to study their equality problem, i.e., to characterize those pairs of functions (f, g) and (F, G) for which M f , g ; μ (x , y) = M F , G ; μ (x , y) (x , y ∈ I) holds. Under at most sixth-order differentiability assumptions for the unknown functions f, g and F, G, we obtain several necessary conditions in terms of ordinary differential equations for the solutions of the above equation. For two particular measures, a complete description is obtained. These latter results offer eight equivalent conditions for the equality of Bajraktarević means and of Cauchy means. [ABSTRACT FROM AUTHOR]

In this paper, we study the Charlier statistical structures -E, S, μi, i ε I}. The sufficient and necessary conditions are given for the existence of consistent estimates of parameters for various definitions of strong separability of statistical structures and for various σ-algebras S. [ABSTRACT FROM AUTHOR]

Flexible job shop scheduling (FJSS) is derived by inheriting the features of the job-shop scheduling problem. It has an extra routing sub-problem of the job-shop scheduling. FJSS is well known as an NP-hard problem in the literature. A new hybrid scatter search method is proposed to solve the FJSS problem. The objective function of the proposed hybrid scatter search method is minimizing the maximum completion time (Cmax) for FJSS problems. The proposed hybrid scatter search method is integrating a local and global search for generating an initial population. The performance of the proposed new hybrid scatter search method is dependent on the selected parameters. These parameters are the size of the initial population and reference set; the number of subsets, reference set updating and population sub updating; reproduction, crossover, and mutation operators, and their ratio. A full factorial experimental design is made to determine the best values of control parameters and operators for the proposed new hybrid scatter search to solve the FJSS problems. The proposed new hybrid scatter search method is tested on a set of the well-known benchmark flexible job shop scheduling instances from the literature. The computational results indicated that the proposed new hybrid scatter search is an effective method for solving the FJSS problems. [ABSTRACT FROM AUTHOR]

In the paper, we establish the complete moment convergence and complete convergence for weighted sums of arrays of rowwise m-asymptotic negatively associated random variables. As an application, the strong law of large numbers for weighted sums of m-ANA random variables is presented. The obtained results generalize the corresponding ones for NA random variables and ρ* -mixing random variables. [ABSTRACT FROM AUTHOR]

In this paper, we present some concepts related to ωpre open set and study some of its basic properties, facts and some examples are given to illustrate our work. Several theoretical results are stated and proved throughout this paper. [ABSTRACT FROM AUTHOR]

For a graph G(V (G),E(G)), a set S is semitotal dominating set if both the set S is a dominating set and every vertex in S must be within 2 distance of another vertex in S. The minimum cardinality of a semitotal dominating set is called semitotal domination number and is denoted by ?t2(G). The semitotal bondage number, denoted by bt2(G), of G is the minimum number of edges to be removed from the graph to increase the semitotal domination number. We determine the semitotal domination number and semitotal bondage number of some wheel and cycle related graphs such as friendship, gear, helm, fan and n-gon book. [ABSTRACT FROM AUTHOR]

Let (S , τ) be a nontrivial compact metric space with metric τ and g : S → S be a continuous self-map, ℬ (S) be the sigma-algebra of Borel subsets of S , and ν be a Borel probability measure on (S , ℬ (S)) with ν (V) ∈ (0 , + ∞) for any open subset V ≠ ∅ of S. This paper proves the following results : (1) If the pair (g , ν) has the property that for any β > 0 , there is r (β) > 0 such that ν p ∈ S : 1 m ∑ i = 0 m − 1 V (g i (p)) − ∫ V d ν > β ≤ e − m r (β) , for any open subset V ≠ ∅ of S and all n ≥ 1 sufficiently large (where V is the characteristic function of the set V), then the following hold : (a) The map g is topologically ergodic. (b) The upper density μ ¯ (N g (p , V)) of N g (p , V) is positive for any open subset V ≠ ∅ of S , where N g (p , V) = { m ∈ { 0 , 1 , ... } : g m (p) ∈ V }. (c) There is a g -invariant Borel probability measure ν having full support (i.e. supp (ν) = S). (d) Sensitivity of the map g implies positive lower density sensitivity, hence ergodical sensitivity. (2) If μ ̲ (N g (A , B)) = 1 for any two nonempty open subsets A , B , then there exists λ > 0 satisfying μ ̲ (N g (C , λ)) = 1 for any nonempty open subset C ⊂ S , where N g (C , λ) = { l ∈ { 0 , 1 , ... } : there exist a , b ∈ C with τ (g l (a) , g l (b)) > λ }. [ABSTRACT FROM AUTHOR]

In this article, we study the existence and uniqueness of nonnegative solutions for the following parabolic problem { H t ω u + ∂ u ∂ t = 0 , in X × (0 , T) , u (x , 0) = u 0 (x) , in X , where T > 0, X is a locally compact separable metric space, Ht is a operator (not necessarily selfadjoint) associated with a regular (not necessarily symmetric)local Dirichlet form E t , the initial value u 0 ∈ L 2 (X , ω 2 d m) and m is a positive Radon measure on Borel subset U of X such that m(U) > 0. Our technical approach for uniqueness is based on Täcklind type uniqueness theorem. [ABSTRACT FROM AUTHOR]

As an instance of a neutrosophic set, a single-valued neutrosophic set (SVNS) can be used to handle uncertainty, inaccuracy, indeterminacy, and inconsistency. In this paper, a new not-sosophisticated distance measure between two SVNSs is defined by considering the crossassessment between characteristic functions for the forward and backward differences. Furthermore, a single-valued neutrosophic similarity measure, a single-valued neutrosophic entropy measure, and their basic properties are presented and proven. In addition, an application to medical diagnosis is shown to illustrate the effective applicability of the proposals. [ABSTRACT FROM AUTHOR]

In this paper, we study some cube packing problems. In particular, we are interested in compact subsets of ℝ[sup n], n ≥ 2, which contain boundaries of cubes with all side lengths in (0,1). We show here that such sets must have lower box dimension at least n - 0.5, and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper. [ABSTRACT FROM AUTHOR]

Let n ∈ Z≥3. Given any Borel subset A of Rn with finite and nonzero measure, we prove that the probability that the set of primitive points of a random full-rank unimodular lattice in Rn does not contain any R-linearly independent subset of A of cardinality (n−2) is bounded from above by a constant multiple, which depends only on n, of (vol(A))−1. This generalizes a result that is jointly due to J. S. Athreya and G. A. Margulis (see Theorem 2.2 [J. Mod. Dyn. 3 (2009), pp. 359-378]). We also generalize independent results of C. A. Rogers (see Theorem 6 [Acta Math. 94 (1955), pp. 249-287]) and W. M. Schmidt (see Theorem 1 [Trans. Amer. Math. Soc. 95 (1960), 516-529]) about primitive lattice points of random lattices to the case of primitive tuples of rank less than n/2. In addition to the work of the authors who were just mentioned, a crucial element of this present paper is the usage of a rearrangement inequality due to Brascamp-Lieb-Luttinger (see Theorem 3.4 [J. Functional Analysis 17 (1974), pp. 227-237]). [ABSTRACT FROM AUTHOR]

We present written naming norms from 153 young adult Dutch speakers for 1397 photographs (the BOSS set; see Brodeur, Dionne-Dostie, Montreuil, & Lepage, 2010; Brodeur, Guérard, & Bouras, 2014). From the norming study, we report the preferred (modal) name, alternative names, name agreement, and average object agreement. In addition, the data base includes Zipf frequency, word prevalence and Age of Acquisition for the modal picture names collected. Furthermore, we describe a subset of 359 photographs with very good name agreement and a subset of 35 photos with two common names. These sets may be particularly valuable for designing experiments. Though the participants typed the object names, comparisons with other datasets indicate that the collected norms are valuable for spoken naming studies as well. [ABSTRACT FROM AUTHOR]

This article deals with the problem of when, given a collection $\mathcal {C}$ of weakly compact operators between separable Banach spaces, there exists a separable reflexive Banach space Z with a Schauder basis so that every element in $\mathcal {C}$ factors through Z (or through a subspace of Z). In particular, we show that there exists a reflexive space Z with a Schauder basis so that for each separable Banach space X, each weakly compact operator from X to $L_1[0,1]$ factors through Z. We also prove the following descriptive set theoretical result: Let $\mathcal {L}$ be the standard Borel space of bounded operators between separable Banach spaces. We show that if $\mathcal {B}$ is a Borel subset of weakly compact operators between Banach spaces with separable duals, then for $A \in \mathcal {B}$ , the assignment $A \to A^*$ can be realised by a Borel map $\mathcal {B}\to \mathcal {L}$. [ABSTRACT FROM AUTHOR]

Given a finite poset P, we call a family F of subsets of [n] P‐saturated if F does not contain an induced copy of P, but adding any other set to F creates an induced copy of P. The induced saturated number of P, denoted by sat∗(n,P), is the size of the smallest P‐saturated family with ground set [n]. In this paper, we are mainly interested in the four‐point poset called the butterfly. Ferrara et al. showed that the saturation number for the butterfly lies between log2n and n2. We give a linear lower bound of n+1. We also prove some other results about the butterfly and the poset N. [ABSTRACT FROM AUTHOR]

Let Bo(T,τ) be the Borel σ-algebra generated by the topology τ on T. In this paper we show that if K is a Hausdorff compact space, then every subset of K is a Borel set if and only if Bo(C*(K), w* = Bo(C*(K),|⋅|), where w* denotes the weak-star topology and |⋅| is the dual norm with respect to the sup-norm on the space of real-valued continuous functions C(K). Furthermore, we study the topological properties of the Hausdorff compact spaces K such that every subset is a Borel set. In particular, we show that if the axiom of choice holds true, then K is scattered. [ABSTRACT FROM AUTHOR]

In this paper, we offer and study a novel type generalized soft-open sets in topological spaces, named soft Ƅc-open sets. Relationships of this set with other types of generalized soft-open sets are discussed, definitions of soft Ƅ , soft bc- closure and soft bc- interior are introduced, and its properties are investigated. Also, we introduce and explore several characterizations and properties of this type of sets. Keywords: soft Ƅ-open set, soft Ƅc-open set, soft Ƅc- nbd, soft Ƅc-interior, soft Ƅcclosure. [ABSTRACT FROM AUTHOR]

The goal of the research is to introduce new types of maps called semi totally Bccontinuous map and totally Bc-continuous map furthermore, study its properties. Additionally, we study the relationship of these functions and other known mappings are discussed. Keyw [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the essential and closed fuzzy submodules of a fuzzy module X as a generalization of the notions of essential and closed submodules. We prove many basic properties of both concepts. [ABSTRACT FROM AUTHOR]

We study the class of Borel equivalence relations under continuous reducibility. In particular, we characterize when a Borel equivalence relation with countable equivalence classes is Σ0ξ (or Π0ξ). We characterize when all the equivalence classes of such a relation are Σ0ξ (or Π0ξ). We prove analogous results for the Borel equivalence relations with countably many equivalence classes. We also completely solve these two problems for the first two ranks. In order to do this, we prove some extensions of the Louveau-Saint Raymond theorem, which itself generalized the Hurewicz theorem characterizing when a Borel subset of a Polish space is Gδ. [ABSTRACT FROM AUTHOR]

We prove that the Wadge order on the Borel subsets of the Scott domain is not a well-quasi-order, and that this feature even occurs among the sets of Borel rank at most 2. For this purpose, a specific class of countable 2-colored posets $\mathbb{P}_{emb} $ equipped with the order induced by homomorphisms is embedded into the Wadge order on the $\Delta _2^0 $ -degrees of the Scott domain. We then show that $\mathbb{P}_{emb} $ admits both infinite strictly decreasing chains and infinite antichains with respect to this notion of comparison, which therefore transfers to the Wadge order on the $\Delta _2^0 $ -degrees of the Scott domain. [ABSTRACT FROM AUTHOR]

We prove a formula relating the Hausdorff dimension of a deterministic Borel subset of R and the Hausdorff dimension of its image under a conformal map from the upper half-plane to a complementary connected component of an SLE κ curve for κ ≠ 4 . Our proof is based on the relationship between SLE and Liouville quantum gravity together with the one-dimensional KPZ formula of Rhodes and Vargas (ESAIM Probab Stat 15:358–371, 2011) and the KPZ formula of Gwynne et al. (Ann Probab, 2015). As an intermediate step we prove a KPZ formula which relates the Euclidean dimension of a subset of an SLE κ curve for κ ∈ (0 , 4) ∪ (4 , 8) and the dimension of the same set with respect to the γ -quantum natural parameterization of the curve induced by an independent Gaussian free field, γ = κ ∧ (4 / κ) . [ABSTRACT FROM AUTHOR]

In this paper, the concepts of J2 -Cauchy. J2* -Cauchy double sequences in fuzzy n-normed spaces were introduced and some properties and relations of them were studied. We show that if a double sequence (xmr) in X is an 3-double Cauchy sequence, then it is J2*-double Cauchy sequence, where J, denotes the ideal of subsets of NxN. [ABSTRACT FROM AUTHOR]

In this paper, motivated by [F. Vetro, Filomat, 29:9 (2015), 2011-2020] we present some fixed point results for a class of nonexpansive self-mappings and multi-valued mappings in the framework of b-metric spaces. Our results generalize and improve the consequences of [ Khojasteh et al. Abstract and Applied Analysis, vol. 2014, Article ID 325840, 5 pages, 2014.] and [F. Vetro, Filomat, 29:9 (2015), 2011-2020]. Some examples are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper is based on the investigation and characterization of the properties of quasi G-s-topological loops. Moreover, we have also introduced the notion of quasi G-s-topological loop having inverse property respecting semi continuity. [ABSTRACT FROM AUTHOR]

A set X endowed with a coarse structure is called ballean or coarse space. For a ballean (X, E), we say that two subsets A, B of X are close (linked) if there exists an entourage E ∈ E such that A ⊆ E[B], B ⊆ E[A] (either A, B are bounded or contain unbounded close subsets). We explore the following general question: which information about a ballean is contained and can be extracted from the relations of closeness and linkness. [ABSTRACT FROM AUTHOR]

We provide a semilocal analysis of the Newton-Kurchatov method for solving nonlinear equations involving a splitting of an operator. Iterative methods have a limited restricted region in general. A convergence of this method is presented under classical Lipschitz conditions. The novelty of our paper lies in the fact that we obtain weaker sufficient semilocal convergence criteria and tighter error estimates than in earlier works. We find a more precise location than before where the iterates lie resulting to at least as small Lipschitz constants. Moreover, no additional computations are needed than before. Finally, we give results of numerical experiments. [ABSTRACT FROM AUTHOR]