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The aim of this paper is to study the notion of quasi-ideals in semigroups on weak nearness approximation spaces and explain some of the concepts and definitions. Also, it is given an example related to the subject. The features described in this study will contribute greatly to the theoretical developments of the nearness semigroup theory. [ABSTRACT FROM AUTHOR]

The current paper contributes towards the investigation of L-supermerotopic spaces. It is a generalization of merotopy as far as the axiomatic structure is concerned, and proximity, both in terms of axioms and number of elements. Lattice structures of L-supermerotopic spaces are investigated and it is searched through L-superpremerotopy. Some basic and desirable results are also obtained.. [ABSTRACT FROM AUTHOR]

In this paper, we focus on pairs consisting of the affine N-space and multiideals with a positive exponent. We introduce a method flifting to characteristic 0 which is a kind of the inversion of "modulo p reduction". By making use of it, we prove that Mustaffta-Nakamura's conjecture and some uniform bound of divisors computing log canonical thresholds descend from characteristic 0 to certain classes of pairs in positive characteristic. We also pose a problem whose affirmative answer gives the descent of the statements to the whole set of pairs in positive characteristic. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of how to define Γ -nearness ring in the sense of Nobusawa theory which extends the notion of a nearness ring and Γ -rings [N. Nobusawa, Osaka J. Math.1 (1964) 81–89; M. A. Öztürk and E. İnan, Annals of Fuzzy Mathematics and Informatics17(2) (2019) 115–131]. Also, we introduce some properties of approximations and these algebraic structures. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of how to define Γ-nearness semigroup theory which extends the notion of a nearness semigroup and roughness of Γ-semigroups ([6] and [11]) to include the algebraic structures of near sets and rough sets, respectively. Also, we introduce some properties of aproximations and these algebraic structures. [ABSTRACT FROM AUTHOR]

This article proposes the tolerance nearness measure (TNM) as a computationally reduced alternative to the graph edit distance (GED) for performing graph comparisons. The TNM is defined within the context of near set theory, where the central idea is that determining similarity between sets of disjoint objects is at once intuitive and practically applicable. The TNM between two graphs is produced using the Bron-Kerbosh maximal clique enumeration algorithm. The result is that the TNM approach is less computationally complex than the bipartite-based GED algorithm. The contribution of this paper is the application of TNM to the problem of quantifying the similarity of disjoint graphs and that the maximal clique enumeration-based TNM produces comparable results to the GED when applied to the problem of content-based image processing, which becomes important as the number of nodes in a graph increases. [ABSTRACT FROM AUTHOR]

We study the uniform connection properties of uniform local connectedness, a weaker variant of the latter, and a certain property S in the context of nearness frames. We show that the uniformly locally connected nearness frames form a reflective subcategory of the category of nearness frames whose underlying frame is locally connected. Amongst other results we show that these uniform connection properties are conserved and reflected by perfect nearness extensions which are uniformly regular. [ABSTRACT FROM AUTHOR]

Proofs of proximity are proof systems wherein the verifier queries a sublinear number of bits, and soundness only asserts that inputs that are far from valid will be rejected. In their minimal form, called MA proofs of proximity ( MAP ) , the verifier receives, in addition to query access to the input, also free access to a short (sublinear) proof. A more general notion is that of interactive proofs of proximity ( IPP ) , wherein the verifier is allowed to interact with an omniscient, yet untrusted prover. We construct proofs of proximity for two natural classes of properties: (1) context-free languages, and (2) languages accepted by small read-once branching programs. Our main results are: 1. MAP s for these two classes, in which, for inputs of length n , both the verifier's query complexity and the length of the MAP proof are O ˜ ( n ) . 2. IPP s for the same two classes with constant query complexity, poly-logarithmic communication complexity, and logarithmically many rounds of interaction. [ABSTRACT FROM AUTHOR]

Covariance matrices that fail to be positive definite arise often in covariance estimation. Approaches addressing this problem exist, but are not well supported theoretically. In this paper, we propose a unified statistical and numerical matrix calibration, finding the optimal positive definite surrogate in the sense of Frobenius norm. The proposed algorithm can be directly applied to any estimated covariance matrix. Numerical results show that the calibrated matrix is typically closer to the true covariance, while making only limited changes to the original covariance structure. [ABSTRACT FROM AUTHOR]

This paper aims at analyzing all-pairs shortest paths algorithm by Floyd to extract optimal path between any pair of vertices of various path length. To form least cost round tour, vertices of an optimal chain are grouped into cluster. These optimal chains are combined by taking an account of both path length as well as magnitude of the path. The chain which has largest path length and optimal distance will be considered first. Tour is constructed by adding up vertices to optimal chains in suitable positions based on nearness. This approach is a mix of both dynamic and greedy strategies. Illustrations of different variations are focus of the study. [ABSTRACT FROM AUTHOR]

We first study subspaces and product spaces in the context of nearness spaces and prove that U-N spaces, C-N spaces, PN spaces and totally bounded nearness spaces are nearness hereditary; T-N spaces and compact nearness spaces are N-closed hereditary. We prove that N2 plus compact implies N-closed subsets. We prove that totally bounded, compact and N2 are productive. We generalize the concepts of neighborhood systems into the nearness spaces and prove that the nearness neighborhood systems are consistent with existing concepts of neighborhood systems in topological spaces, uniform spaces and proximity spaces respectively when considered in the respective sub-categories. We prove that a net of functions is convergent under the pointwise convergent nearness structure if and only if its cross-section at each point is convergent. We have also proved two Ascoli-Arzelà type of theorems.

The goal of this paper is to focus on the notions of merotopy and also merotopology in the soft universe. First of all, we propose L-soft merotopic (nearness) spaces and L-soft guild. Then, we study binary, contigual, regular merotopic spaces and also relations between them. We show that the category of binary L-soft nearness spaces is bireflective in the category of L-soft nearness spaces. Later, we define L-approach soft merotopological (nearness) spaces by giving several examples. Finally, we define a simpler characterization of L-approach soft grill merotopological space called grill-determined L-approach soft merotopological space. We investigate the categorical structures of these notions such as we prove that the category of grill-determined L-approach soft merotopological spaces is a topological category over the category of L-soft topological spaces. At the end, we define a partial order on the family of all L-approach soft grill merotopologies and show that this family is a completely distributive complete lattice with respect to the defined partial order. [ABSTRACT FROM AUTHOR]

We describe a method to construct hypersurfaces of the complex affine n-space with isomorphic C*-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent cancellation problem, that is, hypersurfaces that are nonisomorphic, although their C*-cylinders are isomorphic as abstract algebraic varieties. We also provide examples of nonisomorphic varieties X and Y with isomorphic Cartesian squares X × X and Y × Y. [ABSTRACT FROM AUTHOR]

Straight spaces are spaces for which a continuous map defined on the space which is uniformly continuous on each set of a finite closed cover is then uniformly continuous on the whole space. Previously, straight spaces have been studied in the setting of metric spaces. In this paper, we present a study of straight spaces in the more general setting of nearness spaces. In a subcategory of nearness spaces somewhat more general than uniform spaces, we relate straightness to uniform local connectedness. We investigate category theoretic situations involving straight spaces. We prove that straightness is preserved by final sinks, in particular by sums and by quotients, and also by completions. [ABSTRACT FROM AUTHOR]

Let Γ be a nonuniform lattice acting on the real hyperbolic n-space. We show that in dimension greater than or equal to 4, the volume of a representation is constant on each connected component of the representation variety of Γ in SO(n, 1). Furthermore, in dimensions 2 and 3, there is a semialgebraic subset of the representation variety such that the volume of a representation is constant on connected components of the semialgebraic subset. Combining our approach with the main result of [2] gives a new proof of the local rigidity theorem for nonuniform hyperbolic lattices and the analogue of Soma's theorem, which shows that the number of orientable hyperbolic manifolds dominated by a closed, connected, orientable 3-manifold is finite, for noncompact 3-manifolds. [ABSTRACT FROM AUTHOR]

This paper is concerned with the solution of large-scale linear discrete ill-posed problems with error-contaminated data. Tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems. The choice of regularization matrix in Tikhonov regularization may significantly affect the quality of the computed approximate solution. This matrix should be chosen to promote the recovery of known important features of the desired solution, such as smoothness and monotonicity. We describe a novel approach to determine regularization matrices with desired properties by solving a matrix nearness problem. The constructed regularization matrix is the closest matrix in the Frobenius norm with a prescribed null space to a given matrix. Numerical examples illustrate the performance of the regularization matrices so obtained. [ABSTRACT FROM AUTHOR]

The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for problems of small to moderate size are Tikhonov regularization and truncated singular value decomposition (TSVD). By considering matrix nearness problems related to Tikhonov regularization, several novel regularization methods are derived. These methods share properties with both Tikhonov regularization and TSVD, and can give approximate solutions of higher quality than either one of these methods. [ABSTRACT FROM AUTHOR]

We describe a ring whose category of Cohen-Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of k-planes in n-space. More precisely, there is a cluster character defined on the category which maps the rigid indecomposable objects to the cluster variables and the maximal rigid objects to clusters. This is proved by showing that the quotient of this category by a single projective- injective object is Geiss-Leclerc-Schröer's category Sub Qk, which categorifies the coordinate ring of the big cell in this Grassmannian. [ABSTRACT FROM AUTHOR]

In quantum theory, solving Schrödinger equation analytically for larger atomic and molecular systems with cluster of electrons and nuclei persists to be a tortuous challenge. Here, we consider, Schrödinger equation in arbitrary N-dimensional space corresponding to inverse-power law potential function originating from a multitude of interactions participating in a many-electron quantum system for exact solution within the framework of Frobenius method via the formulation of an ansatz to the hyper-radial wave function. Analytical expressions for energy spectra, and hyper-radial wave functions in terms of known coefficients of inverse-power potential function, and wave function parameters have been obtained. A generalized two-term recurrence relation for power series expansion coefficients has been established. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the category of filters has a left adjoint. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new conditions for the existence and the representations for the $$(P, Q)$$ generalized reflexive and anti-reflexive solutions to matrix equation $$AX = B$$ with respect to the generalized reflection matrix dual $$(P, Q)$$ . Moreover, in corresponding solution sets of the equation, the explicit expressions of the nearest matrix to a given matrix in the Frobenius norm have been provided. [ABSTRACT FROM AUTHOR]

In this paper we prove a quantitative version of the classical isoperimetric inequality in the hyperbolic space $$\mathbb {H}^n$$ . The constant only depends on the dimension and an upper bound for the volume of the set. [ABSTRACT FROM AUTHOR]

For a bitopological space , where and is a simple extension of the initial topology , we show under which relations between the topologies and such properties as in particular the Blumberg property, pseudocompleteness, connectedness, submaximality, to be a Baire space, to be an H-closed space, to be an H D-space, to be an e D-space and to be a nodec space are passed from over to . Moreover, we give the necessary and sufficient conditions both for the connectedness of a simple extension and for the maximal connectedness of some special topology. We obtain a solution for one of Everett and Ulam's problems dealing with the case of coincidence of two classes of homeomorphisms of a space onto itself. [ABSTRACT FROM AUTHOR]

Stimuli were presented in which values of an outcome variable for a single individual were recorded over 24 time periods, and an intervention was introduced at one of the time periods. Participants judged whether and how much the intervention affected the outcome. Judgements were affected by manipulations of the temporal relation between the intervention and a gradual increase in values on the outcome variable, by the size of the increase, by the time taken for the increase to occur, and by variance in the preincrease data. Most results were predicted by a simple model in which the mean outcome value for the preintervention time periods is subtracted from the mean outcome value for the postintervention time periods, though there was also an effect of temporal contiguity that is not predicted by the simple model. This form of information, which is a kind of quasiexperimental design, is more representative of the kind of information generally available for causal judgement than the more commonly investigated binary variables in which the cause is either present or absent, and the outcome either occurs or does not; as such, it is more revealing of how causal judgements are made under the conditions that prevail in the world. [ABSTRACT FROM PUBLISHER]

We discuss three types of sparse matrix nearness problems: given a sparse symmetric matrix, find the matrix with the same sparsity pattern that is closest to it in Frobenius norm and (1) is positive semidefinite, (2) has a positive semidefinite completion, or (3) has a Euclidean distance matrix completion. Several proximal splitting and decomposition algorithms for these problems are presented and their performance is compared on a set of test problems. A key feature of the methods is that they involve a series of projections on small dense positive semidefinite or Euclidean distance matrix cones, corresponding to the cliques in a triangulation of the sparsity graph. The methods discussed include the dual block coordinate ascent algorithm (or Dykstra's method), the dual projected gradient and accelerated projected gradient algorithms, and a primal and a dual application of the Douglas-Rachford splitting algorithm. [ABSTRACT FROM AUTHOR]

Local domains of n-spaces surrounded by the common Euclidean 3D-space may exist in complex chemical (mineral or synthetic) structures. In this paper, two classes of the simplest clusters embedded in n-dimensional spaces higher than three are designed by operations on maps and their properties discussed. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach to proximity structures based on the recognition of many of the entities important in the theory of ideals. So, we give a characterization of the basic proximity using ideals. Also, we introduce the concept of g-proximities and we show that for different choice of "g" one can obtain many of the known types of generalized proximities. Also, characterizations of some types of these proximities - (g0,h0) - are obtained. [ABSTRACT FROM AUTHOR]

For a Hamiltonian matrix with purely imaginary eigenvalues, we aim to determine the nearest Hamiltonian matrix such that some or all eigenvalues leave the imaginary axis. Conversely, for a Hamiltonian matrix with all eigenvalues lying off the imaginary axis, we look for a nearest Hamiltonian matrix that has a pair of imaginary eigenvalues. The Hamiltonian matrices can be allowed to be complex or restricted to be real. Such Hamiltonian matrix nearness problems are motivated by applications such as the analysis of passive control systems. They are closely related to the problem of determining extremal points of Hamiltonian pseudospectra. We obtain a characterization of optimal perturbations, which turn out to be of low rank and are attractive stationary points of low-rank differential equations that we derive. We use a two-level approach, where in the inner level we determine extremal points of the Hamiltonian $$\varepsilon $$ -pseudospectrum for a given $$\varepsilon $$ by following the low-rank differential equations into a stationary point, and on the outer level we optimize for $$\varepsilon $$ . This permits us to give fast algorithms-exhibiting quadratic convergence-for solving the considered Hamiltonian matrix nearness problems. [ABSTRACT FROM AUTHOR]

We study the fuzzy soft proximity spaces in Katsaras’s sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities. [ABSTRACT FROM AUTHOR]

In this paper, Pitman closeness criterion is used to compare the nearness of record values and order statistics from two independent samples to a specific population quantile of the parent distribution while the underlying distributions are the same. General expressions for the associated Pitman closeness probability are obtained when the support of the parent distribution is bounded and also unbounded. Some distribution-free results are achieved for symmetric distributions. The exponential and uniform distributions are considered for illustrative proposes and exact expressions are obtained in each case. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of how to establish algebraic structures of near sets on nearness approximation spaces. Essentially, our approach is define the near group of all weak cosets by considering an operation on the set of all weak cosets. Afterwards, our aim is to study near homomorphism theorems on near groups, and investigate some properties of near groups. [ABSTRACT FROM AUTHOR]

This paper presents the findings from a qualitative study on the extent to which three dimensions of proximity - geographic, cognitive, and organisational - impact knowledge transfer and innovation post-merger and acquisition (M&A). Findings show that the elements of proximity substantially influence both knowledge transfer and innovation although the nature of the impact varies and is influenced by the type of management interventions or lack thereof post-M&A. [ABSTRACT FROM AUTHOR]

In some previous papers we studiedgeneralizednearness by supernear spaces in connection withunificationsand topologicalextensions, respectively. Now, this last part of series deals with those supernear spaces, whichcoverclosely LODATO spaces, b-supertopologies and hence EF-proximities as well. Moreover, we will show that some special kind of these spaces have alocaltopological extension iff they aresuperbunchspaces. Consequently, thisfundamentalresult leading us to a furthergeneralizationof LODATO's theorem, and in addition Doîtchinov's achievement can be dealt with, but in a modified fashion. [ABSTRACT FROM AUTHOR]

Abstract: The non-symmetric (quasi-)nearness and its generalized admissibility are studied both in its biframe and paircovers aspect and in the perspective of entourages. The necessary and sufficient condition for a biframe to carry such an enrichment is shown to be a biframe variant of subfitness (resp. fitness, in the hereditary case). [Copyright &y& Elsevier]

In this paper, we prove a related fixed point theorem for single-valued mappings in two Menger spaces. [ABSTRACT FROM AUTHOR]

First,we define cyclic (ø)-contractions of different types in a uniformspace.Then,we apply these concepts of cyclic (ø)-contractions to establish certain fixed and common point theorems on a Hausdorff uniform space. Some more general results are obtained as corollaries. Moreover, some examples are provided to demonstrate the usability of the proved theorems. [ABSTRACT FROM AUTHOR]

Fuzzy similar priority ratio method is to select the most suitable one to the specific object from feasible alternatives. However, this method considering only the index values of real number has its disadvantages of inaccuracy in result and complexity in calculation. So, this method was extended to handle mixed attributes including real number, interval number, triangular fuzzy number, and trapezoidal fuzzy number. The proposed method decides the optimal alternative by the minimum of integrated nearness degrees calculated by all index vectors and the fixed index vectors based on the theory of similarity. The improved method can not only address mixed attributes but also simplify the calculation and improve the accuracy of result. A case study illustrated this method. [ABSTRACT FROM AUTHOR]

Let Pn be the projective n-space over the complex numbers. In this note we show that an indecomposable rigid coherent sheaf on Pn has a trivial endomorphism algebra. This generalizes a result of Dr'ezet for n = 2. [ABSTRACT FROM AUTHOR]

The new created conceptBounded Topology, a convenient foundation for topology, (see [9]) deals with a lot kind of structures examined by topologists in the past: Especially, generalized convergence spaces, now defined as b-convergences in [8], appear in a new context with the same of its convenient properties like being a strong topological universe. In this realm we now consider bounded proximities and related nearness by generalizing LODATO spaces and nearness spaces to so calledparanear spaces. Its subclass ofparaclan spacesis in one-to-one correspondence to a certain kind ofsymmetric,stricttopological extension. Hence, Lodato's famous theorem [10] and Bently's framework [2] about bunch determined nearness spaces can be also dealt with. [ABSTRACT FROM AUTHOR]

The problem considered in this paper is how to describe and compare visual objects. The solution to this problem stems from a consideration of nearness relations in two different forms of Efremovič proximity spaces. In this paper, the visual objects are picture elements in digital images. In particular, this problem is solved in terms of the application of rough sets in proximity spaces. The basic approach is to consider the nearness of the upper and lower approximation of a set introduced by Z. Pawlak during the early 1980s as a foundation for rough sets. Two forms of nearness relations are considered, namely, a spatial EF- and a descriptive EF-relation. This leads to a study of the nearness of objects either spatially or descriptively in the approximation of a set. The nearness approximation space model developed in 2007 is refined and extended in this paper, leading to new forms of nearness approximation spaces. There is a natural transition from the two forms of nearness relations introduced in this article to the study of nearness granules. [ABSTRACT FROM AUTHOR]

In this work, we give some new characterizations for inclined curves and slant helices in n-dimensional Euclidean space En: Morever, we consider the pre-characterizations about inclined curves and slant helices and restructure them. [ABSTRACT FROM AUTHOR]

Completeness for metric spaces is traditionally presented in terms of convergence of Cauchy sequences, and for uniform spaces in terms of Cauchy filters. Somewhat more abstractly, a uniform space is complete if and only if it is closed in every uniform space in which it is embedded, and so isomorphic to any space in which it is densely embedded. This is the approach to completeness used in the point-free setting, that is, for uniform and nearness frames: a nearness frame is said to be complete if every strict surjection onto it is an isomorphism. Quasi-uniformities and quasi-nearnesses on biframes provide appropriate structures with which to investigate uniform and nearness ideas in the asymmetric context. In [9] a notion of completeness (called “quasi-completeness”) was presented for quasi-nearness biframes in terms of suitable strict surjections being isomorphisms, and a quasi-completion was constructed for any quasi-nearness biframe. In this paper we show that quasi-completeness can indeed be viewed in terms of the convergence of certain filters, namely, the regular Cauchy bifilters. We use the notion of aT-valued bifilter, which generalizes the characteristic function of a filter. An important tool is an appropriate composition for such bifilters. We show that the right adjoint of the quasi-completion is the universal regular Cauchy bifilter and use it to prove this characterization of quasi-completeness. We also construct the so-called Cauchy filter quotient for a biframe using a quotient of the downset biframe that involves only the Cauchy, and not the regularity, condition. Like the quasi-completion, this provides a universal Cauchy bifilter; unlike the quasi-completion, this construction is functorial. [ABSTRACT FROM AUTHOR]

Abstract: We extend Bishopʼs concept of function spaces to the concept of pre-function spaces. We show that there is an adjunction between the category of neighbourhood spaces and the category of Φ-closed pre-function spaces. We also show that there is an adjunction between the category of uniform spaces and the category of Ψ-closed pre-function spaces. [Copyright &y& Elsevier]

In 1999, Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. In 2002, near set theory was initiated by J. F. Peters as a generalization of Pawlak's rough set theory. In the near set approach, every perceptual granule is a set of objects that have their origin in the physical world. Objects that have, in some degree, affinities are considered perceptually near each other, i.e., objects with similar descriptions. Also, the concept of near groups has been investigated by İnan and Öztürk [30]. The present paper aims to combine the soft sets approach with near set theory, which gives rise to the new concepts of soft nearness approximation spaces (SNAS), soft lower and upper approximations. Moreover, we give some examples and properties of these soft nearness approximations. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to the proof of the Niemytzki-Tychonoff theorem for symmetric topological spaces. The proof uses the concept of completeness in $${\varepsilon}$$ -approach nearness spaces which was introduced by Peters and Tiwari (Appl Math Lett 25:1544-1547, ), and of clusters that are a generalization of Cauchy sequences. [ABSTRACT FROM AUTHOR]

Abstract: We give a predicative construction of a completion of a uniform space in the constructive Zermelo–Fraenkel set theory. [Copyright &y& Elsevier]