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Abstract: Multipliers and factorizations for bounded statistically convergent sequences were studied by Connor et al. [J. Connor, K. Demirci, C. Orhan, Multipliers and factorizations for bounded statistically convergent sequences, Analysis 22 (2002) 321–333] and for bounded -convergent sequences by Yardımcı [Ş. Yardımcı, Multipliers and factorizations for bounded -convergent sequences, Math. Commun., 11 (2006) 181–185]. In this paper, we get analogous results of multipliers for bounded -convergent double sequences. [Copyright &y& Elsevier]

Abstract: The paper deals with states on commutative basic algebras that are a non-associative generalization of MV-algebras or, in other words, the algebraic semantics for a fuzzy logic which generalizes the Łukasiewicz logic in that the conjunction is not associative. States are defined in the same way as Mundici''s states on MV-algebras as normalized finitely additive [0,1]-valued functions, and some results analogous to the results that are known from MV-algebras are proved. [Copyright &y& Elsevier]

As a process of socialization where individuals gain cultural and behavioral awareness, and a means of training the generations according to the canons established by culture, education is of vital importance to any society that aspires to train members able to maintain and develop it. But this would not be possible without pedagogical models to support it. How and from what principles, postures and theoretical/methodological positions do those who practice the pedagogical-training task assume the educational process? Starting from this question, this paper seeks a reflection about cognitive, procedural, philosophical, political and social-historical factors that in some way have idealized pedagogical models. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce certain new sequence spaces of fuzzy numbers defined by -convergence using sequences of Orlicz functions and a difference operator of order . We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. [Copyright &y& Elsevier]

Basic algebras are a generalization of MV-algebras, also including orthomodular lattices and lattice effect algebras. A pre-ideal of a basic algebra is a non-empty subset that is closed under the addition ⊕ and downwards closed with respect to the underlying order. In this paper, we study the pre-ideal lattices of algebras in a particular subclass of basic algebras which are closer to MV-algebras than basic algebras in general. We also prove that finite members of this subclass are exactly finite MV-algebras. [ABSTRACT FROM AUTHOR]

Abstract: An efficient segregated algorithm for non-linear incompressible fluid flow and heat transfer problems, called IDEAL (Inner Doubly-Iterative Efficient Algorithm for Linked-Equations) for short, was proposed in reference [9]. Subsequently, it was extended to the 3D staggered/collocated grid systems. IDEAL includes inner doubly-iterative processes for solving pressure equations at each iteration level, and it could adjust the inner iteration times to control the convergence rate and the stability of iteration process, which is greatly different from other segregated algorithms. The objective of this paper is to analyze the effects of inner iteration times on the performance of IDEAL by four incompressible fluid flow problems, two of which belong to open systems, and the others refer to closed systems. It is found that: (1) the robustness of IDEAL is enhanced greatly with the increase of inner iteration times; (2) at the same time step multiple, the outer iteration number decreases with the increase of inner iteration times and the computation time is not related to the inner iteration times; (3) at the optimal time step multiple, the large inner iteration times of 4&4 and 7&7 could reduce the outer iteration number by about 70% and the computation time by about 40% over the small inner iteration times of 1&1. [Copyright &y& Elsevier]

Abstract: In this paper, following the line of Savas and Das (2011) , we provide a new approach to two well-known summability methods by using ideals, introduce new notions, namely, -statistical convergence and -lacunary statistical convergence, investigate their relationship, and make some observations about these classes. [Copyright &y& Elsevier]

In this paper, a new topic about a vast class of subsets of semigroups and binary systems, which contains all ideals, periodic subsets and sub-semigroups, is introduced and studied. In fact, the 'upper periodic subsets' can be considered as a generalization of the conception 'ideals'. We prove a fundamental theorem which states that if A is a (left) upper B-periodic subset of a semigroup S, then under some conditions, it has a unique direct representation $A=\mathfrak{B}\cdot D\,\dot{\cup}\,B^1\cdot E$, where B1=B ∪ {1} and B ⊆ 픅 ≤ S. Especially, we prove a unique direct representation for upper and lower T-periodic subsets, and classify all sub-semigroups of S containing a fixed element T to three classes. This classification gives us more interesting properties for the real semigroups. At last, we characterize upper and lower T-periodic subsets of semigroups and groups. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we continue our investigation of nets using ideals in line of our earlier work where we had studied -Cauchy nets and asked when -Cauchy nets in complete uniform spaces are -convergent in line of a problem by Di Maio and Kočinac who asked in 2008 when statistically Cauchy sequences are statistically convergent in uniform spaces. To answer this, here we consider another type of Cauchy condition of nets, namely -Cauchy condition and examine its basic properties and in particular its relation with the concept of -Cauchy nets. This helps us to give an answer to the above mentioned open question. [Copyright &y& Elsevier]

At the end of the nineteenth century, a process of modernization and development took place in Argentina, within the frame of the nation-state consolidation. In this context, the country witnessed a discursive profusion that expected to introduce disciplinary instruments into society, among which the creation of a modern maternal ideal can be mentioned. This paper analyzes the main topics of such discourses, through one the main media available to spread them in rural central and southern Buenos Aires in our period: the local press. [ABSTRACT FROM AUTHOR]

Abstract: A sectionally complemented modular lattice L is coordinatizable if it is isomorphic to the lattice of all principal right ideals of a von Neumann regular (not necessarily unital) ring R. We say that L has a large 4-frame if it has a homogeneous sequence such that the neutral ideal generated by is L. Jónsson proved in 1962 that if L has a countable cofinal sequence and a large 4-frame, then it is coordinatizable; whether the cofinal sequence assumption could be dispensed with was left open. We solve this problem by finding a non-coordinatizable sectionally complemented modular lattice L with a large 4-frame; it has cardinality . Furthermore, L is an ideal in a complemented modular lattice with a spanning 5-frame (in particular, is coordinatizable). Our proof uses Banaschewski functions. A Banaschewski function on a bounded lattice L is an antitone self-map of L that picks a complement for each element of L. In an earlier paper, we proved that every countable complemented modular lattice has a Banaschewski function. We prove that there exists a unit-regular ring R of cardinality and index of nilpotence 3 such that has no Banaschewski function. [Copyright &y& Elsevier]

Abstract: In this paper we make a new approach to the notions of -summability and -statistical convergence by using ideals and introduce new notions, namely, -summability and -statistical convergence. We mainly examine the relation between these two new methods as also the relation between -statistical convergence and -statistical convergence introduced by the authors recently. We carry out the whole investigation in normed linear spaces. [Copyright &y& Elsevier]

In this paper, we introduce a new algebraic structure, called SU-algebra. We presented a concept of ideal and congruences of SU-algebras and investigate its properties. Moreover, some consequences of the relations between quotient SU-algebras and isomorphisms are shown. [ABSTRACT FROM AUTHOR]

In this paper, introducing the notion of prime convex subnearlattices the authors generalize the Stone's representation theorem for convex subnearlattices of a distributive medial nearlattice. They also show that a distributive medial nearlattice is relatively complemented if and only if its prime convex subnearlattices are unordered. Then they study the congruences of a distributive medial nearlattice containing a convex subnearlattice as a class. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to give a new, elementary proof of Flanigan’s theorem, which says that a given ring A has a maximal essential extension ME(A) if and only if the two-sided annihilator of A is zero. Moreover, we discuss the problem of description of ME(A) for a given right ideal A of a ring with an identity. [ABSTRACT FROM AUTHOR]

An ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under finite unions. The concept of generalized closed sets was introduced by Levine. In this paper, we introduce and investigate the concept of generalized closed sets with respect to an ideal. [ABSTRACT FROM AUTHOR]

Abstract: With L a complete lattice and M a continuous lattice, this paper demonstrates an adjunction between M -valued L-topological spaces (i.e. (L,M )-topological spaces) and Idl(M )-valued L-topological spaces where Idl(M ) is the complete lattice of all ideals of M . It is shown that the right adjoint functor provides a procedure of generating (L,M )-topologies from antitone families of (L,M )-topologies. This procedure is then applied to give an internal characterization of joins in the complete lattice of all (L,M )-topologies on a given set. [Copyright &y& Elsevier]

In this paper, we study homomorphisms of binary algebras and investigate its properties. Moreover, some consequences of the relations between quotient binary algebras and isomorphisms are shown. [ABSTRACT FROM AUTHOR]

Abstract: A numerical semigroup S is an IPM-semigroup if there exists an ideal I of a proportionally modular numerical semigroup such that . Let S and be numerical semigroups such that . We say that is an ideal extension of S if is an ideal of . Clearly a numerical semigroup is an IPM-semigroup if and only if it admits an ideal extension that is a proportionally modular numerical semigroup. In this paper we characterize all the ideal extensions of an arbitrary numerical semigroup. We also give an algorithm to decide whether or not an arbitrary numerical semigroup is an IPM-semigroup. [Copyright &y& Elsevier]

Abstract: In this paper we extend the idea of usual Cauchy condition of nets to I-Cauchy condition by using the concept of ideals. This Cauchy condition arises naturally from the notion of I-convergence of nets introduced by Lahiri and Das (2008). As the underlying structure for the whole study we take a uniform space so that our notion and results extend the idea of statistical Cauchy sequences very recently introduced in uniform spaces by Di Maio and Kočinac (2008). In particular we try to give partial answers to an open problem posed by Di Maio and Kočinac and examine the relationship between this new Cauchy condition and usual completeness of a uniform space. [Copyright &y& Elsevier]

In this paper, we introduce binary algebra and quotient binary algebra. We show the relation between ideals and congruences on binary algebra. [ABSTRACT FROM AUTHOR]

In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C*-algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A′. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system. [ABSTRACT FROM AUTHOR]

In this paper we introduce several concepts which are useful in the development of the theory of Generalised lattices, including the notions of Strong ideals, Strong filters, R--Strong ideals, R--Strong filters, Homomorphisms, Strong homomorphisms and Strong congruences in Generalised lattices. We also introduce the concepts of Congruence and Modularity in Posets. [ABSTRACT FROM AUTHOR]

Abstract: Given an infinite group G and an infinite cardinal , we say that a subset A of G is κ-large (κ-small) if there exists such that ( is κ-large for each ). The subject of the paper is the family of all κ-small subsets. We describe the left ideal of the right topological semigroup βG determined by . We study interrelations between κ-small and other (-small and κ-thin) subsets of groups, and prove that G can be generated by some 2-thin subsets. We partition G in countable many subsets which are κ-small for each . We show that is dual to provided that either κ is regular and , or G is Abelian and κ is a limit cardinal, or G is a divisible Abelian group. [Copyright &y& Elsevier]

In this paper, we study homomorphisms of KU-algebras and investigate its properties. Moreover, some consequences of the relations between quotient KU-algebras and isomorphisms are shown. [ABSTRACT FROM AUTHOR]

Denote by Mat k,l( F) the algebra M n( F) of matrices of order n = k + l with the grading (Mat( F),Mat( F)), where Mat( F) admits the basis and Mat( F) admits the basis . Denote by M k,l( F) the Grassmann envelope of the superalgebra Mat k,l( F). In the paper, bases of the graded identities of the superalgebras Mat1,2( F) and M1,2( F) are described. [ABSTRACT FROM AUTHOR]

The segregated algorithm-IDEAL (inner doubly-iterative efficient algorithm for linked-equations) is an efficient and stable algorithm. In this algorithm, there exist inner doubly-iterative processes for pressure equation, which almost completely overcome two approximations in SIMPLE algorithm. Thus the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of iteration process. In this paper, implementation of the IDEAL algorithm on a 3D collocated grid system is conducted. The interlace velocity is calculated by the modified momentum interpolation method (MMIM), by which the converged result is independent of the under-relaxation factor. Finally, five three-dimensional incompressible fluid flow and heat transfer problems are provided to compare the convergence rate and robustness between the IDEAL and three other most widely-used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison it can be concluded that the IDEAL algorithm is more robust and efficient than the three other algorithms. [ABSTRACT FROM AUTHOR]

The main result of the paper is a structure theorem concerning the ideal extensions of archimedean ordered semigroups. We prove that an archimedean ordered semigroup which contains an idempotent is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. Conversely, if an ordered semigroup S is an ideal extension of a simple ordered semigroup by a nil ordered semigroup, then S is archimedean. As a consequence, an ordered semigroup is archimedean and contains an idempotent if and only if it is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. [ABSTRACT FROM AUTHOR]

Stone-Čech compactifications derived from a discrete semigroup S can be considered as the spectrum of the algebra ℬ( S) or as a collection of ultrafilters on S. What is certain and indisputable is the fact that filters play an important role in the study of Stone-Čech compactifications derived from a discrete semigroup. It seems that filters can play a role in the study of general semigroup compactifications too. In the present paper, first we review the characterizations of semigroup compactifications in terms of filters and then extend some of the results in Papazyan (Semigroup Forum 41:329–338, ) concerning the Stone-Čech compactification to a semigroup compactification associated with a Hausdorff semitopological semigroup. [ABSTRACT FROM AUTHOR]

We denote by C s (X) the set C (X) of real-valued continuous functions defined on X endowed with the topology of the uniform convergence on the closed separable subspaces of X. In this paper we continue the study of C s (X) initiated in Pseudouniform topologies on C (X) given by ideals (Pichardo-Mendoza et al. (2013) [6]). We prove that C s (X) is a k -space if and only if C s (X) is metrizable, and that compactness, sequential compactness and countable compactness coincide in subspaces of C s (X). In addition, we study the cellularity, density, weight and character of C s (X). We prove that (1) d ((R 2 λ ) s) = λ if λ = λ ω , and (2) the Continuum Hypothesis is equivalent to the statement: Every non-separable space X satisfies χ (C s (X)) = w (C s (X)). [ABSTRACT FROM AUTHOR]

In this paper we consider the idea of I - convergence of nets in a topological space and derive several basic properties. This idea extends the concept of I - convergence of sequences considered so far in various spaces. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose the application of formal methods to Software Engineering. The most used data model is the relational model and we present, within the general framework of lattice theory, this analysis of functional dependencies. For this reason, we characterize the concept of -family by means of a new concept which we call non-deterministic ideal operator (nd.ideal-o). The study of nd.ideal-o.s allows us to obtain results about functional dependencies as trivial particularizations, to clarify the semantics of the functional dependencies and to progress in their efficient use, and to extend the concept of schema. Moreover, the algebraic characterization of the concept of Key of a schema allows us to propose new formal definitions in the lattice framework for classical normal forms in relation schemata. We give a formal definition of the normal forms for functional dependencies more frequently used in the bibliography: the second normal form (2FN), the third normal form(3FN) and Boyce–Codd''s normal form (FNBC). [Copyright &y& Elsevier]

In this paper, the semigroup of primitive generalized circulant Boolean matrices is studied, and some algebraic properties of this semigroup are obtained. Also, an asymptotic formula for the cardinality of the semigroup is given. [ABSTRACT FROM AUTHOR]

In the paper, the notions of radical of an ideal and radical of a submodule are generalized and described. [ABSTRACT FROM AUTHOR]

In this paper, we consider fuzzy notion of a Γ-near ring, introduce the notion of a fuzzy coset and obtained some related important fundamental isomorphism theorems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce m-fold stable ideals and show that m-fold stable range for ideals is invariant under matrix extension. Also we prove that every m-fold stable ideal is right and left symmetric. [ABSTRACT FROM AUTHOR]

This paper deals with rings of real Darboux functions defined on some topological spaces. Results are given concerning the existence of essential, as well as prime Darboux rings. We prove that, under some assumptions connected with the domain X of the functions, the equalities: D(X) = Slf (X), S(X) = dim(ℜ) hold, where D(X) is a D-number of X, S(X) (Slf (X)) denotes the Souslin (lf-Souslin) number of X and dim(ℜ) is a Goldie dimension of an arbitrary prime Darboux ring ℜ. [ABSTRACT FROM AUTHOR]

In this paper we define a θ-Euclidean level subset and a θ-Euclidean level ideal. We also give some properties of a θ-Euclidean level subset. [ABSTRACT FROM AUTHOR]

This paper characterizes ideal structure of the uniform Roe algebra B*(X) over simple cores X. A necessary and sufficient condition for a principal ideal of B*(X) to be spatial is given and an example of non-spatial ideal of B*(X) is constructed. By establishing an one-one correspondence between the ideals of B*(X) and the ω-filters on X, the maximal ideals of B*(X) are completely described by the corona of the Stone-Čech compactification of X. [ABSTRACT FROM AUTHOR]

This paper presents vignettes of a case from the city of Rio de Janeiro in which temporality appears as a fundamental issue. Severe difficulties in validating the past and integrating past, present and future reveal pertinent questions on time and the ideal function in the contemporary world. The author underlines the relevance of such questioning for the practice of psychoanalysis today. [ABSTRACT FROM AUTHOR]

The paper considers several different kinds of ideals defined by some densities. We depict relationships between Erdős-Ulam, density, matrix summability and generalized density ideals. We show that Farah's characterization when density ideals are Erdős-Ulam ideals is incorrect and try to provide a new one while showing that the conditions from the old characterization can be used to determine when density ideals have the Bolzano-Weierstrass property. Moreover, we obtain some results about a class of ideals recently established by Bose, Das and Kwela that we name simple generalized density ideals. [ABSTRACT FROM AUTHOR]

Let S and T be two numerical semigroups. We say that T is an I (S) -semigroup if T ∖ { 0 } is an ideal of S. Given k a positive integer, we denote by Δ (k) the symmetric numerical semigroup generated by { 2 , 2 k + 1 } . In this paper we present a formula which calculates the number of I (S) -semigroups with genus g (Δ (k)) + h for some nonnegative integer h and which we will denote by i (Δ (k) , h) . As a consequence, we obtain that the sequence { i (Δ (k) , h) } h ∈ N is never decreasing. Besides, it becomes stationary from a certain term. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a quasi-uniformity U* that is induced in a natural way on a BCK-algebra X endowed with a topology τ: We build a quasi-uniformity by U✻* -Cauchy filters on a BCK-algebra X: Finally, we prove that bicompletions induced by this quasi-uniformity can be considered a topological BCK-algebra which contains X as a sub-dense-space. [ABSTRACT FROM AUTHOR]

Vanishing component analysis (VCA) method, as an important method integrating commutative algebra with machine learning, utilizes the polynomial of vanishing component to extract the features of manifold, and solves the classification problem in ideal space dual to kernel space. But there are two problems existing in the VCA method: first, it is difficult to set a threshold of its classification decision function. Second, it is hard to handle with the over-scaled training set and oversized dimension of eigenvector. To address these two problems, this paper improved the VCA method and presented a grouped VCA (GVCA) method by grouping strategy. The classification decision function did not use a predetermined threshold; instead, it solved the values of all polynomials of vanishing component and sorted them, and then used majority voting approach to determine their classes. After that, a strategy of grouping training set was proposed to segment training sets into multiple non-intersecting subsets, which polynomials of vanishing component were later acquired through a VCA method, respectively, and finally combined into an integral set of vanishing component polynomial. What is more important is that it uses the bagging theory in ensemble learning to successfully expound and prove the correctness of the strategy of grouping training sets. It also compares the time complexity for training algorithm with and without grouping training sets, thus demonstrating the effectiveness of the grouping strategy. A series of experiments showed that the GVCA method proposed in the paper has a perfect classification performance with a rapid rate of convergence compared to other statistical learning methods. [ABSTRACT FROM AUTHOR]