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AbstractLet V be a vector space and U a fixed subspace of V. We denote the semigroup of all linear transformations on V under composition of functions by L(V). In this paper, we study the semigroup of all linear transformations on V whose restrictions belong to the general linear group GL(U), denoted by LGL(U)(V). More precisely, we consider the subsemigroup LGL(U)(V)={α∈L(V):α|U∈GL(U)} of L(V). In this work, Green’s relations and ideals of this semigroup are described. Then we also determine the minimal ideal and the set of all minimal idempotents of it. Moreover, we establish an isomorphism theorem when V is a finite dimensional vector space over a finite field. Finally, we find its generating set. [ABSTRACT FROM AUTHOR]

This paper examines how the Durkheimian approach to the 'ideal' delineates a possible way of straddling the dilemma between the normative orientation of 'powerful knowledge' accounts and the critical orientation of 'knowledge of the powerful' accounts. It argues that the normative aims are embedded in the fabrics of the sociological description with which the Durkheimian notion of 'elementary form' is concerned. To see where this enterprise can lead, this paper turns to the sociology of education of Bourdieu and Bernstein. Both draw on Durkheim's writings on primitive classifications in education and society, working towards uncovering the regularities of the world of knowledge classifications. Keeping in line with Bourdieu and Bernstein, this paper argues that one has to make the same refusal to the advocates of an abstract ideal of educational knowledge that is dissociated from its social conditions of historical realization in pedagogic contexts, and to the advocates of a cynical relativism of ideal that rejects any necessities socially established. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the structure of the variety of Lie algebras with a finite number of ideals and their graph representations using Hasse diagrams. The large number of necessary conditions on the algebraic structure of this type of algebras leads to the explicit description of those algebras in the variety with trivial Frattini subalgebra. To illustrate our results, we have included and discussed lots of examples throughout the paper. [ABSTRACT FROM AUTHOR]

In order to enhance the calculation efficiency of steady-state incompressible fluid flow, based on the existing IDEAL (i.e. the inner doubly iterative efficient algorithm for linked equations) algorithm, a novel segregated pressure-based algorithm (named as IDEALC) has been developed in this paper. The novel algorithm inherits the superiorities of the original IDEAL algorithm and at the same time improves its potential shortcomings. The specific promotions of the IDEALC algorithm consist of three aspects, including the first approximation of the SIMPLE algorithm, the approach to solving the momentum equation and the second approximation of the SIMPLE algorithm. Detailed comparisons between the IDEAL and the IDEALC algorithms are carried out by three numerical experiments on structured collocated grids. The numerical results demonstrate that the IDEALC algorithm can accurately predict the information of the flow field and has substantial advantages over the IDEAL algorithm in terms of the efficiency because of the consistent property of the former. The superiority of the IDEALC algorithm over the IDEAL algorithm is especially remarkable when the time step multiplier gets a moderate value. [ABSTRACT FROM AUTHOR]

The problem of 'applicability' of mathematics to modern physical sciences has been labeled as an 'unreasonably effective' and unexplainable 'miracle' by prominent physicists such as Eugene Wigner and Paul Dirac. Philosophers of science from contending traditions have also contributed to the debates at large. While some have tried to trivialize the problem, others, in particular those with a phenomenological orientation, have attempted to eliminate this riddle, claiming that the two domains are 'identical'. This paper, while challenging some of these interpretations, proposes a solution from a dialectical materialist position. Drawing on Evald Ilyenkov's concept of the 'ideal' as the objectivized form of human activity in social nature, it is suggested that the two realms are necessarily interconnected as schemata of human activity which aim for a highly quantified conceptualization of reality. [ABSTRACT FROM AUTHOR]

In this paper, congruences, ideals, and prime ideals of an EMV-semiring and of its associated EMV-algebra are studied. Then EMV-semirings are characterized and it is proved that each EMV-semiring can be embedded into a direct product of a family of MV-semirings as an EMV-semiring. Moreover, another representation of EMV-semirings are presented by EMV-semirings of continuous sections in a sheaf of commutative semirings whose stalks are localizations of EMV-semirings over prime ideals. Also, using the categorical equivalence between EMV-semirings and EMV-algebras, a representation of EMV-algebras are obtained. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the intuitionistic fuzzy I-convergent sequence spaces S(μ, ν)I(T) and S0(μ, ν)I(T) defined by compact operator and study the fuzzy topology on the above said spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the notion of BCI/BCK-algebras. This structure is studied in detail. Also we introduce a way to make an eBCK-algebra from a BCK-algebra and vice versa. [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]