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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]

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]

Let denote a field with characteristic not 2 and fix a nonzero such that. Let be the quantum enveloping algebra over and let be its equitable generators. Denote by the subalgebra of generated by. In this paper, we solve two open problems concerning and , respectively, which are proposed by Bockting-Conrad and Terwilliger. [ABSTRACT FROM AUTHOR]

A ring R is called filial (left weakly filial) if it satisfies the following condition: for all subrings J and I of R, if J is an ideal of I and I is an ideal of R, then J is an ideal (left ideal) of R. If every subring of R is filial (left weakly filial), then R is called fully filial (fully left weakly filial). In this paper, some new characterizations of left weakly filial rings in terms of the prime radical are given. Left weakly filial rings that are matrix rings, polynomial rings and the direct sum of copies of a ring are also investigated. Recently, in [3], [4] and [13], classification theorems for semiprime torsion fully filial rings and for torsion-free fully filial rings were presented. We study fully left weakly filial rings and show that semiprime torsion rings and semiprime torsion-free rings are fully left weakly filial if and only if they are fully filial. [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]

Let H m , n be the mn2-dimensional Radford Hopf algebra over an algebraically closed field of characteristic zero. In this paper, we show that any finite dimensional indecomposable H m , n -module is a cyclic module. According to the structure of any indecomposable module under the adjoint action of H m , n , we prove that the Radford Hopf algebra H m , n is a principal ideal ring. Furthermore, we give explicitly the generators of all 28 ideals of 9-dimensional Radford Hopf algebra H 1 , 3 . [ABSTRACT FROM AUTHOR]

In this paper, we present the notions of α-ideal and α-congruence on a distributive nearlattice. We prove that the α-ideals and α-congruences of a normal distributive lattice A are in a one-to-one correspondence with the ideals and congruences of the distributive nearlattice R(A) of the annihilators of A, respectively. [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]

In this paper we primarily introduce an ideal version of τ -covers studied in [18, 19]. We establish the inter-relationships between ℐ-τ -covers and ℐ-γ, ℐ-large [3, 5] and κ-covers[2, 7]. We also make some investigations involving the splittability and preservation properties. Our results extend the earlier results proved in [18, 19, 2, 7] and present a more general version with respect to ideals. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite unions of ideals and modules. The first main result is that, ifN ⊆ N1∪N2 ∪ … ∪Nsis a covering of a moduleNby submodulesNi, such that all but two of theNiare intersections of strongly irreducible modules, thenN ⊆ Nkfor somek. The special case whenNis a multiplication module is considered. The second main result generalizes earlier results on coverings by primary submodules. In the last section unions of cosets is studied. [ABSTRACT FROM AUTHOR]

Let R be a semiprime ring and I a nonzero ideal of R. A map F:R→R is called a multiplicative generalized derivation if there exists a map d:R→R such that F(xy) = F(x)y+xd(y), for all x,y∈R. In the present paper, we shall prove that R contains a nonzero central ideal if any one of the following holds: i) ii) iii) F is SCP on I, iv) F(u)∘F(v) = u∘v, for all u,v∈I. [ABSTRACT FROM AUTHOR]

In this paper we study dimensions of the type dim for the class of ideal topological spaces. We shall start from the classical definition of the dimension functions dim and dim*, continue with the dimension -dim and finally, give two different kinds of functions of covering dimensional type. [ABSTRACT FROM AUTHOR]

This paper seeks to understand Keats's early poems as an attempt to shape his poetic identity. While his first volume of poetry can be seen in its entirety as the place where Keats plays out his desire (or even his urge/necessity) to discover his poetic self, two important poems, 'I Stood tip-toe' and 'Sleep and Poetry' fully illustrate his tribute to literature, imagination, and the poetic mind. Like other Romantic poets, Keats has not been spared criticism for being solipsistic. However, as these early poems already demonstrate, his celebration of the poet or poetry is not solipsistic, but rooted in a profound belief in the power of literature to reach out and elevate the human soul above sorrow and loss. In 'Sleep and Poetry' Keats attacks the 'elitist' neoclassicism in order to bridge rather than increase the gap between poetry and society. He is trying to assimilate his poetry and art in general into the culture and lives of the people. Writing after the Enlightenment, which glorified reason and science, Keats is committed to shedding new light on the role of the imagination and poetry, tapping into man's most intimate and authentic feelings. Circulating underneath his enchantment with poetry is the lingering concern with the legitimation of the poetic imagination. In 'I Stood tip-toe' the lyrical 'I' finds education in nature and goes back to myth and to the narrative of poetic beginnings in order to articulate a poetic vision. Keats's later poetry-writing, or, poetry-making, has evolved but has never abandoned the early tenets of his poetic design. [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]

We consider algebraic systems with several products, including unary products, S (as examples we can take linear spaces, algebras, superalgebras, hom-algebras, triple systems, hom-triple systems, Poisson algebras, Bol algebras, n-algebras, etc.) We show that any basis of S gives rise to a decomposition of S as a direct sum of indecomposable well-described ideals (fine decomposition). The simplicity of the components in this decomposition is also characterized. There are as many non-isomorphic fine decompositions as orbits in a determined action. [ABSTRACT FROM AUTHOR]

In this article, we study the non-Newtonian version of C ∗ − algebras. Further, we generalize some results which hold for the classical C ∗ − algebras. We also discuss some illustrative examples to show accuracy and effectiveness of the new findings. If we take the identity function I instead of the generators α and β in the construction of the set C (N) , then non-Newtonian C ∗ − algebras turn into the classical C ∗ − algebras, so our results are stronger than some knowledge and facts in the most existing literature. [ABSTRACT FROM AUTHOR]

Weakly separable algebras are investigated in this article. For this purpose their cohomologies are studied. Conditions are found under which normed algebras have a zero cohomological dimension. Abundant families of algebras satisfying these conditions are described. Their relations with operator algebras are scrutinized. [ABSTRACT FROM AUTHOR]

Background: The motherhood myth has been associated with perceptions of idealised motherhood which makes it difficult for women to express related struggles or distress. This is a second follow-up study focusing on the experiences of mothers from the United Kingdom (UK) and Israel. Methods: Forty-one women were interviewed about their experience of motherhood, body-image, feeding and well-being. Interviews were analysed thematically. Data were driven by the following questions: 1. how do Israeli and UK women experience motherhood 6–12 months postpartum? 2. Are these experiences associated with body satisfaction and well-being? 3. Whether perceptions of motherhood remained stable or changed from early (<6 months) to 12 months postpartum. Results: Three meta-themes were derived from the data relating to motherhood as ideal, good enough or burdened. Such experiences were associated with body acceptance and well-being. The ideal mother was associated with lack of preoccupation with body image whereas the good enough mother aspired to reclaim her mind and her old body. Our findings suggested that the burdened mothers' struggles in relating to motherhood often correlated to a negative body image. Israeli women perceived motherhood as ideal in the early and later postpartum whereas UK mothers continued to relate to their motherhood as ideal 6–12 months postpartum. Conclusions: Perceptions of motherhood varied between Israeli and UK mothers suggesting a diversity positively associated with culture and country. Encouraging mothers to openly share their perceptions of motherhood could lead to improvements in maternal well-being and more positive interactions with the newborn. [ABSTRACT FROM AUTHOR]

The notation of I-convergence was introduced and studied by Kostyrko, Macaj, Salat, and Wilczynski. Recently, the concept of I-convergent for a sequence of bounded linear operators has been studied by Khan and Shafiq. This has motivated us to introduce and study some new spaces of double sequences of bounded linear operators and their basic topological and algebraic properties of these spaces. And we study some of their basic topological and algebraic properties of these spaces. We prove some inclusion relations on these spaces. [ABSTRACT FROM AUTHOR]

In 1990 Kantor defined the conservative algebraW(n) of all algebras (i.e. bilinear maps) on then-dimensional vector space. Ifn>1, then the algebraW(n) does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or Leibniz algebras). We describe automorphisms, one-sided ideals, and idempotents ofW(2). Also similar problems are solved for the algebraW2of all commutative algebras on the 2-dimensional vector space and for the algebraS2of all commutative algebras with trace zero multiplication on the 2-dimensional vector space. [ABSTRACT FROM AUTHOR]

A partial frame is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. The designated subsets are specified by means of a so-called selection function, denoted byS; these partial frames are calledS-frames. We construct free frames over S-frames using appropriate ideals, calledS-ideals. TakingS-ideals gives a functor fromS-frames to frames. Coupled with the functor from frames toS-frames that takesS-Lindelöf elements, it provides a category equivalence betweenS-frames and a non-full subcategory of frames. In the setting of complete regularity, we provide the functor takingS-cozero elements which is right adjoint to the functor takingS-ideals. This adjunction restricts to an equivalence of the category of completely regularS-frames and a full subcategory of completely regular frames. As an application of the latter equivalence, we construct the Stone-Č ech compactification of a completely regularS-frame, that is, its compact coreflection in the category of completely regularS-frames. A distinguishing feature of the study of partial frames is that a small collection of axioms of an elementary nature allows one to do much that is traditional at the level of frames or locales and of uniform or nearness frames. The axioms are sufficiently general to include as examples of partial frames bounded distributive lattices, σ-frames, κ-frames and frames. [ABSTRACT FROM PUBLISHER]

Fuzzy rings are, on the one handside, an appropriate tool for a unified approach to representable, oriented, and valuated matroids. On the other hand, they also serve to unify the relatively new field of “Tropical Geometry” and “Classical Algebraic Geometry.” Therefore, these fuzzy rings deserve a more thorough examination. We study the arithmetic in fuzzy rings and related structures as well as polynomials over these coefficient domains. [ABSTRACT FROM AUTHOR]

Abstract—This article presents a thorough comparative analysis study for various kinds of single-diode model based photovoltaic power source. The main target is to explore the effect of increasing the embedded degree of complexity of the single-diode model on the simulated behavior of a particular photovoltaic module by comparing the dynamic performance of such photovoltaic models with the experimental data from the manufacturer's data sheet under varying atmospheric conditions. The relative errors between each photovoltaic single-diode model output and the experimentally validated data are computed at three indicative points, namely open-circuit voltage, short-circuit current, and maximum power point. The result of this comparison leads to determining the best photovoltaic single diode modulethe one that is more suitable than the others in the context of single diode modelto be applied in different power system applications irrespective of changing environmental conditions over different periods of the day. The comparison study in this article concludes by determining the relevant single-diode model at low, medium, and high temperatures and irradiance levels as well as at standard test conditions. [ABSTRACT FROM PUBLISHER]