Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras

The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic). However, this algebra structure does not have enough characteristics to describe residual implications in depth, so we propose a new concept of strong BI-algebra, which is exactly the algebraic abstraction of fuzzy implication with pseudo-exchange principle (PEP). Furthermore, in order to describe the characteristics of the algebraic structure corresponding to the non-commutative fuzzy logics, we extend strong BI-algebra to the non-commutative case, and propose the concept of pseudo-strong BI (SBI)-algebra, which is the common extension of quantum B-algebras, pseudo-BCK/BCI-algebras and other algebraic structures. We establish the filter theory and quotient structure of pseudo-SBI- algebras. Moreover, based on prequantales, semi-uninorms, t-norms and their residual implications, we introduce the concept of residual pseudo-SBI-algebra, which is a common extension of (non-commutative) residual lattices, non-associative residual lattices, and also a special kind of residual partially-ordered groupoids. Finally, we investigate the filters and quotient algebraic structures of residuated pseudo-SBI-algebras, and obtain a unity frame of filter theory for various algebraic systems.

The lattice properties of 𝔛-local formations of finite groups

Let [Formula: see text] be a class of simple groups with a completeness property [Formula: see text]. Förster introduced the concept of [Formula: see text]-local formation in order to obtain a common extension of well-known theorems of Gaschütz–Lubeseder–Schmid and Baer [Publ. Mat. UAB 29(2–3) (1985) 39–76]. In this paper, it is proved that the lattice of all [Formula: see text]-local formations of finite groups is modular.

A Common Extension of Arhangel’skĭ’s Theorem and the Hajnal–Juhász Inequality

We present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s solution to Alexandroff’s problem: A survey, Topology Appl. 153(2006), 2199–2217).In contrast to previous attempts, we do not need any separation axiom beyond $T_{2}$.

Impeccability and Temptation

The scriptures and the councils teach that Christ was tempted. One common extension to Conciliar Christology, the extension discussed in this chapter, is the claim that Christ not only did not sin, but in fact Christ was unable to sin. Some thinkers see a contradiction looming here. For to be genuinely tempted, they argue, requires having the ability to sin. If Christ was unable to sin, then he could not be tempted, contrary to scripture and council. And so this particular extension of Conciliar Christology, the extension produced by conjoining Conciliar Christology with the thesis that Christ was unable to sin, is false. This chapter responds to this argument against Extended Conciliar Christology.

LEAN Production issues in the organization of the company - the first stage

Today’s market determinants and most importantly, very dynamically changing customer requirements significantly shortened the product life cycle. This situation reflects in companies by common extension of the assortment offered and personalised serial production. The result of a flexible approach to market changes is the implementation of LEAN concept, which, both in terms of management and production aims to develop efficiency within an organisation, which will then enable quick and dynamic response to changes in the environment. The popularity of LEAN concept (in management and production) among managers comes from its universality and a wide range of instruments used to maximise the use of existing potential. The main assumptions of LEAN concept are aimed at the maximum use of an organisation’s resources, defining the activities necessary to execute an order and identifying the areas generating losses and then minimising them and eventually eliminating. LEAN concept is based on flagship-main tools for identification and modernisation of processes, the difficulty in using them results from the need to recognise and select the most effective ones that meet the expectations of a given organisation. The article presents issues related to the first stage of implementing LEAN concept in a company’s structures, i.e. identification of opportunities and selection of appropriate tools.

Private Security Work in Turkey: A Case Study of Precarity, Militarism and Alienation

With one of the largest and fastest growing private security sectors in the greater EU area, Turkey offers an interesting case study for examining the effects of neoliberal policing on private security labour. The analysis is based on unstructured interviews (N = 20) with private security guards, media reports and government documents. Focusing on (1) precarity, (2) militarism and (3) alienation, we find that while private security has been decisive in the militarization of urban space and the exercise of authoritarian control in daily social relations, it is also characterized by class contradictions manifested in the lived experiences of security labour. The growth of Turkish private security and its effects are both part of the common extension of pacification yet uniquely conditioned by the emergence of a single-party, authoritarian regime that has deliberately extended its reach, in part, through the expansion of private security.

Fast Algorithms for Local Similarity Queries in Two Sequences

In sequence comparison, finding local similarities in given strings is a very important well-known problem. In this work we introduce two local sequence similarity query problems, and present algorithms for them. Our algorithms use a data structure that supports constant time longest common extension queries. This data structure is created only once, and in time linear in the size of the input strings. After this step all subsequent local similarity queries can be answered very fast. Existing algorithms take significantly more time in answering these queries.