The 'associative' discrimination fiction: part 1

Associative discrimination is a consequence of the open formulas used in the UK (and EU) equality legislation to define direct discrimination. The treatment needs only to be ‘because of a protected characteristic’ (such as race, sexual orientation, etc) rather than because of his (or her) protected characteristic. Hence, a white worker dismissed for marrying a black person could sue for direct (racial) discrimination. The open formula is not limited to such cases and, so, treating associative discrimination as a term of art is a mistake, as this could unnecessarily restrict the reach of the deliberately open legislative formula. This article identifies the Supreme Court judgment in Lee v Ashers as an example of this mistake. It further asserts that any compromise for conflicting rights is found in the Human Rights Act 1998 (HRA 1998), and not by distorting the definition of discrimination.

Roman Ingarden and Our Times: Recent Trends in Phenomenology and Contemporary Philosophy

The present book is an illustration of current approach to Roman Ingarden’s philosophy and to contemporary philosophy in general. Significantly, the articles contained herein are the works of authors representing various research centers around the world. This clearly demonstrates that Ingarden’s philosophical thought continues to be inspiring, regardless of whether individual researchers interpret it positively or negatively. At the same time, it should be emphasized that the present volume is not a commemorative publication devoted solely to the person and thought of Ingarden. The open formula of the book was intended to encourage and invite researchers representing various schools of philosophical thinking (both close to as well as distant from phenomenology) to publish in the present monographic volume. This applies to polemics both within and without the realm of phenomenology. In each case, we are dealing with an in-depth discussion which may serve as an inspiration for readers interested in a plethora of philosophical problems. The statements presented in this volume are offered in the spirit of research and creative exchange of views.

Extreme nonuniqueness of end-sum

We give explicit examples of pairs of one-ended, open [Formula: see text]-manifolds whose end-sums yield uncountably many manifolds with distinct proper homotopy types. This answers strongly in the affirmative a conjecture of Siebenmann regarding nonuniqueness of end-sums. In addition to the construction of these examples, we provide a detailed discussion of the tools used to distinguish them; most importantly, the end-cohomology algebra. Key to our Main Theorem is an understanding of this algebra for an end-sum in terms of the algebras of summands together with ray-fundamental classes determined by the rays used to perform the end-sum. Differing ray-fundamental classes allow us to distinguish the various examples, but only through the subtle theory of infinitely generated abelian groups. An appendix is included which contains the necessary background from that area.

Effects of standard diets from different sources on growth and some organ parameters of rats

This study aims to determine the effects of open and closed formulated standard diets supplied from different sources on growth performance and internal organ development of laboratory rats. Five-week-old 32 Wistar rats were used. A special control group diet was produced in accordance with the criteria determined by the National Research Council (NRC) (1995). Three different most preferred commercial open and closed-formula diets produced by international and local companies were used as trial groups’ diets. The experiment was carried out for 12 weeks. Weekly feed consumption, body weight change, internal organ weight, intestinal organ weigths and lengths, intestinal villi heigth and crypt depth were measured in groups. The body weight values of the control group and the first group fed with open-formula diet were found at the highest level (P <0.05). The control group diet had a positive effect on small intestine villi heigth and crypt depth (P <0.05). The nutrient contents and energy values of the diets of experimental groups were determined as different from the commercial firm notifications. As a result of the research, it is concluded that the diets prepared with open-formula give more reliable results in the growth performance and development of internal organs of Wistar rats.

Z-scan theoretical model for simultaneous n- and (n+1)-photon absorption

We present a theoretical analysis of multi-photon absorption processes. We find an approximate closed-form expression of the normalized transmittance for a thin sample with two successive nonlinear absorption processes at a time ([Formula: see text]- and [Formula: see text]-photon absorption) in the presence of residual linear absorption. Our approach allows for simultaneous identification and evaluation of the nonlinear absorption coefficients and Rayleigh lengths of the incident elliptic Gaussian beam by fitting the open [Formula: see text]-scan traces.

An algorithm for regular solutions of systems of exp-subanalytic equations and o-minimality of ℝan,exp

We describe an algorithm which reduces (the problem of finding regular solutions of) a system of [Formula: see text]-subanalytic equations to (the same problem for) a finite number of systems of subanalytic equations, by using the following operations: restriction to an open [Formula: see text]-subanalytic subset, smooth [Formula: see text]-subanalytic change of variables and restriction to a linear subspace. An application of this together with a theorem of Lion is that the structure [Formula: see text] is o-minimal.

Distal actions on coset spaces in totally disconnected locally compact groups

Let [Formula: see text] be a totally disconnected locally compact (t.d.l.c.) group and let [Formula: see text] be an equicontinuously (for example, compactly) generated group of automorphisms of [Formula: see text]. We show that every distal action of [Formula: see text] on a coset space of [Formula: see text] is a SIN action, with the small invariant neighborhoods arising from open [Formula: see text]-invariant subgroups. We obtain a number of consequences for the structure of the collection of open subgroups of a t.d.l.c. group. For example, it follows that for every compactly generated subgroup [Formula: see text] of [Formula: see text], there is a compactly generated open subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and such that every open subgroup of [Formula: see text] containing a finite index subgroup of [Formula: see text] contains a finite index subgroup of [Formula: see text]. We also show that for a large class of closed subgroups [Formula: see text] of [Formula: see text] (including for instance all closed subgroups [Formula: see text] such that [Formula: see text] is an intersection of subnormal subgroups of open subgroups), every compactly generated open subgroup of [Formula: see text] can be realized as [Formula: see text] for an open subgroup of [Formula: see text].

Generalized μ(m,n)b-open and closed functions in bigeneralized topological spaces

The purpose of this paper is to introduce the notions of [Formula: see text]-open, [Formula: see text]-closed, quasi [Formula: see text]-open, and quasi [Formula: see text]-closed functions in bigeneralized topological spaces. Basic properties, characterizations and relationships between these functions are obtained.