An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction

23 p. -- An extended abstract of this work appears in the proceedings of the 2012 ACM/IEEE Symposium on Logic in Computer Science

An arithmetical theorem for partially ordered sets

The simplest multiplicative systems in which arithmetical ideas can be defined are semigroups. For such systems irreducible (prime) elements can be introduced and conditions under which the fundamental theorem of arithmetic holds have been investigated (Clifford (3)). After identifying associates, the elements of the semigroup form a partially ordered set with respect to the ordinary division relation. This suggests the possibility of an analogous arithmetical result for abstract partially ordered sets. Although nothing corresponding to product exists in a partially ordered set, there is a notion similar to g.c.d. This is the meet operation, defined as greatest lower bound. Thus irreducible elements, namely those elements not expressible as meets of proper divisors can be introduced. The assumption of the ascending chain condition then implies that each element is representable as a reduced meet of irreducibles. The central problem of this thesis is to determine conditions on the structure of the partially ordered set in order that each element have a unique such representation.

Part I contains preliminary results and introduces the principal tools of the investigation. In the second part, basic properties of the lattice of ideals and the connection between its structure and the irreducible decompositions of elements are developed. The proofs of these results are identical with the corresponding ones for the lattice case (Dilworth (2)). The last part contains those results whose proofs are peculiar to partially ordered sets and also contains the proof of the main theorem.

Lq estimates for rearrangements of Fourier series

This work is concerned with estimating the upper envelopes S* of the absolute values of the partial sums of rearranged trigonometric sums. A.M. Garsia [Annals of Math. 79 (1964), 634-9] gave an estimate for the L₂ norms of the S*, averaged over all rearrangements of the original (finite) sum. This estimate enabled him to prove that the Fourier series of any function in L₂ can be rearranged so that it converges a.e. The main result of this thesis is a similar estimate of the L_q norms of the S*, for all even integers q. This holds for finite linear combinations of functions which satisfy a condition which is a generalization of orthonormality in the L₂ case. This estimate for finite sums is extended to Fourier series of L_q functions; it is shown that there are functions to which the Men’shov-Paley Theorem does not apply, but whose Fourier series can nevertheless be rearranged so that the S* of the rearranged series is in L_q.

A New Type of Coincidence and Common Fixed Point Theorem with Applications

Coincidence and common fixed point theorems for a class of 'Ciric-Suzuki hybrid contractions involving a multivalued and two single-valued maps in a metric space are obtained. Some applications including the existence of a common solution for certain class of functional equations arising in a dynamic programming are also discussed..

An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.

On the theorem of Reichert

This paper reworks and amplifies Reichert's proof of his theorem (1969) which asserts that any impedance function of a one-port electrical network which can be realised with two reactive elements and an arbitrary number of resistors can be realised with two reactive elements and three resistors. © 2012 Elsevier B.V. All rights reserved.

Radiation effects on the immiscible polymer blend of nylon1010 and high-impact polystyrene (HIPS) I: Gel/dose curves, mathematical expectation theorem and thermal behaviour

This paper studies the radiation properties of the immiscible blend of nylon1010 and HIPS. The gel fraction increased with increasing radiation dose. The network was found mostly in nylon1010, the networks were also found in both nylon1010 and HIPS when the dose reaches 0.85 MGy or more. We used the Charleby-Pinner equation and the modified Zhang-Sun-Qian equation to simulate the relationship with the dose and the sol fraction. The latter equation fits well with these polymer blends and the relationship used by it showed better linearity than the one by the Charleby-Pinner equation. We also studied the conditions of formation of the network by the mathematical expectation theorem for the binary system. Thermal properties of polymer blend were observed by DSC curves. The crystallization temperature decreases with increasing dose because the cross-linking reaction inhibited the crystallization procession and destroyed the crystals. The melting temperature also reduced with increasing radiation dose. The dual melting peak gradually shifted to single peak and the high melting peak disappeared at high radiation dose. However, the radiation-induced crystallization was observed by the heat of fusion increasing at low radiation dose. On the other hand, the crystal will be damaged by radiation. A similar conclusion may be drawn by the DSC traces when the polymer blends were crystallized. When the radiation dose increases, the heat of fusion reduces dramatically and so does the heat of crystallization. (C) 1999 Elsevier Science Ltd. All rights reserved.

The Rawls-Tawney theorem and the digital divide in postindustrial society.

The digital divide continues to challenge political and academic circles worldwide. A range of policy solutions is briefly evaluated, from laissez-faire on the right to “arithmetic” egalitarianism on the left. The article recasts the digital divide as a problem for the social distribution of presumptively important information (e.g., electoral data, news, science) within postindustrial society. Endorsing in general terms the left-liberal approach of differential or “geometric” egalitarianism, it seeks to invest this with greater precision, and therefore utility, by means of a possibly original synthesis of the ideas of John Rawls and R. H. Tawney. It is argued that, once certain categories of information are accorded the status of “primary goods,” their distribution must then comply with principles of justice as articulated by those major 20th century exponents of ethical social democracy. The resultant Rawls-Tawney theorem, if valid, might augment the portfolio of options for interventionist information policy in the 21st century