There are currently no fewer than four dedicated logics for equality reasoning over nominal sets: nominal algebra, nominal equational logic, nominal equational logic with equality only, and permissive-nominal algebra. In this survey and research paper we present these logics side-by-side in a common notation, survey their similarities and differences, discuss their proofand model-theories, and ...

In this correspondence we give several new families of binary sequences of period with optimal three-level autocorrelation, where 2(mod 4). These sequences are either balanced or almost balanced. Our construction is based on cyclotomy.

We study quadratic forms that can occur as trace forms qL/K of Galois field extensions L/K, under the assumption that K contains a primitive 4th root of unity. M. Epkenhans conjectured that qL/K is always a scaled Pfister form. We prove this conjecture and classify the finite groups G which admit a G-Galois extension L/K with a nonhyperbolic trace form. We also give several applications of thes...

This paper presents the results of a study on the preference ranking of six layout principles (Cohesion, Economy, Regularity, Sequence, Symmetry, and Unity). Preference judgments were conducted using a forced-choice paired comparisons method. The findings of the present study indicate that, contrary to suggestions in previous literature, an interface was most preferred when it corresponded to a...

Alcohol, with its impact on both communicable and non-communicable diseases, is considered as the third global public health priority. Alcohol ranked third among causes of ill health and premature death, and ranked second in terms of cost among all the substances of abuse, after tobacco, even though nearly half the world’s population drinks alcohol. In most countries, where alcohol is considere...

Abstract. We show that for any prime number l > 2 the minus class group of the field of the l-th roots of unity Qp(ζl) admits a finite free resolution of length 1 as a module over the ring Ẑ[G]/(1 + ι). Here ι denotes complex conjugation in G = Gal(Qp(ζl)/Qp) ∼= (Z/lZ)∗. Moreover, for the primes l ≤ 509 we show that the minus class group is cyclic as a module over this ring. For these primes we...

Explicit formulae for τ ′ r(L(p, q)) and τ(L(p, q)) are obtained for all L(p, q). There are three systems of invariants of Witten-type for closed oriented 3manifolds: 1. {τr(M), r ≥ 2; τ ′ r(M), r odd ≥ 3}, where τr was defined by Reshetikhin and Turaev [1], and τ ′ r was defined by Kirby-Melvin [2] 2. {Θr(M,A), r ≥ 1,whereA is a 2r-th primitive root of unity} defined by Blanchet, Habegger, Mas...

We introduce here the notions of identity and unity as they have been discussed in Philosophy, and then provide additional clarifications needed to use these notions as fundamental tools in a methodology for ontology-driven conceptual analysis. We show how identity and unity complement each other under a general notion of individuality, and conclude with an example of how these tools can be use...

We replace the group of group-like elements of the quantized enveloping algebra Uq(g) of a finite dimensional semisimple Lie algebra g by some regular monoid and get the weak Hopf algebra w q (g). It is a new subclass of weak Hopf algebras but not Hopf algebras. Then we devote to constructing a basis of w q (g) and determine the group of weak Hopf algebra automorphisms of w q (g) when q is not ...

In this paper, a new voltage-mode quadrature oscillator using minimum number of active and passive component is proposed. The proposed circuit employs single modified DVCC, two grounded capacitor and two grounded resistors, which is ideal for IC implementation. The active and passive sensitivity are no more than unity. The proposed circuit is verified through PSPICE simulation results.