The modal systems S1–S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which generalizes a reference rule of S1. In system S1+SP, the relation of strict equivalence φ ≡ ψ satisfies the identity axioms of R. Suszko’s non-Fregean logic adapted t...

An algebra A is called a GI-algebra if its group of units A satisfies a group identity. We provide positive support for the following two open problems. 1. Does every algebraic GI-algebra satisfy a polynomial identity? 2. Is every algebraically generated GI-algebra locally finite? 2000Mathematics Subject Classification. 16R40; 16R50; 16U60; 17B35.

Recently, Chen-Chu-Gu [4] and Guo-Zeng [6] found independently that Watson’s quintuple product identity follows surprisingly from two basic algebraic identities, called finite forms of Watson’s quintuple product identity. The present paper shows that both identities are equivalent to two special cases of the q-Chu-Vandermonde formula by using the (f, g)-inversion.

From Hamilton’s principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity connecting equations of momentum, mass, energy and entropy is obtained by extending the Gibbs identity in dynamics. The obtained system is hyperbolic for sma...

where df{n) denotes the number of divisors of n, d = i (mod 4). In literature there are several proofs of (1) and (2). For instance, M. D. Hirschhorn [7; 8] proved (1) and (2) using Jacobi's triple product identity. S. Bhargava & Chandrashekar Adiga [4] have proved (1) and (2) as a consequence of Ramanujan's ^ summation formula [10]. Recently R. Askey [2] has proved (1) and also derived a formu...

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for today's revival on interest to nonassociativity. Our reflections keep wandering back to the Brahmagupta-Fibonacci Two-Square Identity and then via the Euler Four-Square Identity up to the...

Abstract In a recent paper, Caracciolo, Sokal and Sportiello presented, inter alia, an algebraic/combinatorial proof for Cayley’s identity. The purpose of the present paper is to give a “purely combinatorial” proof for this identity; i.e., a proof involving only combinatorial arguments. Since these arguments eventually employ a generalization of Laplace’s Theorem, we present a “purely combinato...

We propose a critical spin liquid ground state for S=1/2 antiferromagnets on the square lattice. In a renormalization group analysis of the "staggered flux" algebraic spin liquid, we examine perturbations, present in the antiferromagnet, which break its global SU(4) symmetry to SO(5). At physical parameter values, we find an instability towards a fixed point with SO(5) symmetry. We discuss the ...

This paper aims to address the relation between a magic square of odd order n and a group, and their properties. By the modulo number n, we construct entries for each table from initial table of magic square with large number n. Generalization of the underlying idea is presented, we obtain unique group, and we also prove variants of the main results for magic cubes.