Superimposed D–branes have matrix–valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is nonabelian. Quantisation further introduces noncommutativi...

Counterexamples explain why a desired temporal logic property fails to hold, and as such are considered to be the most useful form of output from model-checkers. Multi-valued model-checking, introduced in [4] is an extension of classical model-checking. Instead of classical logic, it operates on elements of a given De Morgan algebra, e.g. the Kleene algebra [14]. Multi-valued modelchecking has ...

A novelWeyl-Heisenberg algebra in Clifford-spaces is constructed that is based on a matrix-valued H extension of Planck’s constant. As a result of this modified Weyl-Heisenberg algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, px); (x, py); (x, pz); (y, px), ... with absolute precision. New Klein-Gordon and Dirac wave equations and dispersion relations in...

It is shown that Bell’s theorem fails for the Clifford algebra valued local realistic variables. This is made evident by exactly reproducing quantum mechanical expectation value for the EPR-Bohm type spin correlations observable by means of a local, deterministic, Clifford algebra valued variable, without necessitating either remote contextuality or backward causation. Since Clifford product of...

We prove a multiplication theorem of a quantum Caldero-Chapoton map associated to valued quivers which extends the results in [8][6]. As an application, when Q is a valued quiver of finite type or rank 2, we obtain that the algebra A H |k|(Q) generated by all cluster characters (see Definition 1) is exactly the quantum cluster algebra E H |k|(Q) and various bases of the quantum cluster algebras...

We begin by taking the point of view of a physicist investigating the charge algebra of integrable field theories in 1+1 dimensions which have a Lie algebra valued, curvature-free, conserved current (of which notable examples are the principal chiral model and the GrossNeveu model and its generalizations). Such theories thus contain a charge Qa0, valued in a Lie algebra A, which acts additively...

Based on the general form of -resolution principle for a lattice-valued logic with truth-values defined in a latticevalued logical algebra structure lattice implication algebra, the further extended -resolution method in this lattice-valued logic is discussed in the present paper in order to increase the efficiency of the resolution method. Firstly, -quasi-lock semantic resolution method in lat...

In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...

This paper deals with the determination of the absolute valued algebras with a nonzero idempotent commuting with the remaining idempotents and satisfying x2x = xx2 for every x. We prove that, in addition to the absolute valued algebras R, C, H, or O of the reals, complexes, division real quaternions or division real octonions, one such absolute valued algebra A can also be isometrically isomorp...

In 1965, in his pioneer paper L.A. Zadeh [9] introduced the concept of fuzzy set to handle the uncertainties in our daily life. After that many generalizations of fuzzy sets are presented, for example, interval valued fuzzy sets [10] and intuitionistic fuzzy sets [1]. Fuzzy sets are extremely useful to solve many problems in applied mathematics, information sciences and theory of automata [2]. ...