In this contribution we present some interesting constructions of non-continuous triangular norms. The first approach is based on strictly increasing sequences of natural numbers. An associative commutative monotone and bounded by minimum binary operation on these sequences induces a t-norm. The corresponding t-norm is left continuous and therefore it is applicable in the fuzzy logic. Several o...

We use a “weakly formulated” Sylvester equation A 1/2 TM −1/2 − A −1/2 TM 1/2 = F to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known results of Davis and Kahan. Another application is a bound for the square root of a positive selfadjoint operator which extends the known rule: “The relative error in th...

We show that Leitgeb’s dependence operator of [2] is a Π11-operator and that this is best possible. In [2] Hannes Leitgeb introduced a dependence operatorD as a relation between sets of sentences in a language LTr such as that for arithmetic (which we shall take here) augmented with a predicate symbol Ṫr to represent truth. We shall assume the reader has a familiarity with this article and its ...

study of the limit-point concept [16]. Which factors could dictate the introduction of a topology for a given system of informational formulas? In informational cases, different kinds of reasonable topologies, corresponding intuitive ideas what an understanding, interpretation, conception, perception and meaning should be, are coming to the consciousness, that is, into the modeling foreground. ...

The List Edge Colouring Conjecture asserts that, given any multigraph G with chromatic index k and any set system fSe : e 2 E(G)g with each jSej = k, we can choose elements se 2 Se such that se 6 = sf whenever e and f are adjacent edges. Using a technique of Alon and Tarsi which involves the graph monomial Q fxu ? xv : uv 2 Eg of an oriented graph, we verify this conjecture for certain families...

The coordinate-free one-way wave equation is transferred in spherical coordinates. Therefore it necessary to achieve consistency between gradient, divergence and Laplace operators establish, beside the conventional radial Nabla operator ∂Φ/∂r, a new variant ∂rΦ/r∂r. two variants differ near field term Φ/r whereas far r≫0 there asymptotic approximation. Surprisingly, more complicated gradient ∂r...

We suggest two grand unified models where the fifth dimensional coordinate is compactified on an S1/(Z2 × Z ′ 2) orbifold. Before showing the models, let us see the compactification of the fifth dimension. We denote the five dimensional coordinate as y, which is compactified on an S1/(Z2 × Z ′ 2) orbifold. Under the parity transformation of Z2 and Z ′ 2, which transform y → −y and y ′ → −y (y =...

The Nevanlinna counting function is used to give several different characterizations of inner functions. The results all assert that a holomorphic selfmap of the unit disc is inner if and only if its Nevanlinna counting function is, in various pointwise, asymptotic, and operator-theoretic senses, as large as it can be. Although many of the results in this note are known, the asymptotic and oper...

I promised a second part. Here it is. I hesitated, because I don’t like being destructive, and unfortunately, to deal with the current state of affairs in quantum theory means just doing this: I show you that the current gauge theory is fundamentally ill-designed, along with it fall Weinberg model and Wightman theory. 1. Continuing with the Lagrangian Formalism Let me continue from where I left...

We construct some separable infinite dimensional homogeneous Hilbertian operator spaces H ∞ and H m,L ∞ , which generalize the row and column spaces R and C (the case m = 0). We show that separable infinitedimensional Hilbertian JC∗-triples are completely isometric to an element of the set of (infinite) intersections of these spaces . This set includes the operator spaces R, C, R ∩ C, and the s...