A Dirichlet operator algebra is a nonself-adjoint $\mathcal{A}$ with the property that $\mathcal{A} + \mathcal{A}^*$ norm-dense in C$^*$-envelope of $\mathcal{A}.$ We show that, under certain restrictions, has family completely contractive representations $\{\pi_i\}$ invariant subspaces $\pi_i(\mathcal{A})$ are totally ordered, and such for all $a \in \mathcal{A}, ||a|| = \sup_i ||\pi_i(a)||.$...

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and ...

When Zadeh first introduced the notion of a fuzzy set, it was laughed away by the ruling caste of 'serious' mathematicians and logicians. Driven by ignorance, the main reason for it was probably strategic: as fuzzy set theory touches upon the very building block of mathematics, it might be better to deny it than to risk being taken out of business. Even the ample practical realizations had no e...

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an binary operations (not necessarily t-norms) defined the fixed subintervals may not be t-norm. Some necessary and sufficient conditions are presented in this article for ensuring that two is, fact, In particular, results here provide answer open problem put forward by Ertuğrul Yeşilyurt, <italic...

Quantum chaotic states over a noncommutative monoid, a unitalization of a noncommutative Ito algebra parametrizing a quantum stochastic Levy process, are described in terms of their infinitely divisible generating functionals over the simple monoid-valued fields on an atomless ‘space-time’ set. A canonical decomposition of the logarithmic conditionally posive-definite generating functional is c...

The study of pseudospectra of linear transformations has become a significant part of numerical linear algebra and related areas. A large body of research activity has focused on how to compute these sets for a given spectral problem with, possibly, certain underlying structure. The theme of this paper was motivated by the question: How effective are path-following procedures for tracing the ps...

We discuss a generalization of the Cohn–Umans method, a potent technique developed for studying the bilinear complexity of matrix multiplication by embedding matrices into an appropriate group algebra. We investigate how the Cohn–Umans method may be used for bilinear operations other than matrix multiplication, with algebras other than group algebras, and we relate it to Strassen’s tensor rank ...

BACKGROUND Given the benefits of radiographic cephalometric studies in determining patterns of dental-skeletal-facial normality in orthodontics, the aim of this study was to investigate the association between mandibular dental arch shape and cross-sectional and vertical facial measurements. MATERIALS AND METHODS It was analyzed plaster casts and teleradiographs in frontal and lateral norm be...