In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.

We describe simple finitely generated associative conformal algebras of Gel’fand–Kirillov dimension one.

This paper demonstrates the use of exact predictive likelihood functions for simple non-linear models. A measure of predictive efficiency based on the concept of expected information loss is introduced as a way of comparing alternative prediction functions. It is shown that the predictive likelihood function minimizes expected information loss over a wide class of potential prediction functions...

We show that any non-zero orbit under a non-compact, simple, irreducible linear group is dense in the Bohr compactification of the ambient space.

A new low order facet type triangular shell finite element is presented. The element is combined from the Arnold-Falk plate bending element and the membrane element based on the noncorming element of Crouzeix-Raviart with conforming drilling rotation. Formulation of the membrane element is based on the variational principle of Hughes and Brezzi employing independent rotation field. Interpolatio...

Let P and Q be simple polygons with vertex sets fp1; : : : ; png and fq1; : : :, qng, respectively. We present an algorithm to construct a piecewise linear homeomorphism between P and Qmapping each vertex pi 2 P to qi 2 Q by constructing isomorphic triangulations of P and Q. These isomorphic triangulations consist of O(M log n+n log2 n) triangles where M is the size of the optimal (minimum size...

Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The fundamental concepts of neutrosophic set, introduced by Smarandache in [7, 8]. Recently, Salama et al. in [14, 15, 16, 32 ], introduced the concept of correlation coefficient of neutrosophic data. In this paper, we introduce and study the concepts of correlation and correlation coeffici...

A suffix array represents the suffixes of a string in sorted order. Being a simpler and more compact alternative to suffix trees, it is an important tool for full text indexing and other string processing tasks. We introduce the skew algorithm for suffix array construction over integer alphabets that can be implemented to run in linear time using integer sorting as its only nontrivial subroutin...

We call a linear time property simple if counterexamples are accepted by a Büchi automaton that has only singleton strongly connected components. This class contains interesting properties such as LTL formulas G(φ =⇒ Fψ) or φUψ which have not yet received support beyond general LTL preserving approaches. We contribute a stubborn set approach to simple properties with the following ingredients. ...

We present a simple linear time combinatorial algorithm for the Betweenness problem. In the Betweenness problem, we are given a set of vertices and betweenness constraints. Each betweenness constraint of the form x {y, z} requires that vertex x lies between vertices y and z. Our goal is to find a linear ordering of vertices that maximizes the number of satisfied constraints. In 1995, Chor and S...