We show that the E +-class can be decided by a liftable order, when it is applied a posteriori. This is a surprising result, because the E +-class was one of the motivations for the study of non-liftable orders. Also surprising is the behaviour of the resolution process. Initially the variable depth of the clauses may grow, but it will not grow deeper than a certain bound. We do not make use of...

and |g′′(x)| = M. We will show that |f(x)| ≤ g(x) on [0, 1]. The desired conclusion follows. Suppose however that this is false, that there is a number q ∈ [0, 1] for which f(q) > g(q). (The other case, f(q) < −g(q), is similar.) Our strategy will be to show that there are real numbers s and t with s < t such that f ′(s) > g′(s) and f ′(t) < g′(t). See figure. We will then apply the Mean Value ...

We systematically study wreath product Schur functions and give a combinatorial construction using colored partitions and tableaux. The Pieri rule and the Littlewood-Richardson rule are studied. We also discuss the connection with representations of generalized symmetric groups.

This paper provides a characterization of dominant strategy mechanisms with quasi-linear utilities and multi-dimensional types for a variety of preference domains. These characterizations are in terms of a monotonicity property on the underlying allocation rule.

Are Plurality voting, the Kemeny rule, Approval voting, and the Borda Mean Dichotomy rule all versions of the same voting rule? Yes, in a sense. In an extension of work by Barthélemy and Monjardet [3], we consider functions F that assign real number scoring weights F (R1, R2) to pairs of binary relations on a finite set A of alternatives, serving as symmetric measures of similarity between R1 a...

We consider the possible ways of the homogenization of nongraded non-commutative algebra and show that it should be combined with the cancellation rule to get the mathematically adequate correspondence between graded and non-graded algebras.

Class Sm variable transformations with integer m for finite-range integrals were introduced by the author about a decade ago. These transformations ‘‘periodize’’ the integrand functions in a way that enables the trapezoidal rule to achieve very high accuracy, especially with even m. In a recent work by the author, these transformations were extended to arbitrary real m, and their role in improv...

In this study, we propose an approach to determine the shortest path length between a pair of specified nodes s and t on a network whose edge weights are represented by trapezoidal neutrosophic numbers. Finally, an illustrative example is provided to show the applicability and effectiveness of the proposed approach. Keywords—trapezoidal fuzzy neutrosophic sets; score function; Shortest path pro...

in this paper the solution of a second order linear dierential equations with intu-itionistic fuzzy boundary value is described. it is discussed for two dierent cases: coecientis positive crisp number and coecient is negative crisp number. here fuzzy numbers aretaken as generalized trapezoidal intutionistic fuzzy numbers (gtrifns). further a numericalexample is illustrated.