A boolean predicate f : {0, 1} → {0, 1} is said to be somewhat approximation resistant if for some constant τ > |f −1(1)| 2k , given a τ -satisfiable instance of the MAX k-CSP(f) problem, it is NP-hard to find an assignment that strictly beats the naive algorithm that outputs a uniformly random assignment. Let τ(f) denote the supremum over all τ for which this holds. It is known that a predicat...

In this paper the concept of somewhat pairwise fuzzy faintly -continuous functions and somewhat pairwise fuzzy faintly -open functions are introduced. Some interesting properties of these functions are investigated besides giving some characterizations of these functions.

Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the somewhat intricate case when the surface is nonorientable.

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.

BACKGROUND Low back pain is a common and disabling condition leading to large health service and societal costs. Although there are several treatment options for back pain little is known about how to improve patient choice in treatment selection. The purpose of this study was to pilot a decision support package to help people choose between low back pain treatments. METHODS This was a single...

Blum Cucker Shub and Smale have shown that the problem P NP has the same answer in all algebraically closed elds of characteristic We generalize this result to the polynomial hierarchy if it collapses over an algebraically closed eld of characteristic then it must collapse at the same level over all algebraically closed elds of characteristic The main ingredient of their proof was a theorem on ...

The aspect markers -te iku and -te kuru in Japanese (where the verbs iku and kuru, when used as main verbs, mean ‘go’ and ‘come’, respectively) exhibit somewhat puzzling entailment patterns with open-scale and closed-scale change of state predicates. Specifically, as shown in (1)–(3), while the two markers behave in the same way with closed-scale predicates in inducing an entailment to the posi...

Example 1. The set R+ is a closed, convex, pointed cone. The half plane {x ∈ R2 : x2 ≥ 0} is a closed, convex cone that is not pointed. The union of the open half plane {x ∈ R2 : x2 > 0} and 0 is a somewhat pathological example of a convex cone that is pointed but not closed. Remark 1. There are several different definitions of “cone” in the mathematics. Some, for example, require the cone to b...