The notion of functionality is not cast in stone, but depends upon what we have as types in our language. With partial equivalence relations (pers) as types we show that the functional relations are precisely those satisfying the simple equation f = f ◦ f∪ ◦ f , where “∪” is the relation converse operator. This article forms part of “A calculational theory of pers as types” [1].

Leaving the land of algebraic functions behind us, we find the notion of a monotone function most appealing. The definition of this notion presumes a partial order on the domain of the function and a total order on its range. We say that f : D → R is monotone if, for every x, y ∈ D if x < y (according to the partial order on D), then f(x) ≤ f(y) (according to the order on R). The most natural p...

The purpose of our study was to examine exercise dependence (EXD) in a large community-based sample of runners. The secondary purpose of this study was to examine differences in EXD symptoms between primary and secondary EXD. Our sample included 2660 runners recruited from a local road race (M age = 38.78 years, SD = 10.80; 66.39% women; 91.62% Caucasian) who completed all study measures online...

We study the two dimensional least gradient problem in convex polygonal sets plane, \(\Omega \). show existence of solutions when boundary data f are attained trace sense. The main difficulty here is a possible discontinuity f. Moreover, due to lack strict convexity \), classical results not applicable. state admissibility conditions on datum f, that sufficient for establishing an result. One t...

The use of anomalous X-ray scattering to obtain the first differences and partial structure factors normally obtained with isotopic substitution neutron diffraction is described and compared with the neutron technique. Both the problems associated with the X-ray technique and the situations in which it is highly valuable are discussed. The availability of tunable, intense synchrotron radiation ...

Let F be an infinite field with characteristic different from two. For a graph G = (V,E) with V = {1, . . . , n}, let S(G;F) be the set of all symmetric n × n matrices A = [ai,j ] over F with ai,j 6= 0, i 6= j if and only if ij ∈ E. We show that if G is the complement of a partial k-tree and m ≥ k + 2, then for all nonsingular symmetric m ×m matrices K over F, there exists an m× n matrix U such...

Given a C-function f on a compact riemannian manifold (X, g) we give a set of frequencies L = Lf (ε) depending on a small parameter ε > 0 such that the relative L-error ‖f−f ‖ ‖f‖ is bounded above by ε, where f L denotes the L-partial sum of the Fourier series f with respect to an orthonormal basis of L(X) constituted by eigenfunctions of the Laplacian operator ∆ associated to the metric g.

antivenoms have been used successfully for more than a century and up to now constitute the only effective treatment for snakebites .the production of antivenin started long time ago when the calmette was prepared the antivenom in 1894.the method currently used to prepare antivenom by most of the manufacturers are originated from the method of pope which was develop in 1938. several new appr...

We consider equation $$-\Delta u+f(x,u)=0$$ in smooth bounded domain $$\Omega \in \mathbb {R}^N$$ , $$N\geqslant 2$$ with $$f(x,r)>0$$ \times {R}^1_+$$ and $$f(x,r)=0$$ on $$\partial \Omega $$ . find the condition order of degeneracy f(x, r) near which is a criterion existence-nonexistence very singular solution strong point singularity Moreover, we prove that mentioned sufficient for uniquenes...

In this paper, we prove the following reversed Hardy–Littlewood–Sobolev inequality with extension kernel: $$\int _{\mathbb R_+^n}\int _{\partial\mathbb R^n_+}\frac{x_n^\beta}{|x-y|^{n-\alpha}}f(y)g(x)\,dy\,dx\geq C_{n,\alpha ,\beta ,p}\|f\|_{L^{p}(\partia