We discuss some Lagrangian and presymplectic models concerning test particles in electromagnetic and gravitational fields, with the aim of describing an upper bound to the acceleration. Some models are based on the relativistic phase space and others on the bundle of the Lorentz frames. For the second case, an appropriate version of the methods of analytic mechanics, including the Noether theor...

Cohen, G.D., S.N. Litsyn, On the covering radius of Reed-Muller codes, Discrete Mathematics 106/107 (1992) 147-155. We present lower and upper bounds on the covering radius of Reed-Muller codes, yielding asymptotical improvements on known results. The lower bound is simply the sphere covering one (not very new). The upper bound is derived from a thorough use of a lemma, the ‘essence of Reed-Mul...

In [1, 2] Zhang shows how the complexity of cut elimination depends primarily on the nesting of quantifiers in cut formulas. By studying the role of contractions in cut elimination we can refine that analysis and show how the complexity depends on a combination of contractions and quantifier nesting. With the refined analysis the upper bound on cut elimination coincides with Statman’s lower bou...

In this article λ-method of Mitrinović-Vasić [1] is applied to improve the upper bound for the arc sin function of L. Zhu [4]. 1. Inequalities of Shafer-Fink’s type D. S. Mitrinović in [1] considered the lower bound of the arc sin function, which belongs to R. E. Shafer. Namely, the following statement is true. Theorem 1.1 For 0 ≤ x ≤ 1 the following inequalities are true: 3x 2 + √ 1− x2 ≤ 6( √...

We determine the combinatorial discrepancy of the hypergraph H of cartesian products of d arithmetic progressions in the [N ]d–lattice ([N ] = {0, 1, . . . ,N − 1}). The study of such higher dimensional arithmetic progressions is motivated by a multi-dimensional version of van der Waerden’s theorem, namely the Gallai-theorem (1933). We solve the discrepancy problem for d–dimensional arithmetic ...

calculation of lateral earth pressure on retaining walls is one of the main issues in geotechnics. the upper and lower bound theorems of plasticity are used to analyze the stability of geotechnical structures include bearing capacity of foundations, lateral earth pressure on retaining walls and factor of safety of slopes. in this paper formulation of finite element limit analysis is introduced ...

Minc conjectured, and Brégman proved, a sharp upper bound on the permanent of an n by n 0-1 matrix with given row sums (equivalently, on the number of perfect matchings in a bipartite graph with each partition class having size n and with fixed degree sequence for one of the two classes). Here we present Radhakrishnan’s entropy proof of Brégman’s theorem, and Alon and Friedland’s proof of an an...

Abstract. A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with exactly i > 0 interior lattice points. We will show that the same bound is true for the normalized volume of lattice polytopes of degree 2 even in higher dimensions. The finiteness of lattice polytopes of degree 2 up to standard pyramids and affine unimodular transformation follows from a theore...

Abstract. A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with exactly i > 0 interior lattice points. We will show that the same bound is true for the normalized volume of lattice polytopes of degree 2 even in higher dimensions. The finiteness of lattice polytopes of degree 2 up to standard pyramids and affine unimodular transformation follows from a theore...

The notion of a partitionable simplicial complex is extended to that of a signable partially ordered set. It is shown in a unified way that face lattices of shellable polytopal complexes, polyhedral cone fans, and oriented matroid polytopes, are all signable. Each of these classes, which are believed to be mutually incomparable, strictly contains the class of convex polytopes. A general suffici...