In this article we give a purely topological characterization for a topology 3 on a set X to be the order topology with respect to some linear order R on X, as follows. A topology 3 on a set X is an order topology iff (X, 3) is a TVspace and 3 is the least upper bound of two minimal 7Vtopologies [Theorem 1 ]. From this we deduce a purely topological description of the usual topology on the set ...

Nowadays, thanks to the new manufacturing processes, indentation is becoming an essential part of the new arising processes such as the Incremental Forming Processes. This work presents the experimental validation of the analytical model developed for an indentation-based process. The analytical model is originated from the Upper Bound Theorem application by means of its new modular distributio...

Sums of Betti numbers in arbitrary characteristic Nicholas M. Katz Introduction In [Mil], Milnor gave an explicit upper bound for the sum of the Betti numbers of a complex affine algebraic variety V. If V is defined in ^N, N ≥ 1, by r ≥ 1 equations Fi, i =1 to r, all of degree ≤ d, Milnor showed ‡i h i(V, $) ≤ d(2d-1)2N-1. Oleinik [Ol] and Thom [Th] gave similar results. It is standard (cf. the...

Abstract By using the eigenvalue inclusion field theorem and commutability of Hadamard product, new upper bound estimations ρ ( E ∘ F ) are given. The can be expressed only by elements two nonnegative matrices, which operable easy to calculate. Finally, an example is given verify that estimation formulas in this paper more accurate than related conclusions.

We use term regular directed graph (r. d. g.) for the graph of irreflexive binary relation with the constant number outputs (or inputs) for each vertex. The paper is devoted to studies of maximal size ER(d, v) of r. d. g. of order v without commutative diagrams formed by two directed passes of length < d with the common starting and ending points. We introduce the upper bound for ER(d, v), whic...

Among the mostly investigated parameters for noisy channels are code size, error probability in decoding, block length; rate, capacity, reliability function; delay, complexity of coding. There are several statements about connections between these quantities. They carry names like “coding theorem”, “converse theorem” (weak, strong, ...), “direct theorem”, “capacity theorem”, “lower bound”, “upp...

For a complete Riemannian manifold M with (1,1)-elliptic Codazzi self-adjoint tensor field A, we use the divergence type operator $${L_A}(u): = div(A\nabla u)$$ and an extension of Ricci to extend some major comparison theorems in geometry. In fact such as mean curvature theorem, Bishop–Gromov volume Cheeger–Gromoll splitting theorem their famous topological consequences. Also get upper bound f...

In this paper, we investigate even-order linear difference equations and their criticality. However, restrict our attention only to several special cases of the general Sturm–Liouville equation. We wish on such a possible converse known theorem. This theorem holds for second-order as an equivalence; however, one implication is equations. First, show in sense term Later, upper bound criticality ...

Suppose a finite group G acts on manifold M. By theorem of Mostow, also Palais, there is G-equivariant embedding M into the m-dimensional Euclidean space Rm for some m. We are interested in explicit bounds such First we provide an upper bound: exists Rd|G|+1, where |G| order and embeds Rd. Next lower bound cyclic action G: If l points having pairwise co-prime lengths G-orbits greater than 1 Rm,...

in this paper we give sharp upper bounds on the zagreb indices and characterize all trees achieving equality in these bounds. also, we give lower bound on first zagreb coindex of trees.