Ideal on an arbitrary non-empty set $\Omega$ it's a family of subset $\mathfrak{I}$ the which satisfies following axioms: $\Omega \notin \mathfrak{I}$, if $A, B \in then $A \cup \mathfrak{I}$ and $D \subset A$, \mathfrak{I}$. The ideal theory is very popular branch modern mathematical research. In our paper we study some classes ideals all positive integers $\mathbb{N}$, namely statistical conv...

A method for calculating the distributions of the components of stiffness and compliance tensors of cubic polycrystalite material from parameters of single crystals is developed. Their mathematical form is derived under the assumption of normal distributions for the members of the rotation group SO(3). Finally the impact of texture on the distributions of Young’s modulus E, shear modulus G and ...

Theoretical Model To design a simple teardrop-shaped membrane, two circles with radii of 2 mm and 0.5 mm, were connected by tangent lines. The two circles were spaced as much as 5 mm apart, from center to center. The shape of the chamber underneath the teardrop-shaped membrane was also the same as that of the membrane. The thickness of the membrane and the height of the chamber were 20 μm and 2...

Let C be a subset of R (not necessarily convex), f : C → R be a function, and G : C → R be a uniformly continuous function, with modulus of continuity ω. We provide a necessary and sufficient condition on f , G for the existence of a convex function F ∈ C(R) such that F = f on C and ∇F = G on C, with a good control of the modulus of continuity of ∇F in terms of that of G. On the other hand, ass...

and Applied Analysis 3 It is known that a uniformly convex Banach space is reflexive and strictly convex. The function δ : 0, 2 → 0, 1 which is called the modulus of convexity of E is defined as follows: δ ε inf {

Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity δΩ of a set Ω. We also show that limε→0 δΩ(ε)/ε 2 exists whenever Ω is closed and convex.

This research explored the effect of a chemical treatment on the stiffness of three southern hardwoods, yellow-poplar, sweetgum, and red oak, with the aim of broadening the potential feedstocks for structural composite lumber. Water-saturated 3 15 150 mm samples from each species were heated at 150 C for 30 min in three solutions: 1.0% H2SO4, water, and 1.0% NaOH. The specimens were nondestruct...