A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of Cr endomorphisms with singularities. A map that is stable in this sense will be conjugated to each perturbation that is equivalent to it in a geometric sense. It will be shown that this kind of stability implies Axiom A, Omega-stability and that every critical point is wanderin...

Let φ be a modulus function, i.e., continuous strictly increasing function on [0,∞), such that φ(0) = 0, φ(1) = 1, and φ(x + y) ≤ φ(x) + φ(y) for all x, y in [0,∞). It is the object of this paper to characterize, for any Banach space X, extreme points, exposed points, and smooth points of the unit ball of the metric linear space `(X), the space of all sequences (xn), xn ∈ X, n = 1, 2, . . . , f...

In this paper, we explain the mechanical properties of single-crystalline silicon with respect to deflectional and torsional motions. Young's modulus, Poisson’s ratio, and shear modulus are isotropic on silicon (111), whereas the variations on silicon (100) and (110) are quite significant. We newly derive formulae for bulk shear modulus of silicon (100), (110) and (111) and show that bulk shear...

Polymer-clay nano-composite materials, in which nano-meter thick layers of clay dispersed in polymer matrix, have generally higher mechanical properties than normal polymeric materials. A new three-dimensional unit cell model has been developed for modeling three constituent phases including inclusion, interphase and matrix. The total elastic modulus of nano-composite is evaluated.  Numerical r...

We present some sufficient conditions for which a Banach space X has normal structure in terms of the modulus of U-convexity, modulus of W∗-convexity, and the coefficient R 1, X , which generalized some well-known results. Furthermore the relationship between modulus of convexity, modulus of smoothness, and Gao’s constant is considered, meanwhile the exact value of Milman modulus has been obtai...

the deformation modulus of a rock mass is an important input parameter in any analysis of rock mass behavior for geotechnical projects such as dams. the determination of this parameter by in situ tests are time consuming and expensive. therefore, different researchers have proposed empirical relationships for estimating the value of rock mass deformation modulus. this work has been done by usin...