For a Lipschitz $ \mathbb{Z}- $periodic function \phi:\mathbb{R}\to \mathbb{R}^2 such that \mathbb{R}^2\setminus\{\phi(x):x\in\mathbb{R}\} is not connected, an integer b\ge 2 and \lambda\in (c/{b^{\frac12}},1) $, we prove the following for generalized Weierstrass-type W(x) = \sum\limits_{n 0}^{\infty}{{\lambda}^n\phi(b^nx)} $: box dimension of its graph equal to 3+2\log_b\lambda where c constan...

— In this article we review some recent work on fourth order equations in conformal geometry of three and four dimensions. We discuss an existence result for a Yamabe-type equation in dimension three. We examine a generalization of the Cohn-Vossen inequality to dimension four. Finally, we review an application of the fourth order equation to a fully nonlinear equation in dimension four that inv...

quantifying spatial structure is one of the most important components, describing natural ecosystems and their biodiversity. in this study, a set of indices and functions related to spatial structure using 102 established plots with an area of 1000 m2 were presented. to achieve spatial structure of carpinus-fagus type, a set of indices (clark & evans, uniform angle, shannon-wiener, mingling and...

It is known that in general range spaces of VC-dimension d > 1 require "-nets to be of size at least (d " log 1 "). We address the question whether this general lower bound is valid for the special range spaces that typically arise in computational geometry. We show that disks and pseudo-disks in the plane as well as halfspaces in R 3 allow "-nets of size only O(1 "), which is best possible up ...

We solve exactly the 6-vertex model on a dynamical random lattice, using its representation as a large N matrix model. The model describes a gas of dense nonintersecting oriented loops coupled to the local curvature defects on the lattice. The model can be mapped to the c = 1 string theory, compactified at some length depending on the vertex coupling. We give explicit expression for the disk am...

objectives: this study aimed to evaluate the effect of storage period on dimensional stability of alginplus and hydrogum 5. materials and methods: in this in vitro experimental study, 60 impressions were taken of an upper jaw typodont, including 10 impressions for each storage period to be tested (12 minutes, 24 and 120 hours) for each type of alginate. then, the impressions were stored in an i...

Educational inequality is one of the types of inequality which always pervades on an educational system. The existence of the educational inequality alongside other inequalities and their interaction are the most important in a society. This paper attempts to examine the factors that affect educational inequality in Kazeroon city. The method of present study is survey and data collection tool i...

The subgroups of GL3(k) which are completions of the Goldschmidt G4-amalgam are determined. We also draw attention to five related graphs which are remarkable in that they have large girth and few vertices.