the plate girders are used in important structural systems. the earlier design of plate girders was restricted to their critical bukling capacity. experimental and theoretical studies show the plate girders with vertical stiffners can carry load over than their critical buckling loads and then in modern design codes is permitted to use post- buckling capacity of them. in this case the out- of- ...

Geometric algebras of dimension $n < 6$ are becoming increasingly popular for the modeling 3D and 3+1D geometry. With this increased popularity comes need efficient algorithms common operations such as normalization, square roots, exponential logarithmic maps. The current work presents a signature agnostic analysis these in all geometric 6$, gives numerical implementations most $\mathbb{R}_{4}$...

Objective: The use of miniature X-ray source in electronic brachytherapy is on the rise so there is an urgent need to acquire more knowledge on X-ray spectrum production and distribution by a dose. The aim of this research was to investigate the influence of target thickness and geometry at the source of miniature X-ray tube on tube output.Method: Five sources were simulated based on problems e...

This paper studies the eeect of slow cyclic variation of parameters on the phase of the oscillating Morris-Lecar model. In chemical oscillators it is known that a phase shift, called the geometric phase shift, is observed upon return to an initial point in parameter space. We nd geometric phase shifts for a two-parameter variation in the Morris-Lecar model. As with the chemical oscillator, the ...

Relationships that exists between the classical, Shannontype, and geometric-based approach to sampling are investigated. Some aspects of coding and communication through a Gaussian channel problem are considered. In particular, a constructive method to determine the quantizing dimension in Zador’s theorem is provided. A geometric version of Shannon’s Second Theorem is introduced. Applications t...

Bisection (of a real interval) is a well known algorithm to compute eigenvalues of symmetric matrices. Given an initial interval [a, b], convergence to an eigenvalue which has size much smaller than a or b may be made considerably faster if one replaces the usual arithmetic mean (of the end points of the current interval) with the geometric mean. Exploring this idea, we have implemented geometr...

Let q be a prime or a prime power ≥ 3. The purpose of this paper is to give a necessary and sufficient condition for the existence of an (n, r)-arc in PG(2, q) for given integers n, r and q using the geometric structure of points and lines in PG(2, q) for n > r ≥ 3. Using the geometric method and a computer, it is shown that there exists no (34, 3) arc in PG(2, 17), equivalently, there exists n...

Exact rounding is provided for elementary oating-point arithmetic operations (e.g. in the IEEE standard). Many authors have felt that it should be provided for other operations, in particular for geometric constructions. We show how one may round modular representation of numbers to the closest f.p. rep-resentable number, and demonstrate how it can be applied to a variety of geometric construct...

An experience of a Geometry Lab based on Mathematica for a Geometry course for Computer Science students, intended to be a basis for later courses in Computer Graphics, CAD and CAGD, is presented. Students combine their knowledge of basic geometry topics like polyhedra, curve and surface generation, aane and perspective transformations, among others, by means of lists manipulation and a clever ...