studying gaussian beam is a method to investigate laser beam propagation and abcd matrix is a fast and simple method to simulate gaussian beam propagation in different mediums. of the abcd matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. however in previous work the incident beam and the principle axis of surface are in parallel...

In contemporary convex geometry, the rapidly developing Lp-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the Lp-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original Lp-affi...

Highly monodispersed concave gold nanobars with 24 high-index {730} facets are synthesized through a seed-mediated growth in aqueous solution. The transformation from the truncated rectangular nanobars to rectangular nanobars, then transitional products, and final concave rectangular nanobars is observed with the fine control of silver nitrate in the growth solution, and their corresponding tra...

This paper’s origins are in two papers: One by Colesanti and Fragalà studying the surface area measure of a log-concave function, one Cordero-Erausquin Klartag regarding moment convex function. These notions same, this paper we continue same construction as well its generalization. In first half prove variation formula for integral functions under minimal optimal conditions. We also explain why...

Curved structures are used in buildings and may be integrated with photovoltaic modules. Self-shading occurs on non-flat (curved) surface collectors resulting a non-uniform distribution of the direct beam diffuse incident solar radiation along curvature surface. The present study uses analytical expressions for calculating analyzing general parabolic concave Concave surfaces facing north, south...

in this study the land surface in western half of hyper-arid lut desert, in south east of iran, which is covered by yardangs, a worldwide typical landform for aeolian erosion, were classified by self organizing maps (som) method. in the first step by using digital elevation model with 10 m resolution and matlab software, 22 morphometric parameters were calculated based on derivative of the surf...

In the past few decades, the quantitative computation of surface roughness has received increasing attention due to its importance in numerical surface study. In this paper, concepts of mathematical morphology are employed to compute and characterize the surface roughness of catchments extracted from a simulated digital elevation model (DEM). Morphological smoothing is implemented on the simula...