Let SH denote the homothety class generated by a convex set S ⊂ R: SH = {a + λS | a ∈ R, λ > 0}. We determine conditions for the Minkowski sum BH + CH or the Minkowski difference BH ∼ CH of homothety classes BH and CH generated by closed convex sets B,C ⊂ R to lie in a homothety class generated by a closed convex set (more generally, in the union of countably many homothety classes generated by...

Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P .

In this paper, we use the Mittag-Leffler addition formula to solve Green function of generalized time fractional diffusion equation in whole plane and prove convergence function.

Under the extra assumption that the boundary is of class C this was proven by S. Nakajima (= A. Matsumura) in 1926 Theorem 1 solves this problem. For convex bodies with C boundaries and positive curvature Nakajima’s result was generalized by Chakerian [?] in 1967 to “relative geometry” where the width and brightness are measured with with respect to some convex body K0 symmetric about the origi...

in this paper, the stability of a functionally graded magneto-electro-elastic (fg-mee) micro-beam under actuation of electrostatic pressure is studied. for this purpose euler-bernoulli beam theory and constitutive relations for magneto-electro-elastic (mee) materials have been used. we have supposed that material properties vary exponentially along the thickness direction of the micro-beam. gov...

Vacuum.-By creating a vacuum the process of decalcification can be characterized as follows: Insoluble calciurn-salts+acid o-soluble calciumsalts+CO2. The carbon dioxide, rapidly extracted, will disturb the balance of the chemical equilibrium, and, according to Le Chatelier, result in an acceleration of the reaction. Waerhaug (1949), however, points out that there will be a more intensive conta...

zinc ferrite (znfe2o4) nanoparticles were synthesized via the auto-combustion assisted sol-gel method of zn2+ and fe3+ ions (molar ratio 1:2) in ammonia solution. the prepared nanomagnetic catalyst was characterized by ir, xrd, sem and icp. the diameter of the znfe2o4 mnps (63.7 nm) was determined by debye-scherre equation via their xrd pattern. nanomagnetic znfe2o4 efficiently catalyzes oxidat...

Multiplication is a basic operation in any signal processing application. Multiplication is the most important one among the four arithmetic operations like addition, subtraction, and division. Multipliers are usually hardware intensive, and the main parameters of concern are high speed, low cost, and less VLSI area. The propagation time and power consumption in the multiplier are always high. ...