Elliptic curves find numerous applications. This paper describes a simple strategy to speed up their arithmetic in right-to-left methods. In certain settings, this leads to a non-negligible performance increase compared to the left-to-right counterparts.

BiFeO3 (BFO), Bi0.86Sm0.07Eu0.07FeO3 (BSEFO), and Bi0.86Sm0.07Cd0.07FeO3 (BSCFO) nano powders were prepared by the sol-gel combustion method and the catalytic performances were evaluated in the acetylation reaction of benzyl alcohol. The physical chemical properties of the catalysts were character...

Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear systems Ax = b for x, where A is a given n-by-n matrix, and b a given n-vector. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG STABilized (Bi-CGSTAB), BiCGStab2, BiCGstab(`), Generalized Product-type Bi-CG (GPBiCG), and BiCG×MR2 have been developed to improve the convergence of Bi-CG and to...

In this thesis, we consider bi-intuitionistic logic and tense logic, as well as the combined bi-intuitionistic tense logic. Each of these logics contains a pair of dual connectives, for example, Rauszer’s bi-intuitionistic logic [100] contains intuitionistic implication and dual intuitionistic exclusion. The interaction between these dual connectives makes it non-trivial to develop a cut-free s...

Dispersion, as the characteristic variation of refractive index with wavelength, is more pronounced, where the wavelength is approaching to the absorption band. In ultra-optical glasses, the nonlinear refractive index, concerning to the light intensity dependent phenomenon, becomes considerable. Here, two ultra-optical property glass systems; TiO2-Bi2O3-PbO (TBP...

Pricing is one of the major aspects of decision making in supply chain. In the previous works mostly a centralized environment is considered indicating the retailers cannot independently apply their decisions on the pricing strategy. Although in a two-echelon decentralized environment it may be possible that supply chain contributors have encountered with different market power situations which...

Sequence assembly from short reads is an important problem in biology. It is known that solving the sequence assembly problem exactly on a bi-directed de Bruijn graph or a string graph is intractable. However, finding a shortest double stranded DNA string (SDDNA) containing all the k-long words in the reads seems to be a good heuristic to get close to the original genome. This problem is equiva...

vendor managed inventory is a continuous replenishment program that is designed to provide major cost saving benefits for both vendors and retailers. previous research on this area mainly included single objective optimization models where the objective is to minimize the total supply chain costs or to maximize the total supply chain benefits. this paper presents a bi-objective mathematical mod...