A topological approach of determining the best one out of four solutions of the Hermitian interpolation problem for quintic Pythagorean hodograph curves is presented. An existence theorem is proved together with complete analysis of uniqueness/nonuniqueness properties. A simple formula of obtaining the best solution without using any curve fairing or curvature integral is also presented.

There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik’s trichotomy theorem. The ‘trichotomy’ here is a case division of the generic minimal counterexamples within odd type, that is, groups with a large and divisible Sylow◦ 2-subgroup. The so-called ‘u...

background: clinical experiences have revealed that patients with breast cancer experience various sexual problems following their treatment. breast cancer negatively impacts the sexual life of the afflicted couples, and as a traumatic event can influence women’s psychosexual functioning and intimate relationship. this review focuses on sexuality after breast cancer and on a growing need for bi...

in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...

Montmorillonite impregnated with bismuth nitrate has been found to be an excellent reagent for the synthesis of several nitro compounds of biological significance in high yield.

We propose that turning on the light can turn on the hot emotional system. Across six studies we show that ambient brightness makes people feel warmer, which increases the intensity of their affective response, including sensation seeking from spicy-hot foods, perception of aggression and sexiness (“hotness”) in others, and generating more extreme affective reactions toward positive and negativ...