Objective Gender selection and family planning have their roots in human history. Despite great interest in these fields, very few scientific propositions exist which could explain why some family do not attain the desired sex. Therefore, the aim of this study was to evaluate whether sex of previous child or children could affect the outcomes of pre-implantation genetic diagnosis (PGD). Materia...

Abstract The aim of this article is to investigate two new classes quaternions, namely, balancing and Lucas-balancing quaternions that are based on numbers, respectively. Further, some identities including Binet’s formulas, summation Catalan’s identity, etc. concerning these also established.

A family of subsets of a ground set closed under the operation of taking symmetric differences is the family of cycles of a binary matroid. Its circuits are the minimal members of this collection. We use this basic property to derive binary matroids from binary matroids. In particular, we derive two matroids from graphic and cographic matroids. Cocycles of the first one are cutsets or balancing...

We consider a society where parents prefer boys to girls, but also value grandchildren. Parental sex selection results in a biased sex ratio that is socially ine¢ cient, due to a congestion externality in the marriage market. Improvements in selection techniques aggravate the ine¢ ciency. These results are robust to allowing prices in the marriage market, if the market is subject to frictions. ...

We propose balancing related numerically reliable methods to compute minimal realizations of linear periodic systems with time-varying dimensions. The rst method belongs to the family of square-root methods with guaranteed enhanced computational accuracy and can be used to compute balanced minimal order realizations. An alternative balancing-free square-root method has the advantage of a potent...

Time and space assembly line balancing considers realistic multiobjective versions of the classical assembly line balancing industrial problems involving the joint optimization of conflicting criteria such as the cycle time, the number of stations, and/or the area of these stations. In addition to their multi-criteria nature, the different problems included in this field inherit the precedence ...

Natural selection, the most important force in evolution, comes in three forms. Negative purifying selection removes deleterious variation and maintains adaptations. Positive directional selection fixes beneficial variants, producing new adaptations. Balancing selection maintains variation in a population. Important mechanisms of balancing selection include heterozygote advantage, frequency-dep...