A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even–odd rule and the winding number, the former leading to ray-crossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algor...

The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4bn/24c+ 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous ...

The notion of an extremal self-dual code has been introduced in 1 . As Gleason 2 remarks onemay use invariance properties of the weight enumerator of a self-dual code to deduce upper bounds on the minimum distance. Extremal codes are self-dual codes that achieve these bounds. The most wanted extremal code is a binary self-dual doubly even code of length 72 and minimum distance 16. One frequentl...

An important factor affecting preference formation is the context in which that preference decision takes place. The current research examined whether one's preference formed for a previously presented stimulus influences the processing of a subsequent preference decision, henceforth referred to as the preference sequence effect. Using a novel sequential rating/judgment paradigm, the present st...

objective: it has been shown that berberine, a major component of berberis vulgaris extract, modulates the activity of several neurotransmitter systems including dopamine (da) and n-methyl-d-aspartate (nmda) contributing to rewarding and reinforcing effects of morphine. drug craving and relapsing even after a long time of abstinence therapy are the most important problems of addiction. in the p...

Female mate preference is central to sexual selection, and all indirect benefit models require that there is genetic variation in female preference. This has rarely been tested however, with relatively few studies documenting heritable variation in female preference and even fewer that have directly selected on mate preference to unequivocally show that it can evolve. Additionally, costs of mat...

Objective: It has been shown that berberine, a major component of Berberis vulgaris extract, modulates the activity of several neurotransmitter systems including dopamine (Da) and N-methyl-D-aspartate (NMDA) contributing to rewarding and reinforcing effects of morphine. Drug craving and relapsing even after a long time of abstinence therapy are the most important problems of addiction. In the p...

For a finite group $G$‎, ‎let $Cent(G)$ denote the set of centralizers of single elements of $G$‎. ‎In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent‎, ‎then $Gcong S_3‎, ‎D_{10}$ or $S_3times S_3$‎. ‎This result gives a partial and positive answer to a conjecture raised by A‎. ‎R‎. ‎Ashrafi [On finite groups with a given number of centralizers‎, ‎Algebra‎ ‎Collo...