A note on Koornwinder's polynomials with weight function (1−x)α(1+x)β+Mδ(x+1)+Nδ(x−1)

We derive the distribution and three-term recurrence relation for the Koornwinder [2] polynomials with weight function shown above using the method developed in our paper [3]. We are able to obtain explicit expressions for the linear functional in terms of the coefficients of the three-term recurrence relation for the Jacobi polynomials and we obtain the distribution using a more direct approach.     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

Sulfur(IV)‐Mediated Unsymmetrical Heterocycle Cross‐Couplings

Despite the tremendous utilities of metal‐mediated cross‐couplings in modern organic chemistry, coupling reactions involving nitrogenous heteroarenes remain a challenging undertaking – coordination of Lewis basic atoms into metal centers often necessitate elevated temperature, high catalyst loading, etc. Herein, we report a sulfur (IV) mediated cross‐coupling amendable for the efficient synthesis of heteroaromatic substrates. Addition of heteroaryl nucleophiles to a simple, readily‐accessible alkyl sulfinyl (IV) chloride allows formation of a trigonal bipyramidal sulfurane intermediate. Reductive elimination therefrom provides bis‐heteroaryl products in a practical and efficient fashion.     

A transformation for the economization of sometoeplitz summation methods

We prove that the solution of a parabolic free boundary problem, arising from a model for some isothermal equimolal non-cathalytic reactions between a fluid and a solid (e.g. oxidization), converges to the solution of the pseudo-steady-state approximation.