Abstract Aichinger’s equation is used to give simple proofs of several well-known characterizations polynomial functions as solutions certain functional equations. Concretely, we use that characterizes solve, for arbitrary commutative groups, Ghurye–Olkin’s equation, Wilson’s the Kakutani–Nagumo–Walsh and a general version Fréchet’s unmixed equation.

We give a unified approach to weighted mixed-norm estimates and solvability for both the usual time fractional parabolic equations in nondivergence form when coefficients are merely measurable variable. In spatial variables, leading locally have small mean oscillations. Our results extend previous result [5] unmixed Lp-estimates without weights.

Resultants are defined in the sparse (or toric) context in order to exploit the structure of the polynomials as expressed by their Newton polytopes. Since determinantal formulae are not always possible, the most efficient general method for computing resultants is as the ratio of two determinants. This is made possible by Macaulay’s seminal result [15] in the dense homogeneous case, extended by...

Globalisation has given birth to medical tourism. Health and medical tourism are the fastest growing segments in not only developed nations but in developing countries too. India has become a hot destination, as the Indian medical standards match up to the highly prescribed international standards at a very low cost. However, it is an unmixed blessing; along with advantages, it has many uninten...