‎this paper obtains the exact solutions of the wave equation as a second-order partial differential equation (pde)‎. ‎we are going to calculate polynomial and non-polynomial exact solutions by using lie point symmetry‎. ‎we demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎a generalized procedure for polynomial solution is pr...

Data-independent methods for dimensionality reduction such as random projections, sketches, and feature hashing have become increasingly popular in recent years. These methods often seek to reduce dimensionality while preserving the hypothesis class, resulting in inherent lower bounds on the size of projected data. For example, preserving linear separability requires Ω(1/γ) dimensions, where γ ...

the omega polynomial(x) was recently proposed by diudea, based on the length of stripsin given graph g. the sadhana polynomial has been defined to evaluate the sadhana index ofa molecular graph. the pi polynomial is another molecular descriptor. in this paper wecompute these three polynomials for some infinite classes of nanostructures.

in this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. we show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

Two conservative approaches are proposed to a semidefinite programming problem nonlinearly dependent on uncertain parameters. These approaches are applicable to general nonlinear parameter dependence not necessarily polynomial or rational. They are based on a mild assumption that the parameter dependence is expressed as the difference of two convex functions. The first approach uses constant bo...

In indirect parameter adaptive control, one updates controller coefficients as new estimates of the plant are obtained. It is often of interest in that context to know if it is possible to design controllers that depend explicitly on plant parameters. For instance, if this dependence is polynomial or rational, the update itself consists simply of an evaluation, with no further computation. In a...

Although many programs use multi-dimensional arrays, the multi-dimensional view of data is often not directly visible in the internal representation used by LLVM. In many situations, the only information available is an array base pointer and a single dimensional offset. For problems with parametric size, this offset is usually a multivariate polynomial that cannot be analyzed with integer line...

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

6 This paper investigates objective Bayesian variable selection when there is a hier7 archical dependence structure on the inclusion of predictors in the model, that, when 8 ignored, makes the variable selection dependent on how the predictors are coded. In 9 particular, we study the type of dependence found in polynomial response surfaces 10 of orders two and higher. We develop three classes o...

Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way polynomial time (Ptime). In this paper we study the complexity of linear logic proof-nets and propose three semantic criteria based on context semantics: stratificatio...