Wu’s elimination method is an important method for solving multivariate polynomial equations. In this paper, we apply interval arithmetic to Wu’s method and convert the problem of solving polynomial equations into that of solving interval polynomial equations. Parallel results such as zero-decomposition theorem are obtained for interval polynomial equations. The advantages of the new approach a...

A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the " projectivized " representation possessing an invariant subspace and the spectral problem for a certain linear differential operator with variable coeffici...

This paper presents a static analysis of laminated composite doubly-curved shells using refined kinematic models with polynomial and non-polynomial functions recently introduced in the literature. To be specific, Maclaurin, trigonometric, exponential and zig-zag functions are employed. The employed refined models are based on the equivalent single layer theories. A simply supported shell is sub...

Inductive databases (IDBs) contain both data and patterns. Here we consider IDBs where patterns are polynomial equations. We present a constraint-based approach to answering inductive queries in this domain. The approach is based on heuristic search through the space of polynomial equations and can use subsumption and evaluation constraints on polynomial equations. We evaluate this approach on ...

Since the advent of Taylor Series, polynomial methods have been used to solve di↵erential equations and learn the properties of di↵erential equations. There are many polynomial methods for solving di↵erential equations and understanding dynamical systems. For example, Taylor polynomials, Chebyshev Polynomials and Adomian Polynomials are used to generate approximate solutions. Automatic di↵erent...

The aim of this investigation was to prepare, characterize and optimize the aceclofenac proniosomes using central composite design and carry out stability studies. Three independent variables selected were molar ratio of drug to lipid (X1), surfactant loading (X2) and volume of hydration (X3). Based on central composite design, 16 batches of proniosomes were prepared by slurry method and evalua...

The aim of this investigation was to prepare, characterize and optimize the aceclofenac proniosomes using central composite design and carry out stability studies. Three independent variables selected were molar ratio of drug to lipid (X1), surfactant loading (X2) and volume of hydration (X3). Based on central composite design, 16 batches of proniosomes were prepared by slurry method and evalua...