let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants. No quadratures are left. These formulas rely on the identification of dual pairs of vertex operators corresponding to dual metrics related by the Kramer-Neug...

Coxeter-Petrie complexes naturally arise as thin diagram geometries whose rankthree residues contain all of the dual forms of a regular algebraic mapM. Corresponding to an algebraic map is its classical dual, which is obtained simply by interchanging the vertices and faces, as well as its Petrie dual, which comes about by replacing the faces by the so-called Petrie polygons. G. A. Jones and J. ...

The foundation of algebraic geometry is the solving of systems of polynomial equations. When the equations to be considered are defined over a subfield of the complex numbers, numerical methods can be used to perform algebraic geometric computations forming the area of numerical algebraic geometry. This article provides a short introduction to numerical algebraic geometry with the subsequent ar...

Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft mixed neutrosophic N-algebraic with the discussion of some of their characteristics. We also introduced soft mixed dual neutrosophic N-algebraic structures, soft weak mixed neutrosophic N-algebraic structures, soft Lagrange mixed neutrosophic N-algebrai...

An introduction to locally compact abelian algebraic groups and the usage of dual groups and Fourier transforms to study them.

In this study, we introduce a new class of generalized quaternions whose components are dual-generalized complex Horadam numbers. We investigate some algebraic properties them.

Kippenhahn's Theorem asserts that the numerical range of a matrix is convex hull certain algebraic curve. Here, we show joint finitely many Hermitian matrices similarly semi-algebraic set. We discuss an analogous statement regarding dual cone to hyperbolicity and prove class bases these cones closed under linear operations. The result offers new geometric method analyze quantum states.

Duality of curves is an important aspect of the “classical” algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using the development of an algebraic “mechanism”, based on “distortion” values, geometric and convexity properties are analyzed. Specifically, we discuss some significant aspe...