LetM be a matroid on ground set E. A subset l ⊆ E is called a line when r(l) ∈ {1, 2}. Given a set of lines L = {l1, . . . , lk} in M , a vector x ∈ RL+ is called a fractional matching when ∑ l∈L xla(F )l ≤ r(F ) for every flat F ofM . Here a(F )l is equal to 0 when l∩F = ∅, equal to 2 when l ⊆ F and equal to 1 otherwise. We refer to ∑ l∈L xl as the size of x. It was shown by Chang et al. that ...

LP relaxation One way to deal with this is to relax the integrality constraints and allow xe ∈ [0, 1] to get a linear program, which can be solved in polynomial-time. However, this gives rise to fractional matchings. Characteristic vectors of matchings in G can be seen as points in R where m = |E|. The convex hull of all the matchings forms a polytope called the matching polytope M. However, th...

Given an algebraically closed field K of characteristic zero, we present the Abhyankar–Jung theorem for any excellent henselian ring whose completion is a formal power series ring K[[z]]. In particular, examples include the local rings which form a Weierstrass system over the field K. The Abhyankar–Jung theorem may be regarded as a higher dimensional counterpart of the Newton–Puiseux theorem. I...

Reduction in hardware complexities is vital in communication. The major contribution to hardware complexity in many technologies is the multiplier utilized. This work present a proposed algorithm based on Farrow differential polynomial interpolation. This interpolator filter is a time varying poly-phase filter that uses fractional delay to reduce the integer sampling rates to fractional rates. ...

For the first time, in this paper, a robust stability test procedure is proposed for linear time-invariant fractional order systems (LTI FOS) of commensurate orders with interval uncertain parameters. For the LTI FOS with no uncertainty, the existing stability test (or check) methods for dynamic systems with integer-orders such as Routh table technique, cannot be directly applied. This is due t...

The present article studies the agitation scenario of SARS‐CoV‐2 (COVID‐19), current pandemic around globe, by applying Atangana–Baleanu–Caputo derivative operator where . Using classical notions, we study various qualitative features, like existence, uniqueness and investigate Hyers–Ulam stability analysis model under consideration. Lagrange's polynomial approach is used for approximation nonl...

In this work, we focus on the long-time behavior of solutions stochastic fractional complex Ginzburg–Landau equation defined Rn with polynomial drift terms arbitrary order. The well-posedness based pathwise uniform estimates and average are proved. Following this, existence uniqueness weak pullback random attractors establsihed.

Discussions are presented by Morita and Sato on the problem of obtaining particular solution an inhomogeneous differential equation with polynomial coefficients in terms Green's function. In present paper, is given without using function, basis nonstandard analysis. It applied to hypergeometric, Hermite, a simple ordinary fractional equation.

the topological index of a graph g is a numeric quantity related to g which is invariant underautomorphisms of g. the vertex pi polynomial is defined as piv (g)  euv nu (e)  nv (e).then omega polynomial (g,x) for counting qoc strips in g is defined as (g,x) =cm(g,c)xc with m(g,c) being the number of strips of length c. in this paper, a new infiniteclass of fullerenes is constructed. the ...

In this paper, we extend the operational matrix method to solve tempered fractional differential equation, via shifted Legendre polynomial. Although is widely used in solving various calculus problems, it yet apply equations defined derivatives. We first derive analytical expression for derivative x p</...