This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

abstract. suppose g is an nvertex and medge simple graph with edge set e(g). an integervalued function f: e(g) → z is called a flow. tutte was introduced the flow polynomial f(g, λ) as a polynomial in an indeterminate λ with integer coefficients by f(g,λ) in this paper the flow polynomial of some dendrimers are computed.

We give a new purely algebraic proof of the Baker-Campbell-Hausdorff theorem, which states that homogeneous components formal expansion $\log(e^Ae^B)$ are Lie polynomials. Our is based on recurrence formula for these and lemma if under certain conditions commutator non-commuting variable given polynomial polynomial, then itself polynomial.

Non-malleable commitments are a central cryptographic primitive that guarantee security against man-in-the-middle adversaries, and their exact round complexity has been a subject of great interest. Pass (TCC 2013, CC 2016) proved that non-malleable commitments with respect to commitment are impossible to construct in less than three rounds, via black-box reductions to polynomial hardness assump...

Glossary Canonical realization: A state-space realization that has specific properties that makes it unique. Characteristic polynomial: The scalar denominator of a transfer function. Column-reduced: A polynomial matrix with non-singular column leading coefficient matrix. Coprime: See relatively prime. Denominator polynomial: The polynomial appearing in the denominator of a rational transfer fun...

Local polynomial regression is a useful non-parametric regression tool to explore fine data structures and has been widely used in practice. We propose a new non-parametric regression technique called local composite quantile regression smoothing to improve local polynomial regression further. Sampling properties of the estimation procedure proposed are studied. We derive the asymptotic bias, v...

the wiener index is a graph invariant that has found extensive application in chemistry. inaddition to that a generating function, which was called the wiener polynomial, who’sderivate is a q-analog of the wiener index was defined. in an article, sagan, yeh and zhang in[the wiener polynomial of a graph, int. j. quantun chem., 60 (1996), 959969] attainedwhat graph operations do to the wiener po...

This paper proposes a strategy for estimating the DA (domain of attraction) for non-polynomial systems via LFs (Lyapunov functions). The idea consists of converting the non-polynomial optimization arising for a chosen LF in a polynomial one, which can be solved via LMI optimizations. This is achieved by constructing an uncertain polynomial linearly affected by parameters constrained in a polyto...

We consider amalgamations of nitely generated nilpotent groups of class c. We show that doubles satisfy a polynomial isoperimetric inequality of degree 2c. Generalising doubles we introduce non-twisted amalgamations and show that they satisfy a polynomial isoperimetric inequality as well. We give a su cient condition for amalgamations along abelian subgroups to be non-twisted and thereby to sat...

In the polynomial approach to systems control, the static output feedback problem can be formulated as follows: given two polynomial matrices D(s) and N(s), nd a constant matrix K such that polynomial matrix D(s) + KN(s) is stable. In this paper, we show that solving this problem amounts to solving a linear matrix inequality with a non-convex rank constraint. Several numerical experiments illus...