A connection is made between certain multiple sequence alignment problems and facility location problems, and the existence of a PTAS (polynomial time approximation scheme) for these problems is shown. Moreover, it is shown that multiple sequence alignment with SP-score and fixed gap penalties is MAX SNP-hard.

let g = (v, e) be a simple graph. hosoya polynomial of g isd(u,v)h(g, x) = {u,v}v(g)x , where, d(u ,v) denotes the distance between vertices uand v. as is the case with other graph polynomials, such as chromatic, independence anddomination polynomial, it is natural to study the roots of hosoya polynomial of a graph. inthis paper we study the roots of hosoya polynomials of some specific graphs.

Optimal sequence alignments depend heavily on alignment scoring parameters. Given input sequences, parametric alignment is the well-studied problem that asks for all possible optimal alignment summaries as parameters vary, as well as the optimality region of alignment scoring parameters which yield each optimal alignment. But biologically correct alignments might be suboptimal for all parameter...

We bound the volume of homotopy groups 2-local Goodwillie approximations a sphere in terms amount 2-torsion stable stems, providing Goodwillie-theoretic refinement result Burklund and Senger. At 2 k $2^k$ -excisive approximation, this is obtained by ‘multiplying answer polynomial degree $k$ ’. The main tool Behrens' Goodwillie–EHP long exact sequence.

This paper focuses on solving methods of multiple internal rates return (MIRR) the series non-conventional cash flow when net present value is equal to zero. The rate a popular rule for project acceptance/rejection. When projects has three or more sign variations, (IRR) not easy obtain returns. In his paper, we introduce Descartes’ maximum positive roots, Bolzano Theorem roots in interval, Buda...

The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants ∆i(u1, . . . , ud, v), i = 0, 1, . . . , is obtained. When l is a classical link, ∆i reduces to the well-known ith Alexander polynomial of the link in the d variables u1v, . . . , udv; in particular, ∆0 vanishes.

In [Butkovič and Zimmermann(2006)] an ingenious algorithm for solving systems of twosided linear equations in max-algebra was given and claimed to be strongly polynomial. However, in this note we give a sequence of examples showing exponential behaviour of the algorithm. We conclude that the problem of finding a strongly polynomial algorithm is still open.

We associate two modules, the \(G\)-parking critical module and toppling module, to an undirected connected graph \(G\). The are canonical modules (with suitable twists) of quotient rings well-studied function ideal ideal, respectively. For each we establish a Tutte-like short exact sequence relating associated \(G\), edge contraction \(G/e\) deletion \(G \setminus e\) (\(e\) is non-bridge). ob...

We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. We focus on the particular cases when the sample points form an arithmetic or a geometric sequence, and we discuss applications, respectively to computations with linear differential operators and to polynomial matrix multiplication.

Sturm’s Theorem is a fundamental 19 century result relating the number of real roots of a polynomial f in an interval to the number of sign alternations in a sequence of polynomial division-like calculations. We provide a short direct proof of Sturm’s Theorem, including the numerically vexing case (ignored in many published accounts) where an interval endpoint is a root of f .