This paper investigates the complexity of steepest descent algorithms for two classes of discrete convex functions, M-convex functions and L-convex functions. Simple tie-breaking rules yield complexity bounds that are polynomials in the dimension of the variables and the size of the effective domain. Combination of the present results with a standard scaling approach leads to an efficient algor...

Ranking functions are qualitative degrees of uncertainty ascribed to events charged by uncertainty and taking as their values non-negative integers in the sense of ordinal numbers. Introduced are ranking functions induced by real-valued possibilistic measures and it is shown that different possibilistic measures with identical ranking functions yield the same results when applied in decision pr...

We derive two new analogues of a transformation formula of Ramanujan involving the Gamma and Riemann zeta functions present in the Lost Notebook. Both involve infinite series consisting of Hurwitz zeta functions and yield modular relations. As a special case of the first formula, we obtain an identity involving polygamma functions given by A.P. Guinand and as a limiting case of the second formu...

By extension of the argument of Kosambi (1944), a family of mapping functions can be derived, which has a parameter regulating the intensity of interference. Different values of this parameter yield the Haldane (1919) and Kosambi mapping functions as special cases. The parameter is the coincidence coefficient for nearby small intervals. The family includes mapping functions for negative interfe...

We consider gate elimination for linear functions and show two general forms of gate elimination that yield novel corollaries. Using these corollaries, we construct a new linear feebly secure trapdoor function that has order of security 5 4 which exceeds the previous record for linear constructions. We also give detailed proofs for nonconstructive circuit complexity bounds on linear functions.

In this paper we prove several inclusion relations associated with ) , (  n neighborhood of certain subclasses of analytic functions of complex order with negative coefficients by making use of the familiar concept of neighborhoods of analytic functions. Special cases of some of these inclusion relations are shown to yield known results.

We study the extended Euler sums and the alternating extended Euler sums and establish their explicit expressions in terms of Riemann zeta functions and Hurwitz zeta functions. Comparing with the existing results, ours are simpler and thus yield significantly better accuracy when Matlab is used for numerical calculation.

We present a single operation for constructing skew diagrams whose corresponding skew Schur functions are equal. This combinatorial operation naturally generalises and unifies all results of this type to date. Moreover, our operation suggests a closely related condition that we conjecture is necessary and sufficient for skew diagrams to yield equal skew Schur functions.

Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of so...

The main object of this paper is to prove several inclusion relations associated with the (n, δ) neighborhoods of various subclasses of starlike and convex functions of complex order by making use of the known concept of neighborhoods of analytic functions. Special cases of some of these inclusion relations are shown to yield known results.