• Volume 102, Issue 2

August 1992,   pages  83-158

• Proof of some conjectures on the mean-value of Titchmarsh series — III

With some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =Σn=1anλn−s be a generalized Dirichlet series with 1 =λ1 &lt;λ2 &lt; …,λnDn, andλn+1 -λnD− 1λn+1− a where α&gt;0 andD(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for$$(1/H)\int {_O^H |} F(it)|^2 dt$$. These results will be applied in other papers to appear later.

• Combinatorial meaning of the coefficients of a Hilbert polynomial

In [1] Abhyankar defines an idealI(p, a) generated by certain minors of a matrixX, the entries ofX being independent indeterminates, and proves that the Hubert function ofI(p, a) coincides with its Hilbert polynomialF(V) and obtains it in the form$$F(V) = \sum\limits_{D \geqslant 0} {( - 1)} ^D F_D (m,p,a)\left( \begin{gathered} c - D + V \hfill \\ V \hfill \\ \end{gathered} \right)$$. He also proves thatF(V) is the number of certain “indexed” monomials of degreeV in the entries ofX and that the coefficientsFD(m,p,a) are non-negative integers and asks for their combinatorial meaning. In this paper we characterize the indexed monomials in terms of certain sets of lattice paths, called frames, and prove that the coefficientsFD(m, p, a) count certain families of such frames.

• A note on two absolute summability methods

In this paper we have established a relation between ¦R,pn;δ¦k and ¦R,qn;δ¦k summability methods which generalizes the results of Bor [1] and Bosanquet [2].

• On deficiencies of differential polynomials

Bounds for deficiencies of differential polynomials have been given and some relations between Nevanlinna characteristic of differential polynomials inf and Nevanlinna characteristic function off have been obtained.

• A note on the identity operators of fractional calculus

The application of an identity operator for Saigo’s fractional calculus operators is shown by evaluating the limit of an indeterminate form. Its special case yields the result which has been used as an infinitesimal generator in the semigroup theory. Also, an identity operator for the recently introduced multi-dimensional fractional operators (due to Srivastava and Raina [8]) is discussed.

• An RSA based public-key cryptosystem for secure communication

A new cryptosystem that uses modulo arithmetic operations is proposed. It is based on Rivest-Shamir-Adleman’s public key cryptosystem. A feature of the proposed system is that the encryption and decryption procedures are computationally less intensive, and hence the system is amenable for high data bit rate communications.

• A note to the paper “An efficient algorithm for linear programming” of V Ch Venkaiah

In Venkaiah [1] an algorithm for solving linear optimization problems based on the idea of the projective algorithm of Karmarkar, is proposed. The essential simplification in the new algorithm is the use of a fixed projection operator. In this way the algorithm requires onlyO(n2) operations to obtain a sufficient exact solution. In this note it is shown that in some special cases the algorithm of Venkaiah yields a feasible solution that is far from the optimal one.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019