The properties of some sequences of functions defined by multiple integrals associated with the Hermite-Hadamard integral inequality for convex functions are studied.

The weighted three point rule is investigated in the current article. It involves $f^{(n)}(t)$ being of bounded variation for $t\in [a,b]$. The rule consists of evaluations at the ends of the interval and at an interior point $x$. Weighted Ostrowski and Trapezoidal rules and their related bounds are recaptured as particular instances of the current development. The unweighted results of Ostrowski, Trapezoidal and three point rules are also procured if we take the weight to be unity.

This paper considers local convergence of secant methods for a non-linear system of equations. The well-known local convergence theory has been developed by Broyden, Dennis and Moré (1973). They used a norm inequality such that the difference between two vectors transformed by some matrix is bounded above by an order of one of the two. Instead, in the present paper, we use an inequality that bounds the angle between the vectors. This inequality has a merit of scale invariance whereas the norm inequality does not.

In the book entitled “Methods of Representation Theory” by Curtis and Reiner they discuss character tables of Hecke algebras. This paper aims to generalize their argument on Hecke algebras to the adjacency algebra of association schemes.

We extend the theorem of A. Saeki and R. Ikehata for the wave equation with linear dissipation.

This paper gives a characterization of totally contact-umbilical semi-invariant submanifolds of a Sasakian manifold.

We determine the ring structure of the Hochschild cohomology $H{H}^{\ast }(\mathbb{Z}{Q}_t)$ of the integral group ring of the generalized quaternion group $Q_t$.