this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

Partitioning 1-variable Boolean functions for various classification of nvariable Boolean functions Ranjeet Kumar Rout, Pabitra Pal Choudhury, Sudhakar Sahoo & Camellia Ray a Applied Statistics Unit, Indian Statistical Institute, Kolkata-700108, India; b Institute of Mathematics and Applications, Bhubaneswar-751003, India Accepted author version posted online: 14 Oct 2014.Published online: 14 N...

A large variety of problems in digital system design, combinational optimization and verification can be formulated in terms of operations performed on Boolean functions. The time complexity of Binary Decision Diagram (BDD) representing a Boolean function is directly related to the path length of that BDD. In this paper we present a method to generate a BDD with minimum path length. The Average...

In many applications like verification or combinatorial optimization, OBDDs (ordered binary decision diagrams) are used as a representation or data structure for Boolean functions. Efficient algorithms exist for the important operations on OBDDs, and many functions can be represented in reasonable size if a good variable ordering is chosen. In general, it is NP-hard to compute optimal or near-o...

We develop non-parametric instrumental variable estimation and inferential theory for econometric models with possibly endogenous regressors whose coefficients can vary over time either deterministically or stochastically, the time-varying uniform versions of standard Hausman exogeneity test. After deriving asymptotic properties proposed procedures, we assess their finite sample performance by ...

This paper proposes programmable architectures and design methods for numeric function generators (NFGs) of two-variable functions. To realize a twovariable function in hardware, we partition a given domain of the function into segments, and approximate the function by a polynomial in each segment. This paper introduces two planar segmentation algorithms that efficiently partition a domain of a...

This paper proposes programmable architectures and design methods for numeric function generators (NFGs) of two-variable functions. To realize a twovariable function in hardware, we partition a given domain of the function into segments, and approximate the function by a polynomial in each segment. This paper introduces two planar segmentation algorithms that efficiently partition a domain of a...