There are some basic real life problems that cannot be solved using classical mathematical techniques. In this paper Functional Networks have been effectively used to solve practical CAD problems related to plant engineering Industry. Modular Construction of plants is becoming popular due to severe weather conditions at plant sites. The modules are transported to and assembled at the actual pla...

1. Introduction In the higher rank paper 17], we reduced Dwork's conjecture from higher rank case over any smooth aane variety X to the rank one case over the simplest aane space A n. In the present paper, we nish our proof by proving the rank one case of Dwork's conjecture over the aane space A n , which is called the key lemma in 17]. The key lemma had already been proved in 16] in the specia...

Several studies conducted during the past decade have suggested that episodic memory is better equipped to handle the future than the past. Here, we consider this premise in the context of motor memory. State-of-the-art computational models for trial-by-trial motor adaptation to constant and stochastic force field perturbations in a horizontal reaching paradigm have shown that motor memory regi...

The ease of understanding, maintaining, and developing a large program depends crucially on how it is divided up into modules, which is constrained by the available modular programming facilities (“module system”) of the programming language being used. Experience with Standard ML’s module system has shown the usefulness of functions mapping modules to modules and modules with module subcompone...

A weight two vector v of a vertex operator algebra is called a conformal vector with central charge c if the component operators Lv(n) for n ∈ Z of Y (v, z) = ∑ n∈Z Lv(n)z −n−2 satisfy the Virasoro algebra relation with central charge c. In this case, the vertex operator subalgebra Vir(v) generated by v is isomorphic to a Virasoro vertex operator algebra with central charge c ([FZ], [M]). Let V...

We prove lifting results for DG modules that are akin to Auslander, Ding, and Solberg’s famous lifting results for modules. Introduction Convention. Throughout this paper, let R be a commutative noetherian ring. Hochster famously wrote that “life is really worth living” in a Cohen-Macaulay ring [7]. For instance, if R is Cohen-Macaulay and local with maximal regular sequence t, then R/(t) is ar...

An integrated model is developed, based on seasonal inputs of reservoir inflow and rainfall in the irrigated area, to determine the optimal reservoir release policies and irrigation allocations to multiple crops. The model is conceptually made up of two modules. Module 1 is an intraseasonal allocation model to maximize the sum of relative yields of all crops, for a given state of the system, us...