Modules with Pure Resolutions

We show that the property of a standard graded algebra R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module corresponding to any degree sequence of length at most depth(R). We also give a relation in terms of graded Betti numbers, called the Herzog-Kuhl equations, for a pure R-module M to satisfy the condition dim(R) - depth(R) = dim(M) - depth(M). When R is Cohen-Macaulay, we prove an analogous result characterizing all graded Cohen-Macaulay R-modules.Comment: 9 page

Multiplication Semigroups on Banach Function Spaces

In this paper we characterize multiplication operators induced by operator valued maps on Banach function spaces. We also study multiplication semigroups and stability of these operators.Comment: We want to withdraw the paper due to the paper needs a careful revision and some proper citations are to be provided. Also there are certain gaps in the results which need to be taken car

Alternative conformal quantum mechanics

We investigate a one dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal transformation such that a scale invariant theory is also invariant under this new conformal transformation

Analytical results connecting stellar structure parameters and extended reaction rates

Possible modification in the velocity distribution in the non-resonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions are used to obtain the stellar luminosity and neutrino emission rates. The composite parameter {C} that determines the standard nuclear reaction rate through the Maxwell-Boltzmann energy distribution is extended to {C}^* by the extended reaction rates through a more general distribution than the Maxwell-Boltzmann distribution. The new distribution is obtained by the pathway model introduced by Mathai in 2005 [Linear Algebra and Its Applications, 396, 317-328]. Simple analytic models considered by various authors are utilized for evaluating stellar luminosity and neutrino emission rates and are obtained in generalized special functions such as Meijer's G-function and Fox's H-function. The standard and extended non-resonant thermonuclear functions are compared by plotting them. Behavior of the new energy distribution, more general than Maxwell-Boltzmann is also studied.Comment: 20 pages, LaTe

DSDV, DYMO, OLSR: Link Duration and Path Stability

In this paper, we evaluate and compare the impact of link duration and path stability of routing protocols; Destination Sequence Distance vector (DSDV), Dynamic MANET On- Demand (DYMO) and Optimized Link State Routing (OLSR) at different number of connections and node density. In order to improve the efficiency of selected protocols; we enhance DYMO and OLSR. Simulation and comparison of both default and enhanced routing protocols is carried out under the performance parameters; Packet Delivery Ratio (PDR), Average End-to End Delay (AE2ED) and Normalized Routing Overhead (NRO). From the results, we observe that DYMO performs better than DSDV, MOD-OLSR and OLSR in terms of PDR, AE2ED, link duration and path stability at the cost of high value of NRO