Using Few Radon Projections to Recover 3-D NMR Spectrum

Given a regular binary function f on R2 with compact support D, we use translation to form a new binary function g from f so that the image representation of g (x, y) is made up of non-overlapping copies of D. Thus, g is made up of discrete entities that are surrounded by regions of space. We devise a procedure that can determine the translation parameters using a minimum number of Radon projections g of g . This model is a mathematical abstraction of an application of the Radon transform in Spectroscopy.Keywords: Radon transforms, transformation of an image, Back projection.

Solutions of General Pentagonal Equation Under Certain Conditions

It was proved by Galois that there are no formulas that can be used to solve “by radicals” general equations of degree 5 or larger. In this paper we solved the general pentagonal equation under certain conditions. We used the “Quartic Formula” and unipodal numbers respectively for condition 1 and conditions 2 to solve the general pentagonal equation. The unipodal case was elaborated with a detailed example.

On Selecting the Normal Population with the Largest Absolute Mean

The problem of selecting the normal population with largest absolute mean is considered. An alternative procedure based on the absolute values of the sample medians and investigate its efficiency relative to Rizvi’s means procedure has been studied.

On -Quasi Irresolute Functions

In this paper we introduce a new class of functions called -quasi irresolute functions. The notion of -quasi graphs are introduced and the relationship between -quasi irresolute functions and -quasi closed graphs is analysed. 2000 Mathematics Subject Classification : 54C08, 54C10.

On   -Homeomorphisms In Topological Spaces

In this paper, we first introduce a new class of closed map called   -closed map. Moreover, we introduce a new class of homeomorphism called   - Homeomorphism, which are weaker than homeomorphism. We also introduce  - Homeomorphisms and prove that the set of all   - Homeomorphisms form a group under the operation of composition of maps.2000 Math Subject Classification: 54C08, 54D05.

Weighted Pseudo Almost Automorphic Solutions to Nonautonomous Semilinear Differential Equations

We consider the existence and uniqueness of Weighted Pseudo almost automorphic solutionsto the non-autonomous semilinear differential equation in a Banach space X :( ) = ( ) ( ) ( , ( )), ' u t A t u t f t u t t Rwhere A(t), t R, generates an exponentially stable evolution family {U(t, s)} andf :R X X satisfies a Lipschitz condition with respect to the second argument.MSC 2010: 43A60; 34G20, 47Dxx

On Regular Pre-Semiclosed Sets in Topological Spaces

The generalized closed sets in point set topology have been found considerable interest among general topologists. Veerakumar introduced and investigated pre-semi- closed sets and Anitha introduced pgpr-closed sets. In this article the concept of regular pre-semiclosed sets is introduced in topological spaces and its relationships with other generalized sets are investigated.

The Sums of Alternating Series of Odd Powers of the Reciprocals of Odd Positive Integers

This paper is an extension of a recent work done by the author [4] and here the sums of alternating series of odd powers (up to fifteen) of the reciprocals of odd positive integers are computed. Following this method, the sum of the series of any higher power could be calculated. In the process of computing these sums, the sums of the series of even powers of reciprocals of odd positive integers have been reestablished and enabled the author to compute the values of Riemann’s zeta function for even positive integers.

Mixed Sampling Product Control for Costly or Destructive Items

This paper presents the derivation of operating characteristics function and associated measures of performance of mixed sampling Plans for costly or destructive items. The first stage is concerned with single sample variable inspection and in the second stage modified Chain Sampling inspection is recommended. If the first stage inspection of mixed plans does not lead to acceptance of the batch or lot then the second stage becomes more important. In the second stage of mixed plans, it is advisable to have small sample size for costly or destructive items. Therefore, in the second stage, the modified chain sampling plan which always utilizes the past lot inspection results in order to achieve very small sample size is taken into consideration. The economic or cost-effective of the sampling plans is measured through Average Sample Number which is smaller compared to any other mixed sampling plans. Designing procedure is given and tables are constructed to facilitate easy application in the production industries.

On Tomography with Limited Data

We give an algorithm for reconstructing a density function f in the plane from limited number of Radon projections on a range of angles −𝝋∗<𝝋<𝝋∗ together with a few well selected angles outside this range. In doing so, we assume that f is subjected to a linear transformation that produces g, and actually recover g. Interpolation is a basic tool in our calculations