Applied Mathematics Research Papers/Topics

On Characterization of Very Rotund Banach Spaces

Abstract/Overview It is known that the Hilbert space H is the most rotund space among all Banach spaces. The question whether if a normed space X is a rotund Banach space implies we can obtain other most rotund spaces is still open and represents one of the most interesting and studied problems. In this paper we investigate if there exists other most rotund Banach spaces. It is shown that Frechet spaces are very rotund and also uniformly rotund.

On Compactness of Similarity Orbits of Norm-Attainable Operators

Abstract/Overview The notion of compactness plays an important role in analysis. It has been extensively discussed on both metric and topological spaces. Various properties of compactness have been proved under the underlying spaces. However, if we consider these sets to be from similarity orbits of norm-attainable operators; little has been done to investigate their compactness. In this paper, we introduce the concept of compactness of similarity orbits of norm-attainable operators in as...

Characterization of Norm-Attainable Operators

Abstract/Overview In this paper we characterize norm-attainable elementary operators, we show that ๐›ฟ ๐‘ƒ,๐‘„ is norm-attainable if both P and Q are norm-attainable and๐›ฟ๐‘ƒ,๐‘„ is norm-attainable ๐›ฟ๐‘ƒ,๐‘„if is normally represented.

On denseness of similarity orbits of norm-attainable operators

Abstract/Overview The notion of dense sets has been extensively discussed on both metric and topological spaces. Various properties of the sets have been proved under the underlying spaces. However, if we consider these sets to be from similarity orbits where a topology has been developed on them, little has been done to investigate their denseness. In this paper, we introduce the concept of denseness of similarity orbits of norm-attainable operators in aspect of generalized sets in topol...

On Centre Properties of Irreducible Subalgebras of Compact Elementary Operators

Abstract/Overview In this paper, we characterize the centre of dense irreducible subalgebras of compact elementary operators that are spectrally bounded. We show that the centre is a unital, irreducible and commutative Cโˆ— -subalgebra. Furthermore, the supports from the centre are orthogonal and the intersection of a nonzero ideal with the centre is non-zero.

Properties of Spectrally Bounded Compact Elementary Operators

Abstract/Overview Spectrally bounded compact elementary operators on dense irreducible subalgebras of C โˆ— -algebras are characterized. Also, it is shown that left multiplications, right multiplications, generalized derivations and basic elementary operators are spec trally bounded compact elementary operators. Furthermore, several properties of spectrally bounded compact elementary operators such as completeness, convergence, continuity and total boundedness in a general Banach setting ...

Numerical Analysis of Holling Type Ii Functional Response Predator-Prey Model with Time Delay Optimal Selective Harvesting

Abstract/Overview Population dynamics indicate the changes in size and composition of population through time, as well as biotic and abiotic factors influencing those changes. Predator-prey (PP) relationship with harvesting and functional response involving prey refuge with Holling type I functional response (HTIFR) has been studied with recommendations on their extension to include Holling type II functional response (HTIIFR). There persists a problem in fifinding the numerical solution ...

On norm preserving conditions for local automorphisms of commutative banach algebras

Abstract/Overview Many studies on preserver problems have been focusing on linear preserver problems in matrix theory. Kadison and Sourour showed that the local derivations of Von Neumann algebras are continous linear maps which coincide with some derivation at each point in the algebra over the field of complex numbers. Most of the studies have been focusing on the spectral norm preserver and rank preserver problems of linear maps on matrix algebras but not on norm preserver problems for...

Estimation of Population Mean Using Three-Stage Optional RRT Model in the Presence of Measurement Errors under Stratified Two-Phase Sampling

Abstract/Overview In the present study, the problem of estimation of the finite population mean of a sensitive study variable using the three-stage optional Randomized Response Technique (RRT) model under measurement errors is addressed. A generalized class of estimators is proposed using a mixture of auxiliary attribute and variable. Some members of the proposed generalized class of estimators are identified and studied. The bias and mean square error expressions for the proposed estimat...

On Norm Estimates for Derivations in Norm-Attainable Classes

Abstract/Overview In this note, we provide detailed characterization of operators in terms of norm-attainability and norm estimates in Banach algebras. In particular, we establish the necessary and su๏ฌƒcient conditions for norm-attainability of the derivations and also give their norm bounds in the norm attainable classes.

Completely Positive Map from M4(C) to M5(C) on Positive Semidefinite Matrices

Abstract/Overview Positive Maps Are Essential In the Description of Quantum Systems. However, Characterization Of The Structure Of The Set Of All Positive Maps Is A Challenge In Mathematics And Mathematical Physics. We Construct A Linear Positive Map From M4 To M5 And State The Conditions Under Which They Are Positive And Completely Positive (Copositivity Of Positive).

Reconstructing Global Earth Observation Based Vegetation Index Records with Stochastic Partial Differential Equations Approach

Abstract/Overview Long-term Earth observation based vegetation index records have been used extensively by researchers to assess vegetation response to global climate variability and change. However, the records exhibit multiple temporal gaps due to spectral and radiometric inconsistencies that inhibit accurate assessment of land surface vegetation dynamics. Here, we propose a new reconstruction procedure that approximates Bayesian time series model by using integrated nested Laplace appr...

Sensitivity Analyses of Population Projection Matrix of Cestrum Aurantiacum

Abstract/Overview The Lefkovitch stage specific matrix population models are divided into discrete stage classes defined by a growth variable such as size, height and diameter at breast height for trees. In matrix model, the deterministic matrix projection models are used to estimate growth rate, stable size distribution, reproductive values, and sensitivities of the growth rate to changes in vital rates. This study sampled five forest blocks (Kiptogot, Kimothon, Suam, Saboti and Kitale w...

Modeling Household Water Demands Using Sinusoidal Models

Abstract/Overview Household water in Kenya is used in agricultural activities, industrial activities and other uses. A lot of water is consumed by indoor appliances. The water management strategy affects the household demand for water. The future demand of water in Kenyan towns has remained uncertain. Therefore this study sought to model household water demand using the non- parametric model in the spectral domain. This study largely relied on the secondary data that was collected from Gu...

Fitting a Markovian Queuing Model to Bus Park Revenue Collection Point in Kisii Town, Kenya

Abstract/Overview In queuing theory one deals with the mathematical analysis of the performance of queuing systems. In our daily lives customers encounter queues while seeking services in institutions. The increase in the number of customers has resulted to congestion at revenue collection points in Kenyan towns. There is therefore need to study the queuing systems to identify possible remedies. This study sought to fit a queuing model to bus park revenue collection point as a preliminary...


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