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.
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...
Abstract/Overview In this paper we characterize norm-attainable elementary operators, we show that ๐ฟ ๐,๐ is norm-attainable if both P and Q are norm-attainable and๐ฟ๐,๐ is norm-attainable ๐ฟ๐,๐if is normally represented.
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...
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 Cโ -subalgebra. Furthermore, the supports from the centre are orthogonal and the intersection of a nonzero ideal with the centre is non-zero.
Abstract/Overview Spectrally bounded compact elementary operators on dense irreducible subalgebras of C โ -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 ...
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 ...
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...
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...
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๏ฌcient conditions for norm-attainability of the derivations and also give their norm bounds in the norm attainable classes.
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).
Abstract *e notion of metric dimension originated in the twentieth century by the work done by Slater [1, 2] and latter independently by Harary and Melter [2]. *e initial concept was introduced to locate the intruder in any network but the development and impact of the notion was far reaching in coming years. Several applications of metric related network parameters can be seen in social networking, navigation, communications, and engineering, pharmaceutical chemistry. *e fault tolerance of ...
Abstract The emergence of Covid-19 posed a great health challenge worldwide. Health care facilitieswere stretched beyond limit, with no space to admit new critical patients. This motivated thisstudy, which sought to understand the dynamics around queues, particularly in hospitals. Themain objective was to analyze the queuing process between the Emergency Department (ED)and Internal Wards (IW) at Moi Teaching and Referral Hospital, in order to understand patientflow with the view to minimizin...
Abstract Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving an optimization problem where the cost function is assembled variously, for example, maximum likelihood and maximum a posteriori methods. However, these methods do not have exact solutions to most real-life problems. It is for this reason that Mont...
Abstract Background. The HIV epidemic varies significantly across different groups in the SSA region, and complicates designing effective general interventions. We aim at uncovering temporal trends in HIV prevalence disaggregated by age, sex, and country. Method. We determined HIV prevalence trends among males and females aged 15-49 years for surveys conducted from the years 2003-2007 (period 1) and 2013-2018 (period 2) in SSA. Countries were divided into three clusters based on their socio-...