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/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...
Abstract/Overview Sugarcane is the main raw material in the production of sugar in Kenya. The supply of sugarcane affects directly the quantity of sugar supplied in the markets. Low supply of sugarcane leads to a decline in the amount of sugar supplied to the markets and vice versa. This creates the need of determining the quantity of sugarcane supplied by the farmers to the industries to facilitate planning. This study employed Box Jenkins predictive models in forecasting the monthly qua...
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...
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...