Abstract/Overview Topological Data Analysis (TDA) is an important aspect in the field of topological data theory since the 21st century’s first decade. Modern TDA utilizes the structural characteristics of Big Data (BD), otherwise known as point cloud data sets. Topology and Geometry are tools used to analyze highly complex and multi-dimensional data by creating a summary of these characteristics to uncover hidden features in these datasets, while preserving feature relationships with...
Abstract/Overview Increased human population has led to increased vulnerabilities to hunger and reduced sources of affordable food. Sweet potato (Ipomoea batatas L.) is a root vegetable with large, starchy, tuberous roots, consumed worldwide. It is a potential food security crop, with high nutritional and economic value. Production of sweet potatoes in Kenya is low due to disease constraints such as sweet potato leaf spot (SPLS). Fungal SPLS results in reduced tuber yield, since the patho...
Abstract/Overview This study investigated the abundance and control of malaria mosquito larvae in a traditional water management agro-ecosystem of Kasagam, Kisumu City, western Kenya. The study of larval habitats of malaria vectors is important in determining abundance and fitness of resultant adult mosquito populations and planning for suitable control measures. Dominant types of plants found in the study site were identified, recorded and categorized. Sampling of mosquito larvae was don...
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 Wave equation is a linear hyperbolic partial differential equation (PDE) which describes the propagation of a variety of waves arising in physical situations. In its simplest form, the one dimension wave equation refers to a scalar function u = u(x, t), which satisfy the PDE utt = C2uxx. When the wave propagates in complex media, form of the governing wave equation changes, so in particular a viscous loss in term µuxxt and the advection term αux are added to the right ...
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 We establish the norm-denseness of the norm-attainable class $NAB(H)$ in the Banach algebra $B(H)$, which consists of all bounded linear operators on a complex Hilbert space $H$. Specifically, for every $O in NAB(H)$ and each $epsilon>0$, there exists $O' in B(H)$ such that $|O - O'| < epsilon$. We achieve this characterization by utilizing the convergence of sequences and the existence of limit points. The properties $A$ and $B$ of Lindenstrauss are sufficient to ensure...
Abstract/Overview The dynamic behavior of a multi-species system that includes a prey refuge and a Holling type III functional response is examined in this work. The pre-requisites for the presence of the equilibrium points, as well as their local and global stabilities, for the suggested system are analyzed and derived. The Routh-Hurwitz criterion and the eigenvalue technique are used to study the local stabilities. On the other hand, the global stabilities have been studied using the Ly...
Abstract/Overview The coexistence of interacting biological species is a vital issue for the management of existing resources and the prediction of the long-term survival of each species. Many species become extinct due to several factors including over-exploitation among others. Suitable measures such as restriction on harvesting, creation of reserved zones among others are key in saving these species. Multi-species models incorporating prey refuge with Holling type I functional response...
Abstract/Overview Purpose: Climate change in Rwanda is a great challenge resulting from increased temperature and causing abnormal variability in weather variables and threatening the socio-economic welfare of human beings. Water resources have been subjected to degradation and pollution due to intensive and frequent rainfall that have negatively impact on water abstractions in their proximity. This study aimed at analyzing the vulnerability of the Nyabarongo river water abstraction to cl...
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 sufficient 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 Jump diffusion processes have been used in modern finance to capture discontinuous behavior in asset pricing. Logistic Brownian motion for asset security prices shows that naturally asset security prices would not usually shoot indefinitely due to the regulating factor that may limit the asset prices. Geometric Brownian motion cannot accurately reflect all behaviors of stock quotation therefore, Merton who was involved in the process of developing the Black-Scholes model...
Abstract/Overview Sub-Saharan Africa still bears the greatest forms of malnutrition. Attention is shifting to the use of edible insects in forms which are acceptable to people irrespective of their social status and level of civilization in efforts to alleviate protein malnutrition. Gonimbrasia zambesina (Lepidoptera: Saturniidae) caterpillars emerge seasonally in the coastal part of Kenya and despite their rich nutritional profile, their consumption is low. This study was thus undertaken...