Department of Mathematics

Permanent URI for this collectionhttp://erepository.kibu.ac.ke/handle/123456789/112

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On convergence of sections of sequences in Banach spaces
(Springer-Verlag, 2000-02-01) Aywa, Shem; Jan, Fourie
An elementary proof of the (known) fact that each element of the Banach spaceℓ w p (X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element ofℓ w p (X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications to spaces of compact operators on Banach sequence spaces are considered.
On summing multipliers and applications
(Journal of Mathematical Analysis and Applications, 2001-01-01) Aywa, Shem; Jan, Fourie
A scalar sequence (αi) is said to be a p-summing multiplier of a Banach space E, if ∑∞i = 1‖αixi‖p < ∞ for all weakly p-summable sequences in E. We study some important properties of the space mp(E) of all p-summing multipliers of E, consider applications to E-valued operators on the sequence space lp, and extend this work to general “summing multipliers.” The case p = 1 shows close resemblance to the work of B. Marchena and C. Piñeiro (Quaestiones Math., to appear), where the results originated from the authors' interest in sequences in the ranges of vector measures.
Spaces of compact operators and their dual spaces
(Springer-Link, 2004-01-13) Aywa, Shem; Jan, Fourie
Theω′-topology on the spaceL(X, Y) of bounded linear operators from the Banach spaceX into the Banach spaceY is discussed in [10]. Let ℒw' (X, Y) denote the space of allT∈L(X, Y) for which there exists a sequence of compact linear operators (T n)⊂K(X, Y) such thatT=ω′−limnTn and let|||T|||:={supn||Tn||:Tn∈K(X,Y),Tn→w′T}. We show that(Lw′,|||⋅|||) is a Banach ideal of operators and that the continuous dual spaceK(X, Y)* is complemented in(Lw′(X,Y),|||⋅|||)∗. This results in necessary and sufficient conditions forK(X, Y) to be reflexive, whereby the spacesX andY need not satisfy the approximation property. Similar results follow whenX andY are locally convex spaces.
Income Source Diversification and Financial Performance of Commercial Banks in Kenya
(Mount Kenya University Journals, 2011-04-01) Rotich, Paul T.; Okaka, Damianus Ochieng; Aywa, Shem
The profitability of commercial banks depends heavily on the net of income generating activities and the related activities’ expense. Due to the problem of profitability and stiff competition in the industry, commercial banks have changed their behavior of income sources, by increasingly diversifying into non-intermediation income generating activities as opposed to the traditional inter-mediation income generating activities. The objective of this paper was to establish the impact of income source diver-sification on financial performance of commercial banks in Kenya. This has been achieved through: establishing the level of income source diversification of commercial banks in Kenya and establish whether income source diversification improves financial position of commercial banks. This was a census study of all registered 44 commercial banks in Kenya and relied heavily on documentary sec-ondary data for 5 year study period (2005-2009) and validated by primary data achieved through key-informant method. Herfindahl-Hirschman Index, Correlations and Regression analysis were mainly used and revealed on aggregate that all commercial banks in Kenya are diversified with large banks in lead while Islamic banks trail. Further, diversification level has a positive influence on financial performance of commercial banks in Kenyan and the two main revenue streams are positively related.
Mathematical model for detecting diabetes in the blood
(Academia, 2011-07-01) Kwach, Boniface Otieno; Ongati, Omolo; Simwa, Richard
This study presents a new mathematical model for Blood Glucose Regulatory System(BGRS) which includes epinephrine as a third variable in the form, Ў= AY, and whose solution has been analyzed for equilibrium and stability to provide the blood glucose concentrations for diabetics and non-diabetics. We establish that the final model is asymptotically stable compared to the existing models, that is, the eigenvalues of the coefficient matrix are complex numbers with negative real parts. Furthermore, the resonance period for the final model, that is, T0 = 2:9847134 hours, is far less than that of the existing model, showing that the glucose concentration returns to normal level within a shorter time.
Equivalent Banach Operator Ideal Norms1
(HIKARI: International Journal of Mathematical Analysis, 2012-01-01) Musundi, Sammy; Aywa, Shem; Jan, Fourie
Let X, Y be Banach spaces and consider the w′-topology (the dualweak operator topology) on the space (L(X, Y),‖.‖) of bounded linearoperators from X into X with the uniform operator norm.Lw′(X,Y) is the space of all T∈L(X, Y) for which there exists a sequence ofcompact linear operators (Tn)⊂K (X, Y) such thatT=w′−limnTn Two equivalent norms, ‖|T‖|:=inf{█(sup@n)┤‖Tn‖:Tn∈K(X,Y),Tnw′→T}and ‖T‖u:=inf{█(sup@n)┤ {max{‖Tn‖,‖T−2Tn‖}}:‖:Tn∈K(X,Y),Tnw→T}on Lw′(X, Y), are considered. We show that (Lw′,|‖.‖|) and (Lw′,‖.‖u) are Banach operator ideals.
Generalized estimation of missing observations in nonlinear time series model using state space representation
(Science Publishing Group, 2013-01-01) Biwott, Daniel Kiprotich; Odongo, Leo O.
The aim of the study was to formulate a Time Series Model to be used in obtaining optimal estimates of missing observations. State space models and Kalman filter were used to handle irregularly spaced data. A non-Bayesian approach where the missing values were treated as fixed parameters. Simulated AR (1) data and corresponding estimated missing values were generated using a computer programme. Values were withheld and then estimated as though they were missing. The results revealed that simple exposition of state space representation for commonly used Time Series Models can be formulated.
Advances in composite integer factorization
(International Knowledge Sharing Platiform, 2013-01-01) Wanambisi, Adrin W.; Aywa, Shem; Maende, Cleophas; Muketha, Geoffrey Muchiri
In this research we propose a new method of integer factorization. Prime numbers are the building blocks of arithmetic. At the moment there are no efficient methods (algorithms) known that will determine whether a given integer is prime or and its prime factors[1]. This fact is the basis behind many of the cryptosystems currently in use.
Building Materials from Stabilized Soils: The use of under-utilized resources for Low Cost Building
(International Journal of Sustainable Construction Engineering and Technology, 2013-01-01) Kwach, Boniface Otieno
A probabilistic data encryption scheme
(international journal sharing platiform ; Journal of Natural Sciences Research, 2013-01-01) Wanambisi, Adrin W.; Maende, cleophas; Muketha, Geoffrey Muchiri; Aywa, Shem
In this paper the author presents a probabilistic encryption scheme that is polynomially secure and has the efficiency of deterministic schemes. From the theoretical construction of Brands and Gill (1996), it is clear that the proof of Pseudo randomness of the quadratic residue generator is complete if it can be shown that there exists a one-way function under the possible assumption that it is infeasible to solve the quadratic residuacity problem provided the factorization of the composite integer is unknown
A Novel Statistical Model for Poverty Estimation
(LAP LAMBERT Academic Publishing, 2013-02-26) Sindayigaya, Samuel; Okoth, Annete w.; Mulati, Nyukuri Omukoba
In this study, individual consumption as a function of income generated by a cow under one-cow-one family program is modelled. The model was applied on sample data collected from Nyaruguru District in Rwanda. The poverty level in the district was estimated and its variance determined. The confidence intervals of the poverty levels were also computed and compared with already established results. It was established that the model is effective
Mathematical model for drug therapy in patients with diabetes mellitus
(International Journal of Engineering, Science and Mathematics, 2013-03-01) Kwach, Boniface Otieno; Ongati, Omolo; Okoya, Oduori; Otedo, Amos
This study presents a new mathematical model for Drug Therapy in Patients with Diabetes Mellitus which includes external rate at which blood glucose, insulin and epinephrine is being increased in the form Y= fi (g,h,e)+ri (t) . The system has been analyzed and solved to provide the systems natural frequency, ω0, which is the basic descriptor of saturation level of the drug. We establish that the resonance period for the final model, that is, T0=3.76912 hrs, agrees well with the data for the existing insulin therapy, showing that the peak, which is the time period for insulin to be most effective in lowering blood sugar, is in the acceptable therapeutic range
Algebraic approach to composite integer factorization
(European Centre for Research, Training and Development : IJMSS, 2013-03-01) Wanambisi, Adrin W.; Aywa, Shem; Maende, cleophas; Muketha, Geoffrey Muchiri
There various algorithms that can factor large integers but very few of these algorithms run in polynomial time. This fact makes them inefficient. The apparent difficulty of factoring large integers is the basis of some modern cryptographic algorithms. In this paper we propose an algebraic approach to factoring composite integer. This approach reduces the number of steps to a finite number of possible differences between two primes.
The relationship between students socio-economic status and accessto public university education in Bungoma West District, Kenya
(International Journal of Advanced Research, 2013-05-29) Mabonga, Reuben Manyonge; Aywa, Shem; Odebero, Stephen; Poipoi, Moses
To access university education in Kenya, one needs to attain grade C+ in Kenya Certificate of Secondary Education and above as a minimum qualification according to Joint Admission Board (JAB) requirements. The sample of students for this study was identified through simple random sampling while Public Universities were purposefully identified. The instruments comprised questionnaire and interviews. The validity of instruments was done through consultation with lecturers who are the experts in the Department of Education Planning and Management of Masinde Muliro University of Science and Technology and supervisors. Data analysis was done on computer based Statistical Package for Social Sciences (SPSS) programme at the ANOVA and Chi-Square value 0.05 level of significance. Both descriptive statistics involving means, mode, frequencies and inferential statistics were used. The study found out that students’ socio economic status influenced the number of those who accessed university education. There is need for the government to establish a comprehensive scholarship and loan system for needy students.
Derivation and solution of the heat equation in 1-D
(International Journal of Engineering, Science and Mathematics, 2013-06-01) Kwach, Boniface Otieno; Ongati, Omolo; Alambo, David; Okaka, Colleta A.
Heat flows in the direction of decreasing temperature, that is, from hot to cool. In this paper we derive the heat equation and consider the flow of heat along a metal rod. The rod allows us to consider the temperature, u(x,t), as one dimensional in x but changing in time, t.
Solutions of second-order partial differential equations in two independent variables using method of characteristics
(International Journal of Engineering and Mathematical Sciences, 2013-06-01) Kwach, Boniface Otieno; Manyonge, Alfred W.; Olambo, David; Aminer, Titus J.O.
Elementary partial differential equations
(Lambert, 2013-06-01) Wanjala, Charles C.; Manyonge, Alfred W.; Kwach, Boniface Otieno
The importance of partial differential equations cannot be gainsaid. They are used in science and engineering. Many natural phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow etc occurring in science and engineering are described by partial differential equations. Partial differential equations often model mathematical systems where many variables exist. They are also used in statistics especially in the field of stochastic processes.
Forensic estimation of time of death: a mathematical model
(International Journal of Management,IT and Engineering (IJMIE), 2013-07-01) Kwach, Boniface Otieno; Ongati, Omolo; Nyakinda, J.O.; Nyang’inja, Rachael
In this paper we establish the exact time of death of a murdered person. This leads to an ordinary differential equations whose solution has been analyzed to provide the approximate time of death. Forensic expert will try to estimate this time from body’s current temperature and calculating how long it would have taken to lose heat to reach this point. This provides an accurate approach to establish the approximate time when crime is committed.
Some Irreducible 2-Modular Codes invariant Under The Symplectic Group S6(2)
(GLASNIK MATEMATIˇ CKI, 2014-01-01) Chikamai, Lucy W.; Moori, Jamshid; Rodrigues, Bernardo G.
We examine all non-trivial binary codes and designs obtained from the 2-modular primitive permutation representations of degrees up to 135 of the simple projective special symplectic group S6(2). The submodule lattice of the permutation modules, together with a comprehensive description of each code including the weight enumerator, the automorphism group, and the action of S6(2) is given. By considering the structures of the stabilizers of several codewords we attempt to gain an insight into the nature of some classes of codewords in particular those of minimum weight.
A HIV/AIDS model in a homogeneous population with time lags in the transmission
(HIKARI Ltd: Applied Mathematical Sciences, 2014-01-01) Wasike, Adu A.M.; Kibwott, Frankline T; Lawi, GO; Mulati, Nyukuri Omukoba
We investigate a simple HIV/AIDS epidemic model in a heterosexual population by by modifying a Susceptible-Infective-Removed (SIR) model. The model considers sexual transmission of HIV where individuals are being recruited into sexually matured age group at a constant rate and incorporates time lags for one to become infective and the other to become fully blown. A complete qualitative analysis of the model, including the boundedness and positivity of the solutions, local stability of the equilibrium points is done. We applly the next generation matrix to determine the disease reproduction number R0. The Model is shown to be completely determined by the reproduction number. The model is numerically analysed to asses the effects of the delay on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Kenya.

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