School of Biological, Physical, Mathematics & Actuarial Sciences
http://ir.jooust.ac.ke/handle/123456789/34
2024-03-29T06:40:23ZThe Exponentially Modified Gaussian Function as a Tool for Deconvolution of Astroparticle Physics data.
http://ir.jooust.ac.ke/handle/123456789/8857
The Exponentially Modified Gaussian Function as a Tool for Deconvolution of Astroparticle Physics data.
Ochilo, Livingstone
In the period 2004 – 2012, the Pierre Auger Observatory has recorded more than two million of ultra-high energy cosmic rays. In seeking to interpret the data recorded for the events, it is necessary to simulate the interaction of primary cosmic rays with the atmosphere. One of the software that is available for this kind of simulation is CONEX. In this study, CONEX is used to simulate various compositions of primary cosmic rays, whose interactions with the atmosphere result in air showers, with a distribution of depths of shower maximum (Xmax), which is treated as the true distribution. Smearing this distribution with a known σ gives the “measured” distribution. By using the Exponentially Modified Gaussian (EMG) function, we have obtained deconvoluted distribution which is generally in good agreement with the original distribution
2018-10-23T00:00:00ZOn norm preserving conditions for local automorphisms of commutative banach algebras
http://ir.jooust.ac.ke/handle/123456789/207
On norm preserving conditions for local automorphisms of commutative banach algebras
Kangogo, Willy; Okelo, Bernad N.; Ongati, Naftali O.
The history of commutative algebra first appeared in 1890 by David Hilbert which was then followed by Banach spaces in 1924 since localization reduces many problems of geometric special case into commutative algebra problems of local ring. So far, many studies on preserver problems have been focusing on linear
preserver problems (LPPs) especially LPPs in matrix theory. Also in consideration has been the characterization of all linear transformation on given linear space of matrices that leave certain functions, subsets and relations invariant. Clearly, we also have spectrum preserver problem or transmission. Kadison and Sourour have also shown that the derivation of local derivation of Von Neumann algebra R are continuous linear maps if it coincides with some derivation at each point in the algebra over C. We employ the concept of 2-local automorphisms introduced by Serml that if we let A be an algebra, then the transformation : A A transformation : A A. is called a 2-local automorphism if for all x, y A there is an automorphism (xy) of A for which ( x) x,y(x) and ( y) x,y(y). In this paper, we characterize commutativity of local automorphism of commutative Banach algebras, establish the norm preserver condition and determine the norms of locally inner automorphisms of commutative Banach algebras. We use Hahn-Banach extension theorems and the great ideas developed by Richard, and Sorour to develop the algebra of local automorphisms, then integrate it with norm preserver conditions of commutative Banach algebras. The results of this work have a great impact in explaining the theoritical aspects of quantum mechanics especially when determining the distance of physical quantities.
1st JOOUST Scientific Conference
0006-01-01T00:00:00ZNorms of derivation associated with idempotents and unitary operators
http://ir.jooust.ac.ke/handle/123456789/204
Norms of derivation associated with idempotents and unitary operators
Moses, Ouma O.; Ongati, Naftali O.; Okelo, Bernad N.
The study of operators has continued to attract the attention of many researchers. Of special interest are the calculations of norms of these operators. Johnson Stampfli wrote a paper on the norms of derivation on algebra of bounded linear endomorphisms of ф. Obonyo and Agure in one of their papers have given their study on the norms of inner derivations on norm ideals followed by another one on norms of derivations implemented by S-universal operators. Ivan Vidar defined a bounded operator acting in a Hilbert space as idempotent if A2 =A. This study is going to concentrate on the norms of derivations induced by orthogonal idempotents and unitary operators. Let H be an infinite dimensional complex Hilbert space and B(H) the algebra of all bounded linear operators on H. A generalized derivation is an operator defined by δA,B(X)=AX- XB, for all X in B(H) and B fixed in B(H). When A=B then we have an inner derivation defined by δA(X)= AX- XA for all X in B(H) and A fixed in B(H). A lot of studies have been done o n characterization of derivations for instance Kittaneh gave commutator inequalities associated with the polar decomposition. Mansour and Bouzenada obtained norm estimates of commutator between subnormal operators but posed a problem that states that if δA(X) = AX-XA is such that A=A + iC and X=B + iD, then what are possible estimates for δA(X) if A,B,C,D stand taken as contractions? Moreover, can there be best estimate for other classes of operators? In this presentation therefore we consider the class of unitary operators and orthogonal idempotents and discuss the norms of derivations associated with the orthogonal idempotents and unitary operators
1st JOOUST Scientific Conference
0006-01-01T00:00:00ZNorm estimates for convexoid operators
http://ir.jooust.ac.ke/handle/123456789/202
Norm estimates for convexoid operators
Onyango, Cecil; Oleche, Paul; Okelo, Bernad N.
Hilbert space operators are important in formulation of principles of quantum mechanics and also in other fields of applied sciences. These operators include normal operators, hyponormal operators, normaloid operators, spectraloid operators, transaloid operators and convexoid operators among others. The norm property has been investigated by several mathematicians for example Dragomir, Kittaneh, Furuta, Bonyo, Agure among others. Important results have been obtained regarding norm inequalities but this has not been fully investigated as stated by Dragomir. Therefore, the problem that persist is to determine norm estimates for convexoid operators. The objectives of this study are: To establish the necessary and sufficient condition for convexoidity of normal operators, to determine upper estimates of convexoid normal operators and to determine the lower estimate of convexoid normal operators. The methodology shall involve the use of known inequalities like Cauchy-Schwarz inequality, Minkowski's inequality and parallelogram law. We shall also use the technical approach of tensor product and numerical ranges in determining the norm estimates. The results obtained are useful in investigating the norm property for other classes of Hilbert space operators when they are normal self-adjoint.
1st JOOUST Scientific Conference
0006-01-01T00:00:00ZNorms and numerical radii inequalities for ( , ) - normal transaloid operators
http://ir.jooust.ac.ke/handle/123456789/200
Norms and numerical radii inequalities for ( , ) - normal transaloid operators
Nyaluke, Wesley K.; Okelo, Bernad N.; Ongati, Naftali O.
The studies on Hilbert spaces for the last decade has been of great interest to many mathematicians and researchers, especially on operator inequalities related to operator norms and numerical radii for a family of bounded linear operators acting on a Hilbert spaces. Results on some inequalities for normal operators in Hilbert spaces for instance numerical ranges W(T), numerical radii w(T) and norm; .; obtained by Dragomir and Moslehian among others due to some classical inequalities for vectors in Hilbert spaces. The techniques employed to prove the results are elementary with some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities. Recently, the new field of operator theory done by Dragomir and Moslehian on norms and numerical radii for ( , ) - normal operators developed basic concepts for our Statement of the problem on normal transaloid operators. M. Fujii and R. Nakamoto characterize transaloid operators in terms of spectral sets and dilations and other non-normal operators such as normaloid, convexoid and spectroid. Furuta did also characterization of normaloid operators. Since none has done on norms and numerical radii inequalities for ( , ) – normal transaloid operators, then our aim is to characterize ( , )- normal transaloid operators, characterize norm inequalities for ( , )- normal transaloid operators and to characterize numerical radii for ( , )- normal transaloid operators. We use the approach of the Cauchy-Schwarz inequalities, parallelogram law, triangle inequality and tensor products. The results obtained are useful in applications in quantum mechanics.
1st JOOUST Scientific Conference
0006-01-01T00:00:00ZCertain properties of normaloid operators
http://ir.jooust.ac.ke/handle/123456789/190
Certain properties of normaloid operators
Mogotu, P.O.; Kerongo, J.; Obogi, R. K.; Okelo, Bernad N.
In this paper we establish new conditions for contractivity of normaloid operators. We employ some results for contractivity due to Furuta, Nakomoto, Arandelovic and Dragomir. A particular generalization is also given.
1st JOOUST Scientific Conference
0006-01-01T00:00:00ZOn shift of mindset: the importance of change of mindset in helping students get better at getting better in mathematics
http://ir.jooust.ac.ke/handle/123456789/188
On shift of mindset: the importance of change of mindset in helping students get better at getting better in mathematics
34; Owiti, Dickson S.O.; Ongati, Naftali O.
That mathematics is important in enhancing creativity, innovativeness and technological development is undisputable. Kenya like any other African country is endowed with reach human resource yet lesscompetitive globally partly due to students’ fear of mathematics and poor performance at almost all levels. A number of measures have been put in place to remedy the situation yet the score card has been poor over the years. There is no such thing as a “math person”. Everyone can and has a capacity to learn mathematics welltoat least improve in it provided they could be helped to overcome the fear for failure. This paper presents and discusses the importance of a shift in mindset for students of mathematics where working on challenging work and making mistakes enhances learning potential. It also proposes some of the interventions by teachers of mathematics that could help students change from fixed mindset to a growth mindset in the 21st century.
1st JOOUST Scientific Conference
0006-01-01T00:00:00ZOn numerical radius attainability for normal self-adjoint operators
http://ir.jooust.ac.ke/handle/123456789/187
On numerical radius attainability for normal self-adjoint operators
Omaoro, Sabasi; Okelo, Bernad N.
The numerical range and numerical radius are very useful in studying linear operators acting on Hilbert spaces. The operators include normal, hyponormal, normaloid, transaloid, self-adjoint, subnormal, compact and unitary. Norm attaining and numerical radius attaining operators have been studied by many mathematicians including Acosta, Paya, Ruiz, and Cardassi among others. The question of whether the numerical radius is attainable for normal operators has not yet been fully investigated, especially for self-adjoint operators. The question arising from Kittaneh is whether the numerical radius is attainable for normal self-adjoint operators. If so, what are the necessary and sufficient conditions for numerical radius attainability for normal self-adjoint operators? The objective of this paper is to establish necessary and sufficient conditions for numerical radius attainability for normal self-adjoint operators. We have the results on conditions for numerical radius attainability and denseness for Hilbert space operators. We have considered normal and self-adjoint operators. The methodology involved the use of the technical approach of tensor products in our calculations. The obtained results are important in investigating the relationship between numerical radius attainable normal operators and other norm attainable operators.
1st JOOUST Scientific Conference
0006-01-01T00:00:00ZEcological niche modelling and spatial distribution of rift valley fever vectors in Baringo County, Kenya
http://ir.jooust.ac.ke/handle/123456789/181
Ecological niche modelling and spatial distribution of rift valley fever vectors in Baringo County, Kenya
Ochieng, A.; Gachie, T; Ondiba, I M.; Nanyingi, M; Olago, D.; Amimo, Fred A.; Oludhe, C.
The Rift Valley fever (RVF) is a vector-borne zoonotic disease that has an impact on human health and animal productivity. It is caused by the Rift Valley Fever Virus (RVFV) which is primarily transmitted by flood water Aedes mosquitoes. Culex spp and Mansonia spp are secondary vectors which pick up the RVFV from domestic animals and amplify the infection to other domestic animals and humans. This study used ecological niche modelling algorithms to predict the effect of climatic variables on habitat suitability and the spatial distribution of RVF vectors in Baringo County. We ran the Boosted Regression trees and Random Forest algorithms to model the spatial distribution of Culex spp. using species occurrence data and AFRICLIM climate data. The species occurrence data was obtained from longitudinal sampling of mosquito larvae in four strata within the study area between June and December 2014. The AFRICLIM climate data consisting of 21 variables was downloaded from https://webfiles.york.ac.uk/KITE/AfriClim. Preliminary results indicate that rainfall, moisture and temperature ranges are the key factors that affect the spatial distribution of Culex spp in Baringo County. Culex spp. is likely to be found in the riverine zone along Kerio River and in the lowlands around Lakes Baringo, 94 and Bogoria.
1st JOOUST Scientific Conference
2015-06-24T00:00:00ZAn automatic teller machine for HIV test based on digital image processing techniques
http://ir.jooust.ac.ke/handle/123456789/179
An automatic teller machine for HIV test based on digital image processing techniques
Adem, Jack A.
Many kinds of HIV testing kits have recently become available to be used in determining whether an individual's blood contains HIV virus or not. In the determine method of the HIV rapid test procedure, when a drop of blood is introduced at the lower testing region of the test kit, a red horizontal line appears on the test section indicating the presence of the HIV virus. The absence of the red line shows that the blood does not contain the virus. However, a similar red line must appear at the control section of the kit to show that the test procedure is successful and complete. The reading, interpretation and confidentiality of the HIV test result has often been abused by the medics and the counselors. There has been an immense widespread of HIV due to people’s ignorance of their status. The spread can be curbed by introducing a human friendly, confidential, automatic and reliable testing system that has been developed by this study. In this study, an electronic system that automatically acquires the red color signals that appear on the test kits has been developed. The system analyses the color signals, processes them, displays and relays the test result to the client. The main objective of the study was to design and develop a real-time HIV test analyzer based on computer aided image processing technique. An image processing software in a client/server system using Graphics Device Interface plus (GDI+) Library tool was created. The system used Complementary metal-oxide- semiconductor (CMOS) digital camera to capture the image and the programmed software, developed in C#, processes the captured image and sends the testing results to the display unit. This technique will not only eliminate the human error associated with the use of HIV testing kits, but will also improve the testing productivity in comparison to those achieved by the trained technicians. It will also enhance the confidentiality of the test result hence reducing the stigma associated with the disease and encourage more people to know their HIV status. The system can be installed in our medical facilities and at the Voluntary Counseling and Testing (VCT) to aid the medical personnel in HIV screening and testing. The system has been tested successfully and the testing results show a high degree of efficiency and reliability.
1st Scientific Conference
2015-06-24T00:00:00Z