JOOUST Repository (Jaramogi Oginga Odinga University of Science and Technology)

ITB 1306

   JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY  SCHOOL OF INFORMATICS AND INNOVATIVE SYSTEMS  UNIVERSITY EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN  INFORMATION AND COMMUNICATION TECHNOLOGY  UNIVERSITY EXAMINATION FOR THE   3RD YEAR 2ND SEMESTER 2024/2025 ACADEMIC YEAR  MAIN CAMPUS    COURSE CODE: ITB 1306  COURSE TITLE: E-GOVERNMENT & INSTITUTIONAL CHANGE  EXAM VENUE:   LAB 12    STREAM:   BSC ICT   DATE : 24/4/2025            EXAM SESSION : 15.00-17.00   TIME: 2 HOURS     INSTRUCTIONS:  1. Answer Question 1 (Compulsory) and ANY other two questions  2. Candidates are advised not to write on the question paper  3. Candidates must hand in their answer booklets to the invigilator while in the examination room.      QUESTION ONE – 30 MARKS a) E-Government is a fundamental element in the modernization of Government. It provides a common framework and direction across the public sector and enhances collaboration within and among public sector organizations and institutions, between Government and the business community, and between Government and the citizens that it serves in the implementation of Government Policies. It also identifies ways of developing the skills needed by public servants to realize the new opportunities offered by ICT advancement such as the internet. State FIVE differences between E-Government and E-Governance       (10Marks) b) The overall goal of e-Government is to make the Government more result oriented, efficient and citizen centered. E-Government should enable citizens to access Government Services and Information as efficiently and as effectively as possible through the use of internet and other channels of communication. Mention FOUR specific objectives of e-Government in Kenya  (4Marks) c) Give FOUR reasons as to why we need an e-Government in our country  (4Marks) d) Press reports indicate a global growth in e-governance utilization by people in different categories. State FOUR current trends for the growth.       (4Marks) e) Explain FOUR Types of Interactions in E-Governance     (8Marks) QUESTION TWO – 20 MARKS a) Every government needs a comprehensive cloud governance. Define the term cloud governance (2Marks) b) Explain FOUR key benefits of a cloud governance framework    (8Marks)  c) Discuss FIVE risks associated with a poor cloud governance     (10Marks)  QUESTION THREE – 20 MARKS a) E-government has become a popular focus of government efforts in many countries around the world. To provide trusted services, e-government needs to focus on effectiveness, efficiency and flexibility. If citizens are to derive maximum benefit FROM the provision of e-services through e-governance. State FOUR attributes that an e-service must possess.                      (4Marks)  b) Explain THREE principles that determines an Information Security of an E-government (6Marks)  c) Discuss FIVE approaches for an e-Government security                                             (10Marks)  QUESTION FOUR – 20 MARKS E-Government models provide frameworks for digital interactions between governments, citizens, businesses, and other stakeholders.   a) Discuss the four main e-government models: Government-to-Citizen (G2C), Government-to-Business (G2B), Government-to-Government (G2G), and Government-to-Employee (G2E). Provide real-world examples for each model.        (12Marks) b) Analyze the benefits and challenges of implementing these e-government models, particularly in developing countries. Suggest possible solutions to overcome these challenges.   (8Marks) QUESTION FIVE – 20 MARKS Organizations today rely on Data Warehousing and Data Mining to make informed business decisions.  a) Explain the key differences between Data Warehousing and Data Mining, highlighting their roles in decision-making.           (8Marks) b) Describe how Data Mining techniques such as Classification, Clustering, and Association Rule Mining can be applied to extract valuable insights from a Data Warehouse.   (12Marks)   

E-GOVERNMENT & INSTITUTIONAL CHANGE

AFB 5127

 JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY SCHOOL OF AGRICULTURAL AND FOOD SCIENCES  FIRST YEAR SECOND SEMESTER EXAMINATION FOR THE DEGREE OF MASTER OF SCIENCE IN FOOD SECURITY AND SUSTAINABLE AGRICULTURE.  2024/2025 ACADEMIC YEAR   COURSE CODE: AFB 5127 COURSE TITLE: Innovations for Sustainable Food Systems DATE:                                 STREAM: MSc. (Food Security  and Sustainable                                                                                Agriculture)      TIME: 3   Hours        Instructions: 1. Answer THREE Questions.  2. Question 1 is compulsory.  3. All questions carry equal marks.        OASIS OF KNOWLEDGEQuestion 1 Evaluate the role of technological innovations such as precision agriculture, biotechnology, AI in improving food security and sustainability. What challenges and ethical issues arise from these technologies, especially in developing countries or marginalized communities? Provide examples.                    (20 Marks) Question 2 Discuss how circular economy principles, such as food waste reduction, upcycling, and sustainable packaging, contribute to a sustainable food supply chain. How do these innovations perform in both developed and developing countries.              (20 Marks) Question 3 How can innovations in food systems promote social equity, particularly for marginalized groups like women and smallholder farmers? Discuss both technological and policy solutions.                     (20 Marks) Question 4  Compare alternative proteins (plant-based, insect-based, lab-grown) in terms of their environmental, economic, and social impacts. What limitations do these alternatives face in achieving widespread adoption?                 (20 Marks)  Question 5  How do global food system governance frameworks (e.g., SDGs, UN Food Systems Summit) influence national food policies? What challenges do governments face in aligning policies with food security and sustainability goals, especially in low-resource settings?           (20 Marks)  

Innovations for Sustainable Food Systems

ICM 1103

   JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY SCHOOL OF INFORMATICS AND INNOVATIVE SYSTEMS DEPARTMENT OF COMPUTER SCIENCE & SOFTWARE ENGINEERING UNIVERSITY EXAMINATION FOR THE DEGREE OF MASTERS IN INFORMATION SECURITY AND AUDIT 1st YEAR 1st   SEMESTER 2024/2025 ACADEMIC YEAR KISUMU CAMPUS   COURSE CODE:   ICM 1103  COURSE TITLE: TCP/IP ARCHITECTURE AND ENTERPRISE NETWORK  EXAM VENUE:  STREAM: MASTERS IN INFORMATION SECURITY AND AUDIT  DATE:   24/4/2025   EXAM SESSION: 9.00-12.00 TIME:  3HOURS     INSTRUCTIONS: Answer QUESTION ONE and ANY other TWO questions      QUESTION ONE (20 Marks) a) Describe the following concepts as used in TCP/IP: i) Segmentation                                                                                              (1 mks) ii) Routing                                                                                                      (2 mks) iii) Address resolution                                                                                   (2 mks) b) It is possible to translate between private and public addresses, using Network Address Translation (NAT). NAT allows a host configured with a private address to be stamped with a public address, thus allowing that host to communicate across the Internet. Discuss the following types of NAT: i)  Static NAT                                                                                                 (2 mks) ii) Dynamic NAT                                                                                           (2 mks) iii) NAT Overload/Port Address Translation (PAT)                                     (2 mks) c) A virtual private network (VPN) allows the provisioning of private network services for an organization or organizations over a public or shared infrastructure such as the Internet or service provider backbone network. Discuss the following protocols and technologies used to enable site-to-site VPNs: i) IP Security (IPsec)                                                                                    (2 mks) ii) Generic Routing Encapsulation (GRE)                                                   (2 mks) iii) Layer Two Tunneling Protocol version 3 (L2TPv3)                              (2 mks) d) Bootstrap Protocol (BOOTP) is used to establish a network connection during a computer's initial boot up during the bootstrap process. Originally, the protocol used floppy disks, but it was soon integrated into computer hardware in motherboards and network adapters, so that no external drive is needed. Briefly describe the operation of BOOTP.                                                                                                                   (3 mks) QUESTION TWO (20 Marks) The diagram below shows TCP/IP encapsulation and headers. The unstructured stream of bits represents frames with distinct content.  Discuss the roles played by the following layers during the transfer of data from Device A towards Device B.   i) Physical layer                                                                                                   (4 mks) ii) Data link layer                                                                                                (4 mks) iii) Network layer                                                                                                (4 mks) iv) Transport layer                                                                                               (4 mks) v) Application layer                                                                                             (4 mks) QUESTION THREE (20 Marks) Study the diagram below carefully and use it to answer the questions that follow.  In TCP/IP, it is often said that the network layer (IP itself) offers an “unreliable” or “best effort” service, while the transport layer adds “reliability” in the form of flow and error control. Using the diagram above as a reference, describe the following procedures: i) Connection control                                                                                                 (8 mks) ii) Flow control                                                                                                          (6 mks) iii) Error control                                                                                                         (6 mks) QUESTION FOUR (20 Marks) Network monitoring is the use of logging and analysis tools to accurately determine trafc fows, utilization, and other performance indicators on a network. Good monitoring tools give you both hard numbers and graphical aggregate representations of the state of the network. This helps you to visualize precisely what is happening, so you know where adjustments may be needed. a) Discuss other benefits for implementing a good monitoring system for your network                                                                                                                                    (10 mks) b) Describe some of the tools that can aid you in network monitoring.                      (10 mks)     QUESTION FIVE (20 Marks) In order to create IP subnets, host bits are changed to network bits. This is often called borrowing bits. It is also often referred to as taking host bits and giving them to the network. By borrowing host bits, more IP subnets are created, but each subnet can support fewer hosts. a) Discuss some of the reasons for IP subnetting                                                        (10 mks) b) Describe the steps followed when calculating subnets                                           (10 mks)  

TCP/IP ARCHITECTURE AND ENTERPRISE NETWORK

In this paper, we investigate the spectral properties of a composition operator Cα : ` p → ` p , where 1 ≤ p < ∞ and a null sequence α = (αk)k∈N, defined by Cαx = (0, α1x1, α2x2, . . .). In particular, we prove that the point spectrum, the approximate point spectrum as well as the spectrum of Cα all coincide and is the singleton set containing 0. However, the extended spectrum of Cα turns out to be the complement of the closed unit disc of the complex plane

Otieno, Dancun

Omoke, Priscah

Bonyo, Job

Annals of Mathematics and Computer Science ISSN: 2789-7206Vol 27 (2025) 55-62 https://doi.org/10.56947/amcs.v27.464ON EXTENDED SPECTRUM OF A COMPOSITIONOPERATOR ON SEQUENCE SPACESDANCUN OTIENO1, PRISCAH OMOKE2 AND JOB BONYO3∗Abstract. In this paper, we investigate the spectral properties of a composi-tion operator Cα : `p → `p, where 1 ≤ p <∞ and a null sequence α = (αk)k∈N,defined by Cαx = (0, α1x1, α2x2, . . .). In particular, we prove that the pointspectrum, the approximate point spectrum as well as the spectrum of Cα allcoincide and is the singleton set containing 0. However, the extended spectrumof Cα turns out to be the complement of the closed unit disc of the complexplane.1. IntroductionLet X be an arbitrary Banach space and L(X) be the space of all boundedlinear operators on X. For T ∈ L(X), the resolvent set of T , ρ(T ), is given byρ(T ) = {λ ∈ C : T − λI is invertible} and its spectrum δ(T ) := C \ ρ(T ). Theset of all eigenvalues of T is called its point spectrum denoted by δp(T ), while theapproximate point spectrum of T , δap(T ), is the set of all λ ∈ C for which thereexist unit vectors xn ∈ X such that ‖(T − λI)xn‖ → 0 as n→∞. The spectralradius of T is defined by r(T ) = sup{|λ| : λ ∈ δ(T )}. For a detailed theory onspectra we refer to [3, 6, 13, 19].A complex number λ ∈ C is called an extended eigenvalue of an operatorT ∈ L(X) if there exists a nonzero operator A ∈ L(X) such that AT = λTA.The set of all extended eigenvalues of T will be denoted by δExt(T ) and is calledthe extended spectrum of T , while such an operator A ∈ L(X) is called theextended eigenoperator associated with the extended eigenvalue λ of T . It iswell known that δExt(T ) is a nonempty and closed subset of C. We refer to[7, 10, 14, 15, 16] for a detailed theory on extended spectra.The study of the extended spectrum of bounded operators has been consideredin different settings, see [1, 2, 4, 7, 9, 11] and references therein. Biswas et.al. [2] considered the Volterra operator, while Lacruz et. al. [18] determinedthe extended spectrum for discrete, finite and continuous Cesàro operators. In[9, 16, 12], interesting results on extended spectrum for shift operators are givenon the sequence space `2. It is important to note that sequence spaces still remainDate: Received: Jan 23, 2025; Accepted: Feb 7, 2025.∗ Corresponding author.2020 Mathematics Subject Classification. Primary 47A10, 47B01, 47B37.Key words and phrases. Extended spectrum, Eigenvalues, Sequence spaces, Compositionoperator.5556 D. O. OTIENO, P. M. OMOKE, J. O. BONYOa useful setting for spectral analysis of a variety of operators, see for instance therecent work by Nuray [5]. In this paper, we consider a composition of a rightshift operator and a multiplication operator on the general sequence space `p,1 ≤ p ≤ ∞, and investigate its spectral properties. In particular, we determineexplicitly the extended spectrum of the resulting composition operator.2. Preliminary ResultsLet `p, 1 ≤ p <∞ denotes the space of p-summable sequences of real or complexnumbers while `∞ denotes the corresponding space of bounded sequences of realor complex numbers. It is well known that `p, 1 ≤ p ≤ ∞ are Banach spaceswith respect to the norms ‖ · ‖p given by‖x‖p =(∞∑k=1|xk|p) 1pfor all x = (xk)∞k=1 ∈ `p, 1 ≤ p <∞,while‖x‖∞ = maxk∈N|xk| for all x = (xk)∞k=1 ∈ `∞.The Unilateral right shift operator S : `p → `p is defined bySx = (0, x1, x2, . . .) for all x = (xk)∞k=1 ∈ `p. (2.1)For an arbitrary null sequence (αk)k∈N of real or complex numbers, define aMultiplication operator Mα : `p → `p byMαx = (α1x1, α2x2, α3x3, . . .) for all x = (xk)k∈N ∈ `p. (2.2)We then define the composition of S and Mα on `p by the operator Cα := S◦Mα :`p → `p. Specifically,Cαx = (0, α1x1, α2x2, . . .) for all x = (xk)k∈N ∈ `p. (2.3)For an arbitrary 0 6= λ ∈ C, we define the diagonal operators Dλ and D 1λon `pas follows:Dλ =1λλ2. . .andD 1λ=11λ1λ2. . .It can be easily verified that D 1λ: `p → `p whenever |λ| ≥ 1 while Dλ : `p → `pwhenever |λ| < 1. We end this section by detailing the spectral properties of theoperators S, Mα and Cα as defined on the `p spaces.Theorem 2.1. Let S : `p → `p be the unilateral right shift operator defined byequation (2.1). Then:EXTENDED SPECTRUM OF A COMPOSITION OPERATOR 57(1) S is an isometry with ‖S‖ = 1(2) δp(S) = ∅, that is, S has no eigenvalues(3) δ(S) = {λ ∈ C : |λ| ≤ 1}, which is a closed unit disk D(4) δap(S) = ∂D, where ∂D is the unit circle.(5) r(S) = 1.Proof. To prove (1), for all x ∈ `p, 1 ≤ p <∞, we have‖Sx‖pp = |0|p + |x1|p + |x3|p + . . .= Σ∞k=1|xk|p= ‖x‖pp.That is, ‖Sx‖p = ‖x‖p. Now,‖Sx‖∞ = maxk∈N|xk|= ‖x‖∞.Taking supremum over all x ∈ `p, 1 ≤ p ≤ ∞, with ‖x‖p = 1, we obtain thedesired result. To prove (2), we have that λ ∈ δp(S) if and only if Sx = λx forsome nonzero x ∈ `p. This is equivalent to (0, x1, x2, . . .) = λ(x1, x2, x3, . . .). Ifλ = 0, then clearly x = 0 and if λ 6= 0, then x = 0 as well. Hence there areno eigenvalues. Next we note that S is not surjective since (1, 0, 0, . . .) does notbelong to the range of S. Therefore by using (1), S is a non-invertible isometry.It then follows immediately that δ(S) = ∇(0, 1) and δap(S) = ∂∇(0, 1). Thisproves assertions (3) and (4). Assertion (5) follows from the definition of thespectral radius and assertion (3). Theorem 2.2. Let Mα : `p → `p be the multiplication operator defined as in(2.2). Then(1) ‖Mα‖ = maxn∈N |αn|(2) δp(Mα) = {αn : n ∈ N}(3) δ(Mα)={αn : n ∈ N} ={0} ∪ {αn : n ∈ N}(4) δap(Mα) = δ(Mα) = {αn : n ∈ N}(5) r(Mα) = maxn∈N |αn|.Proof. To prove (1), we have for all x ∈ `p,‖Mαx‖pp =∞∑n=1|αn|pp|xn|pp≤ maxn∈N|αn|pp‖x‖pp.Taking the pth-root on both sides yields ‖Mα‖p ≤ maxn∈N |αn|‖x‖p. The resultnow follows by taking supremum over all x ∈ Ball(`p). On the other hand, leten = (0, 0, ..., 0, 1, 0, ...) the unit vector having 1 at the nth position and zeroelsewhere. Then en ∈ `p with ‖en‖p = 1 and so ‖Mα‖ ≥ ‖Mαen‖p = |αn|.Taking maximum over all n ∈ N completes the proof of (1). Now, λ ∈ δp(Mα)is equivalent to Mαx = λx for some 0 6= x ∈ `p or (α1x1, α2x2, α3x3, . . .) =λ(x1, x2, x3, . . .). If λ 6= 0, then α1 = λ, α2 = λ, . . . and therefore {αn : n ∈58 D. O. OTIENO, P. M. OMOKE, J. O. BONYON} ⊆ δp(Mα). If λ = 0, then x1 = 0 = x2 = x3 = . . . and so λ = 0 is not aneigenvalue. Therefore δp(Mα) = {αn : n ∈ N}, as desired. Following assertion2, we have that δp(Mα) ⊆ δ(Mα) since the spectrum is always closed, whereδp(Mα) = {αn : n ∈ N} ∪ {0}. We now prove that δ(Mα) ⊆ δp(Mα). Letλ ∈ C, λ 6= 0 and λ /∈ δp(Mα). This implies that λ ∈ ρ(Mα) which is equivalentto λI − Mα invertible, that is, λI − Mα : `p → `p is bijective. Therefore forall y ∈ `p, there exists a unique x ∈ `p such that (λI − Mα)x = y. Takingx =(yjλ−αj)j∈N, it follows that x ∈ `p and therefore δ(Mα) = {αn : n ∈ N} whichproves (4). To prove (5), we know that δp(Mα) ⊆ δap(Mα) ⊆ δ(Mα), that is,{αn : n ∈ N} ⊆ δap(Mα) ⊆ {αn : n ∈ N} ∪ {0}. Since δap(Mα) is closed, itfollows that δap(Mα) = δ(Mα). This therefore implies that the spectral radius is,r(Mα) = maxn∈N | αn |, which proves (6). Theorem 2.3. Let Cα : `p → `p, be the composition operator defined by (2.3).Then(1) ‖Cα‖ = maxn∈N |αn|(2) δp(Cα) = {0}(3) δ(Cα) = {0}(4) δap(Cα) = {0}(5) r(Cα) = 0.Proof. For every x ∈ `p and (αn)n∈N ⊆ F such that αn → 0, we have‖Cαx‖pp =∞∑n=1|αnxn|p≤ maxn∈N|αn|p∞∑n=1|xn|p= maxn∈N|αn|p‖x‖pp.Therefore,‖Cα‖ ≤ maxn∈N|αn|.To prove the reverse inequality, take x = en = (0, 0, ..., 1, 0, 0, ...), a unit vectorhaving 1 at the nth position and zero elsewhere. Then,‖Cα‖ ≥ ‖Cαen‖p = |αn| =⇒ ‖Cα‖ ≥ maxn∈N|αn|.Now, λ ∈ δp(Cα)⇔ Cαx = λx for some 0 6= x ∈ `p. Equivalently,(0, α1x1, α2x2, α3x3, . . .) = λ(x1, x2, x3, . . .). Therefore if λ 6= 0, then 0 = x1 =x2 = x3 = . . . and so λ 6= 0 is not an eigenvalue of Cα. For λ = 0, αn = 0 for somen implying that there exists some nonzero eigenvector. Therefore δp(Cα) = {0},which proves (2). To prove (3),C2α(x) = Cα(0, α1x1, α2x2, α3x3, ...)= (0, 0, α2α1x1, α3α2x2, ...).EXTENDED SPECTRUM OF A COMPOSITION OPERATOR 59implying that,‖C2α‖ = supn∈N|αnαn+1|.AlsoC3α(x) = Cα(C2α(x))= Cα(0, 0, α2α1x1, α3α2x2, ...)= (0, 0, 0, α3α2α1x1, α4α3α2x2, ...).and thus,‖C3α‖ = supn∈N|αnαn+1αn+2|.Implying that in general, ‖Ckα‖ = supn∈N |αnαn+1αn+2...αn+k|.Therefore limk→∞ ‖Ckα‖1k = 0 and thus r(Cα) = 0 proving (5). It therefore followsthat δ(Cα) = {0}, which proves (3). Now, obviously δap(Cα) = δ(Cα) = {0},which completes the proof. 3. Extended spectrumWe compute the extended spectrum for the composition operator Cα in compar-ison with the extended spectrum of the operators S and Mα. It turns out thatthere is no obvious relation between the point spectrum δp, the approximate pointspectrum δap, the spectrum δ as well as the extended spectrum of the operatorsS,Mα and Cα.Theorem 3.1. Let S,Mα and Cα be defined on `p as given by equations (2.1),(2.2)and (2.3) respectively. Then the following holds:(1) δExt(S) = {λ ∈ C : |λ| ≥ 1}(2) δExt(Mα) = {1}(3) δExt(Cα) = {λ ∈ C : |λ| ≥ 1}.Proof. Let S : `p → `p be the unilateral right shift operator defined by equation(2.1), and suppose that |λ| ≥ 1 and D 1λis the diagonal operator on `p so thatD 1λ(x1, x2, x3, ...) = (x1,1λx2,1λ2x3, ...) thenSD 1λ(x1, x2, x3, ...) = S(x1,1λx2,1λ2x3, ...)= (0, x1,1λx2,1λ2x3, ...)andλD 1λS(x1, x2, x3, ...) = λD 1λ(0, x1, x2, x3, ...)= λ(0,1λx1,1λ2x2,1λ3x3, ...)= (0, x1,1λx2,1λ2x3, ...).Therefore from the two above equations SD 1λ= λD 1λS. So, {λ ∈ C : |λ| ≥1} ⊆ δExt(S). Now we need to show that δExt(S) ⊆ {λ ∈ C : |λ| ≥ 1}, that is,60 D. O. OTIENO, P. M. OMOKE, J. O. BONYOλ ∈ δExt(S)⇒ |λ| ≥ 1.We use the proof by contrapositive. Let λ ∈ C be such that |λ| < 1 and considerthe diagonal operator Dλ. ThenSDλ(x1, x2, x3, ...) = S(x1, λx2, λ2x3, ...)= (0, x1, λx2, λ2x3, ...),andλDλS(x1, x2, x3, ...) = λDλ(0, x1, x2, x3, ...)= λ(0, λx1, λ2x2, λ3x3)= (0, λ2x1, λ3x2, λ4x3, ...).Thus SDλ 6= λDλS, implying that λ /∈ δExt(S). Therefore δExt(S) ⊆ {λ ∈ C :|λ| ≥ 1}, implying thatδExt(S) = {λ ∈ C : |λ| ≥ 1}.This completes the proof of (1).To prove (2), let Mα : `p → `p be the multiplication operator defined as in (2.2),and suppose that |λ| ≥ 1 and D 1λis the diagonal operator on `p so thatD 1λ(x1, x2, x3, ...) = (x1,1λx2,1λ2x3, ...).ThenMαD 1λ(x1, x2, x3, ...) = Mα(x1,1λx2,1λ2x3, . . .)= (α1x1, α21λx2, α31λ2x3, . . .),andλD 1λMα(x1, x2, x3, ...) = λD 1λ(α1x1, α2x2, α3x3, ...)= λ(α1x1, α21λx2, α31λ2x3, ...)= (α1λx1, α2x2, α31λx3, ...).Thus for λ = 1,MαD 1λ= λD 1λMα and therefore 1 ∈ δExt(Mα).On the other hand, for λ 6= 1,MαD 1λ6= λD 1λMα and so {λ ∈ C : |λ| > 1} *δExt(Mα). Using the proof by contrapositive, Suppose {λ ∈ C : |λ| < 1} and letDλ be the diagonal operator on `p. ThenMαDλ(x1, x2, x3, ...) = Mα(x1, λx2, λ2x3, ...)= (α1x1, α2λx2, α3λ2x3, ...),andλDλMα(x1, x2, x3, ...) = λDλ(α1x1, α2x2, α3x3, ...)= λ(α1x1, α2λx2, α3λx2, α3λ2x3, ...)= (λα1x1, λ2α2x2, λ3α3x3, ...).EXTENDED SPECTRUM OF A COMPOSITION OPERATOR 61Thus for |λ| < 1,MαDλ 6= λDλMα and therefore {λ ∈ C : |λ| < 1} * δExt(Mα).Hence, δExt(Mα) = {1}, which completes proof (2).For the composition operator defined by equation (2.3), given that |λ| ≥ 1 andD 1λis the diagonal operator, thenD 1λ(x1, x2, x3, ...) = (x1,1λx2,1λ2x3, ...),and soCαD 1λ(x1, x2, x3, ...) = Cα(x1,1λx2,1λ2x3, ...)= (0, α1x1,1λα2x2,1λ2α3x3, ...);whileλD 1λCα(x1, x2, x3, ...) = λD 1λ(0, α1x1, α2x2, α3x3, ...)= λ(0,1λα1x1,1λ2α2x2,1λ3α3x3, ...)= (0, α1x1,1λα2x2,1λ2α3x3, ...).ThusCαD 1λ= λD 1λCα,implying that {λ ∈ C : |λ| ≥ 1} ⊆ δExt(Cα}).Now suppose |λ| < 1 and Dλ is the diagonal operator whereDλ(x1, x2, x3, ...) = (x1, λx2, λ2x3, ...).ThenCαDλ(x1, x2, x3, ...) = Cα(x1, λx2, λ2x3)= (0, α1x1, λα2x2, λ2α3x3, ....),andλDλCα(x1, x2, x3, ...) = λDλ(0, α1x1, α2x2, α3x3, ...)= λ(0, λα1x1, λ2α2x2, λ3α3x3, ...)= (0, λ2α1x1, λ3α2x2, λ4α3x3, ...).Thus,CαDλ 6= λDλCα.implying that λ /∈ δExt(Cα).Therefore {λ ∈ C : |λ| ≥ 1} ⊆ δExt(Cα) which completes the proof of (3). 62 D. O. OTIENO, P. M. OMOKE, J. O. BONYOReferences1. A. Biswas, S. Petrovic, On extended eigenvalues of operators, Integral Equ. Oper. Theory,2 (2006), 233-248. https://doi.org/10.1007/s00020-005-1381-52. A. Biswas, A. Lambert, S. Petrovic, Extended eigenvalues and the Voltera operator, MathJ. Glasg, 3 (2002), 521-534. https://doi.org/10.1017/S001708950203015X3. A. Antonevich, A. Akhmatova, On spectral properties of weighted shift operators generatedby linear mappings, Scientific Publications of the State University of Novi Pazar, 1 (2012),17-24. https://doi.org/10.1063/1.30438784. A. Aymen, Z.B. Fatima, J. Aref, On Extended eigenvalues of a 2 × 2 block operators,Faculty of sciences and mathematics university of Nis Serbia, 5 (2023), 1377-1389. https://doi.org/10.2298/FIL2305377A5. F. Nuray, On the spectrum of the Lacunary Cesàro operator, Annals of Mathematics andComputer Science, 26 (2025), 78-91. https://doi.org/10.56947/amcs.v26.4446. D. Emma, M. Martina, On the spectrum of weighted shifts, Rev. Real Aca-demic ciec. Exactas fis.Nat.ser A Mat, 4 (2023), 100-117. https://doi.org/10.1007/s13398-022-01328-z7. C. Gilles, H. Hasan, Extended spectrum and extended eigenspaces of quasi-normal opera-tors, University of Lyon 43 (2015), 1-15. https://www.arXiv:1507.02901v2[math.FA]8. C. Gilles, H Hassan, Extended spectrum, extended eigenspaces and normal operators, Math.J. Anal. Appl, 1 (2014), 305-316. https://hal.archives-ouvertes.fr/hal-008645789. M. Gurdal, On extended eigenvalues and eigenvectors of shift operator on the Wieneralgebra, int.Math. J. anal. 14 (2009), 1722-1729. https:doi.org/10.1016/j.aml.2009.06.00810. H. Alkanjo, On extended eigenvalues and eigenvectors of truncated shift, Transaction ofthe American Math society, 170, (2013). https:doi.org/10.2478/conop-2012-000311. M.T. Karaev, On extended eigenvalues and eigenvectors of some operator classes, Trans-action of the American Math. society, 8 (2006), 2383-2392. https://www.jstor.org/stable/409827712. H. Kareem, A. Buthainah, On extended eigenvalues and eigenoperators of some weightedshift operators, Iraqi Journal of Science, 2 (2023), 804-808. https:doi.org/10.24996/ijs.2023.64.2.2613. E. Kreyzig, Introduction to Functional Analysis book, Canada publications, (1978), 1-703.14. K. S. Laith, A. H. Anas, Some properties on extended eigenvalues and extended eigenvec-tors, Tikrit J. Pure science, 6, (2019), 119-121. https:doi.org/10.25130/tjps.24.2019.11915. S. Meltem, Y. Fatih, On extended spectrum of some quasinormal operators, turkish math.J. anal, 41 (2017), 1477-1481. https://doi:10.3906/mat-1610-9916. L. Miguel , L. S. Fernando, J. M. Luis, Extended eigenvalues for bilateral weighted shifts,int.math. J. anal, 2 (2016), 1501-1602. https:doi.org/10.1016/j.jmaa.2016.07.04517. L. Miguel, L. S. Fernando, J. M. Luis, On extended eigenvalues of composition operators,int.math. J. anal, 504 (2021), 125-427. https:doi.org/10.1016/j.jmaa.2021.12542718. L. Miguel, L. S. Fernando, S. Petrovic, O. Zabeti, On extended eigenvalues for Cesàrooperators, int.math. J. anal and applications, 429 (2015), 623-657. https:doi.org/10.1016/j.jmaa.2015.04.02819. M. Rosenblum, G. Lumer, Linear operator equations, Proc. Amer. Math. Soc, 10, (1959),32-41. https:doi.org/10.1142/70751,2 Department of Pure and Applied Mathematics, Jaramogi Oginga OdingaUniversity of Science and Technology, Bondo, Kenya.Email address: duncano816@gmail.com3 Department of Mathematics, Multimedia University of Kenya, Nairobi, KenyaEmail address: jbonyo@mmu.ac.ke

On Extended Spectrum of a Composition Operator on Sequence Spaces

HDR 2221

 JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY SCHOOL OF HEALTH SCIENCES UNIVERSITY EXAMINATION FOR DIPLOMA IN HEALTH RECORDS  2nd YEAR 2nd SEMESTER 2024/2025 ACADEMIC YEAR MAIN CAMPUS COURSE CODE:      HDR 2221 COURSE TITLE:                   Management of Health information II EXAM VENUE:   STREAM:  (Diploma in Health Records ) DATE:                                       EXAM SESSION:  TIME:       3 HOURS                                                                              ______________________________________________________________________________ Instructions: 1. Answer question 1and AND 3 questions in Section B  2. Candidates are advised not to write on the question paper. 3. Candidates must hand in their answer booklets to the invigilator while in the examination room.        OASIS OF KNOWLEDGESECTION A: ANSWER ALL TOTAL (40MKS)  SECTION A: Question 1.  1) Briefly explain the following terms as applied in Management of Health Information:     12mks i. Electronic Heath Records (EHSs) ii. Data security iii. Data privacy iv. Data quality Assurance  v. Health information Management systems vi. Health information Exchange (HIE) 2) Briefly explain why data security is important in Health Information Management         3mks 3) How would you establish Health Information Exchange    4mks 4) List THREE widely used information systems for data management   3mks 5) Briefly explain how you would maintain data quality assurance   4mks 6) Why is it important to integrate health information exchanges? 4mks 7) Briefly explain how carry out data design 4mks 8) Outline any SIX data collection tools   6mks 9) Outline any FOUR patient information you would capture in your records 4mks  Section B: Answer 3 questions, 60 marks 1. Discuss the steps you would follow to analyze Health data   20mks 2. Processing health data involves a series of steps to organize, clean, analyze, and interpret the information. Explain what happens at every step 3. Explain  a. Best practices to ensure data quality  10mks b. Types of data security    10mks 4. Explain TEN attributes of data quality   20mks  

Management of Health information II

BEB 1202

   JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY  SCHOOL OF BUSINESS & ECONOMICS UNIVERSITY EXAMINATION FOR THE DEGREE OF BACHELOR OF BUSINESS ADMINISTRATION WITH IT 1ST YEAR 2ND SEMESTER 2024/2025 ACADEMIC YEAR MAIN /KISUMU CAMPUS COURSE CODE: BEB 1202 COURSE TITLE: BUSINESS LAW I EXAM VENUE:                               STREAM: (BBA/BED ARTS/SNE)  DATE: 23/04/2025        EXAM SESSION: 15.00 – 17.00 PM TIME: 2   HOURS   Instructions: 1) Answer   QUESTION ONE and any other TWO questions 2) Candidates are advised not to write on the question paper. 3) Candidates must hand in their answer booklets to the invigilator while in the examination room.         OASIS OF KNOWLEDGE  1. a. Onyango and Kalonzo have entered into a contract of sale of a motor vehicle. Onyango is 17 years old while Kalonzo the buyer is 20 years old. Kalonzo has threatened Onyango with dire consequences if Onyango does not sell the Motor vehicle at Kenya Shillings One hundred thousand only (KShs. 100,000/=). Onyango is asking for Kenya Shillings Three Hundred Thousand (KShs.300, 000/-) Onyango has come to you for a legal advice on the validity of a contract.  Advice Onyango                                  (10 marks) b. Define the term “Tort”                                                                                               (5 marks) c. How can a contract be terminated?     (7 marks)                                                                            d. Discuss the jurisdiction of the high court under the constitution of Kenya 2010        (8 marks)  2) a. The principles aim of the Law of Tort is to compensate the victim; discuss therefore the various objectives of tort.                                                                 (10 marks)  b. Contract is an agreement between two parties; enforceable by law, highlight therefore the differences between a tort and a contract.                         (10 marks)        3) a. Define the tort of defamation and explain the defences available to a defendant .       .                                                                                                                 (10 marks) b. What is the scope of the African customary law and under what circumstances may the court be guided by it.                                                               (10 marks)      4) a. Distinguish between the common law, statue law and the doctrines of equity and how are they applicable in Kenya.                                                       (10 marks) b. The High court of Kenya is established under article165 of the Kenyan constitution. Explain the high court of Kenya’s jurisdiction as exercised against surbodinate courts and other administrative authorities through the writ of Habeas Corpus,writ of Certiorari and the writ of Mandamus.                           (10 marks)      5) Write short notes on the following: a. Res Ipsa Loquitur                                                                                   (5 marks) b. Volenti non fit ijuria.                                                                              (5 marks) c. Consideration                                                                                         .(5 marks) d. Statutory Authority.                                                                                 (5 marks)  

BUSINESS LAW I

ABB 2208

JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY   SCHOOL OF AGRICULTURE AND FOOD SECURITY  2nd YEAR, SECOND SEMESTER EXAMINATION (For 2024/2025 Academic Year) FOR THE DEGREE OF BACHELOR OF SCIENCE IN FOOD SECURITY AND AGRICULTURAL EDUCATION COURSE CODE: ABB 2208 COURSE TITLE: World Food Distribution  INSTRUCTION TO CADIDATES                                          Answer Question ONE and any other THREE questions TIME: THREE HOURS   QUESTION ONE             a) Define the term "food security" and list its four pillars [4 marks] b) Define the term the term food distribution and state its importance [5 Marks] c) Explain the concept of "strategic food reserves" and provide one example of a country that maintains such reserves [5 marks] d) What is the role of the Food and Agriculture Organization (FAO) in global food distribution? [2 marks] e) Identify two key differences in food production patterns between the Global North and the Global South [5 marks] f) What are early warning systems in the context of food security, and why are they important? [5 marks]             QUESTION TWO    Describe the role of FAO information systems (e.g., GIEWS - Global Information and Early Warning System) in monitoring global food security and their limitations [15 marks]     QUESTION THREE      Discuss the challenges of maintaining and distributing food reserves during emergencies, such as natural disasters or conflicts [15 marks] QUESTION FOUR       Discuss the disparities in food production, availability, and access between the Global North and the Global South [15 marks] QUESTION FIVE     How do factors such as technology, climate, and economic policies contribute to these disparities?  [10 marks]  

WORLD FOOD DISTRIBUTION

HMP 5112

JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGYSCHOOL OF HEALTH SCIENCESUNIVERSITY EXAMINATION FOR THE DEGREE OF MASTER OF SCIENCE(EPIDEMIOLOGY AND DISEASE CONTROL/BIOSTATISTICS)/MPH1ST YEAR 1ST SEMESTER 2024/2025 ACADEMIC YEARKISUMU CAMPUSCOURSE CODE: HMP 5112COURSE TITLE: PRINCIPLES OF EPIDEMIOLOGYEXAM VENUE: STREAM:MSc (Epidemiology &Disease Control/Biostatistics)/MPHDATE: EXAM SESSION:TIME: 3.00 HOURSInstructions:1. Answer FOUR questions2. Candidates are advised not to write on the question paper.3. Candidates must hand in their answer booklets to the invigilator while in theExamination Room.Answer question ONE and other THREE questions (60 marks)1. i. Potentially, screening could be done for every disease for which there is a diagnostictest or diagnostic signs and symptoms. Discuss criteria, of Wilson and Jungner, used toguide the rational development of screening programs (10 marks).ii. State the main ways to assess the performance of screening or diagnostic test. (5marks).2 650 patients known to have a particular disease were screened with a new test. 600controls without this disease were also screened. Of the 650 patients, 567 had a positive test.Of the healthy group without disease, 11 had a positive test.a. Create a 2*2 table and reflect on the interpretation of the data. (5 marks).b. Calculate sensitivity and specificity of the test. (5 marks).c. What are the implications for those wrongly classified by the test (5 marks).3. Figure 1.5 shows the occurrence of a disease event over the course of one year. Use it toanswer questions 2 a. and 2.b.a. If the disease had a seasonal pattern every year, explain what an epidemiologist may learnfrom this graph (6 marks).b. If it was an epidemic, discuss scenarios which may cause it (9 marks).4.i. Why are (point) prevalence rates useful in epidemiology? (5 marks).ii. Explain factors which may lead to either an increase or decrease in the prevalence rate(10marks).5. Make short notes on Epidemic patterns with reference to:i. Common source (5 marks).ii. Propagated source (5 marks).Iii. Mixed source (5 marks).6. (a) Case definition is a set of standard criteria for deciding whether a person has aparticular disease or other health related condition. Explain how epidemiologists carry outcase definition during an outbreak of measles (6 marks).(b) Discuss importance of determining rates after making simple counts of cases (9 marks).

PRINCIPLES OF EPIDEMIOLOGY

ICB 1102

  K      JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY SCHOOL INFORMATICS AND INNOVATIVE SYSTEMS UNIVERSITY EXAMINATION FOR  THE DEGREE OF BACHELOR OF SCIENCE  IN COMPUTER SECURITY & FORENSICS 1ST YEAR 2ND SEMESTER 2024/2025 ACADEMIC YEAR CENTRE: MAIN  COURSE CODE: ICB 1102 COURSE TITLE: SYSTEMS BUILDING EXAM VENUE: LAB 7 STREAM: BSc. Computer Security & Forensics DATE: 24/4/2027 EXAM SESSION: 15.00-17.00 TIME: 2  HOURS   Instructions:  1. Answer ANY three questions. 2. Candidates are advised not to write on the question paper. 3. Candidates must hand in their answer booklets to the invigilator while in the examination room.    QUESTION ONE  (a.) Explain the difference between a data-oriented approach and a functional-oriented approach to requirements elicitation. Provide an example of when each approach would be most appropriate. (10 Marks) (b.) Discuss the importance of control and audit considerations during the requirements capture process.  (5 Marks) (c.) Describe how specifications (e.g., standards, regulations) can be used as requirements elicitation tools. (5 Marks)  QUESTION TWO  (a.) Describe the Systems Development Life Cycle (SDLC) phases, including Planning, Analysis, Design, Implementation, and Maintenance. (10 Marks) (b.) Compare and contrast iterative approaches, such as prototyping, rapid application development (RAD), and extreme programming (XP), as project management methodologies. (10 Marks) QUESTION THREE  Explain the principles of database design and development using the data-oriented approach, emphasizing Entity-Relationship (ER) modeling, relationships, keys, dependencies, and normalization. (20 Marks)  QUESTION FOUR  Compare and contrast the top-down and bottom-up approaches to project management, highlighting the scenarios where each approach might be most appropriate. (20 Marks)  QUESTION FIVE (i.) Which of the following is NOT a core principle of Object-Oriented Programming (OOP)? (4 Marks) a) Encapsulation b) Inheritance c) Polymorphism d) Algorithm Design (ii.) In UML, which diagram is used to represent the interactions between objects in a sequence over time? (4 Marks) a) Use Case Diagram   b) Class Diagram c) Sequence Diagram d) State Diagram (iii.) Which OO concept represents a "has-a" relationship between two classes? (4 Marks) a) Inheritance b) Generalization c) Composition d) Aggregation (iv.) In UML, which diagram is most suitable for depicting the different states of an object and the transitions between those states? (4 Marks) a) Class Diagram b) Use Case Diagram c) State Diagram d) Activity Diagram (v.) What is the purpose of "abstraction" in Object-Oriented Programming? (4 Marks) a) To expose all implementation details to the user. b) To hide complex implementation details and provide a simplified view of an object. c) To create multiple instances of a class. d) To define the relationships between classes. 

SYSTEMS BUILDING

AAB 1402

  1  OASIS OF KNOWLEDGE JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY  SCHOOL OF AGRICULTURAL AND FOOD SCIENCES SECOND YEAR SECOND SEMESTER UNIVERSITY EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN ANIMAL SCIENCE,  FOOD SECURITY, BACHELOR OF SCIENCE IN AGRICULTURAL EDUCATION AND EXTENSION AND BACHLOR OF SCINECE IN AGRIBUSINESS MANAGEMENT 2024/2025 ACADEMIC YEAR RECEIPT COURSE CODE: AAB 1402 COURSE TITLE: BEEF CATTLE AND CAMEL PRODUCTION EXAM VENUE:        SIAYA CAMPUS STREAM: BSc. Animal Science   DATE:                                                               EXAM SESSION:  TIME: 2 HOURS                            Instructions: 1. Answer ALL the questions in section A and any TWO in section B. 2. Candidates are advised not to write on question paper. 3. Candidates must hand in their answer booklets to the invigilator while in the examination room.    2  SECTION A [30 MARKS]   SECTION A: ANSWER ALL QUESTIONS (30 MARKS)  1. (a) Define the following:  i) Estrus synchronization  ii) Stocking rate  iii) Backgrounding  iv) Ranch     v) Finishing  [10 marks]               (b). Differentiate between the breeds of camels   (5 marks)              (c)   State four importance of camel production (5 marks) 2. Explain inbreeding and its side effects in beef animals production    (5 marks)    3.  List and explain five common diseases that affect camels in Kenya. (5 marks)  SECTION B: ANSWER ANY TWO QUESTIONS (40 MARKS)  1. a). Mention and explain  factors that have influence distribution beef animal             Production [10 marks]  b). List any four breeds (2marks) c)  Explain beef production systems practiced in Kenya (8 marks)   2. a. Describe management system under which camels  are kept (10 marks) b. Discuss the adaptations of the camel to ASAL environment. (10 marks) 3. a. Explain the characteristics of Intensive Beef Production (10 marks)      b. Explain the following as used in beef production           i. Cow-Calf Phase          ii. Backgrounding Phase (Stocker Cattle Production)    3    

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