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    On geometrical Aspects of Various Operators and their Orthogonality in Complex Normed Spaces
    (CSRS Publication, 2025-11) Otae, Lamech; Okelo, Benard
    Studies involving orthogonality of operators is an area with various applications with regard to the ever dynamic and emerging technological research outputs. In normed spaces (NS) there are different types of orthogonality. Useful results have come up where operators possessing given conditions are chosen for Range-Kernel orthogonality to be established. However, most of the results have been focussing on one type of orthogonality called the Birkhoff-James which we have given more results on. In this paper we give results on various notions of orthogonality by considering certain geometrical aspects in NS.
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    Nonlinear Geometry of Norm-Attaining Functionals: Variational Principles, Subdifferential Calculus, and Polynomial Optimization in Locally Convex Spaces
    (2025-04-16) Mogoi, N. Evans; Moraa, Priscah
    We develop a unified theory of norm-attainment for nonlinear functionals in locally convex spaces, extending classical results to sublinear, quasiconvex, and polynomial settings. Our main contributions include: (1) nonlinear Bishop-Phelps theorems establishing density of norm-attaining functionals, (2) a subdifferential characterization of attainment via interiority conditions, (3) a KreinMilman principle for convex functionals on compact sets, and (4) a complete solution to the polynomial norm-attainment problem through tensor product geometry. The work combines innovative applications of Choquet theory, variational analysis, and complex-geometric methods to reveal new connections between functional analysis and optimization. Key applications address stochastic variational principles and reproducing kernel Hilbert space optimization, with tools applicable to PDE constraints and high-dimensional data science. These results collectively bridge fundamental gaps between linear and nonlinear functional analysis while providing fresh geometric insight into infinite-dimensional phenomena.
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    From Crop Pest to Plate: The Potential of Giant Long-Horn Beetle Larvae (Tithoes Confinis) as a Sustainable Food and Nutrition Resource in Eastern Tanzania
    (Journal of Current Opinion in Crop Science, 2025-06-30) Mpombeye, Patrick Cleophace; Otieno, Dennis Ochuodho; Watako, Arnold Onyango; Kigeso, Andrea Malima; Mwakalinga, Nicolaus Anania
    Food insecurity remains a persistent challenge in rural Tanzania, particularly in Morogoro Rural District, where seasonal food shortages and limited access to affordable, nutritious food threaten household well-being. This study explored the contribution of edible giant longhorn beetle larvae (Tithoes confinis) to household nutrition and food security in selected villages across the district. Data were collected through household surveys, key informant interviews, and focus group discussions conducted in three purposively selected villages: Mazizi, Maseyu, and Mgodini. A total of 385 households participated in the study, representing a cross-section of food security statuses and insect consumption practices. Quantitative data were analyzed using descriptive statistics and chi-square tests to determine the relationship between food security levels and insect consumption, while qualitative data provided insights into advantages of consumption. The results showed that food insecurity was prevalent, with a notable percentage of households categorized as moderately or severely food insecure. Households experiencing higher levels of food insecurity were more likely to consume T. confinis larvae as coping strategy during food shortage. The larvae were recognized for their high nutritional value, ease of accessibility, and cultural acceptance among the Luguru people. However, consumption was declining due to changing dietary norms, negative perceptions, and lack of policy support. The study concludes that integrating edible insects like T. confinis into local diets and nutrition programme could enhance dietary diversity and resilience among rural populations. Policy support and public education on insect-based value chains are recommended to reposition this food source as part of sustainable nutrition strategies.
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    Cost-Effective PUF and ECC-Based Authentication Protocol for Secure Internet of Drones Communication
    (IEEE Internet of Things Journal, 2025-06-03) Nyangaresi, Vincent Omollo; Ahmad, Musheer; Maghrabi, Louai A.; Althaqaf, Turki
    Internet of Drones (IoD) plays a critical role in remote monitoring operations. It has been heavily deployed in applications such as traffic management, air traffic control, disaster and agricultural monitoring. In such operations, high volumes of sensitive and private data is collected and transmitted to the ground stations. The usage of unreliable and open wireless channels during the message exchange process exposes the IoD to a myriad of security threats. Therefore, numerous authentication protocols have been developed in the recent past to mitigate these threats. However, most of these protocols are still inadequate in the provision of robust security against typical IoD attacks. Because, they involve resource-intensive operations and make them unsuitable for an IoD environment. Therefore, we put forward a new authentication protocol which exhibits cost-effective performance. To develop the new protocol for secure IoD communication, we leverage on biometrics, physically unclonable function and elliptic curve cryptography for the robust performance. Extensive formal security analysis using the random oracle model (ROM) is showing that proposed protocol is provably secure. The informal security analysis is also performed which demonstrates its robustness against all the threat assumptions in the Canetti-Krawczyk (C-K) model. Specifically, it is found to offer conditional privacy, unlinkability, anonymity, mutual authentication, session key establishment and perfect key secrecy. Moreover, it is capable enough to mitigate numerous threats such as forgery, impersonation, stolen verifier, replay, physical capture, de-synchronization, known secret key and smart card loss attacks. The performance is cost-effective as evident from the comparative analysis showing that the proposed protocol incurs the lowest energy consumptions and computation overheads at relatively low communication costs compared to many other authentication schemes.
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    Derivation of A Risk Model that Incorporates Inhomogeneous Claim Counts and Financial Risks
    (International Journal of Statistics and Applied Mathematics, 2025-01-10) Motanya, Nyanumba Walter; Brian, Oduor D.; Nyakinda, Joseph O.
    In the insurance industry, ruin or insolvency occurs when an insurer’s total liabilities exceed its assets, rendering it unable to meet future claims. Traditional ruin probability models, such as the Cramer-Lundberg model, assume a homogeneous Poisson claim process with a constant arrival rate, which may not accurately reflect real-world market dynamics. In practice, claim arrivals are often in-homogeneous due to seasonal variations, policyholder behaviors, and external economic factors. Additionally, financial risks including inflation, interest rates, and taxation further influence an insurer’s solvency. This study develops an extended risk model that incorporates in-homogeneous claim counts and financial risks, offering a more realistic framework for estimating ruin probabilities in non-life insurance. The proposed model is derived using integral-differential equations and Cramer-Lundberg approximations, providing a refined approach to risk assessment. The findings offer valuable insights for insurers and regulators in designing risk management strategies to mitigate insolvency risks and ensure financial stability.