Evolution of Kadhis Courts in Zanzibar

Zanzibar, is an Island on the east coast of Africa in Tanzania. The region is mostly populated by Muslims. This region had long time relationship in international trade with the people of near and far-east. The relationship however resulted in the islamization of the island. The early contact had ever lasting impact on the peoples of the region, yet the Islamic Legal System has been treated with a step mother affection since the colonial era. However, in recent times Muslims in the region including the island are asserting for a change of the status of administration of justice system in the region to make it in accordance to Islamic Law. Keywords: Islamic Law, Kadhis Courts, Islamic Legal System and Zanzibar

Electrochemistry of ferrocene derivatives relevant to their use in measuring state of charge of lead acid batteries

The electrochemistry of some ferrocene compounds coated on gold electrodes in concentrated sulphuric acid solutions in the concentration range 1–5 M has been investigated. The objective of this work was to investigate whether such compounds could be used to determine, potentiometrically, the state of charge of lead-acid batteries. The investigated ferrocenes included, simple ferrocene, poly(vinylferrocene), bridged ferrocenes in which the two cyclopentadienyl groups are linked by –CH2– chains of vary lengths and alkanethiol substituted ferrocenes. Each of the investigated ferrocenes were found to undergo one electron reversible oxidation/reduction at the surface of the electrode. Their anodic and cathodic peak potentials were independent of pH in the range 2–10 in aqueous solutions of K2SO4, KCl and NaClO4. However, in concentrated acid solutions (H2SO4, HCl and HClO4) the anodic and cathodic peak potentials shifted, almost linearly, to less positive potentials with increasing acid concentration. The attachment of alkanethiol group to the ferrocene molecules improved the retainability at the gold electrode surface which is possibly linked to strong chemisorption of the thiol group on the gold surface. The retainability and chemical stability of the ferrocene compounds at the gold electrode surface were found to be higher in ClO4– than in Cl– and SO42– media which is postulated to be related to the salt formation between the anion and the ferricenium ion generated on oxidation. The bridged ferrocenes were found to be chemically more stable than simple ferrocene. The presence of a carbonyl group in the alkanethiol chain generally decreased the chemical stability of the ferrocene compounds in aqueous acidic media but more so in SO42– than in ClO4– media. Of all the investigated ferrocenes, the potentiometric response of the 1,1`-Bis(11-mercaptoundecyl)ferrocene redox couple was found to be the most stable and reproducible in concentrated sulphuric acid. Hence this couple has the potential of measuring the change in the acid concentration corresponding to the state of charge of lead-acid battery. Long term stability of the material in concentrated sulphuric acid, however, is not good. The material survived for only 15 days. Further work on identifying more stable ferrocene couples is needed

Brain-like Flexible Visual Inference by Harnessing Feedback-Feedforward Alignment

In natural vision, feedback connections support versatile visual inference capabilities such as making sense of the occluded or noisy bottom-up sensory information or mediating pure top-down processes such as imagination. However, the mechanisms by which the feedback pathway learns to give rise to these capabilities flexibly are not clear. We propose that top-down effects emerge through alignment between feedforward and feedback pathways, each optimizing its own objectives. To achieve this co-optimization, we introduce Feedback-Feedforward Alignment (FFA), a learning algorithm that leverages feedback and feedforward pathways as mutual credit assignment computational graphs, enabling alignment. In our study, we demonstrate the effectiveness of FFA in co-optimizing classification and reconstruction tasks on widely used MNIST and CIFAR10 datasets. Notably, the alignment mechanism in FFA endows feedback connections with emergent visual inference functions, including denoising, resolving occlusions, hallucination, and imagination. Moreover, FFA offers bio-plausibility compared to traditional backpropagation (BP) methods in implementation. By repurposing the computational graph of credit assignment into a goal-driven feedback pathway, FFA alleviates weight transport problems encountered in BP, enhancing the bio-plausibility of the learning algorithm. Our study presents FFA as a promising proof-of-concept for the mechanisms underlying how feedback connections in the visual cortex support flexible visual functions. This work also contributes to the broader field of visual inference underlying perceptual phenomena and has implications for developing more biologically inspired learning algorithms

The Sum-Eccentricity Energy of A Graph

In this paper, we introduce the concept of the sum-eccentricity matrix of a graph and obtain some coefficients of the characteristic polynomial of the sum-eccentricity matrix of . We also introduce the sum-eccentricity energy of a graph . Sum-eccentricity energies of some well-known graphs are obtained. Upper and lower bounds for are estblished. It is shown that if the sum-eccentricity energy of a graph is rational then it must be an even

Traveling wave solutions for two species competitive chemotaxis systems

In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c∗. We also show the non-existence of such traveling waves with speed less than some critical number c∗0 , which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c∗ = c∗0 , which implies that the minimum wave speed exists and is not affected by the chemoattractant

Competition-exclusion and coexistence in a two-strain SIS epidemic model in patchy environments

This work examines the dynamics of solutions of a two-strain SIS epidemic model in patchy environments. The basic reproduction number $\mathcal{R}_0$ is introduced, and sufficient conditions are provided to guarantee the global stability of the disease-free equilibrium (DFE). In particular, the DFE is globally stable when either: (i) $\mathcal{R}_0\le \frac{1}{k}$, where $k\ge 2$ is the total number of patches, or (ii) $\mathcal{R}_0<1$ and the dispersal rate of the susceptible population is large. Moreover, the questions of competition-exclusion and coexistence of the strains are investigated when the single-strain reproduction numbers are greater than one. In this direction, under some appropriate hypotheses, it is shown that the strain whose basic reproduction number and local reproduction function are the largest always drives the other strain to extinction in the long run. Furthermore, the asymptotic dynamics of the solutions are presented when either both strain's local reproduction functions are spatially homogeneous or the population dispersal rate is uniform. In the latter case, the invasion numbers are introduced and the existence of coexistence endemic equilibrium (EE) is proved when these invasion numbers are greater than one. Numerical simulations are provided to complement the theoretical results.Comment: 35 page