Water is essential to life but many people do not have access to clean and safe drinking water while many even die of water borne bacterial infections. The sanitary quality of stream water cannot be predicted due to behavioral differences of the users and their living condition. This investigation was carried out on the seasonal evaluation of the microbiological quality of Agangwu Stream in Enugu State, Nigeria. A total of eighteen (18) stream water samples collected at wet and dry seasons comprised of six (6) water samples each from the upstream, midstream and downstream locations. They were subjected to a wide range of analytical assessments like the multiple tube fermentation method according to APHA, 2016. Then, the bacteria isolates were characterized and identified morphologically and biochemically using standard microbiological techniques. The dilution pattern showed varying coliform concentration especially for MS¹ (3-0-2) and DS¹ (3-1-2). E. coli, the most common fecal coliform appeared in both seasons with the highest (most probable number) MPN index of 75mpn/100ml (95% confidence limits: 14-230) in dry season and the least MPN index of 1.5mpn/100ml (95% confidence limits: 3 - 44) in wet season. Even though the values were statistically insignificant (P=>0.5). The molecular identification of some of the isolates from the stream water samples confirmed various pathogens, including Salmonella enterica subsp. Enterica, Escherichia coli, etc. The MPN index for both seasons reveal a clear gradient of increasing fecal contamination from upstream to downstream sections of Agangwu Stream. These findings demonstrate that Agangwu stream is definitely not safe for direct human consumption or recreational use without adequate treatment. Rather, there is need for regular monitoring, effective water treatment, and public health interventions to mitigate the risks associated with waterborne diseases.

This system presents the classical Geometric Brownian Motion (GBM) benchmark with constant initial price. The Stochastic Differential Equation (SDE) assumes no deterministic trend, seasonality or regime effects. The simulation results for Fidelity Bank share prices were presented using a constant GBM model with varying sample paths. Four graphical solutions were analyzed to examine path behavior, expected growth, and sensitivity to drift and volatility. The results highlight the interaction between deterministic trend and stochastic noise in shaping Fidelity’s price dynamics. The model serves as a benchmark for market efficiency with no deterministic trend. Also, the existence and uniqueness of the strong solution is proved under standard Lipschitz conditions. This system serves as the null model for comparing the other stochastic systems.

Miniature hearing aids operate under severe constraints in volume, mass, battery capacity, acoustic performance, moisture resistance, and user comfort. This paper investigates whether otherwise dissipated mechanical motion associated with the ear canal and temporomandibular joint can be converted into supplementary electrical energy by piezoelectric transduction. The study uses a physics-based contemporary review and conceptual engineering analysis. Direct piezoelectric constitutive relations, transducer capacitance, open-circuit voltage, time-varying power, mechanical strain energy, resonance, acoustic intensity, storage energy, and end-to-end efficiency are used to establish a quantitative framework. Published in-ear studies demonstrate that jaw-related ear-canal deformation is a measurable mechanical energy source and that flexible PVDF structures can generate electrical output in the microwatt range under defined conditions. A free-field acoustic calculation also shows why ordinary sound alone is a weak source for a hearing-aid-sized capture area. Literature from 2024-2026 emphasizes flexible PVDF-based harvesters, mechanically amplified structures, MEMS integration, and ultra-low-power power-management circuits. The proposed architecture combines a compliant piezoelectric transducer, low-loss rectification, energy buffering, an ultra-low-power power-management unit, and micro-storage or an auxiliary load. The analysis does not support continuous full self-powering of the hearing aid; the more defensible near-term application is battery support, gradual energy accumulation, or intermittent operation of low-power auxiliary electronics. The governing physics establishes plausibility, while experimental validation remains necessary to determine the net energy benefit in a real device.

Many institution-level credential-verification systems generate a random-looking reference code and treat it as secure by virtue of being unique, without examining whether that code is actually resistant to guessing. This paper re-examines a deployed reference-number scheme built for the Academic Document Verification System at Northwest University (NWU), Kano, and shows that its uniqueness suffix - four hexadecimal characters drawn from a UUID4 - carries only 16 bits of entropy (65,536 possible values). We show analytically and by Monte Carlo simulation that, while the system's retry-on-collision loop guarantees no reference is ever issued twice, the same 16-bit space can be exhaustively enumerated against the public verification endpoint in under 11 minutes at a modest 100 requests per second, since no rate limiting is applied. We then design, specify, and analyse a drop-in replacement: an HMAC-SHA256-derived tag computed over the year, document-type, department, and a monotonic serial number, keyed by a server-side secret. At a 48-bit truncation this raises brute-force exhaustion time to an estimated 89,000 years under the same attack rate, at a measured computational cost of 3.2 microseconds per generation or verification - statistically negligible against the system's sub-second query latency. The two schemes are compared against manual, QR-code-based, blockchain-anchored, and zero-knowledge credential-verification approaches reported in the literature on a five-dimension feature matrix, supplemented by a quantitative verification-time comparison. The system was validated through 34 functional test cases (100% pass rate) and an exploratory, formative user-acceptance evaluation (n=8; overall satisfaction 4.5-4.8/5.0, not powered for statistical inference), in which security confidence was the lowest-rated criterion - a finding consistent with, though not statistically proof of, the entropy weakness this paper identifies and addresses. The contribution of this paper is therefore not the verification system as an artefact, but a transferable method for quantifying and closing the guessability gap in identifier-based credential-verification schemes generally.