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In this paper, we study the soliton solutions of the fourth-order nonlinear partial differential equations (NPDE). The Riccati-Bernoulli (RB) sub-ODE method is applied to the fourth-order NPDE to investigate the exact and traveling wave solutions. We secure singular periodic wave solutions, kink-type soliton solution, dark soliton and singular soliton solution, which have unlimited application in mathematical physic, science and engineering. Some figures for the obtained solutions are demonstrated.

This paper studies commutativity of sixth-order differential systems with zero and nonzero initial conditions (ICs). Given a sixth-order differential system A, we find its commutative pair, that is a new differential system B of order m≤6; the obtained result will be used to show the input–output equivalency between the cascaded-connected systems AB and BA. Necessary and sufficient conditions for commutativity of sixth-order continuous-time linear time-varying systems (CTLTVSs) are derived. Based on our findings, we discovered that only a small group of sixth-order CTLTVSs has commutative pairs other than their feedback conjugates obtained by constant feedback and forward path gains. The explicit results obtained in this paper will help to fill the gap on commutativity theory, system behaviors which has significant application to science and play an important role in engineering. This research will also address the problems of sensitivity due to changes in ICs or parameters, and also disturbance as a result of external noise. The results are well verified by examples as well as validated by Matlab Simulink tool and Wolfram Mathematica 11.

Decomposition is an important tool that is used in many differential systems for solving real engineering problems and improving the stability of a system. It involves breaking down of high-order linear systems into lower-order commutative pairs. Commutativity plays an essential role in mathematics, and its applications are extended in physical science and engineering. This paper explicitly expresses all form of necessary and sufficient conditions for decomposition of any kind of fourth-order linear time-varying system as commutative pairs of two second-order systems. Regarding the nonzero initial conditions, additional requirements are derived in order to satisfy the decomposition process. In this paper, explicit method for reducing fourth-order linear time-varying systems (LTVS) into two second-order commutative pairs is derived and solved. The method points out the effect of disturbance and sensitivity on the systems and also highlights the necessary and sufficient conditions for commutativity of the decomposed systems. The results are illustrated by solving some examples.

This paper presents decomposition of the fourth-order Euler-type linear time-varying system (LTVS) as a commutative pair of two second-order Euler-type systems. All necessary and sufficient conditions for the decomposition are deployed to investigate the commutativity, sensitivity, and the effect of disturbance on the fourth-order LTVS. Some systems are commutative, and some are not commutative, while some are commutative under certain conditions. Based on this fact, the commutativity of fourth-order Euler-type LTVS is investigated by introducing the commutative requirements, theories, and conditions. The fourth-order Euler-type LTVSs are investigated into commutative pairs of twice Euler-type second-order linear time-varying systems (LTVSs). The decomposition theories and conditions are derived, proved, and solved to simplify the use of commutativity for practical and industrial uses. Some fourth-order systems are sensitive toward change in initial conditions or parameters while others are not, and the effect due to disturbance also varies within systems. Furthermore, the stability and robustness of systems have so many issues. But we consider fourth-order Euler-type LTVS to observe, investigate, and tackle these issues. Lastly, the realization of fourth-order LTVS from cascaded two second-order systems can be laboratory experimented which is an open problem for future engineers to investigate. However, the theoretical results show a good agreement with the simulation results is considered in this work. Perhaps it might have unlimited physical applications in science and engineering as well as theoretical contribution. But beyond any reasonable doubt, the novelty is guaranteed because this study is the first of its kind that introduces the decomposition of the fourth-order Euler-type linear time-varying system (LTVS) as a commutative pair of two second-order Euler-type systems. Illustrative examples are presented to support the results.

The Tiga Dam, a primary hydraulic structure in northern Nigeria, is subjected to intense hydrological stress during the rainy season, posing potential risks to its structural integrity. This study investigates the geotechnical properties and stability of the Tiga Dam in Kano State, Nigeria. Twelve soil samples from the downstream area were analyzed for specific gravity, grain size distribution, Atterberg limits, compaction parameters, permeability, and shear strength. The dam’s stability was assessed using Plaxis 2D under various reservoir conditions. Soil erodibility was evaluated using the Revised Universal Soil Loss Equation (RUSLE), and a linear regression model with noise was developed to predict soil expansion rates. The results showed heterogeneous soil properties, with specific gravity ranging from 2.11 to 2.63 and permeability from 3.40 × 10−9 to 1.49 × 10−7 m/s. Stability analysis revealed factors of safety of 1.322, 1.006, 1.002, and 1.147 for high reservoir, rapid drawdown, slow drawdown, and low reservoir conditions, respectively. The RUSLE K factor ranged from 0.055 to 0.145, indicating low to moderate soil erodibility. The expansion rate model demonstrated high accuracy (R2 = 0.989) in predicting seasonal and long-term soil expansion trends, with peak rates increasing from 16.94 mm/month in 2010–2013 to 19.45 mm/month in 2017–2020. This comprehensive analysis provides crucial insights into the Tiga Dam’s geotechnical behavior, highlighting potential vulnerabilities and the need for targeted management strategies to ensure long-term stability and safety.

The Benjamin-Bona-Mahony (BBM) equation is a nonlinear partial differential equation that describes the propagation of long waves in a shallow water channel. In this work, we present a comprehensive solution for the BBM equation using the Riccati-Bernoulli sub-ODE method. The method involves transforming the BBM equation into a Riccati equation, which is then further transformed into a Bernoulli equation. The Bernoulli equation is then solved analytically, and the solution is used to obtain the solution for the original BBM equation. Our results show that the Riccati-Bernoulli sub-ODE method provides an efficient and accurate solution for the BBM equation. The dfmethod can be extended to solve other nonlinear partial differential equations (NPDEs), making it a valuable tool for researchers in various fields.

As long as the genetically modified crops are gaining attention globally, their proper approval and commercialization need accurate and reliable diagnostic methods for the transgenic content. These diagnostic techniques are mainly divided into two major groups, i.e., identification of transgenic (1) DNA and (2) proteins from GMOs and their products. Conventional methods such as PCR (polymerase chain reaction) and enzyme-linked immunosorbent assay (ELISA) were routinely employed for DNA and protein based quantification respectively. Although, these Techniques (PCR and ELISA) are considered as significantly convenient and productive, but there is need for more advance technologies that allow for high throughput detection and the quantification of GM event as the production of more complex GMO is increasing day by day. Therefore, recent approaches like microarray, capillary gel electrophoresis, digital PCR and next generation sequencing are more promising due to their accuracy and precise detection of transgenic contents. The present article is a brief comparative study of all such detection techniques on the basis of their advent, feasibility, accuracy, and cost effectiveness. However, these emerging technologies have a lot to do with detection of a specific event, contamination of different events and determination of fusion as well as stacked gene protein are the critical issues to be addressed in future.

Subclinical mastitis is an important constraint to small ruminant productivity and a public health concern due to its association with antimicrobial-resistant bacteria. However, information on the prevalence of subclinical mastitis and antimicrobial resistance patterns of associated bacterial pathogens in sheep and goat in Northern Nigeria, particularly Kaduna State, remains limited. A cross-sectional study was conducted between August-October 2024 in Igabi Local Government Area, Kaduna, Nigeria. Milk samples were collected from 488 lactating small ruminants (384 goats, 104 sheep) from farms, households, and markets. Subclinical mastitis was screened using the California Mastitis Test (CMT). Bacterial isolates were recovered from the milk samples and identified using standard cultural and biochemical methods, and antimicrobial susceptibility testing was performed using the Kirby-Bauer disk diffusion method. In addition to commonly used veterinary antimicrobials, imipenem was included to assess resistance to critically important antimicrobials of last resort. Overall, 41.0% (200/488) of animals were positive for subclinical mastitis, with a significantly higher prevalence in sheep (96.2%; 100/104) than in goats (26.0%; 100/384) (χ²=163.44, p  < 0.0001). Bacterial isolates were identified from milk samples of all 488 animals using standard cultural and biochemical methods. A total of 705 bacterial isolates were recovered. The predominant isolates were Staphylococcus aureus (49.5%; 349/705) and Escherichia coli (48.0%; 338/705), while Streptococcus species accounted for 2.6% (18/705). The bacterial isolates showed the highest susceptibility to ciprofloxacin with 92.7–98.9% of Escherichia coli , 85.5–95.0% of Staphylococcus aureus , and 100% of Streptococcus species isolates being susceptible. High resistance was observed to tetracycline (82.6–100%), cefuroxime (88.6–100%), and imipenem (99.6–100%). All isolates exhibited MDR (100%), with MAR indices ranging from 0.20 to 1.00, predominantly 0.80–0.90. The high burden of subclinical mastitis and widespread multidrug resistance among small ruminants in Igabi LGA highlight significant animal health and public health risks. These findings underscore the need for routine mastitis surveillance and strengthened antimicrobial stewardship in small ruminant production systems.

Diabetic retinopathy is one of the leading diseases affecting eyes. Lack of early detection and treatment can lead to total blindness of the diseased eyes. Recently, numerous researchers have attempted producing automatic diabetic retinopathy detection techniques to supplement diagnosis and early treatment of diabetic retinopathy symptoms. In this manuscript, a new approach has been proposed. The proposed approach utilizes the feature extracted from the fundus image using a local extrema information with quantized Haralick features. The quantized features encode not only the textural Haralick features but also exploit the multiresolution information of numerous symptoms in diabetic retinopathy. Long Short-Term Memory network together with local extrema pattern provides a probabilistic approach to analyze each segment of the image with higher precision which helps to suppress false positive occurrences. The proposed approach analyzes the retina vasculature and hard-exudate symptoms of diabetic retinopathy on two different public datasets. The experimental results evaluated using performance matrices such as specificity, accuracy, and sensitivity reveal promising indices. Similarly, comparison with the related state-of-the-art researches highlights the validity of the proposed method. The proposed approach performs better than most of the researches used for comparison.

In this work, we realised the soliton solutions of nonlinear Schrödinger equation (NLSE) that arise from optical fibers, we considered the modified Sardar sub-equation method (MSSEM) to find solitary solutions analytically. The stability of the retrieved soliton solutions realised from the NLSE are investigated. We demonstrate the soliton solutions that are stable and can last for a very long time without losing its form or energy under specific circumstances and those soliton solutions that are unstable. The MSSEM is a frequently employed technique in research for addressing specific mathematical modeling or physical phenomena problems. Its selection in this specific study might stem from its proven efficacy in handling the particular problem under investigation. The decision to utilize MSSEM could be driven by several considerations, including its precision, computationally efficient, effectiveness, greater accuracy and capability to manage intricate systems. Finally, our method offers greater flexibility in modeling various physical phenomena, which makes it particularly useful in applications in diverse fields such as quantum mechanics and nonlinear optics. The findings have ramifications for the architecture of optical fiber communications and offer significant new insights into the behavior of solitons in optical systems. The NLSE has proven to be an effective tool for understanding wave behavior in fiber optics. Its applications have helped engineers and scientists optimize the design of optical fibers and predict the behavior of various conditions. Moreover, our study provides insights into the fundamental properties of solitary solutions in the NLSEs and their practical implications in physical systems.