E. T. Whittaker produced two papers in 1903 and 1904 that, although sometimes considered mere mathematical statements (Barrett, 1993), held important implications for physical theory. The Whittaker 1903 paper united electrostatic and gravitational attraction as resulting from longitudinal waves-waves whose wavefronts propagate parallel to their direction. The Whittaker 1904 paper showed that electromagnetic waves resulted from the interference of two such longitudinal waves or scalar potential functions. Although unexplored, the implications of these papers are profound: gravitational lensing, gravitational waves, the Aharonov-Bohm effect, the existence of a hyperspace above or behind normal space, the elimination of gravitational and point charge singularities, MOND, and the expansion of the universe. This last implication can be related to the recent finding that black holes with posited vacuum energy interior solutions alongside cosmological boundaries have a cosmological coupling constant of k=3, meaning that black holes gain mass-proportional to a 3 in a parameterization equation within a Robertson-Walker cosmology and are a cosmological accelerated expansion species (Farrah et al., 2023). This expansion and many features of General Relativity can be explained by the mass-proportionality and preferred direction of the longitudinal waves within the two underlying non-local Whittaker potentials (Titleman, 2022). Whittaker potential theory also offers a simple explanation for expansion of the universe-it is produced as longitudinal motion within the Whittaker potentials only when dynamic electromagnetism is separate from time-static gravity in intergalactic space.

The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality

This proposal incorporates three experiments concerning perceptual disturbances: one analyzing eye movement and associated electrical activity in hallucinating patients, another assessing dream recall perceptual patients exposed to weak pulsed electromagnetic fields (EMF), perceptual finally the examination of phosphene induction via transcranial magnetic stimulation (TMS) perceptual perceptual eye activity. The direct link between movement noise, noise in and brain’s and activity, and and disturbancescan be established and and analysis and and associated electrical EEG readings electrical electrical in in their differences dream to treatment the control groups. Another pulsed the can the uncovered via the generation the the the the between EMF the of disturbances examination be form of improved of recall. Finally, of effects of TMS on reducing via disturbancesand inducing phosphenes direct link compared within between noise group be related treatment control can group.

Research Proposal: Perceptual Disturbances in Relation to Perceptual and Electrical Noise

The aim of conducting this research was to determine the effect of strategy formulation, implementation and evaluation on the performance of small and medium enterprises. To carry out this study, the researchers have used a descriptive and explanatory research design to determine the relationship and effect of strategic management (strategy formulation, implementation, and evaluation) on performance. The study targeted 152 small and medium enterprises (SMEs) and from these 50 small and medium enterprises (SMEs) were determined as a sample but out of which 4 respondents did not return the questionnaire. Stratified probability sampling method was applied and data were collected from 46 SME managers through structured questionnaire using 5-point Likert scale. Primary data have been edited, classified, organized and coded to get descriptive and inferential statistics outputs using a professional software called Statistical Package for Social Science (SPSS) version 19. Regression analysis was done to determine the effect of strategy formulation, implementation and evaluation on performance and correlation analysis was also conducted to determine the relationship between strategy formulation, implementation, evaluation and performance through inferential statistics. Finally, the finding shows that strategic management practice had a positive effect on performance. However, the only variable that affected performance was strategy implementation. Based on the findings, the researchers have recommended that all enterprises should have a written strategic intent, get training from strategic management consultants/ strategists, involve in training programs prepared by the authorities regarding enterprises and actively engaged in strategic management practice to increase their profit, output, market share, customer satisfaction and reduction of waste.

Strategic Management Practice on Performance of Small and Medium Enterprises (The Case of Gullele Sub City, Addis Ababa, Ethiopia)

This comprehensive survey paper explores the diverse landscape of cryptocurrency forecasting, tracing its evolution from an alternative to traditional monetary systems to its significant growth in the global financial arena. It consolidates existing research by categorizing and analyzing 234 scholarly articles, organizing them into machine learning, deep learning, deep reinforcement learning, and statistical methodologies, and evaluating the related metrics. The case study titled "Examining the performance differences between backtesting and forward testing" highlights the challenges investors face, as strategies that appear effective in backtesting often fail in practical use. Another case study, "Social Data Exploration in Cryptocurrency Trends," examines how social media data can provide insights into market movements and investor sentiment, revealing the impact of social trends on cryptocurrency prices. The findings section provides a detailed view, illuminating trends such as yearly publication rates, methodological distributions, input features, training/testing splits, the total number of data samples considered, and forecasting time horizons. This survey paper serves as a valuable resource, providing researchers and investors with a solid foundation for understanding and navigating the dynamic field of cryptocurrency forecasting.

A Comprehensive Survey of Cryptocurrency Forecasting: Methods, Trends, and Challenges

Sawdust,  by-product of wood processing, poses disposal challenges and environmental concer. This study investigates the valorization of sawdust in construction applications in Cameroon, particularly in the production of particle boards. Following ASTM (D143-09) standards, sawdust from local workshops was analyzed for its physio-mechanical properties. Key findings include variations  in apparent density, thickness swelling, water absorption, and Flexural properties, indicating that sawdust particle boards meet industry standards. The research highlights the potential for sawdust to reduce deforestation and promote sustainable practices in the wood industry

Valorization of Local Waste Materials: Utilizing wood chips in Particle board production. 

This research explores two foundational concepts in complex analysis: the Cauchy Integral Formula and the Residue Theorem. Beginning with a historical and theoretical introduction to complex integration, the study examines the derivation and implications of Cauchy's integral formulas, providing both first and higher-order versions. These formulas not only offer a method for evaluating contour integrals but also reveal the analyticity and differentiability properties of complex functions. The research then transitions to the theory of residues, introducing Laurent series as a framework for analyzing functions with isolated singularities. The residue theorem is developed and applied to evaluate complex integrals efficiently, especially those involving singularities within closed contours. Several illustrative examples and theorems are provided to demonstrate the practical use of these powerful analytical tools in simplifying otherwise difficult integrals. The project emphasizes both the theoretical elegance and the wide applicability of these techniques in mathematics, physics, and engineering.

Cauchy integral formula and Residues 

The purpose of this action research project is to investigate the influence of employing infographics on the development of reflective thinking in fifth-grade mathematics students. In fifth grade, I utilized infographics to teach the operations unit on mixed numbers. The study's sample size was supposed to be 38 fifth-grade pupils, but due to the teachers' strike in public schools, the sample size was reduced to one.

This study looked at how infographics may be used to motivate and strengthen observation and judgment abilities. Teacher observations, interviews, and assessments were used to collect data. According to the data analysis, the infographics enhanced and strengthened students' deep comprehension of rational number ideas and operations on them.

This study found that infographics had a good influence on reflective thinking. Students began studying, relating, and comprehending the infographics, as well as applying the information from them to solve issues by making judgments and even generalizations for their replies. In a nutshell, the students began to practice reflective thinking.

Following this, the students began to ask more in-depth inquiries. They also began producing and Analyzing infographics for the course. Students' performance improved as a result of their increased grasp of the content. They began to outperform their predecessors in terms of grades. As a result, their enthusiasm and attitudes toward mathematics improved.

As a math instructor, I would advise every teacher to apply the infographics employed in this study to enhance the condition of their classroom, assist students in making academic progress, and make students love what they are studying.

Finally, this study marked the start of my research journey to enhance my teaching skills and upgrade my teaching style and strategies.

Utilizing Infographics to Improve 5th-grade Students' Reflective Thinking Practices

The differential transformation method (DTM) was first introduced by Zhou 37 years ago. This method is a semi-analytical numerical method for solving homogeneous or inhomogeneous linear ordinary differential equations. Indeed, the differential transform method is based on Taylor series expansion in a different way, in which the differential equation is turned into a recurrence relation to provide a series solution in terms of polynomials. This research is concerned with the differential transformation method for both ordinary and partial differential equations. To solve initial value and boundary value problems for ordinary differential equations, we use the one-dimensional differential transform technique. Furthermore, we present new modifications to the differential transformation method that improve its algorithm. The differential transformation method is capable to reduce the size of calculations and handles homogeneous or inhomogeneous linear ordinary differential equations directly. Seven examples are considered for the numerical illustrations of this method. The results demonstrate the reliability and efficiency of this method for such problems.

Using The Differential Transformation Method (DTM) to Solving Ordinary Differential Equations

Metacognition, or the ability of a system to reason about its own cognitive processes, is increasingly recognized as an essential component for the development of robust, adaptable, and safe artificial intelligence (AI) systems. However, current computational approaches to metacognition remain fragmented, divided between classic symbolic architectures, which offer explicit control but can be brittle, and modern sub-symbolic models, which demonstrate flexible learning but lack transparency and reliable self-assessment mechanisms. This paper addresses this "Metacognitive Gap" by proposing a balanced path forward: a Hybrid and Hierarchical Metacognitive Architecture (HHMA). The HHMA is a novel framework that integrates principles from cognitive psychology and computer science to create a multi-level system. The lowest level of the architecture (Level 1) implements probabilistic monitoring, inspired by Bayesian models of human metacognition, to generate fast, continuous signals of confidence and uncertainty about the performance of the core cognitive system (Level 0). The highest level (Level 2) uses a symbolic reasoning engine, informed by a declarative model of the agent itself, to perform explicit diagnostics and exert strategic control. It is argued that this hybrid structure, which computationally implements dual-process theory, reconciles the strengths of competing paradigms. By combining sub-symbolic monitoring with symbolic control, the HHMA offers a promising path to improve the adaptability, explainability, and safety of AI, addressing some of the most pressing challenges in the field of assured autonomy and human-machine collaboration.

1. Hierarchical Separation of Concerns: It is recognized that different computational paradigms are better suited for different types of tasks. The HHMA assigns these tasks to distinct layers. Learning from high-dimensional, noisy data is relegated to sub-symbolic components, while deliberate reasoning and strategic decision-making are managed by symbolic components. 2. Probabilistic Monitoring: Uncertainty is an inescapable feature of cognition and

Towards a Balanced Metacognitive Model for Artificial Intelligence: A Hybrid and Hierarchical Architecture

A foundational challenge in neuroscience is the "binding problem": how the brain integrates disparate neural signals into a unified conscious experience with near-instantaneous coherence, a feat that appears to exceed the temporal limits of classical electrochemical signaling. This paper introduces a novel, testable hypothesis positing that the myelin sheath, traditionally viewed as a passive electrical insulator, functions as an active quantum optical component. Drawing upon recent theoretical models in cavity quantum electrodynamics (QED), we propose that the cylindrical structure of myelin acts as a biological resonant cavity, facilitating the generation and preservation of entangled bio-photon pairs via cascade emission from C-H bond vibrations in lipid molecules. This mechanism could establish a non-local, instantaneous communication network supplementing classical axonal conduction. We present a comprehensive, phased experimental roadmap to validate this hypothesis, beginning with Finite-Difference Time-Domain (FDTD) computational modeling, followed by in vitro verification using advanced neurophotonic techniques, including Hanbury Brown and Twiss interferometry and Bell's inequality tests on co-cultures of myelinated neurons. If validated, this research would not only offer a physical substrate for solving the binding problem but also establish a new paradigm for understanding neural computation, provide novel quantum-based biomarkers for demyelinating diseases, and present a robust biological system for studying quantum coherence in complex, "warm, wet, and noisy" environments.