We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.

This work introduces the mathematical framework of the novel “First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (1st-CASAM-NODE)” which yields exact expressions for the first-order sensitivities of NODE decoder-responses to the NODE parameters, including encoder initial conditions, while enabling the most efficient computation of these sensitivities. The application of the 1st-CASAM-NODE is illustrated by using the Nordheim-Fuchs reactor dynamics/safety phenomenological model, which is representative of physical systems that would be modeled by NODE while admitting exact analytical solutions for all quantities of interest (hidden states, decoder outputs, sensitivities with respect to all parameters and initial conditions, etc.). This work also lays the foundation for the ongoing work on conceiving the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-CASAM-NODE)” which aims at yielding exact expressions for the second-order sensitivities of NODE decoder-responses to the NODE parameters and initial conditions while enabling the most efficient computation of these sensitivities.

In the face of the burgeoning electricity demands and the imperative for sustainable development amidst rapid industrialization, this study introduces a dynamic and adaptable framework suitable for policy-makers and renewable energy experts working on integrating and optimizing renewable energy solutions. While using a case study representative model for Sub-Saharan Africa (SSA) to demonstrate the challenges and opportunities present in introducing optimization methods to bridge power supply deficits and the scalability of the model to other regions, this study presents an agile multi-criteria decision tool that pivots on four key development phases, advancing upon established methodologies and pioneering refined computational techniques, to select optimal configurations from a set of Policy Decision Making Metrics (PDM-DPS). Central to this investigation lies a rigorous comparative analysis of variants of three advanced algorithmic approaches: Swarm-Based Multi-objective Particle Swarm Optimization (MOPSO), Decomposition-Based Multi-objective Evolutionary Algorithm (MOEA/D), and Evolutionary-Based Strength Pareto Evolutionary Algorithm (SPEA2). These are applied to a grid-connected hybrid system, evaluated through a comprehensive 8760-hour simulation over a 20-year planning horizon. The evaluation is further enhanced by a set of refined Algorithm Performance Evaluation Metrics (AL-PEM) tailored to the specific constraints. The findings not only underscore the robustness and consistency of the SPEA2 variant over 15 runs of 200 generations each, which ranks first on the AL-PEM scale but also validate the strategic merit of combining multiple technologies and empowering policymakers with a versatile toolkit for informed decision-making.

This article explores the cutting-edge advancement of gypsum and cement building boards infused with shape-stabilized n-octadecane, an organic phase change material (PCM). The primary focus is on improving energy efficiency and providing electromagnetic interference (EMI) shielding capabilities for contemporary buildings. The research investigates the integration of these materials into construction materials, using red-mud Carbon Foam as a stabilizer for n-octadecane (OD@CCF). Various analyses, including microstructural examination, porosity assessment, and additive dispersion, were conducted using X-ray microtomography and density measurements. Thermal conductivity measurements demonstrated the enhancement of composite boards as the OD@CCF content increased, while mechanical tests indicated an optimal additive content of up to 20%. The thermal-regulated capabilities of these advanced panels were evaluated in a custom-designed room model equipped with a homemade environmental chamber, illustrating a consistent temperature environment during heating and cooling cycles. The incorporation of OD@CCF into cement boards exhibited improved thermal energy storage properties. Moreover, the examined composite boards displayed efficient electromagnetic shielding performance within the frequency range of 3.2–7.0 GHz, achieving EMI values of approximately 18 and 19.5 dB for gypsum and cement boards, respectively, meeting the entry-level value required for commercial applications.

In this paper, we first define the concepts of r-fuzzy soft α-open (semi-open and δ-open) sets on fuzzy soft topological spaces based on the article Aygunoglu et al. (Hacet. J. Math. Stat., 43 (2014), 193-208), and the relations of these sets with each other are established. In addition, we introduce the concepts of fuzzy soft δ-closure (δ-interior) operators, and study some properties of them. Also, the concept of r-fuzzy soft δ-connected sets is introduced and studied with help of fuzzy soft δ-closure operators. Thereafter, we define the concepts of fuzzy soft α-continuous (β-continuous, semi-continuous, pre-continuous and δ-continuous) functions, which are weaker forms of fuzzy soft continuity, and some properties of these functions along with their mutual relationships are discussed. Moreover, a decomposition of fuzzy soft α-continuity and a decomposition of fuzzy soft semi-continuity is obtained. Finally, as a weaker form of a fuzzy soft continuity, the concepts of fuzzy soft almost (weakly) continuous functions are defined, and some properties are specified. Additionally, we explore the notion of continuity in a very general setting called, fuzzy soft (L, M, N, O)-continuous functions and a historical justification is introduced.

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system's lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two non parametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets.

A typical halogen-free flame-retardant (HFFR) formulation for electric cables may contain polymers, various additives, and fire-retardant fillers. In this study, composites are prepared by mixing natural magnesium hydroxide (n-MDH) with linear low-density polyethylene (LLDPE) and a few types of ethylene-octene copolymers (C₈-POE). Depending on the content of LLDPE and C₈-POE, we obtained composites with different crystallinity that affected the final mechanical properties. The nucleation effect of the n-MDH and the variations in crystallinity caused by the blending of C₈-POE/LLDPE/n-MDH were investigated. In the C₈-POE/LLDPE blend, we found a decrease in the crystallization temperature of LLPDE compared to pure LLDPE and an increase in the crystallization temperature of C₈-POE compared to pure C₈-POE. On the contrary, the addition of n-MDH led to an increase in the crystallization temperature of LLDPE. As expected, the increase in the crystallinity of the polyolefin matrix of composites led to higher elastic modulus, higher tensile strength, and lower elongation at break. Overall, these results show how to obtain the required mechanical features for halogen-free flame-retardant compounds for electric cable applications depending on the quantities of the two miscible components in the final blend.

Glycosylation, a prevalent post-translational modification, plays a pivotal role in regulating intricate cellular processes by covalently attaching glycans to macromolecules. Dysregulated glycosylation is linked to a spectrum of diseases, encompassing cancer, neurodegenerative disorders, congenital disorders, infections, and inflammation. This review delves into the intricate interplay between glycosylation and protein conformation, with a specific focus on the profound impact of N-glycans on the selection of distinct protein conformations, characterized by distinct interactomes – namely protein assemblies - under normal and pathological conditions across various diseases. We begin by examining the spike protein of the SARS virus, illustrating how N-glycans regulate the infectivity of pathogenic agents. Subsequently, we utilize the prion protein and the chaperone glucose-regulated protein 94 as examples, exploring instances where N-glycosylation transforms physiological protein structures into disease-associated forms. Unraveling these connections provides valuable insights into potential therapeutic avenues and a deeper comprehension of the molecular intricacies that underlie disease conditions. This exploration of glycosylation's influence on protein conformation effectively bridges the gap between the glycome and disease, offering a comprehensive perspective on the therapeutic implications of targeting conformational mutants and their pathologic assemblies in various diseases. The goal is to unravel the nuances of these post-translational modifications, shedding light on how they contribute to the intricate interplay between protein conformation, assembly and disease.

Manzamines are complex polycyclic marine-derived β-carboline alkaloids with reported anticancer, immunostimulatory, anti-inflammatory, antibacterial, antiviral, antimalarial, neuritogenic, hyperlipidemia and atherosclerosis suppression bioactivities, putatively associated with inhibition of glycogen synthase kinase-3, cyclin-dependent kinase 5, and vacuolar ATPases. We hypothesized that additional and yet undiscovered molecular targets might be associated with Manzamine A (MZA) reported pharmacological properties. We report herein for the first time to our knowledge that MZA inhibited a 90kDa ribosomal protein kinase S6 (RSK1) when screened against a panel of 30 protein kinases. Furthermore in vitro RSK kinase assays demonstrated a 10-fold selectivity in potency of MZA against RSK1 versus RSK2. MZA’s differential binding and selectivity toward the two isoforms is also supported by computational docking experiments. Specifically, the RSK1-MZA (N- and C-termini) complexes appear to have stronger interactions and preferable energetics contrary to the RSK2-MZA ones. In addition, our computational strategy suggests that MZA binds to the N-terminal kinase domain of RSK1 rather than the C-terminal domain. RSK is a vertebrate family of cytosolic serine-threonine kinases that act downstream of the ras-ERK1/2 (extracellular-signal-regulated kinase 1/2) pathway, which phosphorylates substrates shown to regulate several cellular processes including growth, survival and proliferation. Consequently, our findings have lead us to hypothesize that MZA and the 80 currently known manzamine-type alkaloids isolated from several sponge genera, may have novel pharmacological properties.