Paving blocks are concrete pieces placed in exposed places to the weather, which are sub-jected to loads and wear. Hence, quality control in the manufacture of paving blocks is es-sential to guarantee the properties and durability of the product in construction projects. In Ecuador, the requirements are described in the Ecuadorian technical standard "NTE INEN 3040", and tensile splitting strength is a fundamental requirement to guarantee product quality. It is analyzed using quality control measurements such as dimensions, the weight of the fresh paving block in the vibro-compacted process, and the percentage of water absorption in order to know how the variables influence and manage to predict the tensile splitting strength to avoid product non-conformity in advance, having a timely and better control of the manufacturing process. The data was obtained from a company that can produce 30 000 units per day of rectangular paving blocks with 6 cm thickness. Mul-tivariate models such as multiple linear regression, regression trees, random forests and neural networks are performed to predict the tensile splitting strength variable through two groups of predictors; the first group is the thickness mm, width mm, length mm, mass of fresh paving block g and percentage of water absorption %. The second group of pre-dictor variables is the density of the fresh paving block kg/m3 and the percentage of water absorption %. It is concluded that the multiple linear regression method performs better in predicting the first group of predictor variables with a mean square error (MSE) of 0.110086, followed by the neural network without hidden layers resulting in an MSE of 0.112198. The best method for the second set of predictors was the neural network with-out hidden layers with a mean square error ( MSE ) of 0.112402, closely followed by the multiple linear regression model with an MSE of 0.115044.

The results of physico-chemical studies of individual fruit parts, including crusts, partitions, juice and seeds themselves, extracted from immature (green), unripe and mature fruits of three harvest periods are presented: 20.VII, 01.IX and 15.X. The analyses were carried out in 2019-20 during the period of active growth and ripening of fruits in the varieties Spring, Iridanaly, Guleisha pink and wild pomegranate from the Geokchay region (Azerbaijan) using standard and generally accepted physico-chemical methods. The ripe fruit (130-288 g) consisted of 60-113% of the peel (peel together with partitions), 53-140% of the juice and 17-85% of the seeds themselves. The edible part of the ripened fruits (53.85-73.2 of the total weight of the fruit) consisted of 58.54-78.65% juice and 21.35 -41.46% seeds, fresh juice contained 15.7-17.7% solids, including 12.04-13.84% sugar, 0.17-0.30% protein, 0.15—0.23% pectin, 0.30-0.40% ash and 0.26-0.57% total polyphenols. The concentrations of solids, protein, ash and total polyphenols in the seeds themselves, remaining after the extraction of juice from the grains of ripe fruits, were 50.0-58.2, 4.13-5.75, 0.60-1.0 and 0.08-0.32%, respectively. There were fewer total polyphenols, flavonoids, chlorogenic acids, catechins and leucoanthocyanins in ripe fruits, and more ascorbic acid, anthocyanins and proanthocyanidins than in unripe ones. The period from the second half of July to the beginning of September is the time of a real “boom” of common polyphenols.

High temperature Ni-superalloys are limited by reliance on critical elements and complex processing steps. High entropy alloys (HEAs) have demonstrated stable single/dual phase microstructures with strong ordering tendencies. A dual phase (FCC+BCC) Al0.5Co0.5CrFeNi1.5Ti0.25 alloy (developed using CALPHAD) was tested for room and high temperature compression behavior. The microstructure mainly comprises of coarse ordered FCC(L12) surrounding decomposed lamellae of ordered FCC(L12) and BCC(L21) phases, which coarsened upon annealing at high temperature (1100 °C) into a bi-continuous structure of disordered FCC+BCC(B2). Additionally, cold rollability of the cast alloy increased from <5% to ~40% after annealing, with a corresponding softening observed in room temperature compression mainly due to disordering of FCC and BCC phases. Peak flow stresses of 793.45MPa, 535.12MPa, and 324.40MPa were achieved at 800oC, 900oC, and 1000oC respectively for the high temperature annealed alloy.

The study of the surface thermodynamic properties of solid materials is primordial for the determination of the dispersive surface energy, polar enthalpy of adsorption and Lewis’s acid base properties of solid particles. Inverse gas chromatography technique (IGC) at infinite dilution is the best surface technique for the determination of the surface physicochemical properties of materials. (1) Background: This paper was devoted to study the surface properties of solid materials such as alumina particles by using IGC technique. (2) Methods: Different methods and molecular models such as spherical, cylindrical, van der Waals, Redlich-Kwong, Kiselev and geometric models, were used to determine the London dispersive surface energy of solid surfaces. Hamieh model was also used and highlighted the thermal effect on the surface area of solvents. (3) Results: The variations of the dispersive surface energy and the free energy of adsorption were determined for alumina particles as a function of the temperature as well as their Lewis’s acid base constants. Alumina surfaces were proved to exhibit a strong Lewis amphoteric character three time more basic than acidic (4) Conclusions: The new methodology based on Hamieh model gave the more accurate results of the physicochemical properties of the particle surfaces.

The article obtains large deviation asymptotic for sub-critical communication networks modelled as signal-interference-noise-ratio(SINR) random networks. To achieve this, we define the empirical power measure and the empirical connectivity measure, as well as prove joint large deviation principles(LDPs) for the two empirical measures on two different scales. Using the joint LDPs, we prove an Asymptotic equipartition property(AEP) for wireless telecommunication Networks modelled as the subcritical SINR random networks. Further, we prove a Local Large deviation principle(LLDP) for the sub-critical SINR random network. From the LLDPs, we prove the large deviation principle, and a classical McMillan Theorem for the stochastic SINR model processes. Note that, the LDPs for the empirical measures of this stochastic SINR random network model were derived on spaces of measures equipped with the $\tau-$ topology, and the LLDPs were deduced in the space of SINR model process without any topological limitations. We motivate the study by describing a possible anomaly detection test for SINR random networks.

In this work we identify combinations of technological activities that signal the presence local capabilities in a country to successfully export a product. We use country-level patent and trade data to generate a multi-layer network, and we apply maximization of entropy to generate synthetic data to effectively divide signal from noise. We show that in several sectors the signal far exceed the noise. Our exercise provides robust evidence of the presence of synergies between technologies to explain trade performances in specific markets. This can be highly useful for policy makers, to inform industrial and innovation policies.

Neck circumference (NC), neck circumference to height ratio (NHtR) and neck circumference to weight ratio (NWtR) appear to be good candidates for the non-invasive management of non-alcoholic fatty liver disease (NAFLD). This study aimed to evaluate the ability of routine variables to assess and manage NAFLD in participants with obesity and NAFLD included in a 2-year nutritional intervention program. Anthropometric measurements, biochemical variables and imaging techniques were performed at different study time-points (baseline, 6, 12 and 24 months). The nutritional intervention significantly improved all anthropometric measurements as well as the glucose profile and the hepatic enzymes. NC and neck ratios combined with ALT levels and HOMA-IR showed good prediction ability for the hepatic fat content and hepatic steatosis at all the study time-points in a ROC analysis. The prediction ability of the combination panels improved when the weight loss variable was also considered. NC and neck ratios are easy anthropometric measurements that in combination with routine biochemical variables (ALT and HOMA-IR) showed good prediction ability of NAFLD. More research studies are necessary to validate the utility of these simple and easy variables as surrogate markers of NAFLD since their application could improve the prevention and management of this prevalent disease.

The self-assembly is an intriguing process of great importance in general soft matter and thus re-ceives an ever-growing scientific interest. Its most trivial example is the entropy-driven crystalli-zation of hard spheres. Past works have established the similarities and differences in the phase behavior of monomers and chains made of hard spheres. In the present work, inspired by the dif-ference in the melting points of the pure components, we study, through Monte Carlo simulations, the phase behavior of athermal mixtures composed of fully flexible polymers and individual monomers of uniform size. We analyze how the relative number fraction and the packing density affect crystallization and the established ordered morphologies. A synergetic effect is observed in the crystallization leading to synchronous crystallization of the two species. Structural analysis of the resulting ordered morphologies shows perfect mixing and thus no phase separation, which could split the system into polymer-rich and monomer-rich domains. Due to the constraints imposed by chain connectivity, the local environment of the individual spheres is systematically more spherical and more symmetric compared to the one of spheres belonging to chains. In general, increasing polymer content leads to reduction of the degree of crystallinity. According to the present findings, relative concentration is another determining factor to control the phase behavior of hard colloidal systems based on polymers.

The rapid convergence of Artificial General Intelligence (AGI), autonomous drones, and applied robotics presents a transformative opportunity for many sectors. However, this advancement also raises critical ethical and existential questions, particularly in warfare. This paper explores the concept of entropy as a metaphor for the potential disorder introduced by these increasingly complex technologies. We examine the risks of AGI surpassing human control in conflict situations, where autonomous decision-making could have disastrous consequences. We then analyze autonomous drones, scrutinizing their impact on warfare tactics and the ethical dilemmas surrounding independent, real-time decision-making. Finally, we investigate applied robotics in military operations, focusing on the delicate balance between enhanced capabilities and the potential for uncontrollable systems. Through a multidisciplinary lens, drawing on technology ethics, military strategy, and AI safety, this paper utilizes the concept of entropy to highlight the need for caution in developing these technologies. We propose a scientifically grounded and ethically sound framework to guide policymakers, technologists, and ethicists in navigating the path between innovation and global stability. This framework concludes with recommendations for responsible development and deployment strategies that can mitigate the risks associated with these powerful tools.

The theory of Ismail's non-extensive maximum entropy solution (NME) is described in detail. It is used as an inductive inference technique for heavy-tailed queues with a non-robust mean queue length and a non-extensive "long-range" interaction. In our novel method, we substitute the non-robust mean queue length for the conventional Pollaczeck-Khinchin mean queue length. In other words, the new non-extensivity parameter q will be included in the resulting state probability function. Numerical portraits are provided to capture the influential effect of the derived formalism, , on the stable M//1 queue with heavy tails. More potentially, some applications of Hurst Exponent to social computing and connected health are provided. Conclusion with some challenging open problems and possible future research pathways are given.

My innovative entropy measure, Ismail entropy, namely, (IE) is an ultimate generalization to numerous generalized entropies within the literature. The fractal dimension of IE is identified in this paper. On another applicative note, this paper offers some potential applications of fractal dimension to smart cities. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.

The temporo-spatial theory of consciousness postulates that the brain implements its own inner time and space for conscious processing of outside world. In line with this hypothesis, I present a mechanistic model of mutually connected processes that encode the inner space and time. The model is used to elaborate the binding mechanism between two sets of processes representing the inner space and time, respectively. Further, a stochastic version of the model is developed to investigate the interplay between the binding strength and noise. The spectral entropy is used to characterize the noise effects on the systems of processes when the binding strength is varied. The stochastic modeling results reveal that the spectral entropy values for strongly bound systems have similar entropy values for weakly bound or even decoupled systems. Thus, the analysis performed in this study allows to conclude that the binding mechanism is noise-resilient.

In this paper, the problem of predicting future failure times based on a jointly type-II censored sample from k exponential populations is considered. The Bayesian prediction intervals and point predictors were then obtained. Generalized Bayes is a Bayesian study based on a learning-rate parameter. This study investigated the effects of the learning rate parameters on the prediction results. The loss functions of squared error, Linex, and general entropy were used as point predictors. Monte Carlo simulations were performed to show the effectiveness of the learning rate parameter in improving the results of prediction intervals and point predictors.

Black hole temperature T_BH = T_P/2πd as a function of its Planck length real diameter multiplier d is derived from black hole surface gravity and Hawking temperature w.l.o.g. It is conjectured d = 1/2π describes primordial Big Bang singularity as in this case T_BH = T_P. A black hole interacts with the environment and observable black holes have uniquely defined Delaunay triangulations with a natural number of spherical triangles having Planck areas (bits), where a Planck triangle is active and has gravitational potential of -c² if all its vertices have black hole gravitational potential of -c²/2 and is inactive otherwise. As temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy a black hole is a fundamental, one-sided thermodynamic equilibrium limit for a dissipative structure. Black hole blackbody radiation, informational capacity fluctuations, and quantum statistics are discussed. On the basis of the latter, wavelength bounds for BE, MB, and FD statistics are derived as a function of the diameter multiplier d. It is shown that black holes feature wave-particle duality only if d ≤ 8π, which also sets the maximum diameter of a totally collapsible black hole. This outlines the program for research of other nature phenomena that emit perfect blackbody radiation, such as neutron stars and white dwarfs.

There are currently around 78 Nuclear Power Plants (NPP) in the world based on Boiling Water Reactors (BWR). The current parameter to assess BWR instability issues is the linear Decay Ratio (DR). However, it is well known that BWRs are complex non-linear dynamical systems that may even exhibit chaotic dynamics that normally preclude the use of the DR when the BWR is working at a specific operating point during instability. In this work a novel methodology based on an adaptive Shannon Entropy estimator and on Noise Assisted Empirical Mode Decomposition variants is presented. This methodology was developed for real-time implementation of a stability monitor. This methodology was applied to a set of signals stemming from several NPPs reactors (Ringhals-Sweden, Forsmark-Sweden and Laguna Verde-Mexico) under commercial operating conditions, that experienced instabilities events, each one of a different nature

This paper constitutes an original and new methodology for the determination of the surface properties of carbon fibers in the two oxidized and untreated forms by inverse gas chromatography technique at infinite dilution based on the effect of the temperature on the surface area of the various organic molecules adsorbed on the carbon fibers. The studied thermal effect proved a large deviation of the classical methods or models relative to the new determination of the surface properties of carbon fibers, such as the dispersive component of their surface energy, the free surface energy, the free specific energy, the enthalpy and entropy of adsorption of molecules on the carbon fibers. The obtained specific enthalpy and entropy of adsorption for the polar solvents led to the determination of the Lewis’s acid-base constants of carbon fibers. Different molecular models and chromatographic methods were used to quantify the surface thermodynamic properties of carbon fibers and compared to the thermal model. The obtained results proved that the oxidized carbon fibers gave more specific interaction energy and greater acid-base constants than that of the untreated carbon fibers and thus highlighting the important role of the oxidization on the acid-base of fibers. The determination of the specific acid-base surface energy of the two carbon fibers showed greater values of the oxidized carbon fibers relative to the untreated carbon fibers. An important basic character was highlighted for the two studied carbon fibers, larger than the acidic character. It was observed that the Lewis’s acid-base constants of the oxidized carbon fibers are larger than that of the untreated fibers with more accentuated basic charterer. This result was confirmed by all molecular models and chromatographic methods.

Computationally modelling a nuclear reactor startup core for a benchmark against the existing models is highly desirable for an independent assessment informing nuclear engineers and energy policymakers. This work presents a startup core model of the UK’s first Evolutionary Pressurised Water Reactor (EPR) based on Monte Carlo simulations of particle collisions using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup code. Coupling between neutronics and thermal-hydraulic conditions with the fuel depletion is incorporated into the multi-dimensional branches, obtaining the thermal flux and fission rate (power) distributions radially and axially from the three dimensional (3D) single assembly level to a 3D full core. Shannon entropy is employed to characterise the convergence of the fission source distribution, with 3 billion neutron histories tracked by parallel computing. Source biasing is applied for the variance reduction. Benchmarking the proposed Monte Carlo 3D full-core model against the traditional deterministic transport computation suite used by the UK Office for Nuclear Regulation (ONR), a reasonably good agreement within statistics is demonstrated for the safety-related reactivity coefficients, which creates trust in the EPR safety report.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

Ontological premises have profound theoretical implications. This analysis posits a single, universal structure composed of two ontic entities: discrete, quantized units of space ("Planck Spheres") and a State of Absolute Nothingness (the "SOAN"). Planck Spheres and the SOAN form a physical, ultra-high (3 x N) dimensional space ("Planck Space") and a discrete 3D space (or "4D spacetime"). Together, Planck Space and 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the "Dual Ontology"). Critically, a one-to-one mapping and identity exists between the Planck Spheres comprising 4D spacetime and Planck Space. The Dual Ontology conjecture supports radically simplified physical explanations for three distinct areas of theoretical physics: First, the conjecture reconciles fundamental issues in Special Relativity and quantum mechanics by explaining why single and N-body quantum states (a) dynamically evolve in 4D spacetime subject to the speed of light and (b) instantaneously collapse in a physical Planck Space that is not subject to Special Relativity. Second, the temporal and physical asymmetry between the dynamic evolution of quantum states in 4D spacetime subject to Special Relativity and the instantaneous collapse of quantum states in a Planck Space where Special Relativity is inapplicable explains quantum path irreversibility and the arrow of time. Third, at or near the heat death of 4D spacetime, the instantaneous collapse of the energy content of Planck Space and the simultaneous transition of 4D spacetime's extremely widely dispersed energy content to a non-singular, generally localized volume at t = 0 explains 4D spacetime's isotropy, homogeneity, extremely high energy, pressure, and temperature, flatness, and low gravitational entropy. It also explains the horizon and fine-tuning problems.

In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. The doping-induced and concentration-dependent phase transition of zirconium dioxide under the influence of yttrium oxide was studied, after which the position of the Fermi level changes and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of -0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The calculations showed that ab initio research methods are capable of describing the mechanism of phase transitions of materials under the influence of alloying. That is, by optimizing the parameters of DFT calculations, it is possible to observe the effects of doping on other physical and chemical properties of materials, which are still beyond the scope of quantum chemical modeling. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.

We present results on the spontaneous crystallization of freely-jointed polymers of hard spheres obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous configuration and after a transitory dominance of the hexagonal closed packed (HCP) polymorph, the system crystallizes in a final, stable, face centered cubic (FCC) crystal of very high perfection. Through refined metrics we gauge the degree of ordering and identify the regions of the phase transition and the corresponding morphologies. An analysis of chain conformational characteristics, of the spatial distribution of monomers and of the volume accessible to them shows that the phase transition is caused by an increase in translational entropy that is larger than the loss of conformational entropy of the chains in the crystal compared to the amorphous state. Polymer chains in the crystal adopt ideal random walk statistics as their great length renders local conformational details, imposed by the geometry of the FCC crystal, irrelevant.

According to the current European and Italian scenario related to urban re-generation, cultural and landscape heritage, valorisation is being also enhanced by the activation of innovative processes. These involve the development of methodologies and tools that are able to address decision-making processes among low entropy economy, complex values and creative practices. In this perspective, the research aims to investigate the possibilities of developing a Cultural Heritage Low Entropy Enhancement (CHLEE) approach by considering how the complex values of cultural heritage can vary not only through a physical transformation of spaces but also through a program of uses and activities able to produce new values, where the human experience is essential. This type of model modifies the objectives that characterise the valorisation of cultural heritage and landscape, recognising that the fruition is no longer “consumerist” but “experiential”. A crucial role is represented by the heterogeneity of creative practices that contribute to the identificationidentifying and implementation ofimplementing innovative management and governance models. The present paper explores the components of creative regenerative processes, based upon the ex-post evaluation of some Italian experiments, across the PROMETHEE-GAIA multi-criteria method, to understand how creative experiences are building innovation ecosystem thanks to low entropy economy and improve the ex-ante evaluation for new strategies and policies.

In this paper we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau's symplectic model of statistical mechanics, its polysymplectic extension, Koszul model, and approaches developed in quantum information geometry. We emphasize the role of equivariance with respect to Lie group actions and the role of several concepts from geometric mechanics, such as momentum maps, Casimir functions, coadjoint orbits, and Lie-Poisson brackets with cocycles, as unifying structures appearing in various applications of this framework to information geometry and machine learning. For instance, we discuss the expression of the Fisher metric in presence of equivariance and we exploit the property of the entropy of the Souriau model as a Casimir function to apply a geometric model for energy preserving entropy production. We illustrate this framework with several examples including multivariate Gaussian probability densities, and the Bogoliubov-Kubo-Mori metric as a quantum version of the Fisher metric for quantum information on coadjoint orbits. We exploit this geometric setting and Lie group equivariance to present symplectic and multisymplectic variational Lie group integration schemes for some of the equations associated to Souriau symplectic and polysymplectic models, such as the Lie-Poisson equation with cocycle.

The vast majority of patients with pancreatic ductal adenocarcinoma (PDAC) suffer cachexia. Although cachexia results from concurrent loss of adipose and muscle tissue, most studies focus on muscle alone. Emerging data demonstrate the prognostic value of fat loss in cachexia. Here we sought to identify the muscle and adipose gene profiles and pathways regulated in cachexia. Matched rectus abdominis muscle and subcutaneous adipose tissue were obtained at surgery from patients with benign conditions (n=11) and patients with PDAC (n=24). Self-reported weight loss and body composition measurements defined cachexia status. Gene profiling was done using Ion proton sequencing. Results were queried against external datasets for validation. 961 DE genes were identified from muscle and 2000 from adipose tissue, demonstrating greater response of adipose than muscle. In addition to known cachexia genes such as FOXO1, novel genes from muscle, including PPP1R8 and AEN correlated with cancer weight loss. All the adipose correlated genes including SCGN and EDR17 are novel for PDAC cachexia. Pathway analysis demonstrated shared pathways but largely non-overlapping genes in both tissues. Age related muscle loss predominantly had a distinct gene profiles compared to cachexia. This analysis of matched, externally validate gene expression points to novel targets in cachexia.

Recently, due to the miniaturization of electronic products, printed circuit boards (PCBs) have also become smaller. This trend has led to the need for high-precision electrical test equipment to check PCBs for disconnections and short circuits. The purpose of this study is to improve the position repeatability of the platform unit up to ±2.5 μm in a linear stage type test equipment. For this purpose, the causes of position errors of the platform unit are analyzed. The platform unit holding the PCB is driven by a single-axis linear ball screw drive system offset from its geometric center due to design constraints. The yaw rotation of the platform is found to have a dominant effect on position repeatability. To address this problem, the methods of adding balancing weights to the platform unit and adjusting the stiffness of LM Guides are proposed. This reduces the yaw rotation by moving the centers of mass and stiffness closer to the linear ball screw actuator. In the verification tests, the position repeatability was decreased to less than ±1.0 μm.

The paper explores the Kullback-Leibler divergence formalism (KLDF) applied to the stable MG1 queue manifold. More potentially, both service time probability and cumulative functions which make KLDF exact are obtained. The credibility of KLDF is justified through consistency axioms. Some potential applications of Kullback-Leibler divergence to Biometry are presented. The paper concludes with closing remarks combined with some challenging open problems and the next phase of research.

The spatial resolution measurement limitation of the position-momentum uncertainty principle is shown to mathematically originate from the Bekenstein entropy bound and the associated second law of thermodynamics, as a special case in which a statistical thermodynamic distribution of energies is specialized to a fixed, definite probe energy equal to the average energy of that distribution. This is used in combination with the Wein displacement law to predict an ultraviolet cutoff for Planck blackbody radiation at about ⅛ of the Wein peak. A new UV photon counting experiment is proposed to test for this. A physical understanding of these results may be provided by a UV-complete, intelligible theory of general relativistic quantum mechanics in which the observation of a blackbody spectrum is simply a remote observation of Hawking radiation emitted from black hole fluctuations in the gravitational vacuum.

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.

In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their "space of evolution" associated to a homogeneous symplectic manifold by a Lagrange 2-form, and defines in case of non null cohomology (non equivariance of the coadjoint action on the moment map with appearance of an additional cocyle) a Gibbs density (of maximum entropy) that is covariant under the action of dynamic groups of physics (eg, Galileo's group in classical physics). Souriau Lie Group Thermodynamics was also addressed 30 years after Souriau by R. F. Streater in the framework of Quantum Physics by Information Geometry for some Lie algebras, but only in the case of null cohomology. Souriau method could then be applied on Lie Groups to define a covariant maximum entropy density by Kirillov representation theory. We will illustrate this method for homogeneous Siegel domains and more especially for Poincaré unit disk by considering SU(1,1) group coadjoint orbit and by using its Souriau’s moment map. For this case, the coadjoint action on moment map is equivariant. For non-null cohomology, we give the case of Lie group SE(2). Finally, we will propose a new geometric definition of Entropy that could be built as a generalized Casimir invariant function in coadjoint representation, and Massieu characteristic function, dual of Entropy by Legendre transform, as a generalized Casimir invariant function in adjoint representation, where Souriau cocycle is a measure of the lack of equivariance of the moment mapping.

During the conceptual and preliminary design stage of a ship, designers need to ensure that the selected principal dimensions and parameters are good enough to deliver a stable ship (statically and dynamically) besides deadweight and speed. To support this, the initial intact stability of the proposed ship is required to be calculated, and in doing so, the lightship weight and its detailed breakdown are necessary to be known. After hull steel weight, machinery weight, mainly, marine propulsion and power generation machinery, play a vital role in the lightship weight estimate of a ship due to its robustness. The correct estimation of respective weights improves the accuracy of calculating a ship's initial stability typically to be designed and built. Hence, it would be advantageous for the designer to convince the ship owner. A total of 3006 marine propulsion (main marine diesel) engines and 348 power generation (auxiliary marine diesel) engines/generators of various power output (generators output for auxiliary engines), engine RPM and cylinder number of different engine makers are collected. These are analyzed and presented in both tabular and graphical forms to demonstrate the possible relationship between marine propulsion engine weight and power generation engine weight, and their respective power output, RPM, cylinder number, power-RPM ratio and power-RPM ratio per cylinder.In this article, the authors have attempted to investigate the behavior of marine propulsion engine weight and power generation engine/generator weight regarding engine power output, generator power output, engine RPM and cylinder number (independent variables). Further attempts have been made to identify those independent variables that influence the weight of the marine propulsion engine and power generation engine/generator (dependent variables), and their interrelationships. A mathematical model has thus been developed and proposed, as a guiding tool, for the designer to estimate the weight of main and auxiliary engines more accurately during the conceptual and preliminary design stage.

The determination of the specific surface free energy, specific properties and Lewis’s acid base of solid materials is of capital importance in many industrial processes such as adhesion, coatings, two dimensional films and adsorption phenomena. (1) Background: The physicochemical properties of many solid particles were characterized during the last forty years by using the retention time of injected well-known molecules into chromatographic column containing the solid substrates to be characterized. The obtained net retention time of the solvents adsorbed on the solid allowing the determination of the net retention volume directly correlated to the specific surface variables, dispersive, polar and acid-base properties. (2) Methods: Many chromatographic methods were used to quantify the values of the different specific surface variables of the solids. However, one found a large deviation between the different results. In this paper, one proposed a new method that quantify the specific free energy of adsorption as well as the Lewis’s acid-base constants of many solid surfaces. (3) Results: The new applied method allowed us to obtain the specific enthalpy and entropy of adsorption of polar model organic molecules on several solid substrates such as silica, alumina, MgO, ZnO, Zn, TiO2 and carbon fibers. (4) Conclusions: our new method based on the separation between the dispersive and polar free surface energy allowed to better characterize the solid materials.

Research for a theory of quantum gravity has recently led to the use of presheaf topos. Quantum uncertainty is linked to the truth values of intuitionistic logic. This paper proposes transposing this model into a classic probability context, that of conditional mathematical expectations. A simulation of Brownian motion is offered for illustrative purposes.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

A simple line of reasoning, based on the most fundamental concepts of thermodynamics, yields some intriguing results for a better understanding of the processes occurring in the observable Universe. Gravitational mass must be continuously generated within an expanding thermodynamic system for this system to remain closed. The Second Law is a direct consequence of this production of mass. Simple expressions for the entropy and temperature of the Universe were obtained and the results agree well with observable values. Furthermore, it is demonstrated that the conservation laws within the Universe are independent of its energy density. Based on the solution for the quantum state of the Universe, it is conjectured that the Second Law is incomplete and must be complemented to a conservation law, which takes into account the growth of the amount of information within the Universe. Once the Second Law is complemented to a conservation law, the importance of mass generation within the Universe becomes well pronounced – not only gravitational effects play the role of an organising force, but also the amount of mass within the Universe defines both the amount of information within the Universe and the level of the Universe’s complexity.

In the present work we revise and extend the Characteristic Crystallographic Element (CCE) norm, an algorithm used to simultaneously detect radial and orientational similarity of computer-generated structures with respect to specific reference crystals and local symmetries. Based on the identification of point group symmetry elements, the CCE descriptor is able to gauge local structure with high precision and finely distinguish between competing morphologies. As test cases we use computer-generated monomeric and polymer systems of spherical particles interacting with the hard-sphere and square-well attractive potentials. We demonstrate that the CCE norm is able to detect and differentiate, between others, among: hexagonal close packed (HCP), face centered cubic (FCC), hexagonal (HEX) and body centered cubic (BCC) crystals as well as non-crystallographic fivefold (FIV) local symmetry in bulk 3-D systems; triangular (TRI), square (SQU) and honeycomb (HON) crystals, as well as pentagonal (PEN) local symmetry in thin films of one-layer thickness (2-D systems). The descriptor is general and can be applied to identify the symmetry elements of any point group for arbitrary atomic or particulate system in two or three dimensions, in the bulk or under confinement.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.

Information geometry (IG) seeks to characterize the structure of statistical geodesic models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.