Environmental legislation is moving towards global standards for ease of application and to impose sanctions and penalties when necessary, without compromising human health and biota. International environmental measures for control and monitoring of atmospheric air only monitor emissions of SO_x, NO_x, O₃, and Pb. In general, most research work in air pollution done using the analysis of elements in rainwater show analysis of trace metals such as Na, Mg, Zn, and Mn. In this work, trace metals in the rainwater at the city of Goiânia, capital of the State of Goiás, were analyzed. Goiânia is a large city set in a predominantly agricultural province located in central Brazil. Presence of trace metals in rainwater was detected, indicating atmospheric air pollution levels higher than occupational limits set by WHO.

Policing duties may inherently be dangerous due to stab, blunt trauma and ballistic threats. The addition of individual light armour vests (ILAVs) has been suggested as a means to protect officers. However, the addition of the extra load of the ILAV may affect officer ability to conduct occupational tasks. The purpose of this study was to determine if wearing any of 3 different ILAVs (ILAV A, ILAV B, & ILAV C) affected occupational task performance when compared to that in normal station wear. A prospective, within-subjects repeated measures design was employed, using a counterbalanced randomization in which each ILAV was worn for an entire day while officers completed a variety of occupationally relevant tasks. These tasks included a victim drag, car exit and 5 meter sprint, step down and marksmanship task. Results showed that performance in each task did not vary between any of the ILAV or normal station wear conditions. There was less variability in the marksmanship task with ILAV B, however. The results suggest that none of the ILAVs used in this study were heavy enough to significantly affect task performance in the assessed tasks when compared to wearing normal station wear.

This study examines the significant impact of Houthi insurgent activities on maritime traffic within the strategic Red Sea and Suez Canal routes, essential conduits for global trade. It explores the correlation between regional instability, exemplified by Houthi actions from November 19, 2023, to February 5, 2024, and changes in maritime traffic patterns and operational efficiency. This study seeks to answer a critical question in transport geography: How does regional instability, exemplified by Houthi insurgent activities, affect maritime traffic patterns and the operational efficiency of the Red Sea and Suez Canal? Using descriptive statistics, qualitative analysis, and geospatial methods, the research highlights recent trends in maritime traffic and incidents, revealing spatial and geopolitical challenges in this crucial trade route.Findings indicate a notable decline in maritime activity in the Gulf of Aden and Suez Canal due to security concerns from Houthi attacks, prompting a significant shift to alternative routes, particularly around the Cape of Good Hope. This shift underscores the broader implications of regional instability on global trade and the importance of maintaining uninterrupted maritime flow. The study also emphasizes the economic ramifications, such as increased operational costs and freight rates due to longer transit times and enhanced security measures.The research concludes with a call for improved maritime security protocols and international cooperation to protect these strategic maritime pathways. It contributes to the discourse on transport geography by quantifying the direct impacts of regional conflicts on maritime logistics and proposing strategies for future resilience, highlighting the interconnected nature of global trade and security and the need for collective action against evolving geopolitical challenges.

This paper reviews the ethical issues involved and argues that each of the usual policies for handling conscientious refusals faces serious challenges. Healthcare providers who refuse to provide medical services should be expected to explain their reasons, make prompt referrals, and bear some of the resulting costs or burdens.

Although evolutionary theory has yet to furnish a comprehensive rationale for the underlying mechanism of natural selection, it is pertinent to note that the phenomenon transcends the confines of biological systems, exhibiting analogous patterns in physical systems as well. Specifically, isolated and closed systems tend to evolve towards states of progressively increasing entropy. In scenarios where multiple paths for entropy increase are accessible, such systems tend to favor combinations of paths that exhibit the most rapid entropy increase rates. Among the various processes in nature, life activities constitute a salient means of achieving entropy increase. Genetic variation within organisms generates individuals that vary in their rates of entropy increase. As these organisms interact, compete and combine, they form diverse combinations of entropy-increasing pathways. Nature, in turn, selects among these combinations, favoring those that culminate in the fastest entropy increase, thereby propelling the evolution of life. Essentially, the evolution of life is an ongoing exploration of diverse combinations of pathways that maximize entropy increase across various energy pools. Amidst continuous genetic variation and the selective pressure imposed by nature for maximum entropy production rates, information accumulates, leading to a corresponding acceleration in the rate of entropy increase. This natural selection, which favors maximizing the entropy at the fastest possible rate, serves as the ultimate driving force for the origin and evolution of life.

International law faces numerous challenges in the 21st century, ranging from the traditional issues of sovereignty to emerging threats like cyber warfare and climate change. This article explores the evolving landscape of international law, discussing both the challenges it faces and the prospects for its future. By examining the role of international organizations, the impact of technological advancements, and the growing influence of non-state actors, this article provides a comprehensive overview of the current state of international law and offers insights into how it can adapt to meet the demands of an increasingly interconnected world.

This study presents a comparative analysis of length deformation in Classical and Relativistic Mechanics, specifically investigating 10-gram objects accelerating to 1% of the speed of light. By employing Hooke's Law in Classical Mechanics and the Relativistic Lorentz Factor, the research explores the implications of acceleration dynamics and the limitations inherent in Relativistic Mechanics. The results reveal significant differences in predicted length changes between the two frameworks, emphasizing the necessity of considering relativistic effects beyond velocity alone. This study underscores the critical importance of addressing the incomplete treatment of acceleration dynamics in Relativistic Mechanics to achieve a more accurate depiction of length deformation in high-speed scenarios.

In 1911, A. Einstein suggested that gravity affects at the electromagnetic radiation originating from the distant sources, namely, it shifts the spectral lines in the red side of the spectrum and derived the gravitational redshift formula. A modern science claims that Einstein’s formula is mathematically immaculate. We show that this is not true: in fact, this formula is approximate. Using the law of conservation of mechanical energy, we derived two exact formulas оf the gravitational redshift.

This paper proposed a time two-mesh (TT-M) finite difference numerical scheme to improve the efficiency of solving the symmetric regularized long wave (SRLW) equation. The TT-M Crank-Nicolson discretization and finite difference method are employed in time and space approximation respectively. The scheme involves three main steps: firstly, the time interval is divided into coarse and fine time meshes, then the nonlinear system is solved on the coarse time mesh; secondly, coarse numerical solutions on the fine time mesh are computed using an interpolation formula based on the solutions derived in the step one; lastly, the TT-M finite difference numerical solutions can be obtained through constructing the linearized fine time mesh system using Taylor’s formula. Compared to the currently existing TT-M numerical methods, the novelty of this study is that the nonlinear term including derivatives is linearized by Taylor’s formula for a function with three variables, whose error analysis is more complex. Finally, some numerical examples, including computational time and accuracy, preservation of conservation laws, are given to verify the efficiency of the scheme. By comparing it with the standard nonlinear finite difference scheme, this method can reduce CPU time without sacrificing accuracy.

Law of conservation of energy is the most well-established law of modern physics. But, inflationary cosmological model which assumes the universe to be created from a point of singularity has not been able to identify the source of energy for creation of this universe. As per uncertainty principle, a quantum vacuum fluctuation can at most create energy of ~10^-8 kg in a Planck time of ~5.4 ×10^-44 s whereas total positive energy due to matter/vacuum existing in the universe is more than ~10⁵⁴ kg. To solve this problem, we have recently published a new cosmological model (Biswaranjan Dikshit, Canadian Journal of Physics, 100, 218-225, [2022]) in which we have mathematically proved that the total energy of the universe can be zero right from the beginning of the universe to till date due to negative gravitational potential energy and thus law of conservation of energy can be satisfied during creation of the universe from nothing. In this article, starting from a simple argument, we explain why net energy of the universe can be zero only in our model, not in standard cosmological model. An interesting fact pointed out in this paper is that the factor ~10⁶² by which radius of universe has increased from its starting value of ~10^-36 m to present value of ~10²⁶ m is same as the factor by which positive energy has increased from Planck energy ~10^-8 kg to present value ~10⁵⁴ kg. This is in agreement with our new model that predicts the positive energy of universe to be proportional to the radius of universe. We also bring out to the notice that zero energy universe is possible only if smallest possible length in nature is, l_min=l_p(π/2)^1/2 = 2.0×10^-35 m. Minimum possible length is important in theory of quantum gravity and string theory.

The photoelectric effect induced by blackbody radiation could be a mechanism to harvest ambient thermal energy at a uniform temperature. Here, I describe (without going too much into mathematical details) the theoretical model I developed starting from 2010 to study that phenomenon, and I summarize the results of the numerical simulations. Simulations tell us that the process must be there. Moreover, at least two experimental tests have been performed in the past years that seem to corroborate, although not definitely, the alleged functioning of the proposed mechanism. Unfortunately, at present, the obtainable power density is extremely low and inadequate for immediate practical applications.

The extrusion of food for human and animal consumption is a unit operation that includes mixing, shearing and force to the materials related to the rheological properties of the materials in the extruder. The present work aims to study the rheological behavior of an extruded fish diet incorporating hydrolyzed protein flour processed by extrusion. The measurement was carried out online with a slit die rheometer, defining the rheological models and parameters that fit the process. During the extrusion process, the raw materials used were hydrolyzed protein meal, fish meal and cassava starch. For the results, the evaluated treatments were adjusted to the Power Law, where an increase in the shear rate decreases the viscosity of the material, corresponding to a pseudoplastic behavior. The incorporation of hydrolyzed protein flour presented a significant effect on the value of n and Klp, increasing the viscosity with the increase in the percentage of inclusion of HPH. The models obtained for the prediction of the viscosity are adjusted to the changes in shear rate, temperature and humidity of the system.

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. Preferably based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].

The police occupy a very important position in the entire criminal justice system in Nigeria. The nature of police relationship with the people and the manner in which the public were handled at the station and on the street daily within the community affects the way the people perceive them and the level of cooperation they get from the people in curbing crime in the society. The study took place in Zaria, Kaduna state, Northern Nigeria .The study population was the police in Zaria. Three police stations (Zaria City, Sabon Gari and Samaru police stations) were purposively selected reflecting the socio-cultural and demographic backgrounds of Zaria residence and population. The Divisional Police officers and police officers in-charge of crime were interviewed. The police crime and incidence records were examined while the general conduct and social atmosphere of the police and police stations were observed. Using in- depth interview, observational method and police records, it was discovered that the socio economic status of suspects affected how they were treated by the police in the police stations studied. Also the environment a suspect lives affected how they were treated too by the police. It was recommended that the police make the rule of law their guide in the handling of suspects in the police stations irrespective of socio-demographic variable or area of habitation of the suspects. Police brutality and violations of citizen’s rights should be checked by senior police officers while community-policing style should be implemented across communities in Nigeria.

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

Shot peening is an attractive technique for fatigue enhanced performance of metallic components, because it promotes crack initiation retardation and later crack growth. Engineering design based on fatigue crack propagation predictions applying the principles of fracture mechanics is commonly used in aluminum structures for aerospace engineering. The main purpose of present work was to analyze the effect of shot peening on the fatigue crack propagation of the 7475 aluminum alloy, under both constant amplitude loading and periodical overload blocks. The tests were performed on 4 and 8 mm thickness specimen's with stress ratios of 0.05 and 0.4. The analysis of the shot-peened surface showed a small increase of the micro-hardness values, due to the plastic deformations imposed by shot peening. The beneficial effect of surface peening on fatigue crack growth rates is quite limited to an increasing near the threshold. The specimens’ thickness has only marginal influence on the crack propagation, in opposite to the stress ratio. Periodic overload blocks of 300 cycles promotes a reduction of the fatigue crack growth rate for both intervals of 7,500 and 15,000 cycles.

In this paper, we study a one-dimensional Bresse-Cattaneo system with infinite memories and time-dependent delay term (the coefficient of which is not necessarily positive) in the internal feedbacks. First, it is proved that the system is well-posed by means of the Hille-Yosida theorem under suitable assumptions on the relaxation functions. Then, without any restriction on the speeds of wave propagations, we establish the exponential or general decay result by introducing suitable energy and Lyapunov functionals.

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.

Keywords: conservation; cultural pluralism; environmental regulation; community-based natural resource management; Indigenous law

Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems—thermal, externally loaded, internally reactive, open and closed––are developed via selection of suitable thermodynamic potentials. Here we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented––and demonstrated on grease degradation, battery charging and discharging, metal fatigue and pump flow––can be used for design, analysis, and support of diagnostic monitoring and optimization.

Hund's rule of maximum multiplicity is a powerful empirical tool for determining the electron population of electronic shells. It was recently discovered that it is also the rule of minimum Shannon entropy. This study extends these findings to the Aufbau rule and discusses them from the perspective of emergent dimensionality, providing a monotonically increasing entropy function. We observed that some elements that violate the Aufbau rule have the same entropies in the actual and Aufbau electron configurations. On the other hand, lower entropies of all actual elements' configurations are associated with higher or equal numbers of unpaired electrons in these configurations compared to the Aufbau configurations. The only exception to this rule is palladium.

The fatigue delamination damage is one of the most important fatigue failure modes of laminated composite structures. However, the developments of the theoretical framework, mathematical/physical model and numerical simulation of fatigue delamination are still challenging issues, and there is a lack of systematic classification. This article reviews the experimental phenomena of the onset and propagation stage of delamination under fatigue loading, and summarizes the commonly used phenomenological models for laminated composite structures. The research methods, general modeling formulas and development prospects of the phenomenological models are presented in detail. In the light of the analysis of finite element model (FEM) for the laminated composite structures, a number of simulation methods of fatigue delamination crack propagation damage model are carefully classified. Furthermore, within the theoretical framework of strength theory model (SM), fracture mechanics model (FM), damage mechanics model (DM) and hybrid model (HM), the complete procedure, application, capability assessment, advantages and limitations of the models are also discussed in detail. Finally, several valuable suggestions are given for the research interests, and challenging technical problems that need to be overcome on the fatigue delamination prediction of laminated composite structures in the future.

This study investigates via Lie symmetry analysis the Hunter-Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation derived from first-order multipliers. Conservation laws of the Hunter-Saxton equation, in combination with the Lie point symmetries of the equation, enable us to perform symmetry reductions through employment of the double reduction method. The method exploits the relationship between Lie point symmetries and conservation laws to effectively reduce both the number of variables and the order of the equation. Five nontrivial conservation laws of the Hunter-Saxton equation are derived, four of which are found to have associated Lie point symmetries. Applying the double reduction method to the Hunter-Saxton equation results in a set of first-order ordinary differential equations, the solutions of which represent invariant solutions for the equation.

The results of measuring the capacity of a thin-film solid-state lithium-ion battery (SSLIB) Ti|Si@O@Al|LiPON|LiCoO₂|Ti at different charge currents are reported. It is shown that the dependence of the capacity on the current density follows the Peukert's law, which is characterized by a low value of the Peukert’s exponent in the region of low currents and a high value of the exponent in the region of high currents. A capacity model for a SSLIB based on the balance of diffusion and migration currents is proposed and the dependence of the capacity on the charge current is derived. The obtained dependence is well approximated by Peukert's law with an exponent of 1.39, which is intermediate between the exponents for lithium-ion batteries with liquid electrolyte and SSLIBs.

Given a square matrix $A$, we are able to construct numerous equalities that involve reasonable mixed operations of $A$ and its conjugate transpose $A^{\ast}$, Moore--Penrose inverse $A^{\dag}$, and group inverse $A^{\#}$. Such kind of equalities can be generally represented in the equation form $f(A, \, A^{\ast}, A^{\dag}, A^{\#}) =0$. In this article, the author constructs a series of simple or complicated matrix equalities, as well as matrix rank equalities involving the mixed operations of the four matrices. As applications, we give a sequence of necessary and sufficient conditions for a square matrix to be range-Hermitian.

It is a classic topic in algebras to construct and verify equalities that are composed of various algebraic operations of elements and their inverses or generalized inverses. In this note, the author constructs a matrix equality $(AB)^{\dag} = B^{\ast}(A^{\ast}ABB^{\ast})^{\#}A^{\ast}$ (called a mixed reverse-order law), where $A$ and $B$ are two matrices of appropriate sizes, $(\cdot)^{\ast}$, $(\cdot)^{\dag}$, and $(\cdot)^{\#}$ denote the conjugate transpose, the Moore--Penrose inverse, and the group inverse of a matrix, respectively, and shows that the mixed reverse-order law always holds. A list of variation forms of this matrix equality are also given, and necessary and sufficient conditions are obtained for them to hold. Especially, we show a remarkable fact that the two reverse-order laws $(AB)^{\dag} = B^{\dag}A^{\dag}$ and $(A^{\ast}ABB^{\ast})^{\#} = (BB^{\ast})^{\#}(A^{\ast}A)^{\#}$ are equivalent.

This paper proposes how to reduce the consumption of active electrical energy (kwh) by 90.3% while maintaining the same mechanical work speed (RPM) at variable torque loads (fans or air-fluid blowers, centrifugal pumps are not included). of water and similar fluids), by using the “Fan Law” in an innovative way in PMSM-type synchronous motors (a comparative study never before carried out on the Fan Law). The work is carried out comparatively between brushless a-synchronous motors with starting loop (or motor with a short-circuited loop) versus brushed a-synchronous motors and PMSM-type synchronous motors without the need to use VDF (variable frequency drives), simplifying technology (electronics) and saving costs in an innovative way (R+D+i). The case study was developed on a design applied to a centrifugal air extractor/blower with PMSM/IPM type synchronous motor. Applying one of the fan affinity laws –with the impeller diameter 10.5 (mm) constant- the electrical power absorbed by the blower motor is proportional to the cube of the shaft speed: . Being “P” power (Watts) and “N” speed (RPM). Carrying out a comparative study between power (watts), active energy consumption (kwh) and rotational speed (RPM). This has a direct impact on the costs of residential and commercial single-phase active electrical energy consumption, measured in kilowatt-hours (kwh). Carrying out a comparative study between three (3) types of alternating current (AC) electrical machines, according to the NEMA (National Electrical Manufacturers Association); AC motors fall into three (3) categories. One (1), synchronous motors (Syncrhonous Motor) of three types: (1a) excitation by DC (DC Excited Motor), (1b) permanent magnet (Permanent Magnet Motor) and (1c) reluctance motor (Reluctance Motor) or motor Step by Step. Two (2), asynchronous induction motors of two types: (2a) Squirrel-Cage Induction Motor and (2b) Wound-Rotor Induction Motor. Three (3) series-wound motor (Series-Wound Motor) also called universal motor (they have carbons).

Power law relationships, which describe scaling relationships of data, are powerful information theoretic descriptive tools in many empirical contexts, including that of music. Zipf’s law (pink noise) describes the optimum case of a power law relation where observations are exactly inversely proportional to their rank. Descriptions that approximate a pink noise signature can be said to maximize the amount of information in a signal, and is thus suggestive of a richness of an understanding. This information density of pink noise signatures is not, however, necessarily a desirable quality for explanations in general, which, by definition, “flattens out” some data while highlighting others, ideally those most relevant to an interpretation. The privileging of data most relevant to comprehension corresponds to a red noise relationship, as opposed to the pink noise of Zipf’s law or the white noise of a description that highlights nothing in particular. Here, I explore and evaluate this concept of red noise explanations in the form of analyses of three comparable short piano works: Robert Schumann’s “Von fremden Ländern und Menschen” (no.1 from Kinderszenen op. 15, 1838), Frédéric Chopin’s Prelude op. 28 no. 20 (1838-9), and Felix Mendelssohn’s “Venetianisches Gondellied” (no. 6 from Lieder ohne Worte op. 19b, 1829-30).

The Benford method can be used to detect manipulation of epidemiological or trial data during the validation of new drugs. We extend here the Benford method after having detected particular properties for the Fibonacci values 1, 2, 3, 5 and 8 of the first decimal of 10 runs of official epidemiological data published in France and Italy (positive cases, intensive care, and deaths) for the periods of March 1 to May 30, 2020 and 2021, each with 91 raw data. This new method – called “BFP” for Benford-Fibonacci-Perez - is positive in all 10 cases (i.e. 910 values) with an average of favorable cases close to 80%, which, in our opinion, would validate the reliability of these basic data.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

Based on detection of elliptic particle tracks, $\simeq 137^2 n^2$ bigger than Bohr-Sommerfeld electron orbits, indicating the possible detection of superluminal electrons masquerading as magnetic monopoles, a new structure emerges leading to: (i) a new set of seven elementary lengths; (ii) replacement of the usual motion (Lorentz) transformations by scale transformations between $v^2<c^2$ and $v^2>c^2$ frames; (iii) equivalence of charge between $v^2<c^2$ and $v^2>c^2$ frames based on the Dirac-Schwinger quantization condition; (iv) a relativistic foundation for the Dirac-Schwinger quantization condition; (v) a possible cause of charge quantization; and (vi) the prospect of symmetry in Maxwell's equations. If the elliptic particle tracks are viewed as a magnification of electron orbits, the effect is suggestive of a spacetime distortion such as those predicted in general relativistic theories.

In this paper, the preparation methods of porous silicon nitride materials with controllable dielectric constant and pore structure were systematically studied. By using microwave sintering technology, porous silicon nitride materials with high closed pore ratio were prepared by adjusting the content of sintering additives and sintering process parameters, and controlling the grain boundary phase and pore structure and size. The effects of sintering conditions on the total porosity, closed porosity, pore structure and dielectric properties of materials were systematically studied.

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

Efficiently solving the problem of computing, in a distributed fashion, the shortest paths of a graph whose topology dynamically changes over time is a core functionality of many today’s digital infrastructures, probably the most prominent example being communication networks. Many solutions have been proposed over the years for this problem that can be broadly classified into two categories, namely Distance-Vector and Link-State algorithms. Distance-Vector algorithms are widely adopted solutions when scalability and reliability are key issues or when nodes have either limited hardware resources, as they result in being very competitive approaches in terms of both the memory and the computational point of view. In this paper, we first survey some of the most established solutions of the Distance-Vector category. Then, we discuss some recent algorithmic developments in this area. Finally, we propose a new experimental study, conducted on a prominent category of network instances, namely generalized linear preference (GLP) power-law networks, to rank the performance of such solutions.

HIGHLIGHTS Mach's principle is linked with inertia and the mass around. Nowadays, physicists believe its effect is infinitesimal, so Mach's principle is simply ignored. This paper looks at the consequence of applying Mach's principle. It could replace dark matter. ABSTRACT After seeing the history of Mach's principle, we will work out a new model of galaxies inspired by Mach’s principle, which is more satisfactory than current dark matter models. This new model is just maths and needs an explanation. One possible explanation is obviously that Mach's principle is at work in a galaxy.

Arduino microcontrollers are being used for a wide range of technological and biomedical applications such as image classification, computer vision, brain-computer interaction and vision experiments. Here I present a new cost-effective mini-device based on RGB LED flicker stimulation for the assessment of polychromatic temporal resolution of visual function. The visual device configuration allows for relative luminance thresholding, mono- and polychromatic critical flicker fusion frequency assessment. The results demonstrate the steady white visual perception of a trichromatic flicker stimulus beyond the critical flicker fusion frequency, as predicted by Talbot´s law for monochromatic stimuli. The trichromatic critical flicker fusion frequency (tFCC) depends on the relative luminance threshold at the light-adaptation level. Finally, wavefront measurements demonstrate that high-order aberrations improve the temporal resolution of visual function.

The normative and safeguarding role of ethics and law in the development of biomedical science and technology, as well as their importance in promoting the progress of the industry, analyzed the key role of ethics and law in the field of biomedical science and technology, by restricting scientific research behavior, protecting the rights and safety of subjects, providing a solid guarantee for scientific research activities, and promoting the healthy development of biomedical science and technology. At the same time, the positive role of ethics and law in promoting international cooperation and exchange of biomedical science and technology is also discussed, which will inject strong impetus into the global development of biomedical science and technology. In addition, through case analysis, the paper demonstrates the key role of ethical review in the field of biomedical science and technology, as well as the importance of law in maintaining market order, protecting subjects' rights and interests, and fairness and justice. The successful practice of ethics and law in the development of biomedical science and technology is emphasized, which proves that following ethical principles and legal framework is the key factor to promote the progress of biomedical science and technology. This paper explores the important role of ethics and law in the development of biomedical science and technology, and provides valuable reference and guidance for practitioners in the industry. By following ethical principles and legal norms, we will jointly promote the prosperity and development of biomedical science and technology, and contribute to the common progress of human health.

Mexico is a well-known seismically active country, which is primarily affected by several tectonic plate interactions along the southern Pacific coastline and by active structures in the Gulf of Baja California. In this paper we investigate this seismicity in the context of a non-extensive statistical approach based on Tsallis entropy. The analysis is performed using data from the corrected Mexican seismic catalogue provided by the National Seismic Service, spanning a period from January 2000 to October 2023. The Gutenberg-Richter law fitting to the earthquake sub-catalogues for all six regions studied indicates magnitudes of completeness between 3.30 and 3.76. All six regions display values of the entropic index in the range 1.52≲q≲1.61, which are lower than the previously estimated range 1.54≲q≲1.70 using catalogue data from 1988 to 2010. The cause of this discrepancy is certainly due to the use of modern recording devices, which are sensitive enough to detect a larger number of low-magnitude events compared to older instrumentation.

{This study investigates the coordinated behaviors and the underlying collective intelligence in biological groups, particularly those led by informed leaders. By establishing new convergence criteria based on real biological group experiments, this research introduces the concept of a volitional term and heterogeneous networks, constructing a coupled force Cucker-Smale model with informed leaders. The inclusion of the informed leader aspect distinctively characterizes the dynamics of leaders and followers, enabling a more accurate representation of biological group behavior. The paper then proposes the Flock Leadership Hierarchy Network (FLH), a model reflecting real biological interactions. By employing time slicing and rolling time windows, the study methodically analyses group behavior stages, using volatility and convergence time as metrics to examine the relationship between group consistency and interactions. Comparative experiments show the FLH network's superior performance. The Kolmogorov-Smirnov test indicates that the FLH network follows a power-law distribution, highlighting the evolutionary intelligence of biological groups. This research offers new perspectives on the evolution of biological groups, contributing to our understanding of both natural and artificial systems, such as animal migration and autonomous drone operations.

Laboratory experiments and investigations into natural phenomena in this research series have unveiled the presence of a gravitational repulsion force that permeates our environment on both microscopic and macroscopic scales, contingent upon the thermal energy present. This paper presents a study exploring novel properties of gravitational forces among gas molecules, employing principles of thermodynamics. A model has been devised based on the interactions between pairs of gas molecules. While traditional models treat gravitational interaction as a singular force, our experimental approach validates it as the composite of two distinct forces: gravitational repulsion and attraction. By utilizing established experimental data on gas thermodynamics, our model demonstrates robust performance both analytically and experimentally. It verifies the coexistence of gravitational repulsion and attraction forces among gas molecules, showcases their Inverse-Cube relationship with distance, and elucidates the direct proportionality of the repulsion force to absolute temperature. This bridges a crucial gap between energy and fundamental forces. The order of magnitudes of gravitational repulsion and attraction forces are found to be considerably large, contrasting with the low values predicted by classical theory, which results from their amalgamation. Recognizing these forces as substantial in magnitude promises unprecedented outcomes and advancements.

This paper aims to argue the fundamental significance of education in addressing notable gaps in the constitutive, performance, and evaluation criteria for corporate social responsibility (CSR) and endeavours to showcase the complementarity between education, human security, sustainable human development, and the pursuit of CSR as an ideal normative paradigm. An abstractive approach to studying CSR engages with corporate philanthropy, which has not been helpful outside traditional CSR paradigms without looking at key dynamics that can robustly underpin successful CSR. It relies on the systematic analysis of written data sources to theoretically explore the central significance, and complementarity between human security, education, and human dignity and how they can orchestrate a holistic CSR paradigm. In 1994, the UNDP in formulating the human security doctrine recognised the syncretic correlation between human security, education, and sustainable human development as fundamental elements that should underpin CSR. This paper contends that these are necessary intrinsic components of human dignity as the central factor that justifies a multi-dimensional and proactive approach to CSR. Despite the criticisms against human security, this paper identifies it as an important concept that could instrumentally orchestrate a model of CSR that uniformly mainstreams sustainable human development and human dignity that leverages education which has routinely and traditionally been seen as a constitutive component of CSR. It reveals how a holistic path to CSR can reinvigorate the central pillars of human security and human dignity using education as a springboard and makes a compelling case for supporting explicit references to education in company law with appropriate human security informed constitutive, performance, and evaluation criteria which are absent in existing legally orchestrated CSR.

In this article, we have tried to extend the Neumann–Kopp law concerning the heat capacity of solid compounds to other physical observables for materials represented as mixtures of chemical compounds, alloys, and ceramics. The main goal of this study is to find the intervals of external or internal parameters for a solid compound, within which its physical observable - the magnetic transition temperature for this work, can be expressed in terms of the atomic or molar weighted sum of the magnetic transition temperatures of the constituent elements of a compound. Outside these intervals, we tried to figure out the structure of the variable by which the weighted sum should be multiplied. Thus, for USb–x(ThSb) mixtures with a mole fraction x from 0.36 to 0.55, the magnetic transition temperature of this mixture is expressed in term of the molar weighted sum of the temperature of uranium structural transition associated with a change in the magnetic properties of uranium and of the temperature at which the nature of the magnetic susceptibility of antimony changes. For the magnetic Laves phase compounds Er(Fe_0.8–xMn_0.2–yCo_x+y)₂, the Curie temperature of the compound is equal to the weighted sum of the Curie temperatures of all elements of the compound, except for Mn, at x = 0.1, y = 0 and y = 0.1. For the paramagnetic Curie temperature of intercalated dichalcogenides Cr_xМоSe₂, it can be expressed in terms of the weighted Neel temperature of chromium multiplied by a variable depending on x, on the atomic numbers of all elements of the compound, and on a parameter proportional to the derivatives with respect to x of the dichalcogenide’s crystal lattice parameters.

In order to study the effect of TiB2 particles on the mechanical properties of TiB2/6061Al composites, a series of TiB2/6061Al 3D representative volume element (RVE) were established based on SEM photos. This model took into account the ductile damage of the matrix and the traction separation behavior of the interface, and the linear damage evolution law was introduced to characterize the stiffness degradation behavior of the matrix elements. The mixed boundary conditions were used for RVE tensile experiments, and the accuracy of the predicted result was verified by the agreement of the experimental stress-strain curve. Results show that the addition of TiB2 particles can effectively promote the load-bearing capacity of the composite, but elongation is reduced. With the weight fraction of TiB2 increasing from 2.5% to 12.5%, the elastic modulus, yield strength, and tensile strength are increased by 8%, 10.37%, and 11.55% respectively, while the elongation decreased by 10%. The clustering rate of the TiB2 particles is also an important factor affecting the toughness of the composites. With the increase in the clustering rate of TiB2 particles from 20% to 80%, the load-bearing capacity of the composites is not improved, and the elongation of the composites is reduced by 8%. Moreover, the high strain region provides a fast expansion path for crack propagation and the particle spacing is a crucial factor that affects the stress field.

We introduce two symmetric concepts to physics: “distance” (space and time in one) and “wavematter” (electromagnetic wave packet and matter in one). We claim that physics has chosen the wrong concept of time: It is not aware that the time of a moving object flows in a direction other than my time. We provide 15 proofs for our claim by solving 15 mysteries of physics graphically! For example, we prove that length contraction and time dilation are actually geometrical effects in a 4D manifold that we call “Euclidean spacetime” (ES). We prove that the discrepancy in calculating the Hubble constant stems from a systematic error in the redshift measurement. We prove that what I deem wave, deems itself matter, which solves wave–particle duality. We even untangle quantum entanglement without the issue of non-locality. We finally understand why alternative theories of Euclidean relativity have failed: They are all based on four dimensions of space rather than distance. A huge amount of energy was injected into ES at a point that we take as origin. Ever since has this energy been moving radially away at the speed of light. We live in the 3D hypersurface of an expanding 4D hypersphere. Hyperspherical coordinates have the great advantage that they reduce all that is ever happening to just one formula. So, it is the Theory of Everything in these coordinates: “Energy is covering radial distance which, divided by Euclidean time, is equal to the speed of light.” Acceleration and force like gravitation emerge from a rotation of objects in ES and a subsequent projection to 3D space. Matching the symmetry simplifies physics.

Intestinal gases are usually discarded as physiologically inert, useless sub-products of colonic fermentation that must be expelled to prevent discomfort and meteorism. Starting from the observation that many living beings use exogenous and/or endogenous gases to attain evolutionary benefits, we question whether intestinal gases in healthy humans could have underestimated physiological effects, either intestinal or extra-intestinal. We examine gaseous volume, composition, source and local distribution in proximal as well as distal gut, providing extensive data that may serve as reference for future studies. We analyze each one of the most abundant intestinal gases and describe their diffusive patterns, active trans-barrier transport dynamics, chemical properties, intra-/extra-intestinal metabolic effects mediated by intracellular, extracellular, paracrine and distant actions. Discussing the physical properties of the whole intestinal gaseous mixture, we illustrate how changes in volume/pressure can be generated by two different mechanisms, namely, physical muscular gut contraction and biological colonic fermentation, with quite different metabolic outcomes. The experimental gas laws suggest that the gaseous exchanges between lumen and bloodstream are impaired by muscular contraction and improved by muscular relaxation. In turn, the surface-area-to-volume ratio suggests that the gaseous exchanges are impaired by microorganismal overproduction and improved by microorganismal reduction. Further, theoretical stochastic approaches from probability theory indicate that the non-turbulent, random paths of gas molecules inside colonic haustra do not homogenously spread over the whole mucosal surface. This means that the intestinal area available for lumen/blood metabolic exchanges is much less than expected not just in disease states, but also in healthy individuals.

Voltage Source Inverters (VSI) are the integral part of Electrical Vehicles (EV) to enhance the reliability of supply power to critical loads in vehicle to load (V2L) applications. Inherent properties of sliding mode control (SMC) makes it one of the best vailable options to achieve desired voltage quality under variable load conditions. Intrinsic characteristic of robustness associated with SMC is achieved generally at the cost of unwanted chattering along the sliding surface. To manage this compromise better, optimal selection of sliding surface coefficient is applied with proposed composite exponential reaching law (C-ERL). The novelty of proposed C-ERL is associated with the intelligent mix of exponential, power and difference functions blended with rotating sliding surface selection (RSS) technique for three phase two level VSI. Moreover, proposed reaching law along with power rate exponential reaching law(PRERL), enhanced exponential reaching law(EERL) and repeatitive reaching law(RRL) are implemented on two level three phase VSI under variable load condtions. Comparative analysis of which strongly advocates the authenticity and effectiveness of proposed reaching law in achieving well regulated output voltage, with high level of robustness, reduced chattering and low %THD.

A quantitative description of the second law of thermodynamics in small scale systems and over short time scales comes from various fluctuation theorems. The applicability of the transient fluctuation theorem in particular to small scale systems perturbed from an initial equilibrium steady-state distribution has been demonstrated both theoretically and experimentally in several works over the past few decades. In addition, some experimental works in the past have also made successful attempts to demonstrate the applicability of the fluctuation theorem to small scale systems evolving from a certain nonequilibrium steady-state distribution over relatively long time scales. To this end, this paper seeks to demonstrate the transient fluctuation theorem for a Brownian particle confined within a power-law trapping potential by following the trajectory of the particle that itself is translating linearly along one dimension with constant acceleration in a viscous fluid. Considered herein is an idealized version of this model, in that it is assumed that the force of the trapping potential is only felt by the translating Brownian particle confined within the trap, and that this Brownian particle moves relative to the fluid molecules that are held stationary. The results presented herein show that the transient fluctuation theorem applies not only to equilibrium steady-state distributions but also to nonequilibrium steady-state distributions of an ideal colloidal system in an accelerated frame of reference in the asymptotic (long-time) limit.

Potential dependent special relativity and Gauss's law for the electric field have been used for gravity by assuming vacuum energy to be generated when the energy is a minimum useful expression for vacuum energy has been found. This expression shows that elementary particles are generated by gravity vacuum filling their hollow balls; using Schrödinger equation for spherically symmetric particles vacuum energy is quantized. Treating mass as vibrating spheres thus solving Schrödinger, coordinate harmonic oscillator energy relation has been found.

Ofloxacin is a highly efficient and widely used antibiotic drug. It is classified as a refractory pollutant due to its poor biodegradability. Consequently, it is commonly found in water sources, requiring efficient methods for its removal. Advanced Oxidation Processes (AOPs) offer efficient alternatives since those yield complete degradation not achieved in adsorption or membrane processes. Previous studies suggest ofloxacin degradation follows a pseudo-first or -second order processes, whereas for full removal of refractory pollutants – lower pseudo-orders are required. Monitoring the actual “pseudo-order” degradation kinetics of ofloxacin is needed to evaluate any proposed AOP process. This study presents a simple procedure to evaluate pseudo-orders of AOPs. Photolysis of 20 mM ofloxacin solutions follow pseudo-zero order kinetics, with half-life times (t_1/2) of approx. 60 min. TiO₂ heterogenous catalyst show to have no influence at low concentration (0.2 mg L^-1) but a significant reduction of half-life time (t_1/2 = 20 min) and increase in pseudo-order (0.8) is measured at 2.0 mg L^-1. Similar results are obtained with homogenous catalysis by 2.0 mg L^-1 H₂O₂. The combination of H₂O₂ and TiO₂ catalysts shows additional reduction in half-time life with increase in the pseudo-order to 1.2. The conclusions are (1) heterogenous and homogenous photocatalysis can effectively degrade ofloxacin, (2) combined photocatalysis yields higher pseudo-order, being less prone to achieve full removal, (3) analysis of specific pseudo-orders in AOPs of refractory pollutants helps to further elucidate the efficiency of the processes.

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches on it, we show that entropy has a universal stochastic definition which is not disorder. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept and promotes entropy as the mother of creativity and evolution. As social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether the maximum entropy, applied to the distribution of wealth quantified by annual income, can give an objective description. Using publicly available income data, we show that the income distribution is consistent with the principle of the maximum entropy. The increase of entropy is associated to increase of society’s wealth yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in development and increase of the entropy of income. Such findings are contrary to the theories of ecological economics and other theories which use the term entropy in a Malthusian perspective.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the ‘probability assumption’ needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann’s Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.

The geometry of structural members can influence the fatigue crack growth rate. In the paper, the T-stress depending on the element's geometry is used to quantify the effect of geometry on the fatigue crack growth rate. A series of fatigue tests on three-point bending specimens with different initial crack lengths were conducted. As a result, the dependence of the crack growth rate on the T-stress value was obtained.

Previous control methods developed by our research team cannot satisfy the high-accuracy requirements of unmanned surface vessel (USV) path-tracking during bathymetric mapping because of the excessive overshoot and slow convergence speed. For this reason, this study developed an adaptive fuzzy integral-derivative line-of-sight (AFIDLOS) guidance law for USV path-tracking control. Integral and derivative terms were added to counteract the effect of the sideslip angle, with which the USV could be quickly guided to converge to the planned path for bathymetric mapping. To obtain a high-accuracy of the look-ahead distance, a fuzzy control method was proposed. The proposed method was verified using simulations and outdoor experiments. The results demonstrate that the AFIDLOS guidance law can reduce the overshoot by 79.85%, shorten the settling time by 55.32% in simulation experiments, and reduce the average cross-track error by 10.91%, and can ensure a 30% overlap of neighboring strips of bathymetric LiDAR outdoor mapping when compared with the traditional method.

The steady rheological behavior of suspensions of solid particles thickened by cellulose nanocrystals is investigated. Two different types and sizes of particles are used in the preparation of suspensions, namely TG hollow spheres of Sauter mean diameter of 69 µm and Solospheres S-32 of Sauter mean diameter of 14 µm. The nanocrystal concentration varies from 0 to 3.5 wt% and the particle concentration varies from 0 to 57.2 vol%. The influence of salt (NaCl) concentration and pH on the rheology of suspensions is also investigated. The suspensions generally exhibit shear-thinning behavior. The degree of shear-thinning is stronger in suspensions of smaller size particles. The experimental viscosity data are adequately described by a power-law model. The variations of power-law parameters (consistency index and flow behavior index) under different conditions are determined and discussed in detail.

This paper examines the response of the ionosphere to the impact of two moderate geomagnetic storms observed in January 17 and 26-27, 2013 under conditions of strong sudden stratospheric warming. The study uses data from ground-based ionosonde measurements at the Alma-Ata ionospheric station (43.25 N, 76.92 E) combined with optical observation data (The Spectral Airglow Temperature Imager (SATI)). Ionosonde data showed that the geomagnetic storms under consideration do not generate ionospheric storms, but demonstrate some unusual types of diurnal foF2 variations with large (up to 60%) deviations of foF2 from median values observed during the night/morning periods on 13-15 and 20-23 January which do not have any relation to solar or geomagnetic activity. Wave-like disturbances in foF2, h’F and daily averaged foF2 values with quasi-period of 5-8 days and peak-to-peak amplitude from about 1MHz to 2 MHz (from 20% to 40%) and ~40 km are observed during the 9-28 January, after registration the occurrence of the major SSW event on 6-7 January. The observed variations in the OH emission rate are found to be quite similar to those observed in the ionosheric parameters that assume a community of processes in the stratosphere/mesosphere/ionosphere system. The study shows that the F-region of the ionosphere is influenced by processes in the lower ionosphere, in this case by processes associated with sudden stratospheric warming SSW-2013, which led to modification of the structure of the ionosphere and compensation of processes associated with the development of the ionospheric storms.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

For many decades, X-ray diffraction (XRD) has been used for material characterization. With the recent development in material science understanding and technology, various new materials are being developed, which requires upgrading the existing analytical techniques such that intricate problems can be solved. Although, XRD is a well-established non-destructive technique, it still requires further improvements in its characterization capabilities, especially when dealing with complex mineral structures. The present review conducts comprehensive discussions on atomic crystal structure, XRD principle, its applications, uncertainty during XRD analysis, and required safety precautions, all in one place. It further discusses the future research directions, especially the use of artificial intelligence and machine learning tools for improving the effectiveness and accuracy of XRD technique for mineral characterization. It has been focused that how XRD patterns can be utilized for a thorough understanding of the crystalline structure, size, and orientation, dislocation density, phase identification, quantification, and transformation, information about lattice parameters, residual stress, and strain, and thermal expansion coefficient of materials. All these important discussions on XRD for mineral characterization are compiled in this short yet comprehensive review that would benefit specialists and engineers in the chemical, mining, iron, metallurgy, and steel industries.

We take a heterodox approach to the ΛFRW Cosmology starting from the modification of Newtonian gravity by explicitly incorporating Mach's Principle through an additional term a great scale in the gravitation. The results show that at the after of the matter-radiation decoupling, the distribution of matter at scales greater than 10Mpc contributes with an inverse Yukawa-like field, which verifies the observations: resulting null in the inner solar system, weakly attractive in ranges of interstellar comoving distances, very attractive in comoving distance ranges comparable to the clusters of galaxies, and repulsive in cosmic scales. This additional term explains dark energy, removes the incompatibility between the density of matter and the flatness of the universe; and also allows the theoretical deduction of the Hubble-Lemaitre Law. Additionally, Birkhoff Theorem, Virial Theorem, the missing mass of Zwicky, the BAO, gravitational redshift are discussed. It is concluded that the dark energy and the missing mass can be approached with the usual physics if a classical, large-scale modification of the Inverse Square Law.

The Newton-Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton’s characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of Green function satisfying the radial Schrödinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb-Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential.

Inspired by amazing result obtained by Semay [1], this study revisits generalised Kepler's third law of an n-body system from the perspective of dimension analysis. To be compatible with Semay's quantum n-body result, this letter reports a conjecture which had not be included in author's early publication [2] but formulated in the author's research memo. The new conjecture for quantum N-body system is proposed as follows: Tq|Eq|^3/2 = πG/√2[(Σ^N_i=1 Σ^N_j=i+1 m_im_j)³/(Σ^N_k=1 m_k)]^1/2. This formulae is, of course, consistent with the Kepler's third law of 2-body system, and exact same as Semay's quantum result for identical bodies.

We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon -- a device that interacts with a memory register (a stream of bits), a thermal reservoir (an ideal gas) and a work reservoir (a mass that can be lifted or lowered). Our device is similar to one that we have briefly described elsewhere [1], but it has the additional feature that it can be programmed to recognize a chosen reference sequence, for instance, the binary representation of $\pi$. If the bits in the memory register match those of the reference sequence, then the device extracts heat from the thermal reservoir and converts it into work to lift a small mass. Conversely, the device can operate as a generalized Landauer's eraser (or copier), harnessing the energy of a dropping mass to write the chosen reference sequence onto the memory register, replacing whatever information may previously have been stored there. Our model can be interpreted either as a machine that autonomously performs a conversion between information and energy, or else as a feedback-controlled device that is operated by an external agent. We derive generalized second laws of thermodynamics for both pictures. We illustrate our model with numerical simulations, as well as analytical calculations in a particular, exactly solvable limit.

In this paper, we investigate the stabilization of a one-dimensional thermoelastic laminated beam with structural damping, coupled to a heat equation modeling an expectedly dissipative effect through heat conduction governed by Gurtin-Pipkin thermal law. Under some assumptions on the relaxation function g, we establish the well-posedness for the problem. Furthermore, we prove the exponential stability and lack of exponential stability for the problem. To achieve our goals, we make use of the semigroup method, the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem.

Aerial image classification has become popular and has attracted extensive research efforts in recent decades. The main challenge lies in its very high spatial resolution but relatively insufficient spectral information. To this end, spatial-spectral feature extraction is a popular strategy for classification. However, parameter determination for that feature extraction is usually time-consuming and depends excessively on experience. In this paper, an automatic spatial feature extraction approach based on image raster and segmental vector data cross-analysis is proposed for the classification of very high spatial resolution (VHSR) aerial imagery. First, multi-resolution segmentation is used to generate strongly homogeneous image objects and extract corresponding vectors. Then, to automatically explore the region of a ground target, two rules, which are derived from Tobler’s First Law of Geography (TFL) and a topological relationship of vector data, are integrated to constrain the extension of a region around a central object. Third, the shape and size of the extended region are described. A final classification map is achieved through a supervised classifier using shape, size, and spectral features. Experiments on three real aerial images of VHSR (0.1 to 0.32 m) are done to evaluate effectiveness and robustness of the proposed approach. Comparisons to state-of-the-art methods demonstrate the superiority of the proposed method in VHSR image classification.

We propose the Ramsey approach for the analysis of behavior of isolated mechanical systems containing interacting particles. The total momentum of the system in the frame of the center of masses is zero. The mechanical system is described by the Ramsey, bi-colored, complete graph. Vectors of momenta of the particles pi serve as the vertices of the graph. We start from the graph representing the system in the frame of the center of masses, the momenta of the particles in this system are pcmi. If (pcmi(t)∙pcmj(t))≥0 is true, vectors of momenta of the particles numbered i and j are connected with the red link; if (pcmi(t)∙pcmj(t))&lt;0 takes place, the vectors of momenta are connected with the green link. Thus, the complete, bi-colored graph emerges. Consider the isolated system built of six interacting particles. According to the Ramsey Theorem, the graph inevitably comprises at least one monochromatic triangle. The coloring procedure is invariant relatively rotations/translations of frames; thus, the graph representing the system contains at least one monochromatic triangle in any of frames emerging by rotation/translation of the original frame. This gives rise to the novel kind of a mechanical invariant. Similar coloring is introduced for the angular momenta of the particles. However, the coloring procedure is sensitive to Galilean/Lorenz transformations. Extensions of the suggested approach are discussed.

53% of adults in the US acknowledge racial bias as a significant issue, 23% of Asian adults experience cultural and ethnic bias, and more than 60% conceal their cultural heritage after racial abuse. AI models like ChatGPT and Google Bard, trained on historically biased data, inadvertently amplify racial and ethnic bias and stereotypes. This paper addresses the issue of racial bias in AI models using scientific, evidence-based analysis and auditing processes to identify biased responses from AI models and develop a mitigation tool. The methodology involves creating a comprehensive database of racially biased questions, terms, and phrases from thousands of legal cases, Wikipedia, and surveys, and then testing them on AI Models and analyzing the responses through sentiment analysis and human evaluation, and eventually creation of an 'AI-BiasAudit,' tool having a racial-ethnic database for social science researchers and AI developers to identify and prevent racial bias in AI models.

It has been empirically observed that the upper tail of the firm size distribution follows either the Pareto distribution or the Zipf distribution, with both patterns being explained by Gibrat’s law (Gabaix, 1999). This article analyzed firm revenue data from China, spanning from 2005 to 2013, to examine the whole range of the firm size distribution. Our empirical analysis revealed that firm revenue data over these years is well fitted by a three-parameter generalized Pareto distribution, with the fitted parameters indicating a dichotomy: The size distribution of large-sized firms, namely the upper tail, is asymptotically characterized by a Pareto distribution or a Zipf distribution, whereas the size distribution of smaller and medium-sized firms is approximated by an exponential distribution. This finding suggests that Gibrat’s law should be extended to account for the emergence of a generalized Pareto distribution.

Despite being stored at 113 K and atmospheric pressure, LNG cold potential is not exploited to reduce green ships’ energy needs. An innovative system based on three Organic Ranking Cycles integrated into the regasification equipment is proposed to produce additional power and recover cooling energy from condensers. A first-law analysis identified ethylene and ethane as suitable working fluids for the first and the second ORC making available freshwater and ice. Propane, ammonia and propylene could be arbitrarily employed in the third ORC for air-conditioning. An environmental analysis that combines exergy efficiency, ecological indices and hazard aspects for marine environment and ship’s passengers, indicated propylene as safer and more environmentally friendly. The exergy analysis confirms more than 20% of the LNG potential can be recovered from every cycle to produce a net clean power of 76 kW, whereas 270 kW can be saved by recovering condensers' cooling power to satisfy some ship needs. Assuming the sailing mode, a limitation of 162 kg in LNG consumptions was determined, avoiding the emission of 1584 kg of CO2 per day. Marine thermal pollution is reduced by 3.5 times by recovering the working fluids' condensation heat for the LNG pre-heating.

Permeability is an important transport property of porous materials, and its accurate evaluation is relevant in studying applied tasks such as CO2 injection into reservoirs and investigating groundwater quality issues. This study examines the dependence of permeability on total and connected porosity, hydraulic tortuosity, specific surface area, and mean pore radius based on the data of 408 cubic sub-volumes extracted from heterogeneous and naturally fractured cylindrical carbonate samples before and after injection of HCl solutions into them. These parameters were computed using pore-scale modeling of fluid flow. It has been shown that permeability correlates well with porosity and mean pore radius with correlation coefficients of R2≈0.65-0.79 for heterogeneous samples. It was found that the presence of natural fractures significantly influenced the relationship between permeability and other parameters. The relationship between permeability k, tortuosity τ, and specific surface area S is described by power laws k~τ-α and k~S-β, with coefficients α and β substantially exceeding those in the Kozeny-Carman equation. It was also found that there is a parabolic relationship between connected and total porosities both before and after rock dissolution with R2≈0.96-0.99. This allowed for estimation of percolation threshold porosity that are in good agreement with the literature data.

The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in the idea of Shlesinger and colleagues about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The close approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman-Holstein approach to the transfer of excitation of a medium by photons, generalized to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson's t3 scaling law to the combined regime of Lévy flights and Lévy walks.

We think of time as one of four dimensions appearing in the equations of motion of Newtonian and quantum physics, but participating independently of space. In these pages we explore the way the time variable affects how space is perceived. We show first that non-commutation may be interpreted as the difference between electron and photon cycling during radiation processes. For every electron cycle of a quantum oscillator there are two photon cycles. Secondly, the difference between relativistic and non-relativistic quantum mechanics is shown to be related to time evolution. Only relativistic models evolve continuously. The reasoning of Einstein is implicit to an understanding of both physical models. Previously obtained derivations of relativistic quantum mechanics are reaffirmed by following the ideas of Dirac.

Global economy, financial markets and technology are on the verge of moving to a new stage of development – information society. Three major world countries the US, Russia and China will play a leading role in this process. However, the specific development path will depend on many factors, including the stability of legal systems, security of computer and financial technologies, the effectiveness of legislation. The focus of this article is to assess the current condition of the economy the major countries, to identify trends and methods of stabilization of legal systems on the basis of balance of rights and obligations of the business, suggest some methods of objective evaluation of the impact factors of the total taxes, fixed costs and the legal system dynamics on financial indicators.

Magnetometric Resistivity(MMR) Method, which can use the power supply method of the traditional apparent resistivity method to measure the magnetic field. At present, the application research abroad is relatively extensive, but the domestic(China) research on the application of the MMR method is very few, and it is not even well-known. This paper is based on the MMR theoretical method under the point source DC condition, combined with the abnormal potential method and the modified Biot-Savart law, and using the three-dimensional numerical calculation method of the finite difference method to calculate the abnormal potential field, electric field, and magnetic field on the matlab2018a platform. Calculate, realize the multi-physics simulation in the electromagnetic field through Matlab platform programming, and verify the correctness of the algorithm by the spherical anomaly model with an analytical solution. Through the visual simulation of the three-dimensional data volume of the multi-physics field in the electromagnetic field, we can better understand the response mechanism of the electromagnetic field under DC conditions and grasp their three-dimensional spatial distribution rules. It is hoped that the research in this article can help the research of MMR Personnel better use this method for exploration.

In the work, the nuclei structure was modeled by a system of shells consisting of combinations of spherical and annular vortices. Having connected the spin and the magnetic moments of the nuclei with the dynamics of the outer shell of the nucleus, we determined its type and carried out a semiempirical calculation of the parameters of its structure for stable and unstable nuclear isotopes in the sequence of the order number Z from 1 to 37. Comparison of the obtained nuclear sizes with the radii of the electron shells of atoms made it possible to reveal a definite correlation. On the basis of it, it was concluded that the periodic law of Mendeleyev can determine the patterns in the change in the structure of the atomic nucleus.

The aim of this work is to study generalizations of the notion of mean. Kolmogorov proposed a generalization based on an improper integral with a decay rate for the tail probabilities. This weak or Kolmogorov mean relates to the Weak Law of Large Numbers in the same way that the ordinary mean relates to the Strong Law. We propose a further generalization, also based on an improper integral, called the doubly weak mean, applicable to heavy-tailed distributions such as the Cauchy distribution and the other symmetric stable distributions, We also consider generalizations arising from Abel-Feynman type mollifiers that damp the behavior at infinity and alternative formulations of the mean in terms of the cumulative distribution and the characteristic function.

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

It has been theorized that black holes are surrounded by firewalls, although there is not universal agreement concerning this. We first review basic concepts pertaining to Schwarzschild black holes and Hawking radiation. Then we discuss the anticipation of Hawking radiation—albeit from non-black holes—initially by R. C. Tolman and shortly thereafter with P. Ehrenfest. We compare evaporation into a vacuum at absolute zero (0 K) of black holes with that of non-black holes, and show that not only black holes but also non-black holes evaporate within a finite time. The times required for evaporation of black holes and non-black holes are compared. Next, we show that (i) if firewalls exist, they can originate via Hawking radiation at the minimum possible ruler distance (the Planck length) beyond the Schwarzschild horizon, where it has not suffered any gravitational redshift, or, alternatively, suffered maximal gravitational blueshift and (ii) the firewall temperature is on the order of the Planck temperature, independently of the mass and hence also of the Schwarzschild radius of a Schwarzschild black hole. We then explain the exponential nature of the gravitational frequency shift as a function of the gravitational potential. Next, we consider the firewall-mass problem, and provide an at least prima facie tentative resolution thereto based on: (i) the mass of a firewall being canceled by the negative gravitational mass = (negative gravitational energy)/c² accompanying its formation, (ii) the unchanged observations of a distant observer upon formation of a firewall, and (iii) Birkhoff's Theorem (actually first discovered by Jørg Tofte Jebsen). We then consider one aspect of thermodynamics in gravitational fields, showing that equilibrium relativistic gravitational temperature gradients cannot be exploited to violate the Second Law of Thermodynamics.

The present study examines the relationship between thermal and configurational entropy in two resistors in parallel and in series. The objective is to introduce entropy in electric circuits analysis by considering the impact of system geometry on energy conversion in the circuit. Thermal en-tropy is derived from thermodynamics, whereas configurational entropy is derived from network modelling. It is observed that the relationship between thermal entropy and configurational en-tropy varies depending on the configuration of the resistors. In parallel resistors, thermal entropy decreases with configurational entropy, while in series resistors, the opposite is true. The impli-cations of the maximum power transfer theorem and constructal law are discussed. The entropy generation for resistors at different temperatures was evaluated, and it was found that the con-sideration of resistor configurational entropy change was necessary for consistency. Furthermore, for the sake of generalization, a similar behavior was observed in time-dependent circuits, either for resistor-capacitor circuits or circuits involving degradation.

We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.

The layout of deep chamber for coal-gangue separation (DCCS) based on the horizon of the weak stratum can affect the stability of its surrounding rocks. First, the work summarized the main structural characteristics of DCCS. Similar simulation tests were performed to analyze the deformation and failure law of surrounding rocks of DCCS under different horizons of the weak stratum. Then, 60 numerical simulation schemes were designed by considering the lateral pressure coefficient and the thickness and horizon of the weak stratum. A comprehensive evaluation method was proposed for the stability of surrounding rocks. The optimal layout methods of the DCCS were determined based on the thickness and horizon of the weak stratum in different ground stress fields. If the thickness of the weak stratum was large and lateral pressure coefficient λ &lt; 0.6 or λ &gt; 1, the stability of surrounding rocks was optimal to arrange the side of DCCS along the weak stratum. When 0.6 ≤ λ ≤ 1, the optimal approach for controlling surrounding rocks was to position the floor of DCCS along the weak stratum. If the thickness of the weak stratum was small and λ&lt;0.6 or λ&gt;1, the stability of surrounding rocks was optimal to arrange the side of DCCS near roof along the weak stratum. When 0.6 ≤ λ ≤ 1, the optimal approach for controlling surrounding rocks was to arrange the side of DCCS near the floor along the weak stratum. The results can provide an important theoretical reference for the spatial layout and support design of DCCS.

The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts interests are often in symmetry and in the rates of change of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. Applying these estimates we obtain Chung's laws of the iterated logarithm for spatial surfaces of operator fractional Brownian motion. Our results show that the precise rates of change of spatial surfaces are completely determined by the self-similarity exponent.

Elucidating physicochemical processes in the degradation of pollutants may optimize their removal from water sources. This work presents a set of elementary steps in the photocatalytic degradation of carbamazepine (CBZ), assuming a steady state approximation in an Advanced Oxidation Process (AOP) combining short-wave ultraviolet radiation (UVC), homogeneous reagent (H₂O₂) and heterogeneous (TiO₂) catalyst. Elementary steps include excitation of both reagent/catalysts by UVC photons, adsorption of CBZ on the excited TiO₂, or its oxidation by hydroxyl radicals. Assuming the steady state approximation on the intermediate products (excited TiO₂, CBZ- excited TiO₂ complex, and hydroxyl radicals), leads to rate laws for degradation of CBZ, in which UVC radiation, TiO₂, and H₂O₂ are pseudo first order at all concentrations or intensities having no direct influence on CBZ pseudo-order, whereas CBZ shifts from pseudo first order at low concentrations to pseudo-zero order at high concentrations. Several experiments to test the mechanism were conducted, by varying CBZ, H₂O₂, and TiO₂ concentrations, and UVC radiation intensities. Measured results indeed fit the suggested mechanism for the first three, but irradiation intensity appears to shift CBZ influence from pseudo-second to pseudo-first order with increased intensities. Corrected elementary steps are proposed to fit the results.

It has been well known that the exponential distribution is the only continuous distribution that has the memoryless property. Here, we observe that, if the exponential distribution dominates an economy as a probability distribution of income acquisition, then the memoryless property imposes equal opportunities on agents in this economy to acquire earnings. Based on this observation, we propose to identify the emergence of an exponential income distribution as a potential necessary condition for guaranteeing the equality of opportunity. Together with other conditions (such as social and economic mobility), it would promote equal opportunities for income acquisition among citizens. Empirically, we employ the latest data available from four representative market-economy countries (the United Kingdom, the United States, Canada, and China) to demonstrate that the exponential distribution is a stylized feature of the income structure of the low- and middle-income class, which occupies the great majority of populations. By contrast, the top income classes in these countries obey the Pareto distribution. To validate the relationship between exponential distribution and equal opportunity, we empirically show how the income structure of the low- and middle-income class in China (from 1978 to 2015) evolved towards an exponential distribution after the market-oriented economic reformation.

Political and legal debate about freedom of religion and belief (FoRB) in Australia has intensified since the Same-sex marriage postal survey in 2017. Central to this debate has been children, their parents and institutions (Schools). This paper outlines the place of children in the Australian FoRB since 2017, focusing on the Same-sex marriage postal survey debate and subsequent reviews into freedom of religion. In particular it highlights the links drawn between same-sex marriage or marriage equality and the Safe School Coalition Australia campaign, the emphasis on parental rights in relation to education about marriage in schools and the ongoing debate about potential reform to Australia’s suit of anti-discrimination laws

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

The Betz limit sets a theoretical upper limit for the power production by turbines expressed as a maximum power coefficient of 16/27. Betz’s theory is accurate and it is based on the calculation of kinetic energy.

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

This article presents a new theory on redshift of light from celestial bodies. Lately it has been found that the Hubble constant calculated from different methods discord so much that calls arise for new physics to explain. Also, in addition to many unsolved puzzles like dark matter and source of expansion force, we shall show in this article that the current theory of redshift implies a few hidden, unreasonale assumptions. By assuming photon has temperature and its thermal energy is fully converted to wave energy, this article shows that photon can have a new redshift called Temperature Redshift, which not only is more significant for remote stars or galaxies, but also better fits the observational data, including those used in Hubble constant calculation. As such, if true, this new theory not only adds to our new understanding of photons, but may totally change our current understanding of the Universe, i.e., the Big Bang theory.

With reference to Planck scale, increasing support for large scale cosmic anisotropy and preferred directions and by considering an increasing ratio of Hubble parameter to angular velocity, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the baby universe in all directions). We would like suggest that, from the beginning of Planck scale, 1) Dark matter can be considered as a kind of cosmic foam responsible for formation of galaxies. 2) Cosmic angular velocity decreases with square of the decreasing cosmic temperature. 3) Increasing ratio of Hubble parameter to angular velocity plays a crucial role in estimating increasing cosmic expansion velocity and decreasing density ratios of dark matter and ordinary matter. 4) There is no need to consider dark energy for understanding cosmic acceleration.

As noted in the introductory quotation, an ideal map was long ago seen as the map of the map, the map of the map, of the map, and so on endlessly. This recursive perspective on maps, however, has received little attention in cartography. Cartography, as a scientific discipline, is essentially founded on Euclidean geometry and Gaussian statistics, which deal with respectively regular shapes, and more or less similar things. It is commonly accepted that geographic features – such as rivers, cities, streets and building – are not regular and that the Earth’s surface is full of fractal or scaling or living phenomena with far more small things than large ones at different levels of scale. This paper argues for a new paradigm in mapping, based on fractal or living geometry and Paretian statistics, and – more critically – on the new conception of space, conceived and developed by Christopher Alexander, that space is neither lifeless nor neutral, but a living structure capable of being more living or less living. The fractal geometry is not limited to Benoit Mandelbrot’s framework, but is extended towards Christopher Alexander’s living geometry and based upon the third definition of fractal: A set or pattern is fractal if the scaling of far more small things than large ones recurs multiple times. Paretian statistics deals with far more small things than large ones, so it differs fundamentally from Gaussian statistics, which deals with more or less similar things. Under the new paradigm, I make several claims about maps and mapping: (1) Topology of geometrically coherent things – in addition to that of geometric primitives – enables us to see a scaling or fractal or living structure; (2) Under the third definition, all geographic features are fractal or living, given the right perspective and scope; (3) Exactitude is not truth – to paraphrase Henri Matisse – but the living structure is; and (4) Töpfer’s law is not universal, but scaling law is. All these assertions are supported by evidence, drawn from a series of previous studies. This paper demands a monumental shift in perspective and thinking from what we are used to on the legacy of cartography and GIS.

The philosophy of testing statistical hypothesis is a natural consequence and functional extension of mathematical analysis of Probability. Along with the concept of recurrence when applied to random sequences and functions, it leads to the analysis of a priori and posterior which implies testing statistical hypothesis. Testing statistical hypothesis also involves algebraic, functional and dimensional considerations, which are found in the works of Laplace. Aspects of mathematical analysis such as universality of solutions, Laws of Large Numbers, Entropy, Information, and various functional dependencies are the main factors explained in the five properties that lead to implication of testing statistical hypothesis. Various interesting examples with modern scientific significance from genetics, astrophysics, and other areas give methodological access to answers of different problems and phenomena which are involved in the logic of testing statistical hypothesis.

Significant global challenges, particularly in the areas of economics, society, and the environment, are posed by urbanization. In this researcher-led study, we look at how Jordan is trying to bring the Sustainable Development Goals (SDGs) to life in its capital, Amman, by bringing urban laws in line with these global goals. The paper finds legislative flaws that prevent SDG incorporation through a thorough analysis of the Amman Building and Regulation Act of 2019. Some of the main points covered are public participation, the use of renewable energy sources, sustainable construction practices, resilience in urban areas, and the management of natural resources. Although a lot of work has gone into it, the analysis shows that if Jordan wants to accomplish the 2030 Agenda and have sustainable urban growth in the future, it must overcome these institutional and legal barriers. As a model for other cities facing a similar challenge, Amman is being asked to lead the way in SDG localization through more public involvement, new laws, and innovative resource management.

This author is not a philosopher nor historian of science, but an engineering thermodynamicist. In that regard and in addition to various philosophical “why & how” treatises and existing historical analyses, the physical and logical “what it is” reflections, as successive Key Points, where a key reasoning infers the next one, along with novel contributions and original generalizations, are presented. We need to keep in mind that in Sadi Carnot’s time (early 1800s) the steam engines were inefficient (below 5%, so the heat in and out were comparable within experimental uncertainty), the conservation of caloric flourished (might be a fortunate misconception), and many critical thermal-concepts, including the conservation of energy (The First Law) were not even established. If Clausius and Kelvin were "fathers of thermodynamics" then Sadi Carnot was the "grandfather" [Kostic, 2023 July 24], or better yet, Sadi Carnot was the "Forefather of Thermodynamics-to-become" [Kostic, 2023 October 29].

It's a method to achieve energy savings in single-phase active power greater than that obtained with the "Fan Law" in electric machines applied to ventilation. Quantitative analysis methods were based on electrotechnical techniques, practiced with the corresponding laboratory equipment on the working materials (three prototypes of electric machines). The results obtained from experimentation on the test bench were recorded in tables that collect data of formulas, values, and physical units. The discussion provides a comprehensive comparative study, mainly between power (watts), active energy consumption (kWh), and rotational speed (revolutions per minute). The permanent magnet synchronous motor (PMSM) with the coupling of an RL circuit design does mechanical work at its maximum speed of 3000 (RPM) with only 6.3 (Watts), which is equivalent to 25.2% of the active power required by the single-phase induction asynchronous motor (or shaded pole motor), which required 25 (Watts) to rotate at 1690 (RPM). This translates to 75% lower active power with a 44% superiority in speed, resulting in a 75% savings in single-phase active energy (measured in kWh). The same occurs when comparing it to the universal AC motor (with brushes and wound rotor) to maintain a speed of 3000 (RPM); since it consumes 64.8 (Watts), which is 90.3% more single-phase active energy than that required to achieve the same rotational speed as the permanent magnet synchronous motor (PMSM). The study was conducted on all motors with the same impeller blade diameter and under identical air temperature and atmospheric pressure conditions.

Block copolymers are a class of materials particularly interesting for their ability to self-assemble into ordered structures. In this context, the coupling between environment and dynamics is particularly relevant, given that movements at the molecular level influence various properties of macromolecules. Mixing the polymer with a second macromolecule appears to be an easy way to study these relationships. In this work, we studied a system based on two diblock copolymers of methyl methacrylate as first block and 3-methyl-4-[6-(methylacryloyloxy)-hexyloxy]-4’-pentyloxy azobenzene as second block and their blends with PMMA. The relaxational properties of these systems were investigated by electron spin resonance (ESR) spectroscopy sensitive to nanometric length-scales. The results of the study on the blends were related to the dynamic behavior of the copolymer. The study evidenced the presence of fast and slow molecular sites for the molecular reorientation at nanoscale, modulated by the ability of block copolymer to form supramolecular structures. For blends, the heterogeneities at nanoscale are still detected. However it was found that the presence of the PMMA as the major component of the blends modified their dynamic behaviour.

The Victorian Government Inquiry into wildfires that killed 173 people in 2009 has driven an Australian policy shift from self-evacuation or staying and defending a well-prepared property (‘go or stay’) to self-evacuation under catastrophic fire weather (‘leave early’). The Inquiry also led to the establishment of national ‘performance standards’ for Private Fire Shelters (PFS, that also known as bunkers). Nonetheless, incorporation of PFS into national bushfire policy remains embryonic with only Victoria having streamlined accreditation and planning approval processes. Arguments against PFS include potentially engendering complacency about preparing dwellings to survive fire and encourage risky behavior in response to a fire threat. Counteracting these arguments is research that shows that residents without PFS have low engagement with bushfire preparation and typically delay evacuation. In any case, because wildfire is unpredictable it is accepted that self-evacuation plans must have fallback positions that include sheltering ‘in place’ from the bushfire, making properly used and well maintained PFS an important element of bushfire safety. A less discussed barrier to PFS uptake outside Victoria appears to hinge on a lack of clarity about obligations for their design, certification, and consistency with planning approvals. The escalating Australian fire crisis demands much greater research and development in legal frameworks, policy and planning processes for PFS, as well as design and construction standards.

The EPR paradox was caused by the provision that quantum variables must have pre-existing values. This type of “hidden property realism” was later falsified by Bell’s Theorem. Accordingly, the physical basis for action-at-a-distance between entangled quanta was removed. Yet, modern interpretations present Bell’s inequality as a Locality Criterion, as if Bell violations can only happen at the quantum level, and only with remote interactions. This is a questionable practice, considering that classical joint measurements also violate such inequalities for mutually exclusive wave properties. In particular, consecutive measurements of polarization produce the same coef-ficients of correlation as parallel measurements with entangled quanta, yet they are explicitly local. Furthermore, it is possible to combine parallel and consecutive measurements of Type I polariza-tion-entangled photons in a single experiment, conclusively showing that quantum Bell violations can be local. Surprisingly, classical phenomena also require nonlocal interpretations if pre-existing properties are taken for granted. Hence, the solution is to reject the models with pre-existing properties for both classical and quantum wave-like phenomena.