In this paper, we derive Jeffreys divergence, generalized Fisher divergence and corresponding De Bruijn identities on space-time random field. First, we determine the relation between Fisher information on the space-time random field in one of the space-time points and the ratio of Jeffreys divergence on a space-time random field at distinct space-time positions to the square of coordinate difference. In addition, we also find identities between the partial derivative of the Jeffreys divergence and the generalized Fisher divergence with respect to space-time variables, i.e. the De Bruijn identities, between two space-time random fields obtained by different parameters under the same Fokker-Planck equations. At the end of this paper, we present three examples of the Fokker-Planck equations on space-time random fields, identify their density functions, and derive the Jeffreys divergence, generalized Fisher information, generalized Fisher divergence, and accompanying De Bruijn identities.

In this paper, we consider the Cauchy problem of a time fractional nonlinear diffusion equation. According to the Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time for some sufficient conditions. We next give sufficient conditions for the existence of global solutions by using the result of Zhang and Sun. In conclusions, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

This work is the first in literature to tackle the difficult open problem of determining the upper bound and threshold theorem for the TDCDP (time-dependent controller parameter) of the (Fokker Planck Kolmogorov) probability density function. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to information theory, graph theory, data science, finance, economics, and beyond. So, this by default adds more taste and credibility to this study. This leads by nature to introducing a different flavor to this ground-breaking research by highlighting the impact of Fokker Planck Kolmogorov(FPK) to revolutionize crypocurrency,which have received its name because it uses encryption to verify transactions, a new debatable digital payment system that doesn't rely on banks to verify transactions. It’s a peer-to-peer system that can enable anyone anywhere to send and receive payments. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.

Biohydrogen is a versatile energy carrier for the generation of electric energy from renewable sources. Hydrogenases can be used in enzymatic fuel cells to oxidize dihydrogen. The rate of electron transfer (ET) at the anodic side between the [NiFe]-hydrogenase enzyme distal iron-sulfur cluster and the electrode surface can be described by the Marcus equation. All parameters for the Marcus equation are accessible from DFT calculations. The distal cubane FeS-cluster has a three cysteine and one histidine coordination [Fe₄S₄](His)(Cys)₃ first ligation sphere. The reorganization energy (inner- and outer-sphere) is almost unchanged upon a histidine-to-cysteine substitution. Differences in rates of electron transfer between the wild-type enzyme and the all-cysteine mutant can be rationalized by a diminished electronic coupling between the donor and acceptor molecules in the [Fe₄S₄](Cys)₄ case. The fast and efficient electron transfer from the distal iron-sulfur cluster is realized by a fine-tuned protein environment which facilitates the flow of electrons. This study enables the design and control of electron transfer rates and pathways by protein engineering.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

The hard open problem of finding the lower bound for the Fokker Planck Kolmogorov’s time-dependent controller parameter probability density function is addressed for the first time in literature in this work. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to multi-interdisciplinary fields of human knowledge, and beyond. So, this by default adds more taste and credibility to this study. Concluding thoughts are included at the end of the work along with a difficult outstanding problem and the direction of future work.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

Understanding user challenges with light dosimeters is crucial for designing more acceptable devices and advancing light exposure research. We systematically evaluated the usability and acceptability of the lido (light dosimeter) by 29 participants who wore the dosimeter near the corneal plane of the eye for 5 days. Common reasons for not wearing the dosimeter included exercise, recharging, wet environments, public settings, and discomfort. Despite these issues, participants adhered to using the dosimeter, with high compliance (89% of recording time). Our findings reveal a significant discrepancy between mean melanopic Equivalent Daylight Illuminance (300 lxmEDI) and median values (51 lxmEDI). This discrepancy indicates that, for most of the time, participants experienced significantly lower light levels. Specifically, participants were exposed to light levels above 250 lxmEDI for only 14% of their wearing time. This highlights the need for increased exposure to recommended light levels. In the evening, participants' light exposure was below the recommended 10 lxmEDI for 58% of the wear time, which is in line with the guidelines for reducing light exposure before sleep. This study highlights the critical need for strategies to enhance daily light exposure, aligning better with circadian health recommendations.

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

A difficult open problem that has never been fully resolved in the literature to date is the behaviour of the (TDCDP) third approximation. As a giant step towards modern control theory, this cutting-edge paper will advance control theory and other relevant inter-disciplinary subjects. Because control theory is important in industry and engineering, this study will be especially beneficial to anyone working in these disciplines who wish to understand more about recent advances in control theory settings. In contrast, the wealth of applications of Fokker Planck Kolmogorov (FPK) equations numerous disciplines As a result, the study instantly gains more taste and credibility. At the end of the paper, there are several challenging open problems, some concluding remarks, and recommendations for further investigation.

The Mononuclear Phagocyte System includes monocytes, macrophages, some dendritic cells and multinuclear giant cells. These cell populations display marked heterogeneity depending on their differentiation from embryonic and bone marrow haematopoietic progenitors, tissue location and activation. They contribute to tissue homeostasis by interacting with local and systemic immune and non-immune cells, through trophic, clearance and cytocidal functions. During evolution they contributed to innate host defense before effector mechanisms of specific adaptive immunity emerged. Mouse macrophages appear at midgestation and are distributed throughout the embryo to facilitate organogenesis and clear cells undergoing programmed cell death. Yolk sac-, AGM- and foetal liver-derived tissue resident macrophages persist throughout postnatal and adult life, supplemented by bone marrow-derived blood monocytes, as required after injury and infection. Nobel awards to Elie Metchnikoff and Paul Ehrlich in 1908 drew attention to cellular phagocytic and humoral immunity, respectively. In 2011, prizes were awarded to Jules Hoffmann and Bruce Beutler for contributions to innate immunity and to Ralph Steinman for discovery of Dendritic Cells and their role in antigen presentation to T lymphocytes. We trace milestones in the history of mononuclear phagocyte research from the perspective of Nobel awards bearing directly and indirectly on their role in cellular immunity.

The correspondence between classical and quaternion quantum equations, permits considering the universe (vacuum) as an ideal elastic solid. Elementary particles would have to be standing or soliton-like waves. Tension induced by the compression and twisting of the elastic medium would increase the energy density, consequently generate a gravity forcing and affect the wave speed. Consequently the gravity could be described by an index of refraction. Theory was created by combining the Cauchy model of the elastic continuum with the Planck-Kleinert crystal hypothesis. The quaternion-imaginary Lagrange’an, the quaternion motion equation and the quaternionic oscillator allowed deriving: - The Schrödinger equation from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. - The 2nd order wave equation system describing both the bosons and the gravity in terms of quaternionic Poisson equation. - The first order quaternionic wave equation system. - The family of the second order wave equation systems describing both the particles and the generated quaternionic force-fields (four-potentials). - The fundamental Planck and gravity constants. - The quaternionic continuity equation in an ideal elastic solid.

In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.

The high radio frequency polarization imaging of non-thermal emission from active galactic nuclei (AGN) is a direct way to probe the magnetic field strength and structure in the immediate vicinity of supermassive black holes (SMBHs) and is crucial in testing the jet-launching scenario. To explore the the magnetic field configuration at the base of jets in blazars, we took advantage of the full polarization capabilities of the GMVA (Global Millimeter VLBI Array). With an angular resolution of ~50 micro-arcseconds at 86 GHz, one could reach scales down to ~900 Schwarzschild radii (for a 10^9 solar mass black hole). We present here the preliminary results of our study on the blazar BL Lac. Our results imply that on sub-mas scales the core and central jet of BL Lac is significantly polarized with two distinct regions of polarized intensity. We also noted a great morphological similarity between the 7mm/3mm VLBI images at very similar angular resolution.

In this paper, we analyze the generalized Ulam-Hyers stability of affine type AQ Functional Equation in various Banach Spaces using Direct and Fixed Methods

Plant growth promoting rhizobacteria (PGPR) are a diverse group of microorganisms including genera such as Pseudomonas, Bacillus, Serratia, Enterobacter and Klebsiella. These bacteria have the ability to colonize roots externally and internally, and to directly enhance plant growth employing various mechanisms like phytohormone production and nutrient mineralization. These microbes can also promote plant growth indirectly by secreting antimicrobial compounds (e.g., siderophores, hydrogen cyanide) to antagonize root pathogens or by inducing defensive responses in the plant. Interestingly, there are also cases where production of antibiotic compounds such as 2,4-Diacetylphloroglucinol have the direct effect of enhancing plant growth and yield, irrespective of their biocontrol effects. The objective of this paper is to review publications showcasing PGPRs that have the capacity to both control root pathogens and stimulate plant growth, and to discuss what mechanisms might be involved.

We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for long-ranged hydrodynamic effects. We derive the fractional Langevin equation governing the dynamics of the active particle, as well as that of any other passive particle (or probe) bound to the elastic system. Our study explores the diffusional behavior emerging for both the active particle and a distant probe.

This article develops a multi-perspective view on motivations and methods for tobamovirus purification through the ages, and presents a novel efficient, easy-to-use approach that can be well-adapted to different species of native and functionalized virions. We survey the various driving forces prompting researchers to enrich tobamoviruses: from the search for the causative agents of mosaic diseases in plants to their increasing recognition as versatile nanocarriers in biomedical and engineering applications. Best practice and also rarely applied options for the serial processing steps required for successful isolation of tobamoviruses are then reviewed. Adaptations for distinct particle species, pitfalls and 'forgotten' or underrepresented technologies are considered as well. The article is topped off with our own development of a method for virion preparation, rooted in historical protocols. It combines selective re-solubilization of polyethylene glycol (PEG) virion raw precipitates with density step gradient centrifugation in biocompatible iodixanol formulations, yielding ready-to-use particle suspensions. This newly established protocol and some considerations for perhaps worthwile further developments could serve as putative stepping stones towards preparation procedures appropriate for routine practical uses of the multivalent soft-matter nanorods.

Autologous platelet-rich plasma (PRP) preparations are prepared at point of care. Centrifugation cellular density separation sequesters a fresh unit of blood into three main fractions: a platelet-poor plasma (PPP) fraction, a stratum rich in platelets (platelet concentrate) and, bioformulation dependent, also leukocyte and erythrocyte fractions. The employment of autologous platelet concentrates facilitates the biological potential to accelerate and support in numerous cellular activities that can lead to tissue repair, tissue regeneration, wound healing, and ultimately functional structural repair. Normally, after PRP preparation the PPP fraction is discarded. One of the less well known, but equally important features of PPP is that particular growth factors (GFs) are not abundantly present in PRP, as they reside outside the platelet alpha granules. Precisely, insulin-like growth factor-1 (IGF-1) and hepatocyte growth factor (HGF) are mainly present in the PPP fraction. In addition to their roles as angiogenesis activators, these plasma-based GFs are also known to inhibit inflammation, fibrosis, and they promote keratinocyte migration and support in tissue repair and wound healing. Additionally, PPP is known for the presence of exosomes and other macrovesicles, exerting cell-cell communication and cell signaling. Newly developed ultrafiltration technologies incorporate PPP processing methods by eliminating in a fast and efficient manner plasma water, cytokines, molecules, and plasma proteins with a molecular mass (weight) less than the pore size of the fibers. Consequently, a viable and viscous protein concentrate of functional, total proteins, like fibrinogen, albumin, and alpha-2-macroglobulin is created. Consolidating a small volume of high platelet concentrate with a small volume of highly concentrated protein-rich PPP creates a protein rich platelet concentrate (PRPC) biological preparation. After the activation of proteins, mainly fibrinogen, the PRPC matrix retains and facilitates interactions between invading resident cells, like macrophages, fibroblast, and mesenchymal stem cells (MSCs), and the embedded concentrated PRP cells and molecules. The administered PRPC biologic will ultimately undergo fibrinolysis, leading to a sustained release of concentrated cells and molecules that have been retained in the PRPC matrix until the matrix is dissolved. We will discuss the unique biological and tissue reparative and regenerative properties of PRPC matrix.

Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, momentum spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Schrödinger equation the wave function is represented by a single complex quantity, in the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors.In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. The Lagrangian densities for the scalar field and for the electron field, along with their corresponding propagators, are presented. An equation of motion for the electron is proposed that is relativistically invariant, in contrast to the Dirac equation, which lacks this invariance. This novel equation permitted the construction of a relativistically invariant procedure for the second quantization of the fermion field in spinor coordinate space.

DiFX is a software VLBI correlator currently adopted by several main correlation sites around the globe. After the launch of the RadioAstron Space-VLBI mission in 2011, an extension was necessary to handle processing of an orbiting antenna, to be correlated with supporting ground arrays. We present here a branch of the main DiFX distribution (2.4), recently uploaded on the publicly available repository, that MPIfR developed to process data of the three AGN-imaging RadioAstron key science projects. It can account for general relativistic correction of an orbiting antenna with variable position/velocity, providing a routine to covert the native RDF format to the more common M5B one. Also, a fringe-finding algorithm able to manage arbitrary large fringe-search window is included, allowing one to increase the search space normally adopted by common software packages like HOPS.

In modern physics, it is assumed that the Planck length is a derived constant from Newton's gravitational constant, the Planck constant and the speed of light, $l_p=\sqrt{\frac{G\hbar}{c^3}}$. This was first discovered by Max Planck in 1899. We suggest a way to find the Planck length independent of any knowledge of Newton's gravitational constant or the Planck constant, but still dependent on the speed of light (directly or indirectly).

With reference to Planck scale, Mach’s relation, increasing support for large scale cosmic anisotropy and preferred directions and by introducing two new parameters Gamma and Beta, 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 is directly proportional to squared cosmic temperature. 3) Ratio of critical temperature to actual temperature plays a heuristic role in understanding ordinary and dark matter density ratios. 4) Cosmic expansion velocity increases with decreasing total matter density ratio. 5) There is no need to consider dark energy for understanding cosmic acceleration.

To understand the biological relevance and mode of action of artificial protein ligands, crystal structures with their protein targets are essential. Here, we describe and investigate all known crystal structures that contain a so-called “molecular tweezer” or one of its derivatives with an attached natural ligand on the respective target protein. The aromatic ring system of these compounds is able to include lysine and arginine side chains, supported by one or two phosphate groups that are attached to the half-moon shaped molecule. We analyse the corresponding crystal structures with 14-3-3 proteins in complex with mono- and diphosphate tweezers. Furthermore, we solved crystal structures of two different tweezer variants in complex with the enzyme 1-Pyrroline-5-carboxyl-dehydrogenase (P5CDH), and found that the tweezers are bound to a lysine and methionine side chain, respectively. The different binding modes and their implications for affinity and specificity are discussed, as well as the general problems in crystallizing protein complexes with artificial ligands.

When limited area models of the hydrodynamics of the atmosphere and of the ocean are 1 run over an extended time, variability unrelated to external "drivers" emerge - this variability is 2 colloquially named "hydrodynamical noise" or just "noise". This article summarises what we have 3 learned in the past few years about the properties of such noise, and the implications for numerical 4 experimentation and analysis. The presence of this noise can be identified easily in ensembles of 5 numerical simulations, and it turns out that the intensity of the noise is closely linked to the scale- 6 dependent "memory". At the system level, this "memory" term as given by Hasselmann’s Stochastic 7 Climate model plays a key role. In the case of marginal seas, the process of baroclinic instability 8 modulated by tides and the formation of seasonal thermoclines are significant aspects. Some more 9 general aspects are discussed, such as the applicability of the Stochastic Climate model to systems 10 outside of atmospheric and oceanic dynamics, the irreversibility of tipping points and the challenges 11 of detecting changes beyond a noise level and of the attribution of causes of change.

In this paper we study a class of impulsive delayed neural networks with parameter uncertainties and reaction-diffusion terms. Using the properties of M-matrices and some inequality techniques, some sufficient conditions are derived to guarantee the global exponential stability of the given system. The results obtained are presented by simple algebraic inequalities, which are certainly more concise than previous methods. Finally, the validity and usefulness of our results are illustrated by arithmetic examples.

Abstract: Short-chain fatty acids (SCFAs) are the major microbial metabolites produced in the gut through the fermentation of non-digestible fibers. SCFAs act through free fatty acid receptor 2 and 3 (FFAR2 and 3), which are known to be expressed on glucagon-like peptide-1 (GLP-1)-secreting L-cells. This pathway is suggested to protect the intestinal mucosa. We aimed to investigate how lack of fiber affects the production of SCFAs and the vulnerability of the co-lon. Additionally, the involvement of FFAR2 and 3 in GLP-1 secretion and intestinal protection. SCFA concentrations in luminal contents from chow- or fiber-free diet-fed mice were analysed by LC‒MS. SCFAs were applied to isolated perfused colons from FFAR2/3 double KO and WT mice, and the secretion of GLP-1 was measured. Dextran sulfate sodium (DSS) colitis was induced in chow- or fiber-free diet-fed mice as well as in FFAR2/3 KO and WT mice. The removal of die-tary fiber significantly decreased total colonic SCFA concentrations, with specific decreases in acetate, propionate, and butyrate. SCFAs significantly increased colonic GLP-1 secretion but not in FFAR2/3 KO mice. In the DSS model, the removal of dietary fiber increased the severity and delayed recovery. Colitis severity was independent of FFAR2 and FFAR3 signaling.

Diffusion magnetic resonance imaging (dMRI) is an imaging technique that provides information on the microstructural organization of biological tissue. dMRI allows for non-invasive visualization and quantitative assessment of white matter architecture in the brain by characterizing restrictions on the random motion of water molecules. Ultra-high field MRI scanners, such as those operating at 7 Tesla (7T) or higher, can boost signal-to-noise ratio (SNR) to improve dMRI compared with what is attainable at conventional field strengths such as 3T or 1.5T. However, at 7T wavelength effects cause lower transmit magnetic field efficiency in the human brain, mainly in the posterior fossa region, manifesting as signal dropouts in this region. Recently, we reported a simple approach of using a wireless radiofrequency (RF) surface array to improve transmit efficiency and signal sensitivity at 7T. Here we demonstrate the feasibility and effectiveness of using this RF enhancer for in-vivo dMRI at 7T. The use of the RF enhancer can effectively recover signal dropouts in the regions with intrinsically lower SNR such as cerebellum, leading to a better depiction of principal fiber orientations and enhanced visualization of extended tracts to the brainstem and pons enabling more comprehensive delineation of the full white matter architecture.

Bicarbonate and CO2 are essential substrates for carboxylation reactions in bacterial central metabolism. In Staphylococcus aureus, the bicarbonate transporter, MpsABC (membrane potential-generating system) is the only carbon concentrating system. A mpsABC deletion mutant can hardly grow in ambient air. In this study, we investigated the changes that occur in S. aureus when it suffers from CO2/bicarbonate deficiency. Electron microscopy revealed that mpsABC has a twofold thicker cell wall thickness compared to the parent strain. The mutant was also substantially inert to cell lysis induced by lysostaphin and the non-ionic surfactant Triton X-100. Mass spectrometry analysis of muropeptides revealed the incorporation of alanine into the pentaglycine interpeptide bridge, which explains the mutant’s lysostaphin resistance. Flow cytometry analysis of wall teichoic acid (WTA) glycosylation patterns revealed a significantly lower -glycosylated and higher ß-glycosylated WTA, explaining the mutant’s increased resistance towards Triton X-100. Comparative transcriptome analysis showed altered gene expression profiles. Autolysin-encoding genes such as sceD, a lytic transglycosylase encoding gene, were upregulated, while genes related to cell wall-anchored proteins, secreted proteins, transporters, and toxins were downregulated. Overall, we demonstrate that bicarbonate deficiency is a stress response that causes changes in cell wall composition and global gene expression resulting in increased resilience to cell wall lytic enzymes and detergents.

Dam breaches have catastrophic consequences, causing severe property damage, life loss, and environmental impact. The Kulekhani reservoir rockfill dam break was studied to evaluate the downstream impact. The appropriate breaching parameter of MacDonald and Langridge (1984) regression equations was selected based on the sixteen observed dam failure cases and cross-sectional geometry of the existing dam of Kulekhani. The 2D Diffusion Wave and Full Dynamic Wave Equation were applied for downstream flood assessment, Full Dynamic Wave was able to capture the physical flow phenomena like river bend effects resulting in higher flow velocity at the outer bend, and formation of eddies considering losses. The application of a Full Dynamic Equation was found to be appropriate for rapidly varying unsteady flow considering steep slopes, and sudden changes in channel geometry. Flood mapping of water depth, flow velocity, flood intensity, and arrival time were carried out for flood hazard assessment classified by the American Society of Civil Engineers (ASCE). Flow depth and extension of the flow area were compared to identify the affected area, higher flow depth and larger extension were observed using a Full Dynamic Wave Equation as a result of less flow velocity considering the losses. Almost 17 minutes of the arrival time of peak difference at the Bagmati River confluence was evaluated between the models which plays an important role in decision-making for selection of the flood model. Flood mitigation with river diversion works through a hydraulic measure of Levee was suggested to protect the highly affected households of Ranche, Nagmar, Khanikhet, and Debaltar towns. Most of the household was found to be safe after the construction of the Levee except for eleven houses that lie along the river below flood elevation of 1269.6 m.a.s.l. This signifies the importance of room for the rivers and the human settlement near the river might be life-threatening.

Additive manufacturing processes offer various options to fabricate metal parts, which show numerous ecological and technological advantages compared to formative and subtractive manufacturing methods. Due to quick availability and high accuracy, they are particularly suitable to produce complex prototypes. Metal fused deposition modeling is a relatively new material extrusion additive manufacturing technique based on the widely used fused filament deposition process. This study focuses on the Inconel 625 metal filament from Markforged Inc., it consists of a mixture of metal powder and a binder system, the latter being removed during washing and sintering. In this article, the mechanical properties of printed and sintered Inconel were investigated using tensile testing specimens with three different infill patterns, solid, triangular, and gyroid, printed in flatwise and upright direction. In addition, investigations into the dimensional accuracy of the printed specimens and the sintering shrinkage were carried out. The results showed that neither the dimensional accuracy nor the sintering shrinkage was significantly influenced by the printing orientation. In the context of lightweight engineering, the structures proofed beneficial especially within the elastic region. Generally, triangular infill patterns resulted in higher stiffness, while gyroids led to more ductile specimens. A mass-related evaluation of tensile testing elucidates that with aid of the infill structures weight savings of 40 % resulted in mechanical performance decreased by only 20 % on average.

In wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

This article shortly introduces Gaussian processes as a new approach for modelling time series in the field of blazar physics. In the second part of the paper, recent results from an application of GP modelling to the multi-wavelength light curves of the blazar PKS 1502+106 are discussed.

Hydrogen storage in general is an indispensable prerequisite for the introduction of a hydrogen energy based infrastructure. In this respect, high-pressure metal hydride (MH) tank systems appear to be one of the most promising hydrogen storage techniques for automotive applications using proton exchange membrane (PEM) fuel cells. These systems bear the potential of achieving a beneficial compromise of comparably large volumetric storage density, a wide working temperature range, comparably low liberation of heat, and increased safety. The debatable term unstable metal hydride stands in the literature short for metal hydrides with high dissociation pressure at comparably low temperature. Such compounds may help to improve the merit of high-pressure MH tank systems. Consequently, in the last few years, some materials for possible on-board applications in such tank systems have been developed. This review summarizes the state-of-the-art developments of these metal hydrides, mainly including intermetallic compounds and complex hydrides and gives some guidelines for future developments. Since typical laboratory hydrogen uptake measurements are limited to 200 bar, a possible threshold for defining unstable hydrides could be a value of their equilibrium pressure of peq > 200 bar for T < 100°C. However, these values would mark a technological future target and most current materials, and those reported in this review, do not fulfill these requirements and need to be seen as current stages of development towards the intended target. For each of the aforementioned categories in the review, special care was taken not only to covers the pioneering and classical research, but also to portrait the current status and latest advances. For intermetallic compounds, key aspects focus on the influence of partial substitution on absorption/desorption plateau pressure, hydrogen storage capacity and hysteresis properties. For complex hydrides, the preparation procedures, thermodynamics and theoretical calculation are presented. Besides, challenges, perspectives, and development tendency of this field are also discussed.

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

We consider a control problem for a diffusive PDE model of heterogeneous population of thermostatically controlled loads (TCLs) aiming to balance the aggregate power consumption within a given amount of time. Using the Green’s function approach, the problem is formulated as an approximate controllability problem for a residue depending on control parameters nonlinearly. A sufficient condition for approximate controllability is derived in terms of initial temperature distribution, operation time of TCLs and threshold value of the aggregate power consumption. Case studies allow to reveal the advantages of the proposed solution from numerical calculations point of view.

Link prediction is a fundamental problem in graphs. Currently, SubGraph Representation Learning (SGRL) methods provide state-of-the-art solutions for link prediction by transforming the task into a graph classification problem. However, existing SGRL solutions suffer from high computational costs and lack scalability. In this paper, we propose a novel SGRL framework called Augmented Feature Diffusion on Sparsely Sampled Subgraph (AFD3S). The AFD3S first uses a conditional variational autoencoder to augment the local features of the input graph, effectively improving the expressive ability of downstream Graph Neural Networks. Then, based on a random walk strategy, sparsely sampled subgraphs are obtained from the target node pairs, reducing computational and storage overhead. Graph diffusion is then performed on the sampled subgraph to achieve specific weighting. Finally, the diffusion matrix of the subgraph and its augmented feature matrix are used for feature diffusion to obtain operator-level node representations as inputs for the SGRL-based link prediction. Feature diffusion effectively simulates the message-passing process, simplifying subgraph representation learning, thus accelerating the training and inference speed of subgraph learning. Our proposed AFD3S achieves optimal prediction performance on several benchmark datasets, with significantly reduced storage and computational costs.

We will apply Pascal’s hydrostatic pressure law to black holes and also to the Hubble sphere. Haug has recently demonstrated how hydrostatic pressure in water can be utilized to determine the Planck length. One can conceptualize the energy in the Hubble sphere as a type of superfluid, and if this is correct, then Blaise Pascal’s hydrostatic pressure formula may also be applicable to such a superfluid, even within the Hubble sphere. By employing the same method on the Hubble sphere and considering it as a Schwarzschild black hole with the critical Friedmann mass, we can estimate the Planck length based on its hypothetical hydrostatic pressure.

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

In this work, we introduce a new concepts for $\alpha$-type $F$-Suzuki contraction and $\alpha$-type $F$-weak-Suzuki contraction in the context of $b$-metric spaces. Compared to the $\alpha$-type $F$-contraction and $F$-Suzuki contraction mappings, these contractions are essentially weaker. For these type of contraction mappings, sufficient conditions are established for the fixed point's existence and uniqueness in $b$-metric spaces. As a result, the findings encompass several generalizations. To show the usability of our obtained results, we provide a supportive example and an application to a non-linear differential equation with fractional order.

Natural systems of units $\{U_i\}$ need to be overhauled to include the dimensionless coupling constants $\{\upalpha_{U_i}\}$ of the natural forces. Otherwise, they cannot quantify all forces in a unified manner. Thus, each force must furnish a system with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts $\{ G, \upalpha_G \}$, thus it cannot account for gravitation. The cosmological system discounts $\{ \slashed{h}, \upalpha_\slashed{h} \}$, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, $\upalpha_G$ is the gravitational coupling constant and $\upalpha_\slashed{h}$ is the fine-structure constant. The speed of light $c$ and the impedance of free space $Z_0$ are resistive properties of the vacuum, thus they must be present in all systems of units. The upgraded Planck system $${\rm UPS} \,:=\,\{ c, Z_0, G, \upalpha_G, \slashed{h}, \upalpha_\slashed{h}, \,\dots\,\!\},$$ describes all physical scales in the universe---it is nature's system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics, and some of which have been designated as mere coincidences. Based on the UPS results, that relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed/measured physical properties are coincidental in this universe.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

We present preliminary results of JVLA wideband full polarization observations of a sample of Active Galactic Nuclei (AGN) with very high Rotation Measure (RM) values, sign of extreme environment. The polarization properties show a complex behaviour with the polarization angle (PA) and the fractional polarization (fp) that dramatically change within the wideband. The measured RM is not constant within the wide band. Its complex behaviour reflects the complexity of the medium with the presence of several Faraday components. The depolarization have been studied, modeling the Stokes parameters Q and U together with the polarization parameters (PA and fp) with wavelength by applying combinations of the simplest existing depolarisation models. With this JVLA study we could spectrally resolve multiple polarized components of unresolved AGN. These preliminary results reveal the complexity of these objects, still improvements have to be done on the depolairzation modeling to better understand the polarization structure of these sources.

For the past few decades, researchers have been intrigued with glassy polymers, which have applications ranging from gas separations to corrosion protection to drug delivery systems. The techniques employed to examine the sorption and diffusion of small molecules in glassy polymers are the subject of this review. Diffusion models in glassy polymers are regulated by Fickian and non-Fickian diffusion, with non-Fickian diffusion being more prevalent. The characteristics of glassy polymers are determined by sorption isotherms, and different models have been proposed in the literature to explain sorption in glassy polymers during the last few years. This review also includes the applications of glassy polymer. Despite having so many applications, current researchers still have difficulty in implementing coating challenges due to issues like as physical ageing, which is briefly discussed in the review.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB = C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB = C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

Natural systems of units $\{U_i\}$ need to be overhauled to include the dimensionless coupling constants $\{\upalpha_{U_i}\}$ of the natural forces. Otherwise, they cannot quantify all forces of nature in a unified manner. Thus, each force must furnish a system of units with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts $\{ G, \upalpha_G \}$, thus it cannot account for gravitation. The cosmological system discounts $\{ \slashed{h}, \upalpha_\slashed{h} \}$, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, $\upalpha_G$ is the gravitational coupling constant and $\upalpha_\slashed{h}$ is Dirac's fine-structure constant. The speed of light $c$ and the impedance of free space $Z_0$ are resistive properties imposed by the vacuum itself, thus they must be present in all systems of units. The upgraded Planck system with fundamental units $${\rm UPS} \,:=\,\{ c, Z_0, G, \upalpha_G, \slashed{h}, \upalpha_\slashed{h}, \,\dots\,\!\},$$ describes all physical scales in the universe---it is nature's system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics, and some of which have been designated as mere coincidences. Based on the UPS results, that relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed/measured physical properties are coincidental in this universe. Furthermore, we derive from first principles Koide's $K=2/3$ enigmatic constant and additional analogous quark and vector boson constants. These are formal mathematical proofs that justify a posteriori the use of geometric means in deriving the quark/boson mass ladder. This ladder allows us to also calculate the Higgs couplings to the vector bosons and the Weinberg angle in terms of only $K$.

In a multivariable system there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux-force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables such that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics.

Plants are subjected to abiotic stresses throughout their developmental period. Abiotic stresses include drought, salt, heat, cold, heavy metals, nutritional element and oxidative stresses. Improving plant response to various environmental stresses is critical for plant survival and perpetuation. The WRKY transcription factors have special structure (WRKY structural domains), which enable WRKY transcription factors to have different transcriptional regulatory functions. The WRKY transcription factors can not only regulate abiotic stresses response and plant growth and development by regulating phytohormone signalling pathways, but also promote or suppress the expression of downstream genes by binding to the W-box [TGACCA/TGACCT] in the promoters of their target genes. In addition, WRKY transcription factors not only interact with other families of transcription factors to regulate plant defence responses in abiotic stresses, but also self-regulate by recognizing and binding to W-boxes in their own target genes to regulate their defence responses to abiotic stresses. However, in recent years, research reviews on the regulatory roles of WRKY transcription factors in higher plants are scarce and shallow. In this review, we focus on the structure and classification of WRKY transcription factors, as well as the identification of their downstream target genes and molecular mechanisms involved in the response to abiotic stresses, which can improve the tolerance ability of plants in abiotic stress and we also look forward to their future research directions, with a view to providing theoretical support for the genetic improvement of crop abiotic stresses tolerance.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

We investigate perovskite oxides from different aspects, namely their pseudoharmonic dynamical properties, their dynamical properties when strong anharmonicity exists and the intriguing functionalities arising from domain walls. Taking these viewpoints together yields a rather complex picture of this material class which was not anticipated in previous approaches. It opens pathways to novel applications and reveals the rich ground states beyond the fictitious belief in ‘simplicity of perovskites and such structures’.

This study addresses the challenge of treating skin cancer effectively, especially in visible areas like the face, where traditional methods may be undesirable. Current options, including surgery and radiation therapy, have limitations such as complexity, expense, and imprecise dose delivery. The proposed solution involves additively manufacturing personalized patches using diagnostic imaging data, offering a targeted and controlled dose of beta-emitting isotopes like Y-90. The patches, tailored to the tumor's shape and depth, aim to minimize damage to healthy tissues and structures. Through 3D printing technology we demonstrated the feasibility of creating individualized applicators filled with radioisotopes, that have the potential to deliver therapeutic doses while ensuring patient comfort and affordability. This innovative approach, based on radiation delivery simulations, offers a promising future alternative to conventional radiation therapy methods. Clinical trials are required to validate its efficacy and safety, but the potential for reduced radiation exposure and enhanced treatment precision positions this personalized and targeted therapy as a valuable advancement in skin cancer treatment.

In 2018, Iran witnessed approximately 21,000 fatalities resulting from road accidents, ranking it as the fifth leading cause of death across all age groups. These incidents carry substantial economic and social burden for the nation, claiming more than 5% of its GDP. Human behavior emerges as a significant contributing factor to high-risk driving offenses. It has been proposed that by influencing general deterrence, a rigorous defense can be established against such violations. Various theories posit that by reinforcing or diminishing influential factors, general deterrence perception can be molded, presenting a potential avenue for an effective deterrent against traffic infractions. This study examines deterrence perceptions prevailing among the public in Iran regarding the enforcement of traffic laws. Employing Structural Equation Modeling (SEM), we delve into the intricate relationships between variables, allowing for a comprehensive exploration of the factors influencing general deterrence. The study draws on the data derived from a survey comprising 548 questionnaires for modeling purposes. An innovative concept, private sector enforcement, is introduced and incorporated into the questioning and modeling process. The findings reveal that socioeconomic status (p-value&lt;0.01), police enforcement (p-value&lt;0.05), private sector enforcement (p-value&lt;0.05), specific deterrence (p-value&lt;0.01), and the use of technology (p-value&lt;0.01) have direct and indirect impacts on the general deterrence perception of drivers.

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.

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.

The resilience of towns and cities refers to their ability to adapt and recover when confronted with pressures or challenges. This study employs ten variables as indicators to assess the resilience of urban areas by analyzing official data and constructing a multilevel mixed-effects structural equation model. The empirical findings demonstrate that enhancing resilience significantly influ-ences urban service functions, such as strengthening healthcare systems, stabilizing the real estate market, and addressing socio-economic challenges. Specifically, factors such as healthcare re-sources, housing demand, population structure, and social security exhibit varying levels of resil-ience, which profoundly impact the spatial distribution of these factors and socio-economic de-velopment. Disparities in healthcare resource allocation, demographic aging trends, and shifts in the housing market closely correlate with resilience levels in different regions. Additionally, the study emphasizes that improving resilience not only boosts the reliability and security of urban services but also ensures that communities receive necessary support and protection during times of adversity. Consequently, policymakers should recognize the pivotal role of urban resilience in resource allocation and social equity, devising corresponding strategies to enhance the resilience of these areas.

Diffusion bonding is often used on pre-machined parts to generate internal cavities, e.g. for cooling injection molding tools close to the mold cavity. Only then, the workpieces are finished to their final dimensions. In the case of micro-process devices, however, it is essential to precisely control the deformation, as otherwise uncontrollable pressure losses will occur with channel cross-sections in the sub-millimeter range. Post-processing is not possible. The most important process parameters for diffusion bonding are temperature, dwell time and contact pressure, with the bonding temperature and contact pressure acting in opposite directions and showing a strong non-linear dependence on deformation. In addition, the deformation is influenced by a number of other factors such as the absolute size of the cross-section and the aspect ratio of the parts, the dimensions and distribution of the internal cross sections and the overall percentage of the cross-section to be bonded. In micro process engineering, small material cross-sections in the range of the materials microstructure can facilitate additional deformation mechanisms such as grain boundary sliding, which are not relevant at all for larger structures. For parts consisting of multiple layers, tolerances in thickness and roughness of multiple surfaces must be levelled, contributing to the percentaged deformation. This makes it difficult, especially in micro process engineering and in single or small series production, to determine suitable joining parameters in advance, which on the one hand do not cause unforeseen large deformations, but on the other hand reliably produce highly vacuum-tight components. Hence, a definition of a fixed percentaged deformation does not work for all kinds of components. This makes it difficult to specify parameters for surely obtain high-vacuum tight parts. For successful diffusion bonding, atoms must diffuse over the bonding planes, forming a monolithic part in which the original layers are no longer visible. Only then, mechanical properties identical to those of the base material, which has been subjected to identical heat treatment, can be achieved. In this paper, the impacts of different material cross section widths as well as of the aspect ratio on deformation were investigated. By accident, it was found that also accuracy of the temperature measurement may have a serious impact in terms of deformation.

Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their complete integrability. The Gardner equation is chosen as the key example for it comprises both the Korteweg-de Vries and modified Korteweg de Vries (mKdV) equations. The Gardner and Miura transformations which connect these equations are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case) whereas the focusing Gardner equation has the standard elastically colliding solitons. The paper’s aim is to provide a review of integrability properties and solutions of the Gardner equation and illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica but can be adapted for major computer algebra systems.

Despite the effectiveness of insulin injections in managing hyperglycemia in Type 1 Diabetes, they fall short in addressing autoimmunity and regenerating damaged islets. This review aims to explore the potential of various treatment modalities for T1DM, including mesenchymal stem cells (MSCs), MSC-derived exosomes, gene therapy, islet allotransplantation, and pancreatic islet cell transplantation. Results: MSCs demonstrate efficacy in T1DM treatment through immunomodulation and tissue regeneration, although further research is warranted to optimize their therapeutic potential. Gene therapy presents a promising approach despite challenges such as donor shortage and immune rejection. Pancreatic islet cell transplantation emerges as a viable option, albeit with associated risks including graft rejection and the need for immunosuppression. Teplizumab, an FDA-approved humanized monoclonal antibody, revolutionizes the treatment landscape of Type 1 Diabetes by significantly delaying its onset, offering a paradigm shift since the discovery of insulin Conclusion: Ongoing studies and technological advancements in T1DM management offer a promising outlook for improved treatments and possibly even eradication on a global scale. MSCs, MSC-derived exosomes, gene therapy, and pancreatic islet transplantation hold considerable potential.

Diffusion Models (DMs) are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech synthesis, and natural language processing due to their ability to produce high-quality samples. As DMs are being adopted in various domains, existing literature reviews that often focus on specific areas like computer vision or medical imaging may not serve a broader audience across multiple fields. Therefore, this review presents a comprehensive overview of DMs, covering their theoretical foundations and algorithmic innovations. We highlight their applications in diverse areas such as media quality, authenticity, synthesis, image transformation, healthcare, and more. By consolidating current knowledge and identifying emerging trends, this review aims to facilitate a deeper understanding and broader adoption of DMs and provide guidelines for future researchers and practitioners across diverse disciplines.

This paper is a brief review of our work on the Planck quantized version of general rela- tivity theory. It demonstrates several straightforward methods to rewrite the same equations that we have already presented in other papers. We also explore a relatively new general relativity-inspired field equation based on the original Newtonian mass, which is very differ- ent from today’s kilogram mass. Additionally, we examine two other field equations based on collision space-time, where both energy and matter can be described simply as space and time. We are thereby fulfilling Einstein’s dream of a theory where energy and mass are not needed, or are just aspects of space and time. If this is extended beyond the 4-dimensional space-time formalism of general relativity theory to a 6-dimensional framework—with 3 space dimensions and 3 time dimensions—this ultimately reveals that they are two sides of the same coin. In reality, it is a three-dimensional space-time theory, where space and time are just two sides of the same coin.

This paper is the third application-oriented paper based on the "unified theory of forces" and also addresses the shortcomings of previous research in fully explaining the origin and nature of the weak force. The main conclusions of this paper are as follows: (1) It is argued that neutrinos are generated by the gravitational field, and their generation mechanism is similar to the radiation of photons from electron orbital transitions. Particles undergoing orbital transitions in a gravitational field will emit neutrinos. (2) We rigorously derive the energy formula for neutrinos and demonstrate that the energy formula for neutrinos does not comply with the Planck energy formula. Neutrinos with higher energy have longer wavelengths and are more easily observed in experiments.

Current physiology attributes the mechanism of membrane potential generation to transmembrane ion transport, but ion adsorption could just as well play this fundamental role. The evidence shows that the ion adsorption mechanism accurately reproduces the experimentally measured membrane potential. The Goldman-Hodgkin-Katz equation (GHK eq.) and the Nernst equation (Nernst eq.) are the typical mathematical formulas representing the membrane potential in current physiology. However, the authors were able to show that the potential formulas by ion adsorption mechanism give identical results to GHK eq. and Nernst. eq. Our experimental and theoretical analyses suggest that there is a special relationship between the membrane potential and the membrane surface charge density, and this unique equation inevitably leads to the establishment of a GHK eq and/or a Nernst eq. The authors found that the unique equation is the foundation of thermodynamics “Boltzmann distribution”. Thus, the GHK eq. and the Nernst eq. are simply the natural consequence of thermodynamics from the view of the ion adsorption mechanism.

The assortment of low-cost 3D printers for “in-practice” use, e.g., for clear aligner therapies, is ever increasing. To address concerns about the accuracy of orthodontic models produced on such printers when cost efficient modes of 3D printing are employed, this study examined the effect of print model body type and print angulation on accuracy. Six printing-configuration groups were included: 2 model types (solid or hollow shell) combined with 3 print angles (0°, 70°, or 90°) with 10 models/group; all models were printed with 100-µm layer thickness using a digital light processing-based 3-dimensional printer. Eleven selected structures and distances were measured on the printed models with a digital microscope and compared to the same measures on a digitized master model. The clinically-acceptability range was set at ±0.25 mm difference from the master model for single tooth measurements (intra-tooth) and ±0.5 mm for cross-arch measurements (inter-tooth). For individual measurements across all models, 98% fell within clinical acceptability. For mean measurements within each model group, only canine height for the shell-0° model had a mean difference (0.26 mm ± 0.03) outside the clinically acceptable range for intra-tooth measurements. Standard deviations for all intra-tooth measurements were within 0.07 mm. While none of the mean inter-tooth measurements exceeded the acceptability range, the standard deviations were larger (0.04 to 0.30 mm). Accuracy of orthodontic models for clear aligner therapies was not impacted beyond the clinically acceptable range when altering model body type and print angulation to improve efficiency of 3D printing. These findings suggest greater flexibility of the practitioner to alter print settings to address time and cost efficiency in various clinical scenarios and still maintain clinically acceptable model accuracy.

This paper concentrates on the general birth-death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth-death processes with two-type catastrophes are is successfully expressed with the Laplace transform of transition probability function of the birth-death processes without catastrophe. The first effective catastrophe occurrence time is considered. The Laplace transform of its probability density function, expectation and variance are obtained.

In the contemporary world of science, continuous observation of specific fixed regions is required, awaiting the emergence of targets or phenomena within those areas to locate and identify them. Astronomy requires continuous monitoring of stars, swiftly pinpointing occurrences, such as flares, and acquiring their spectral data to aid identification. In military contexts, continuous observation of specific areas is essential for promptly locating enemy movements and obtaining target spectral data for deciphering enemy disguises. Additionally, continuous observation of experimental samples in biochemistry is mandatory to pinpoint localized changes and acquire spectral data from those areas. Hence, this paper develops a novel imaging spectrometer solution to monitor localized regions continuously. Specifically, this paper first elaborates on the developed instrument’s characteristics and optical structure, followed by optical design software simulations. The instrument has an F-number of 5, a focal length of 100mm, and a field of view covering the wavelength range from 400nm to 600nm. The optical path diagram indicates that the system’s dispersion and imaging images can be separated, meeting the system’s requirements. Besides, the Modulation Transfer Function (MTF) graph confirms that the image quality meets the requirements. Furthermore, a region-monitoring type imaging spectrometer was constructed to assess the instrument’s capability for spectral observation of fixed regions. The instrument can detect a fixed area, with the target placed within the detection area. Spectral data were successfully obtained by conducting image processing on the acquired images. The correlation coefficient between this data and reference data was as high as 0.9226, indicating the instrument’s successful measurement of the target’s spectrum. Thus, the developed instrument demonstrated that it can image the observed areas and acquire spectral data from targets within those regions.

The sexual reproduction of ascomycetes is controlled by the mating-type(MAT) locus. (Pseudo)homothallic reproduction has been hypothesized based on genetic data from Hirsutella sinensis (Genotype #1 of Ophiocordyceps sinensis). In this study, the differential occurrence of the mating-type genes in the MAT1-1 and MAT1-2 idiomorphs, which constitute the genetic control of O. sinensis reproduction, was analyzed in 237 strains and 5 genomes of H. sinensis. The mating-type genes were differentially transcribed in H. sinensis Strain L0106, and the MAT1-2-1 transcript in H. sinensis Strain 1229 was alternatively spliced, with an unspliced intron I containing stop codons; these findings constitute O. sinensis reproduction controls at the transcriptional and coupled transcriptional-translational levels. The occurrence of the mating-type genes and a-/α-pheromone receptor genes differed among the 5 H. sinensis genomes. The differential occurrence and transcription of these genes are inconsistent with self-fertilization under (pseudo)homothallism but suggest self-sterility of H. sinensis, which therefore needs a mating partner to achieve sexual outcrossing under heterothallism or hybridization. Consistent occurrence and transcription of the mating-type genes of both the MAT1-1 and MAT1-2 idiomorphs have been reported in natural and cultivated Cordyceps sinensis, but these findings are insufficient to determine the reproduction mode(s) because of the co-occurrence of >90 fungal species and multiple genomically independent genotypes of O. sinensis. The mutant MAT1-1-1 and α-pheromone receptor transcripts in natural C. sinensis result in the N-terminus or middle-truncated proteins, with changes in hydrophobicity and secondary structures of the proteins, suggesting heterogeneous fungal source(s) of the proteins and hybridization reproduction.

The generation and maintenance of membrane potential is a fundamental part of Membrane Pump Theory. One of the key points of this hypothesis is based on a natural or facilitated molecular diffusion through several types of ion channels and pumps like the Na/K ATPase. Chemistry, physics and especially electrochemistry, however, bring strong contradictions to this theoretical assumption. By respecting the principles of chemistry and electrostatics, it becomes obvious that this theoretical hypothesis cannot work. The ionic diffusion that would be at the origin of this potential cannot take place. Indeed, the topology and the forces involved definitively exclude the current model, which must absolutely be revised according to the current state of our knowledge and allow an advance in the understanding of the phenomena and open new research perspectives.

The building envelope has the most significant contribution in the reduction of the building energy consumption. Application of new, alternative and improved materials and systems has an important impact on the buildings performances. This paper is focused on the thermal transmittance, as an indicator of the thermal conductance of the construction element. It includes comparisons of the U-values, calculated by software, with those measured in situ on three representative façade walls. The walls have been constructed with the new wall system Fragmat NZ-1, a new product in Macedonian buildings. This research provides basic information on the thermal transmittance of the system. The results of the analysis show that the in situ measuring is a useful tool in validation of the precision of analytically calculated values, since it was difficult to obtain precise results from the analytical calculations only, especially when the layers are with non-uniform thickness.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

With reference to Planck scale, Mach's relation and by introducing two new parameters Gamma and Beta, 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 Planck mass in all directions). In analogy with currently believed cosmic acceleration, with a decreasing trend of total matter density ratio, cosmic expansion velocity can be shown to be increasing. By considering $H_0\cong 70$ km/sec/Mpc, estimated current cosmic mass, radius, total matter density, expansion velocity, temperature and age are: $4.3352\times {10}^{53}\mathrm{kg},$ $3.207\times {10}^{26}\mathrm{m},$ $3.138\times {10}^{-27}\mathrm{kg}{.\mathrm{m}}^{-3},$ $2.43c,$ $2.721\mathrm{K}$ and $19.78\mathrm{Billion}\mathrm{years}$ respectively. Point to be noted is that, with reference to Planck scale, cosmic temperature seems to be redshifted by a factor ${\left(Z_T\right)}_t\cong \sqrt{1+\ln \left(H_{pl}/H_t\right)}-1$ where $\left(H_{pl},H_t\right)$ represent Planck scale and time dependent Hubble parameters respectively. As a peculiar case, considering the equality of current Hubble parameter and current angular velocity, current cosmic rotational kinetic energy can be estimated to be 0.667 times the current critical energy. It needs further study.

We investigate solutions of the classical Mathieu-Hill (MH) equation which characterizes the dynamics of trapped ions, based on the Floquet theory and starting from a well known analytical model. The analytical model we introduce demonstrates that the equations of motion are equivalent to those of the harmonic oscillator (HO). Two independent approaches are used, based on two classes of complex solutions of the MH equation. The paper addresses both the damped HO and parametric oscillator (PO) for an ion confined in an electrodynamic (Paul) trap. Stability and instability regions for the periodic orbits associated to the MH equation which describes a HO (PO) confined in an electrodynamic trap are also discussed, depending on the values of the Floquet exponent, for very small values of the $q$ parameter. The main objective of the paper is to identify stable and bounded solutions for the dynamics of a HO levitated in an electrodynamic trap. This paper represents a follow-up of a recently published article in Photonics, 11 (6) 551.

The study aimed to analyze thoracic and lumbar erector spinae muscle activations during 3D elongation exercises in individuals with adolescent idiopathic scoliosis (AIS). Participants included 24 adolescents, meeting specific criteria such as a Cobb angle between 10° and 20°, and not having undergone surgical or brace treatments. EMG data were collected to evaluate muscle activations. The study found no significant interaction between exercise type and the side of the curve, but a significant main effect of exercise type on muscle activation, irrespective of Cobb angle. Different exercise types significantly affected muscle activity, with the highest activations in the TheraBand exercise, followed by manual and without equipment conditions. This suggests that exercise type significantly impacts muscle engagement in AIS patients, providing valuable insights for targeted exercise program design. The study, however, focused on short-term muscle activation, not long-term Cobb angle progression, pointing to the need for further research in this area.

The reflectance $R$ of monolayer graphene for the normal incidence of electromagnetic radiation is known to be remarkably defined only by $\pi$ and the fine-structure constant $\alpha$. It is shown in this paper that the reflectance (or the sum of transmittance and absorptance) of monolayer graphene, expressed as a quadratic equation with respect to the fine-structure constant $\alpha$ must unsurprisingly introduce the 2$^\text{nd}$ fine-structure constant $\alpha_2$, as the 2$^\text{nd}$ root of this equation, as well as two $\pi$-like constants for a convex and a saddle surface. It turns out that this 2$^\text{nd}$ fine-structure constant is negative, and the sum of its reciprocal with the reciprocal of the fine-structure constant $\alpha$ is independent of the reflectance value $R$ and remarkably equals $-\pi$. Particular algebraic definition of the fine-structure constant $\alpha^{-1} = 4\pi^3 + \pi^2 + \pi \approx 137.036$, containing the free $\pi$ term and agreeing with the physical definition of this dimensionless constant to the 5$^\text{th}$ significant digit, when introduced to this sum, yields $\alpha_2^{-1} = -4\pi^3 - \pi^2 - 2\pi \approx -140.178$. Assuming universal validity of the physical definition of $\alpha$, $\alpha_2$ defines the negative speed of light in vacuum $c_n$. The average of this speed $c_n$ and the speed of light in vacuum $c$ is in the range of the Fermi velocity ($10^6$ m/s). Furthermore, the 2$^\text{nd}$ negative fine-structure constant $\alpha_2$ alone introduces the imaginary set of base Planck units.

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and mass can be rewritten in terms of their densities and the integral over the volume element. The idea find its place in the Hamiltonian formulations, and can be carried over into quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores this concept and runs through various frameworks and equations relevant to this idea, particularly the schrodinger-Newton equation and discusses the cosmological constant as a vacuum energy density.

In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

Concrete is more stable than filler as a false roof in a downward approach type infill quarry, but the mechanical model of a concrete false roof is not clear. As a result, there has been limited application. Therefore, it is necessary to establish the mechanical model of a concrete artificial false roof to enhance the stability of the downward approach infill quarry. This paper combines theoretical analysis, model derivation, finite element analysis and field application methods. Firstly, the basic assumptions of thin plate theory and elasticity mechanics are used as the premise to establish the differential equations of the deflection curve of the concrete thin plate false roof. Then, the three types of bending moment generation of the concrete thin plate false roof are explored. Secondly, the relationship between the location of dangerous surface and dangerous point in hard-supported weak-slab structure and soft-supported weak-slab structure is analyzed, and the type of uniform load and calculation model of concrete thin-slab false roof are improved. Finally, according to the established mechanical model of thin slab false roof, finite element analysis and field application were carried out. The results show that there are three types of deflection curve differential equations in the concrete thin slab false roof perpendicular to the strike, and three extreme points exist in the middle section of the thin slab and on both sides of the surrounding rock. The hazardous surface of the hard-supported weak-slab structure is present at the intersection of the encircling rock and the thin-slab fake ceiling, with the perilous point situated on the top of this surface. The hazardous surface of the soft-supported weak-slab structure can be found in the centre section of the thin-slab fake ceiling, with the perilous point being located at the bottom of this surface. Moreover, the damage mode for both structures is that of maximum tensile stress damage. Upon conducting a finite element analysis, the results indicate that the concrete's maximum tensile stress is significantly high.

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

In the sphere of urban renewal in historic districts, preserving and innovatively reinterpreting traditional architectural styles remains a primary research focus. However, the modernization and adaptive reuse of traditional buildings often necessitate changes in their functionality. To cater to the demands of tourism in historic districts, many traditional residential buildings require conversion to commercial use, resulting in a mismatch between their external form and internal function. This study explores an automated approach to transform traditional residences into commercially viable designs, offering an efficient and scalable solution for the modernization of historic architecture. We developed a methodology based on diffusion models, focusing on a dataset of nighttime shopfront facades. By training a Low-Rank adaptation (LoRA) model and integrating the ControlNet model, we enhanced the accuracy and stability of generated images. The methodology’s performance was validated through qualitative and quantitative assessments, optimizing batch size, repetition, and learning rate configurations. These evaluations confirmed the method’s effectiveness. Our findings significantly advance the modern commercial style transformation of historical architectural facades, providing a novel solution that maintains aesthetic and functional integrity, thereby fostering breakthroughs in traditional de-sign thinking and exploring new possibilities for the preservation and commercial adaptation of historical buildings.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

To conduct high-precision and high-resolution numerical simulation of complex flow structures in turbomachinery, a high-order finite volume weighted essentially non-oscillatory (WENO) scheme for the large eddy simulation (LES) is improved and embedded into the three-dimensional viscous unsteady CFD solver NUAA-Turbo. Firstly, the spectral characteristics and unsteady convergence of the improved WENO scheme are studied. Compared with the classical WENO scheme, the improved WENO scheme has better dissipation and dispersion characteristics and faster convergence speed. Then, the coefficient CW of the Wall-Adapting Local Eddy-viscosity (WALE) model is calibrated by decaying homogeneous isotropic turbulence (DHIT) test case. Finally, the scheme is applied to conduct high-precision LES calculations of turbulent boundary layer flow, supersonic compression corner flow, and low-pressure turbine cascade separation flow. The numerical simulation results show that this WENO scheme has excellent shock wave capture ability and turbulence resolution and can capture more flow field details with less mesh size, greatly reducing the computational cost and laying a foundation for large-scale engineering application of LES.

In this paper, a new axial-type magnetic gear with auxiliary flux-enhancing structure (AFS-AMG) is proposed. Compared to conventional AFS-AMG, it has the higher torque density and higher permanent magnet (PM) utilization factor. Firstly, the design rules and operating principles of proposed AFS-AMG are elaborated. Then, the mapping relation between the radial-type magnetic gears (RMGs) and AMGs are elucidated. Compared to its counterpart in RMGs, AFS-AMGs achieve small size. Then, the geometrical parameters of AFS-AMGs are optimized to obtain the better electromagnetic performances, where the torque density per volume and per PM volume is adopted as the evaluation standard. Finally, three different AMG topologies are constructed in finite element analysis (FEA) software for comparison. It is proven that the AFS-AMG has the largest torque density per volume and per PM volume.

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

This paper designs and fabricates a small-type permanent-magnet linear motor and driver for automation applications. It covers structural design, magnetic circuit analysis, control strategies, and hardware development. Magnetic circuit analysis software JMAG is used for flux density distribution, back electromotive force(back-EMF), and electromagnetic force analysis. To address end effects and cogging force, auxiliary core structures and control strategies are proposed. The motor has a three-phase, six-coil, seven-pole configuration, achieving a peak phase voltage of 3.621 V at 1.0 m/s with a total harmonic distortion(THD) of 0.49 % and the voltages of each phase are balancing a phase voltage error of -0.002 V. The average electromagnetic force is 5.46 N/A. The driver uses a three-phase inverter with voltage space vector pulse width modulation(VSVPWM), dq-axes current closed-loop control, electromagnetic force control, and S-curve motion trajectory control. Simulations with JMAG-RT models in MATLAB/Simulink verify the control strategies. A microcontroller (TMS320F280045) serves as the control core, and a magnetic encoder with a 488 nm resolution provides position feedback. Each phase winding has an equivalent resistance of approximately 3.0 Ω and an inductance of approximately 1.98 mH. The S-curve motion trajectory control achieves a maximum position error of approximately 5.0 μm and a speed ripple of approximately 0.03 m/s at steady speed. With cogging force improvement, the maximum electromagnetic force is 4.90 N, and the q-axis current compensates around 1.05 A based on mover position. S-curve motion trajectory control results in highly stable and responsive performance. Practical tests show that the designed small-type permanent-magnet linear motor and its driver provide efficient, stable, and high-precision solutions for automation applications.

To achieve n-type doping in diamond, extensive investigations employing first principles have been conducted on various models of phosphorus doping and boron-phosphorus co-doping. The primary focus of this study is to comprehensively analyze the formation energy, band structure, density of states, and ionization energy of these structures. It is observed that within a diamond structure solely composed of phosphorus atoms, the formation energy of an individual carbon atom is excessively high. However, the substitution of two carbon atoms leads to the conversion of diamond into a p-type semiconductor. Upon examining the P-B co-doping structure, it is revealed that the doped impurities exhibit a tendency to form more stable cluster configurations. As the separation between the freely doped atoms and the cluster impurity structure increases, the overall stability of the structure diminishes, consequently resulting in an elevation of the ionization energy. Analysis of the electronic density of states demonstrates that the electron orbit of the B atom makes negligible contributions to the impurity levels during P-B doping.

An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses a discretization scheme for the Laplace operator multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is applied, leading to significant time savings. The procedure is successfully tested on some standard black&white natural images.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

This paper is another applied article based on the author's "Unified Theory of Force". The main work of this paper is as follows: (1) Reinterpretation of the Lorentz contraction effect and rigorous proof that the Lorentz contraction is a physical phenomenon based on the conservation of energy and momentum under non-completely symmetrical relative motion effects. This paper proves that the Lorentz contraction effect not only occurs in the direction of motion but also simultaneously in any direction. (2) For the first time, we attempted to explain the physical meaning of the Planck energy formula in theory and associate the Planck energy formula with the Lorentz contraction effect, which can help us to have a deeper understanding of the true physical meaning behind the Planck energy formula. At the same time, we also made reasonable theoretical predictions about the basic structure of photons.

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

Addressing the significant challenge in high-speed cotton dibbling operations in Xinjiang—specifically, the duck bill’s ("Duck bill" is a type of duck-billed bunch planting mechanism or component). shortened opening duration leading to seed throwing and floating—a new crawler-type delayed hole-forming mechanism has been designed. This mechanism extends the duck bill horizontally, thereby prolonging its opening time, enabling cotton sowing speeds of up to 6 km/h. Following agronomic principles for cotton planting, the overall layout of the crawler-type hole-forming mechanism, the structural parameters of the key components and the trajectory of the hole-forming are determined. We use the Discrete Element Method (DEM) and multi-body dynamics coupling method to simulate and analyze the motion process of the device. The fixed the tilt angle of the duck bill α(A), the depth of the duck bill hole-forming into the soil h(B), and the angle of rotation of the moving duck bill β(C) were taken as the experimental factors, with the longitudinal length of cotton seed hole (Y1) and the hole-forming depth of cotton seed hole (Y2) as the response values. The parameter range of each factor and the preliminary influence on the response value were determined through pre-experiments and single-factor simulation test. Based on RecurDyn-EDEM coupling, a quadratic regression orthogonal rotation combination simulation test was carried out. The results show that the order of the primary and secondary factors affecting the Y1 of the time-lapse hole-forming device was: A > C > B. The order of primary and secondary factors affecting the Y2 of the delayed hole forming device was: B > C > A. When the A was 2.4 °, the B was 42.4 mm, and the C was 30.5 °, the performance of the hole-forming was the best, and the Y1 was 26.4 mm, and the Y2 was 25.0 mm. The bench verification test results show that under the optimized combination of operating parameters, the average Y1 was 29.1 mm, and the average Y2 was 23.2 mm. Compared with the results of the previous coupled simulation model, the average relative errors of the two are 7.23 % and 4.36 %, respectively, indicating the accuracy and effectiveness of the established DEM simulation model and virtual test analysis. The hole-forming area and the opening time of the duck bill after the stable operation of the machine were recorded and measured. The calculated hole dislocation rate Hc was 4.33 %, which did not exceed the national standard requirement of 6 %. The qualified rate of hole distance Hx was 94.33 %, which was much higher than the national standard requirement of 80 %. The average opening time of the duck bill at a speed of 6 km/h is 0.45 s, which is much longer than the time required for cotton seeds to fall from the duck bill 0.11 s. It meets the requirements of high-speed cotton planting in China and facilitating advancements in future high-speed planter technology.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

As the number of end-of-life vehicles continues to grow, the field of separation technology for broken copper and aluminium parts of end-of-life vehicles has emerged as a significant area of research. As a key technology for the separation of non-magnetic non-ferrous metals, such as copper and aluminium, eddy current separation can achieve efficient separation of non-magnetic non-ferrous metals according to their differing conductivity and density. Nevertheless, further research is required in the separation of large-scale broken copper and aluminium parts of end-of-life vehicles. This paper presents a novel magnetic roller model comprising circumferential and axial periodic arrangements of permanent magnets. A single permanent magnet was constructed as an equivalent current model, and the magnetic scalar potential equations were solved using simulation tools. This allowed the distribution of the magnetic field outside the magnetic roller to be studied. The results demonstrate that the novel permanent magnet array magnetic roller can enhance the magnetic field intensity and action distance of the external magnetic field, which is more conducive to the separation of large-scale broken copper and aluminium parts of scrap cars. The findings of this research provide a theoretical foundation for the separation of scrap car broken copper and aluminium parts.

An adequate representation of the water infiltration process in the soil allows improving the efficiency in application and the uniformity in surface irrigation. The Green and Ampt model has shown a good representation of the process, and researchers from the United States Department of Agriculture (USDA) determined the values of their parameters for soils of that country, which are shown in tables or through functional relationships and this information is used as reference in several parts of the world, although there is no certainty that they are representative of the soils in Mexico. In this study, the parameters of the Green & Ampt equation were determined and evaluated in some soils of agricultural importance in Mexico. The parameters were obtained in four ways: one of them applied a methodology adapted from Brooks and Corey to quantify the wetting front capillary pressure head and used an permeameter under constant hydraulic head to determine the saturated hydraulic conductivity, and the other three consisted in taking them from three studies reported by the USDA. The values of the parameters suggested in Mexico drastically underestimated the results with relative errors (RE) in a range of -49.0 to -94.0% and the most representative were those obtained with the methodology proposed in this research with RE of -15.0 to 6.0%.