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, impulse 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. At the end of the paper the question on a possibility of second quantization of the electron field in the spinor coordinate space is touch upon. The statement that the electron and positron have the same, and exactly positive energy, and have opposite signs of charge and opposite signs of mass is also justified. Accordingly, in the process of annihilation their total energy, momentum, charge and mass do not change. It is shown that if we take as an axiom the conservation at interaction of the total mass of the system of particles taking into account its sign, then it is possible to explain the difference between bosons and fermions in the statistics to which they obey.

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.

UV SO₂ cameras have become a common tool to measure and monitor SO₂-emission-rates, mostly from volcanoes but also from anthropogenic sources (e.g. power plants or ships). In the past years, the analysis of UV SO₂ camera data has seen many improvements. As a result, for many of the required analysis steps, several alternatives exist today. This inspired the development of Pyplis, an open-source software toolbox written in Python 2.7, which aims to unify the most prevalent methods from literature within a single, cross-platform analysis framework. Pyplis comprises a vast collection of algorithms relevant for the analysis of UV SO₂ camera data. These include several routines to retrieve plume background radiances as well as routines for cell and DOAS based camera calibration. The latter includes two independent methods to identify the DOAS field-of-view within the camera images. Plume velocities can be retrieved using an optical flow algorithm as well as signal cross-correlation. Furthermore, Pyplis includes a routine to perform a first order correction of the signal dilution effect. All required geometrical calculations are performed within a 3D model environment allowing for distance retrievals to plume and local terrain features on a pixel basis. SO₂-emission-rates can be retrieved simultaneously for an arbitrary number of plume intersections. Pyplis has been extensively and successfully tested using data from several field campaigns. Here, the main features are introduced using a dataset obtained at Mt. Etna, Italy on 16 September 2015.

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.

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.

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.

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 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.

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.

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.

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 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.

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.

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.

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.

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.

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.

An active power dispatch method for a microgrid (MG) with multi-type loads, renewable energy sources (RESs) and distributed energy storage devices (DESDs) is the focus of this paper. The MG operates in a grid-connected model, and distributed power sources contribute to the service for load demands. The outputs of multiple DESDs are controlled to optimize the active power dispatch. Our goal with optimization is to reduce the economic cost under time-of-use (TOU) price, and to adjust the excessively high or low load rate of distributed transformers (DTs) caused by the peak-valley demand and load uncertainties. To simulate a practical environment, the stochastic characteristics of multi-type loads are formulated. The transition matrix of system state is provided. Then, a finite-horizon Markov decision process (FHMDP) model is established to describe the dispatch optimization problem. A learning-based technique is adopted to search the optimal joint control policy of multiple DESDs. Finally, simulation experiments are performed to validate the effectiveness of the proposed method, and the fuzzification analysis of the method is presented.

Nanocrystalline silicon oxide (nc-SiOx:H) is a multipurpose material with its varied application in solar cells as a transparent front contact, intermediate reflector, back reflector layer and even tunnel layer for passivating contacts, owing to easy tailoring of its optical properties. In this work, we systematically investigate the influence of gas mixture (SiH4, CO2, PH3 and H2), RF power and process pressure on the optical, structural and passivation properties of thin n-type nc-SiOx:H films prepared in an industrial, high throughput, plasma-enhanced chemical vapor deposition (PECVD) reactor. We provide a detailed description of the n-type nc-SiOx:H material develop-ment using various characterization techniques (SEM, EDX, Raman spectroscopy, and spectro-scopic ellipsometry) with a focus on the relationship between the material properties and the pas-sivation they provide to n-type c-Si wafers characterized by their effective carrier lifetime (τeff). Further, we also outline the parameters to be kept in mind while developing different n-type nc-SiOx:H layers for different solar cell applications. We report a tunable optical gap (1.8 – 2.3 eV) for our n-type nc-SiOx:H films as well as excellent passivation properties with τeff up to 3.5 ms (iVoc ~ 715 mV) before annealing. Oxygen content plays an important role in determining the crystallinity and hence passivation quality of the deposited nanocrystalline silicon oxide films.

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.

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

Spinocerebellar ataxia type 3 is a neurodegenerative disease caused by an abnormal expansion of CAG repeats in the disease gene ATXN3, leading to prolonged polyglutamine (polyQ) tracts in the respective protein ataxin-3. The polyQ-expanded protein forms polyQ-containing aggregates in several brain regions which leads to neuronal cell loss. Autophagy is thought to play a significant role in clearing these polyQ-containing protein aggregates. Therefore, the autophagy mechanism was investigated in SCA3 with focus on the autophagic protein p62/sequestosome-1. Human and mouse RNA sequencing data were analyzed to determine RNA expression level of autophagic genes. Additionally, autophagy was studied in the SCA3 304Q knock-in mouse model and through several cell culture experiments using HEK-293T cells transfected with ATXN3 of differ-ent polyQ lengths. For cell culture experiments, autophagy was induced with rapamycin treat-ment, proteasomal degradation was blocked with MG132 and degradation of autophagic pro-teins was investigated using cycloheximide treatment. Here, we report an increased autophagy impairment with SCA3 disease progression seen in HEK-293T cells transfected with ATXN3 plasmid with expanded polyQ tracts, higher aged 304Q-knock-in mice, or human post-mortem brain material. Furthermore, co-localized aggregation of the autophagic protein p62 and the dis-ease protein ATXN3 was observed in the course of SCA3 disease. Therefore, we suggest a signifi-cant role for p62 in aggregate formation seen in the neurodegenerative disease SCA3.

Existing research indicates that mineralization of Carlin-type gold deposit is related to geological structures, but current studies mostly focus on the qualitative association, and lack quantitative analysis of the relationship between mineralization and structural features, which limits the potential for predictive mineral exploration. In this study, the Nibao Carlin-type gold deposit was selected as the research area to conduct three-dimensional geological modeling, spatial analysis, and three-dimensional prospectivity modeling. Spatial analysis revealed that the majority of gold ore bodies are situated near the main fault, with gold mineralization primarily occurring within a spatial range of approximately -80 meters to 20 meters from the main fault plane. This spatial distribution predominantly aligns in a SW-NE direction. Spatial characteristic extraction of fault slope indicators suggests that the slope angles are conducive to the migration and accumulation of ore-forming hydrothermal fluids, with ore body metal content rapidly increasing within an angle range of approximately 20° to 60°. The shape analysis of the mainfault indicates that the principal spaces of mineralization enrichment are within -10m to 20m of the fault plane undulations, where gold resources are concentrated in a relatively flat area. However, the degree of mineralization is more pronounced in the protruding sections than in the depressed areas. The areas with significant dip changes in faults display higher variations in orebody attitudes, with mineralization noticeably weaker in areas where the fault steepness changes markedly. Ore-bearing units exhibit significantly higher grades within the -17° to 3° interval of fault steepness transition. This interval also sees a rapid accumulation of gold resources. The Nibao gold mine's mineralization is derived from deep, ore-bearing hydrothermal fluids ascending along major fractures, precipitating, and accumulating in favorable ore-hosting spaces (faults, anticline cores) and lithological combinations (sedimentary tuffs, tuffs). Three deep potential gold targets were identified, highlighting the deep western edge of the F1 fault and the deep southeast-trending lower plate as prospective areas for future exploration. This study underscores the effectiveness of 3D prospective modeling as an indispensable tool for elucidating the spatial distribution of fault-controlled Carlin-type gold deposits and their tectonic determinants.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

Background and Objectives Neurofibromatosis 1 (NF1 MIM # 162200), also known as von Recklinghausen disease, is among the most common autosomal dominantly transmitted disorders characterized mainly by neurocutaneous manifestations such as café au lait spots, intertriginous freckling, various types of neurofibromas (cutaneous neurofibromas or plexiform tumors), neurological manifestations, and bone abnormalities. It occurs with an incidence of 1:3000–1:4000 cases. Cone-rod dystrophies belong to the large group of retinal dystrophies, a highly heterogeneous group of disorders clinically manifested mainly by damage to cone and rod cells and have a broad spectrum of clinical manifestations. Many genes are involved in their etiology, with more than 100 currently identified, including the CRX gene responsible for the autosomal dominant form of cone-rod dystrophy (ad CORD). Materials and Methods: The authors present an intriguing case of a patient diagnosed with Neurofibromatosis type 1 (NF1) as an infant and ocular involvement (myopia and astigmatism onset at age 15), which yielded a surprising molecular testing result. Results: Molecular DNA analysis identified a rare occurrence of two mutational variants, including a pathogenic variant in the NF1 gene, c.3871-2A, and a likely pathogenic variant in the CRX gene c.119G>A. Conclusions: The authors present this case to highlight the surprises offered by molecular testing in a condition where the diagnosis is usually based on clinical criteria, thus providing patients with competent genetic advice.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

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.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

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.

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.

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.

To assess the community health workers’ (CHWs) knowledge, attitude, and practices (KAP) in type-2 diabetes (T2D) and hypertension (HTN) management. We thus also sought to assess the potential health system barriers for incorporating CHWs in T2D and HTN management. Mixed-method study comprised (1) a survey among 153 active CHWs to assess their KAP of T2D and HTN, and (2) semi-structured interviews with key informants to understand challenges of the health system and proposed solutions in incorporating CHWs in T2D and HTN management. The majority of CHWs correctly answered general knowledge questions on NCDs, risk factors, and prevention; however, only one-quarter correctly answered questions on smoking, family history, or tobacco use as risk factors. Most respondents appeared to have positive attitudes and have been practicing some activities related to T2D and HTN. Both financial and non-financial resource constraints were cited as challenges of the health system; therefore, re-structuring the role definition of CHWs and task of responsibilities, and assessment the need and workload have been proposed as ways forwards to effectively incorporate CHWs in T2D and HTN care. CHWs in Cambodia have shown their potential in T2D and HTN management; however, a well-designed strategy including technical training, clearly defined roles and responsibilities, and strong supporting structure are important to maximize their potential in the health system.

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%.

The three-pronged sliding universal coupling is a new kind of three-pronged coupling. To study its kinematic and dynamic characteristics, directional cosine matrices are utilized as tools to analyze the coordinate systems by establishing simplified geometric models and corresponding motions. Through the analysis of the motions of the input and output shafts and employing the method of single-force element, a set of equilibrium equations for the forces acting on the output shaft and the input shaft are formulated for solution analysis. The research indicates that during the rotation process, there exists a small angular difference between the input shaft and the intermediate shaft, demonstrating the quasi-constant angular velocity characteristics of the new tripod sliding universal coupling. The curves of the forces and torques acting on each component of the coupling approximate sinusoidal curves. The optimal operating angle range for the new tripod universal coupling is at angle , during which the system exhibits good transmission and mechanical performance.

Protein tyrosine phosphatase receptor type E (PTPRE) is a member of the “classical” protein tyrosine phosphatase subfamily and regulates a variety of cellular processes in a tissue-specific manner by antagonizing the function of protein tyrosine kinases. PTPRE plays a tumorigenic role in different human cancer cells, but its role in retinoblastoma (RB), the most common malignant eye cancer in children, remains to be elucidated. Etoposide resistant RB cell lines and RB patients display significant higher PTPRE expression levels compared to chemosensitive counterparts and the healthy human retina, respectively. PTPRE promotor methylation analyses revealed that PTPRE expression in RB is not regulated via this mechanism. Lentiviral PTPRE knockdown (KD) induced a significant decrease in growth kinetics, cell viability, and anchorage independent growth of etoposide resistant Y79 and WERI RB cells. Caspase-dependent apoptosis rates were significantly increased and a re-sensitization for etoposide could be observed after PTPRE depletion. In vivo chicken chorioallantoic membrane (CAM) assays revealed decreased tumor formation capacity as well as reduced tumor size and weight following PTPRE KD. Expression levels of miR631 were significantly downregulated in etoposide resistant RB cells and patients. Transient miR631 overexpression resulted in significantly decreased PTPRE levels and concomitantly decreased proliferation and increased apoptosis levels in etoposide resistant RB cells, impacts mirroring PTPRE KD effects and indicating PTPRE regulation via this miR. Additionally, PTPRE KD led to altered phosphorylation of protein kinase SGK3 and - dependent on the cell line - also AKT and ERK1/2, suggesting potential PTPRE downstream signaling pathways. In summary, these results indicate an oncogenic role of PTPRE in chemoresistant retinoblastoma.

Background and Objectives: In this current state, Type 2 Diabetes Mellitus (T2DM) is more prevalent in the population, and metformin is used as a first-line medication for treating it. There was up surge in the utilization of alternative therapies in the management of diabetes. Especially in diabetes, Herbal medicines are considered safe and reliable by majority of the population. Aim: The purpose of this research is aimed to estimate the safety and efficacy of Polyherbal Metabolite Compounds (PHMC) capsules in adults with T2DM. Materials and Methods: In this study, 60 T2DM patients aged 18-60 years were randomly assigned to Groups A (30) receiving Metformin 500 mg twice a day after food and Group B (30) receiving PHMC capsule 500 mg twice a day after food in a prospective, randomized and open-label clinical study. The in-silico simulation study was performed to selected plants major compounds on target protein Insulin-like Growth Factor-1 (1K3A). Result: The PHMC is found to be safe and effective in the management of T2DM. The FBS, PPBS and HbA1c were significantly lowered (p

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.

Background and Objectives: Cancer as the second leading cause of death in the United States poses a huge healthcare burden. Barriers to access to advanced therapies influence the outcome of cancer treatment. In this study, we examined whether insurance types affect the quality of cancer clinical care regarding access to an important monoclonal antibody, ramucirumab. Materials and Methods: Data for 13,340 cancer patients with Purchased or Medicaid insurance from the All of Us Database were collected for this study. The Chi-square test of proportions was employed to determine the significance of patient cohort characteristics and ramucirumab usage between Purchased and Medicaid insurance groups. The independent t-test was utilized to assess the influences of other determinants on insurance types. Results: Cancer patients who are African American, with lower socioeconomic status, or with lower educational attainment are more likely to be insured by Medicaid. Analysis of survey questions demonstrated the relationship between income and education level with insurance type as Medicaid cancer patients were less likely to receive primary care and specialist physician access and more likely to request lower cost medications. In addition, those with Medicaid insurance were identified to have poorer access to expensive therapeutics like ramucirumab compared to those with Purchased insurance.  Conclusions: The inequities of the US healthcare system are observed for cancer patient care; access to physicians and therapeutics are highly varied and dependent on insurance types. Socioeconomic status determines insurance type, which unfortunately generates a significant impact on cancer treatment and disease outcome.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

The effects on Raychaudhuri's equation of an intrinsically discrete or particle nature of spacetime are investigated, through consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. This is done from an effective point of view, meaning through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point; this on top of resulting non vanishing the limiting cross-sectional area itself of the congruence.

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

The process of sexual reproduction in eukaryotes starts when gametes from two different sexes encounter each other. Paramecium, a unicellular eukaryote, undergoes conjugation and uses a gametic nucleus to enter the sexual reproductive process. The molecules responsible for recognizing mating partners, hypothetically called mating-type substances, are still unclear. We have identified an O3-type mating substance polypeptide and its gene sequence using protein chemistry, molecular genetics, immunofluorescence, RNA inter-ference, and microinjection. The O3-type substance is a polypeptide found in the ciliary membranes, located from the head to the ventral side of cells. The O3-type substance has a kinase-like domain in its N-terminal part located outside the cell and four EF-hand motifs that bind calcium ions in its C-terminal part located inside the cell. RNA interference and immunofluorescence revealed that this polypeptide positively correlated with the expression of mating reactivity. Microinjection of an expression vector incorporating the O3Pc-MSP gene induced additional O3 mating type in the recipient clones of different mating types or syngen. Phylogenetic analysis indicates this gene is widely present in eukaryotes and exhibits high homology among closely related species. The O3Pc-MSP gene had nine silent mutations compared to the complementary mating type of the E3 homologue gene.

(1) Background: Among the chronic complications of type 2 diabetes mellitus, cancer became the leading cause of death in several countries. Our objective was the determination of whether prevalent type 2 diabetes mellitus is associated with a higher incidence of cancer. (2) Methods: This study is a nationwide analysis performed in Hungary. Study population was divided into a group with type 2 diabetes mellitus and into a non-diabetic group. The primary outcome was the risk related to overall cancer incidence. A key secondary outcome was the overall incidence of cancer in distinct study years. Further outcomes were the annual percent changes. (3) Results: The odds ratio related to the overall incidence of cancer was 2.50 (95% confidence interval: 2.46-2.55, P<0.0001) in patients with diabetes as related to controls. The odds ratio was higher in males than in females. The highest risk was found in the 18-39-year-old subgroup. The annual cancer incidence rate declined in controls, but not in patients with diabetes. Several types of cancer showed a decreasing tendency in non-diabetic controls.; (4) Conclusions: type 2 diabetes is associated with a higher risk of cancer. High risk in young patients with type 2 diabetes suggests that these young individuals should be considered as a risk group.

(1) Background: Patients with type 2 diabetes mellitus (T2DM) are at higher risk of cancer but how these two diseases associate is still debated. The goal was the assessment of the overall incidence of cancer among patients with newly diagnosed T2DM in Hungary. Summarizing, incident T2DM is associated with a significantly higher overall risk of incident cancer, with a reverse correlation of age. Newly registered T2DM patients were suggested to be screened for cancer within 6 months. (2) Methods: A nationwide, retrospective, longitudinal study was performed using a Hungarian database. The incident T2DM and diabetes free Hungarian population were included in the study. The primary endpoints were the overall and site-specific incidence and annual percentage change of the incidence of cancer in both populations. (3) Results: The overall incidence of cancer in patients amounted to 29.4/1000 and 6.6/1000 with or without T2DM, respectively, and the OR (95%CI) of cancer of the T2DM group was 4.32 (4.14-4.53), p<0.0001. The risk of having cancer was age-dependent, having the highest odd in the age group 18-39. The incidence of cancer was declining in the non-diabetic but was unchanged in T2DM population. The average lag time of diagnosing a cancer after the detection of T2DM was 3.86 months.; (4) Conclusions: Iincident T2DM is associated with a significantly higher overall risk of incident cancer, with a reverse correlation of age. Newly registered T2DM patients were suggested to be screened for cancer within 6 months.

Diabetes mellitus (DM) poses a significant challenge to global health, with its prevalence projected to rise dramatically by 2045. This narrative review explores the bidirectional relationship between periodontitis (PD) and type 1 diabetes mellitus (T1DM), focusing on cellular and molecular mechanisms derived by the interplay between oral microbiota and the host immune response. A comprehensive search of literature published between 2008 and 2023 was conducted to elucidate the association between these two diseases. Preclinical and clinical evidence suggests a bidirectional relationship, with individuals with T1DM exhibiting heightened susceptibility to periodontitis, and vice versa. The review includes recent findings from human clinical studies, revealing variations in oral microbiota composition in T1DM patients, including increases in certain pathogenic species such as Porphyromonas gingivalis, Prevotella intermedia, and Aggregatibacter actinomycetemcomitans, along with shifts in microbial diversity and abundance. Molecular mechanisms underlying this association involve oxidative stress and dysregulated host immune responses, mediated by inflammatory cytokines such as IL-6, IL-8, and MMPs. Furthermore, disruptions in bone turnover markers, such as RANKL and OPG, contribute to periodontal complications in T1DM patients. While preventive measures to manage periodontal complications in T1DM patients may improve overall health outcomes, further research is needed to understand the intricate interactions between oral microbiota, host response, periodontal disease, and systemic health in this population.

The vomeronasal system serves as a pivotal element in mammalian sensory biology, allowing the perception of chemical signals essential for social communication via the activation of two main receptor families, V1R and V2R. The expression of V1Rs and V2Rs is linked with that of the G-protein alpha-subunits, Gαi2 and Gαo, respectively. The exploration of the evolutionary pathways of V1Rs and V2Rs across all mammalian species remains a main challenge, juxtaposing available genomic data against emerging immunohistochemical evidence. However, recent investigations, in contrast to what is predicted by the currently annotated genomic sequences, have revealed the expression of Gαo in the vomeronasal neuroepithelium of wild canids, including wolves and foxes. In the present study, the employment of a specific antibody raised against the mouse V2R2, member of the C-family of vomeronasal receptors, V2Rs, has confirmed the expression of this receptor in the fox and wolf, but it has revealed the lack of expression in the dog. This may reflect the impact of domestication on the regression of the VNS in this species, in contrast to their wild counterparts, and underscores the effects of artificial selection on sensory functions. Thus, these findings suggest a more refined chemical detection capability in wild species.

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.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium.This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect.Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction.Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully .

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.

Recently quantum cosmology in tomographic representation was considered. as an important tool to analyze the quantum states of the early universe in relation with the subsequent classical evolution. Given a wave function the correspondent tomogram is defined proportional to the square modulus of its fractional Fourier transform. The classical limit obtained by taking the limit ℏ→0 can be compared with the classical tomogram obtained from the classical hamiltonian formalism. In this paper we show that a set of tomograms can be derived as exact solutions of a third order equation when a de Sitter quantum universe is considered. We finally discuss the limits of this approach to quantum cosmology because the extension to equations with arbitrary potentials can become extremely complicated for potentials given by algebraic polynomials of degree greater than two and therefore also for potentials expressible by arbitrary functions.

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 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 focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

The paper presents a new type of hydraulic clutch operating with magnetorheological (MR) fluids and the results achieved from both theoretical analysis and experimental measurement. The hy-draulic clutch system of its own design with MR working fluid and a rotating magnetic field lo-cated is designed. The principle of this clutch is to use a rotating magnetic field created by an al-ternating current electromagnet to set the MR fluid in motion. In the tests of the hydraulic clutch with a rotating magnetic field, MR fluid produced on their own, consisting of solid iron particles of various diameters mixed with a silicone oil, are used as working fluids. The rheological properties of MR fluids are assessed on the basis of tests carried out with a Brookfield DV2T rheometer equipped with a magnetic device for generating the magnetic field of its own design. The char-acteristics of the hydraulic clutch with MR working fluid and the rotating magnetic field are tested on a specially built test stand. As a result of the research, it has been found that the torque transmitted by the clutch is the greater, the higher the rotational speed of the magnetic field and the lower the rotational speed of the beaker in which the working fluid is placed, and that the greatest torque occurs for the working fluid with the highest iron content. Based on the analysis of the structure and characteristics of the clutch in which the magnetic field is used, it has been shown that the design of the developed clutch is similar to that of an induction clutch, and its characteristics correspond to the characteristics of the eddy current clutch. Therefore, the proposed new clutch working with MR fluid and the rotating magnetic field can be applied to stationary power transmission system similarly to an eddy current clutch.

We still do not have satisfactory answers about the inflationary and accelerating expansions of the universe, the missing mass problem, and the origins of the four fundamental forces and the quantum phenomena. Here, we introduce a new model of matter and space and a postulate on a constant of motion, and then show that an equation of motion derived from the constant of motion could provide new understandings of the above problems. For example, we show that there is a natural inflation scenario and that the co-moving distance to the closest accelerating supernova is clearly given as $c/(\sqrt{3} H)$ ($\sim$8.1 billion ly). In addition, we show that, in a system including a proton and an electron, the equation of motion has eight acceleration terms, some of which are suspected to be responsible for the four fundamental forces and the galaxy rotation anomaly. From further discussion, we conjecture that in order to understand the gravitational and strong interactions and the quantum phenomena, it is necessary to consider the expansion of the universe. The lensing mass distribution is explained, based on another postulate on a method of representing superposition.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

This paper secures the analytical soliton solutions of the perturbed NLSE gives to (1). The existence criteria have been demonstrated and the wave speed of the soliton befall out. To achieve all the results obtained we used the mathematical technique. In view of the results obtained, some new additional one have been reported in left-handed metamaterials.

PHA synthases (PhaC) are grouped into four classes based on the kinetics and mechanisms of reaction. The grouping of PhaC enzymes into four classes is dependent on substrate specificity, according to the preference in forming short chain length (scl) or medium chain length (mcl) polymers: class I, class III, and class IV produce scl-PHAs depending on propionate, butyrate, valerate and hexanoate precursors, while class II phaC synthesize mcl-PHAs based on the alkane (C6 to C14) precursors. PHA synthases of class I, in particular PhaC_Cs from Chromobacterium USM2 and PhaC_Cn/RePhaC1 from Cupriavidus necator/R. eutropha, have been analysed and the crystal structures of the C-domains have been determined. PhaC_Cn/RePhaC1 was also studied by small angle X-ray scattering (SAXS) analysis. Models have been proposed for dimerization, catalysis mechanism, substrate recognition and affinity, product formation and product egress route. The assays based on amino acid substitution by mutagenesis have been useful to validate the hypothesis on the role of amino acids in catalysis and in accommodation of bulky substrates, for the synthesis of PHB co-polymers and medium chain length-PHA polymers with optimized chemical properties.

The kinetics and efficacy profiles of photoinitiated polymerization are theoretically presented. For the same dose, lower light intensity achieves a higher steady-state-efficacy (SSE) in type-I; in contrast, type-II has an equal SSE. Higher light intensity has a faster rising efficacy, due to faster depletion of photoinitiator (PS) concentration. However, type-II process is also affected by the available oxygen. Higher light intensity produces more efficient singlet oxygen, resulting a higher transient efficacy, in which all intensities reach the same SSE when oxygen is completely depleted. With external oxygen, type-II efficacy increases with time, otherwise, it is governed only by the light dose, i.e., same dose achieves same efficacy. Moreover, type-II has an efficacy follows Bunsen Roscoe law (BRL), whereas type-I follows non-BRL. The measured type-I efficacy and gelation profile are analyzed by our analytic formulas. Schematics of the photocrosslinking stage defined by the availability of oxygen is developed, where both type-I and –II coexist until the oxygen is depleted. The overall efficacy may be enhanced by resupply of PS or oxygen during the light exposure. The roles of light dose and PS concentration on the efficacy of photoinitiated polymerization should be are governed a new concept of a volume efficacy (Ve), defined by the product of the crosslink (or gelation) depth (CD) and local [efficacy].

Among the many Lysosomal Storage Disorders (LSDs) that would benefit from the establish-ment of novel cell models, either patient-derived or genetically engineered, is Mucopolysaccha-ridosis type II (MPS II). In fact, even though a specific therapeutic approach does exist for this disorder (Enzyme Replacement Therapy, ERT, with recombinant human IDS) and haematopoiet-ic stem cell transplantation (HSCT) may also hold promise whenever the disorder is diagnosed soon enough, both approaches have their own drawbacks. Here we present our results on the establishment and characterization of two MPS II pa-tient-derived stem cell line(s) from deciduous baby teeth. To the best of our knowledge, this is the first time a stem cell population is isolated from LSD patient samples obtained from the oral cavity. Taking into account our results on the molecular and biochemical characterization of those cells and our first insights on their subcellular MPS phenotype, we consider these cells will be a valuable tool for both pathophysiological assessments and drugs screenings. Ultimately, we believe patient-derived dental pulp stem cells (DPSC) may represent a feasible alternative to induced pluripotent stem cells (iPSC) in many labs with standard cell culture con-ditions and limited (human and economic) resources.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations converting the defined Lax pairs to some simpler forms and reducing the variety of the Lax pairs this way are found. The direct method and its possible applications to other types of evolution equations are discussed.

In this paper, two double Jordan-type inequalities are introduced based on the papers [1]-[5]. These inequalities generalize the inequalities obtained in [1]-[5]. As a result, some new upper and lower bounds of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions elaborated in [6]. Based on this approach, some optimal approximations of the sinc function are derived by determining corresponding minimax approximants, also described in the paper [6].

The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but it does not admit solutions where the receiver is allowed to move. To overcome this limitation, the new wave equation is derived, permitting both the receiver and the source to move. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by the stationary point source. From this purely mathematical definition, the wave equation for the stationary source and the moving receiver is derived together with the corresponding free-space Green's function. Utilizing the derived Green's function, it was shown that this new wave equation also permits the solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for the moving source and the moving receiver governs the waves emitted by the moving point sources and received by the moving receivers.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

This study aimed to elucidate the similarities and differences between amyloid-forming corpora amylacea (CA) in the prostate and lung, examine the nature of CAs in cystic tumors of the atrioventricular node (CTAVN), and clarify the distinctions between amyloid-forming CA and spheroid-type amyloid deposition. We conducted proteomics analyses using liquid chromatography–tandem mass spectrometry with laser microdissection and immunohistochemistry to validate the characteristics of CAs in the lung and prostate. Our findings revealed that CAs in these organs primarily consist of common proteins (β2-microglobulin and lysozyme) and locally produced proteins. Moreover, we observed a discrepancy between the histopathological and proteomic analysis results in CTAVN-associated CAs. In addition, while the histopathological appearance of amyloid-forming CAs and spheroid-type amyloid deposits were nearly identical, the latter deposition lacked β2-microglobulin and lysozyme, and exhibited evident destruction of surrounding tissue. A literature review further supported these findings. These results suggest that amyloid-forming CAs in the lung and prostate are formed through a shared mechanism, serving as waste containers (wasteosomes) and/or storage for excess proteins (functional amyloids). In contrast, we hypothesize that while amyloid-forming CA and spheroid-type amyloid deposits are formed, in part, through common mechanisms, the latter are pathological.

Soil erosion and sediment transport are quite complex processes as they depend on physical, biological, mechanical, and chemical processes within a particular catchment. Therefore, it is highly essential to better explain engaged physical processes and means of accounting for site-specific conditions, for soil loss and sediment yield estimation. This paper mainly focuses on physical explanations behind soil erosion and common soil erosion models like Universal or Revised Universal Soil Loss Equation(USLE/RUSLE) and Modified Universal Soil Loss Equation(MUSLE). Based on the physical explanations and overall limitations, the MUSLE is selected for the application of sediment yield estimation. The main objective of this paper is to estimate the best exponent of the MUSLE, and to estimate the best combination of the exponent and topographic factor of the MUSLE under hydro-climatic conditions of Ethiopia. For the sake of calibration procedure, the main parameters of the MUSLE which directly affect soil erosion process such as cover, conservation practice, soil erodibility, and topographic factors are estimated based on the past experiences from literature and comparative approaches, whereas the other parameters which do not directly affect the erosion process or which have no any physical meaning (i.e coefficient a and exponent b) are estimated through calibration. It is verified that the best exponent of the MUSLE is 1 irrespective of the topographic factor, which results in the maximum performance of the MUSLE (i.e approximately 100\%). For the best combination of the exponent and topographic factor, the performance of the MUSLE is greater than or equal to 80\% for all four watersheds under our consideration, we expect the same for other watersheds of Ethiopia.

Background Homologous recombination deficiency (HRD) evolved into a major diagnostic marker in high grade ovarian cancer (HGOC) predicting the response to poly (Adenosine diphosphate-ribose) polymerase inhibitors (PARPi) and also platinum-based therapy. In addition to HRD, the type of peritoneal tumor spread influences treatment response and patient survival; miliary type tumor spread has poorer predicted outcome than non-miliary type tumor spread. Methods Known methods for HRD assessment were adapted for our technical requirements and the Predictive-value Integrated Genomic Instability Score (PIGIS) for HRD assessment evolved as an outcome. PIGIS was validated in HGOC samples from 122 patients. We used PIGIS to analyze whether the type of tumor spread correlated with HRD status and whether this had an impact on survival. Results We demonstrated that PIGIS can discriminate HRD positive from HRD negative samples. Tumors with miliary tumor spread are HRD negative and have a very bad prognosis with a progression free survival (PFS) of 15.6 months and an overall survival (OS) of 3.9 years. However, HRD negative non-miliary spreading tumors in our cohort had a much better prognosis (PFS 35.4 months, OS 8.9 years), similar to HRD positive tumors (PFS 34.7 months, OS 8.9 years). Conclusions Our results indicate that in a predominantly PARPi naïve cohort the type of tumor spread might be a better predictor of response to platinum sensitivity than HRD. It remains to be determined, whether this also applies for sensitivity to PARPi.

On the H-type group G⊂Rm×Rn, we study the existence of solutions for the Brezis-Nirenberg problem

This paper presents the perturbation theory for the double–sine–Gordon equation. We obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution.. In the particular case λ = 0 we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ=-1/8, we derive a phase-locked solution with the same frequency of the linear case. In general we obtain both coherent (solitary waves, lumps and so on) solutions as well as fractal solutions. We can demonstrate the existence of envelope wobbling solitary waves, because of the phase modulation depending on the solution amplitude and on the position. The main conclusion is that it is too reductive focus only on coherent solutions for the double sine-Gordon equation, because of the very rich behavior for the DSG nonlinear equation, including wobbling chaotic and fractal solutions.

Although there is a common physiological notion that the origin of the membrane potential is attributed to transmembrane ion transport, it is theoretically possible to explain its generation by the mechanism of ion adsorption. It was previously suggested that the ion adsorption mechanism led even to the potential formulas which are even identical to either the famous Nernst equation or Goldman-Hodgkin-Katz equation. Our further analysis shown in this paper indicates that the potential formula based on the ion adsorption mechanism leads to one equation which is the function of material surface charge density and the material surface potential. Furthermore, we confirmed that the equation holds in all the different experimental systems we studied. Although we have not succeeded in elucidating why such an equation is established, the equation appears to be the key equation governing the characteristics of the membrane potential regardless of the systems in question.

HU is the Hypergeometrical Universe Theory (HU)[1-8], proposed in 2006, where the Universe is a Lightspeed Expanding Hyperspherical Hypersurface and Gravitation is an absolute-velocity-dependent, epoch-dependent force. Here we introduce the Big Pop Cosmogenesis and show our calculations associated with the Equation of State of the Universe. This article is the first in a series of articles[9-22] supporting the paradigm shift.

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple codes for these.

Recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the Universe is undergoing a phase of accelerated expansion and it has been proposed that this cosmological behavior is caused by a hypothetical dark energy which has a strong negative pressure that allows explain the expanding universe. Several theoretical ideas and models related dark the energy includes the cosmological constant, quintessence, Chaplygin gas, braneworld and tachyonic scalar fields. In this paper, we have obtained new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution which could represents a potential model of a dark energy star. In order to investigate the effect of a quadratic equation of state in this anisotropic model we specify particular forms for the gravitational potential that allow solving the Einstein-Maxwell field equations. For these new solutions we checked that the radial pressure, metric coefficients, energy density, anisotropy factor, charge density , mass function are well defined and are regular in the interior of the star. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions but the causality condition and strong energy condition are violated. We expect that these models have multiple applications in astrophysics and cosmology.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and provide an analytical expression for the eigenvalues of the results. The holomorphicity of the resulting eigenvalues is examined. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, from the holomorphicity of the eigenvalues it is shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

This study delves into the Schrödinger equation's new invariants, shedding light on their crucial implications for theoretical physics and beyond. Specifically, it explores the behavior of scattering amplitudes and bound states concerning the choice of coordinate systems. The research unveils that while the energy of bound states remains invariant under coordinate transformations, the phase of scattering amplitudes undergoes variations, underscoring its pivotal role in theories reliant on phase normalization. Moreover, these findings have played a pivotal role in constructing estimates for three-dimensional Navier-Stokes equations, enhancing our ability to model complex fluid dynamics with greater precision and reliability. Additionally, in seismic exploration, tomography, and ultrasound imaging, these properties allow researchers to optimize phase selection, facilitating the most effective interpretation of measurement results. This strategic phase manipulation ensures clearer insights into subsurface structures, tissue composition, and fluid dynamics, with the flexibility to seamlessly transition back to the original coordinate system post-interpretation. This interdisciplinary synergy underscores the profound impact of fundamental theoretical research on advancing practical applications across diverse scientific domains.

The mind-body problem is the central issue in both of philosophy and life science for several centuries. To date, there is still no conclusive theory to interpret the relation between the mind and the body, even just the mind alone. Here, we promote a novel model, a derived mathematic equation called the entropic system equation, to describe the innate characters of the mind and the mechanism of the mind-body coupling phenomenon. As the semi-open thermodynamic systems far from equilibrium, the living organisms could be logically considered as an entropic system. In the living organisms or the entropic systems, there also are three essential existing elements including mass, energy and information, in which the mind and the body are hypothetically coupled by free energy and entropic force.

An extension of the Stoney formula for the case of a back side metallized 8” silicon taiko wafer has been developed, in the elastic regime, within the frame of the theory of elasticity. A good correlation between the calculated warpage, determined by the stress released by a given back side metallization (BSM), and the corresponding experimental warpages of the same thick metal layers deposited on an 8” silicon taiko wafer provides evidences of the correctness of the developed theory. This development suggests the possibility to extend this approach to the case of 8” taiko wafers based on a wide band gap semiconductor such as silicon carbide (SiC).

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

Orthohepadnavirus causes chronic hepatitis in a broad range of mammals, including primates, cats, woodchucks, and bats. Hepatitis B virus (HBV) X protein inhibits type-I interferon (IFN) signaling, promoting HBV escape from the innate immune system to establish persistent infection. However, whether X proteins of Orthohepadnavirus viruses in the other species have similar inhibitory activity remains unknown. Here, we investigated the anti-IFN activity of 17 Orthohepadnavirus X proteins derived from various hosts. We observed conserved activity of Orthohepadnavirus X proteins in inhibiting TIR-domain-containing adaptor protein inducing IFN-β (TRIF)-mediated IFN-β signaling pathway through TRIF degradation. X proteins from domestic cat hepadnavirus (DCH), a novel member of Orthohepadnavirus, inhibited mitochondrial antiviral signaling protein (MAVS)-mediated IFNβ signaling pathway comparable with HBV X. These results indicate that inhibition of IFN signaling is conserved in Orthohepadnavirus X proteins.

Hepatocellular carcinoma (HCC) is a heterogeneous malignancy with complex carcinogenesis. Although there has been significant progress in the treatment of HCC over the past decades, drug resistance to chemotherapy remains a major obstacle in its successful management. In this study we were able to reduce chemoresistance in cisplatin-resistant HepG2 cells by either silencing the expression of transglutaminase type 2 (TG2) using siRNA or by pre-treatment of cells with the TG2 enzyme inhibitor cystamine. Further analysis revealed that, whereas the full-length TG2 isoform (TG2-L) was almost completely cytoplasmic in its distribution, the majority of the short TG2 isoform (TG2-S) was membrane-associated in both parental and chemoresistant HepG2 cells. Following induction of cisplatin toxicity in non-chemoresistant parental cells, TG2-S together with cisplatin quickly relocated to the cytosolic fraction. Conversely, no cytosolic relocalisation of TG2-S or nuclear accumulation cisplatin was observed following identical treatment of chemoresistant cells, where TG2-S remained predominantly membrane-associated. This suggests that deficient subcellular relocalisation of TG2-S from membranous structures into the cytoplasm may limit the apoptic response to cisplatin toxicity in chemoresistant cells. Structural analysis of TG2 revealed the presence of binding motifs for interaction of TG-S with the membrane scaffold protein LC3/LC3 homologue that could contribute to a novel mechanism of chemotherapeutic resistance in HepG2 cells.

The Diophantine equation for which p is prime 2^n = p^2 + 7 and n is integers with p > 0, is examined in this work. It is demonstrated by examining the characteristics of the equation that the only solutions meeting these requirements are p = 3 with n = 5 and p = 5 with n = 7. In order to analyze the above equation, it is necessary to look at the properties of primes and how they relate to powers of two. These results advance our knowledge of prime numbers and how they behave in certain mathematical problems.

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics and others. Due to its application in control theory, the matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C over the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of the dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for the dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

We present set-theoretical solutions of the Yang-Baxter equation in BCK–algebras. Some solutions in BCK−algebras are not solutions in other structures (such as MV −algebras). Related to our investigations we also consider some new structures: Boolean coalgebras and a unified braid condition – quantum Yang-Baxter equation. Finally, we will see how poetry has accompanied the development / history of the Yang–Baxter equation.

We give an operator solution to an advanced-retarded differential equation. The application of the operators involved produces a solution in terms of Bessel functions.

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov method for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations, as a result of various steps, which on solving the so obtained equation systems yields the analytical solution. By this way various exact solutions including complex structures are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of solutions.

The current study compared the goodness of fit and estimation precision of Bayes and maximum likelihood (ML) structural equation modeling across sample sizes. Data consisted of Markov Chain Monte Carlo generated samples of 50, 75, 100, 125, 150, 200, 250, 500, 750, 1000, and 1500 observations. The Bayes and ML methods were used to estimate a structural equation model with 40 parameters, including 12 continuous observed indicators, four latent variables, and three structural paths. Analyses were conducted with the Mplus 8.0 statistical software and were replicated 500 times with each of the 22 conditions (11 sample sizes x 2 estimation methods). Indices of model fit were the Bayes information criterion, the Tucker-Lewis index, the comparative fit index, the root mean square error of approximation, the posterior predictive p-value (for Bayes models), and the ꭓ2 test (for ML models). Results showed that as the sample size increased, both estimation methods exhibited improved model fit and enhanced estimation precision, and both methods performed well with samples of 200 or larger; however, ML demonstrated a marginally superior fit with smaller samples. These findings were not consistent with previous research and suggest that ML remains a better choice with continuous data and small samples.

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb-Douglas functions embed the endogenous space factor as new capital to form the space travel firm's production function, which is also transformed into the consumer's utility function. Thus, the market equilibrium occurs at the equivalence of supply and demand functions, like the GRT presents the equivalence between the spatial geometric tensor and the energy-momentum tensor, which explains the principles of gravity and the motion of space matter in the spacetime framework. The mathematical axiomatic set theory of the accounting equation explains the equity premium effect that causes a short-term accounting equation inequality, then reaches the equivalence by suppliers' incremental equity through the closing accounts process of the accounting cycle. On the demand side, the consumption of space travel can be assumed as a value at risk (VaR) investment to attain the specific spacetime curvature in an expected orbit. Spacetime market equilibrium is then achieved to construct the space travel pricing model. The methodology of econophysics and analogy method was applied to infer the space travel pricing by the model of profit maximization, single-minded, and envy-free pricing in unit-demand markets. A case study with simulation was conducted for empirical verification of the math models and algorithm. Results show that space travel pricing remains the principle of market equilibrium but needs to be extended to the spacetime tensor of GRT.

We propose a generalization of Nambu-Hamilton equation in superspace $\mathbb R^{3|2}$ with three real and two Grassmann coordinates. We construct the even degree vector field in the superspace $\mathbb R^{3|2}$ by means of the right-hand sides of proposed generalization of Nambu-Hamilton equation and show that this vector field is divergenceless in superspace. Then we show that our generalization of Nambu-Hamilton equation in superspace leads to family of ternary brackets of even degree functions defined with the help of Berezinian. This family of ternary brackets is parametrized by the infinite dimensional group of invertible second order matrices, whose entries are differentiable functions on the space $\mathbb R^{3}$. We study the structure of ternary bracket in a more general case of a superspace $\mathbb R^{n|2}$ with $n$ real and two Grassmann coordinates and show that for any invertible second order functional matrix it splits into the sum of two ternary brackets, where one is usual Nambu-Poisson bracket, extended in a natural way to even degree functions in a superspace $\mathbb R^{n|2}$, and the second is a new ternary bracket, which we call $\Psi$-bracket, where $\Psi$ can be identified with invertible second order functional matrix. We prove that ternary $\Psi$-bracket as well as the whole ternary bracket (the sum of $\Psi$-bracket with usual Nambu-Poisson bracket) is totally skew-symmetric, satisfies the Leibniz rule and the Filippov-Jacobi identity (Fundamental Identity).

(1) Background Diabetic Retinopathy (DR) is the primary cause of poor vision in young adults. Screening for DR is important but many patients do not attend; (2) Methods: We validated an algorithm for predicting DR and its progression by conducting a retrospective study of 11 children in a population of 120,389 T2DM (3) Results: By applying the algorithm to the population showed an AUC of 0.93 (95% CI, 0.92–0.94) for any-DR and 0.90 (95% CI, 0.89–0.91) for referable-DR(4) Conclusions: The algorithm is useful for predicting patients who could develop referable forms of DR and also for any-DR. This would allow a personalized screening plan to be drawn up for each patient.

D-type cyclins encode G1/S cell cycle checkpoint proteins, that play a crucial role in defining cell cycle exit and progression. Precise control of cell cycle exit is vital during embryonic development, with defects in the pathways regulating intracellular D-type cyclins resulting in abnormal initiation of stem cell differentiation in a variety of different organ systems. Furthermore, stabilisation of D-type cyclins is observed in a wide range of disorders characterised by cellular over-proliferation, including cancers and overgrowth disorders. In this review, we will summarise and compare the roles played by each D-type cyclin during development and provide examples of how their intracellular dysregulation can be an underlying cause of disease.

Lacunary polyoxometalates (POMs) are negatively charged metal−oxo clusters, formally obtained from plenary topologies via fragment removal. Owing to the fragment removal, the lacunary POMs archetypes are rich in nucleophilic terminal oxo ligands, making them suitable for post-synthetic coordination with various heterometals. Trilacunary heteropolytungstates (het-ero-POTs) based on bowl-shaped {W9O30} framework incorporating a central lone-pair containing {XO3} hetergroup (X = AsIII, SbIII, and BiIII) function as all-inorganic scaffolds that in the presence of d-block metal cations typically construct sandwich-like dimers of Hervé and/or Krebs. Herein we review the preparative approaches, compositional and magnetic versatility of the constructing Hervé and Krebs type dimers and discuss prospective use as POMtronics.