We study the existence of positive solutions for a system of Hadamard fractional differential equations on an infinite interval with nonnegative nonlinearities, subject to coupled nonlocal boundary conditions which contain Hadamard fractional derivatives and Riemann-Stieltjes integrals. In the proof of the main results, we use the Guo-Krasnosel'skii fixed point theorem and the Leggett-Williams fixed point theorem.

Viral contamination in the aquaculture industry is a significant challenge that requires further research. Emerging evidence suggests that long noncoding RNAs (lncRNAs) play a role in regulating various biological processes, including immunity. However, most studies have focused on model organisms, and little is known about non-coding RNAs in the immune response to viral hemorrhagic septicemia (VHS) in rainbow trout. In this study, we investigated the listing of non-coding RNAs (ncRNAs) in rainbow trout challenged with VHS virus. We explored their potential role in defense-like responses based on transcriptomic analysis of the virus-treated and control groups. As a result of this research, 4207 lncRNAs were identified, of which 182 lncRNAs were differentially expressed between treated and untreated samples. Among 7753 lncRNA transcripts, 1920 were novel intergenic (class code “u”), and 3748 transcripts were potentially novel isoform of lncRNAs. Gene ontology analysis revealed biological pathways associated with the stress response and immune signaling. Pairs of genes such as TP63-MSTRG.62, IL10-MSTRG.9783, IL10-MSTRG.9784, TK1-MSTRG.22826, and MSTRG.17881-GLI1 showed cis interactions, while DOCK10-MSTRG.30015, MSTRG.36357-LOC101268921, and MSTRG.34190-ENPP2 showed trans interactions. In this study, the role of lncRNAs in regulating the expression of the target genes was clearly identified. This finding is consistent with the regulatory processes of immune system responses mediated by cytokines, as well as the regulation of oxygen levels in response to viral infection. The information presented here highlights the various regulatory mechanisms of lncRNAs in the expression of immune system genes in fish treated with VHS virus.

Standard cell culture is routinely performed at supraphysiological oxygen concentrations (~18% O2). Conversely, oxygen levels in most tissues range from 1%–6% (physioxia). Such hyperoxic conditions can alter reactive oxygen species (ROS) production, energy metabolism, mitochondrial network dynamics, and response to drugs and hormones. The aim of this project was to investigate the transcriptional response to different oxygen levels and whether it is similar across cell lines, or cell-line specific. Using RNA-seq, we performed differential gene expression and functional enrichment analyses in four human cancer cell lines, LNCaP, Huh-7, PC-3, and SH-SY5Y cultured at either 5% or 18% oxygen for 14 days. We found that oxygen levels affected transcript abundance of hundreds of genes, with the affected genes having little overlap between cell lines. Functional enrichment analysis also revealed different processes and pathways being affected in each cell line. Interestingly, we found that the top differentially expressed genes are involved in cancer biology. Further, we observed several hypoxia-inducible factor (HIF) targets upregulated at 5% oxygen, suggesting a role of HIF at physiological oxygen conditions. Finally, oxygen strongly induced transcription of mitochondrial genes in most cell lines, in a cell-type specific manner too. We conclude that cellular response to oxygen is widely cell-type specific, emphasizing the importance of maintaining physioxia in cell culture.

With continued scaling of semiconductor devices , the value of predictive analysis through 1 accurate quantum transport modeling is exponentially increasing. Quantum transmitting Boundary 2 method (QTBM) has been a well-known method of choice to model quantum transport in simple 1-D 3 devices. Here, we present an extension of the QTBM to the 2-D domain and apply it for more realistic 4 devices for accurate performance analysis.

We investigate the exact travelling wave solutions of the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations, appear in nonlinear optics, using simple ansatz approach. We use the Painlevé and traveling wave transformations to convert the mentioned nonlinear equations into nonlinear ordinary differential equations. Then, the simple ansatz approach has been employed to procure wave solutions, in terms of bright, singular soliton and trigonometric functions, for the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations. The study shows that the simple ansatz approach is straightforward and easy to implement for solving nonlinear problems.

Every subset S of a Cartesian spaces Rd, endowed with differen- tial structure C∞(S) generated by restrictions to S of functions in C∞(Rd), has a canonical partition M(S) by manifolds, which are or- bits of the family X(S) of all derivations of C∞(S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney’s conditions A and B. If M(S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces.

We study different aspects of an exactly solvable master equation (ME). Its simplicity allows one direct access to the details of its workings, highlighting significant features and peculiarities. The existence of phase transitions is unveiled.

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.

Variable during practice is widely accepted to be advantageous for motor learning and therefor a valuable strategy to effectively reduce high-risk landing mechanics and prevent primary anterior cruciate ligament (ACL) injury. Few attempts have examined the specific effects of variable train-ing in athletes who have undergone ACL reconstruction. Thereby it is still unclear to what extent the variations in different sensor areas lead to different effects. Accordingly, we compared the effects of versatile movement variations (DL) with variations of movements with emphasis on disrupting visual information (VMT) in athletes who had undergone ACL reconstruction. For-ty-five interceptive sports athletes after ACL reconstruction were randomly allocated to a DL group (n= 15), VT group (n= 15) or control group (n= 15). The primary outcome was functional performance (Triple Hop Test). The secondary outcomes included dynamic balance (Star Excur-sion Balance Test (SEBT)), biomechanics during single-leg drop-landing task hip flexion (HF), knee flexion (KF), ankle dorsiflexion (AD), knee valgus (KV), and vertical ground reaction force (VGRF), and kinesiophobia (Tampa Scale of Kinesiophobia (TSK)) assessed before and after the 8-weeks of interventions. Data were analyzed be means of 3×2 repeated measures ANOVA fol-lowed by post hoc comparison (Bonferroni) at the significance level of p≤0.05. Significant group × time interaction effects, main effect of time and main effect of group were found for triple hop test, all eight directions of SEBT, HF, KF, AD, KV, VGRF and TSK. There was no significant main ef-fect of group in HF and triple hop test. Also, significant differences in triple hop test, seven direc-tions of SEBT, HF, KF, KV, VGRF and TSK were found between control group with the DL and VMT groups. Between group differences in AD and medial direction of SEBT were not signifi-cant. Also, there was no significant differences between VMT and control groups in triple hop test and HF variables. Both motor learning (DL and VMT) programs improved outcomes in patients after ACL reconstruction. Findings suggest that DL and VMT training programs lead to compa-rable improvements in rehabilitation.

A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.

The space time fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz method. A simple compatible wave transformation in one dimension is employed to reduce the governing equations to integer ordered ODEs. Then, the ansatz approximation is used to derive exact solutions. Some illustrative examples are presented for some particular choices of parameters and derivative orders.

We propose a description of the electromagnetic field in the form of a four-component complex spinor, from which a vector of electromagnetic potential with two degrees of freedom, calibrated by two conditions - zero length and zero component along the y-axis - is obtained by using Pauli matrices. A similar approach is applied to the field of a fermion, in particular, the electron. It is known that the quantum field of the electron and the electron itself is a four-component complex spinor, so, existing in the Minkowski vector space, we cannot observe it directly. But with the help of Pauli matrices a vector is formed from the electron spinor, which is known to us as an electric current vector, and this current vector describes exactly a single particle. As a vector, it is available to us for observation in our vector space. Similarly, the electromagnetic field and its photon particle is also a four-component spinor, from which the universal formula using Pauli matrices produces a vector, it is known to us as the electromagnetic potential vector, and it too describes even a single photon. All the differences in the properties of the current vector and the electromagnetic potential vector, and hence the electron and the electromagnetic field, are due only to a slight difference in the structures of their four-component spinors and inextricable linked to them momentum spinors and coordinate spinors. Expressions for the electric and magnetic fields of a photon during its interaction with an electron.Thus, a unified way to describe bosons and fermions in spinor space is proposed. Each spinor using the same formula corresponds to a vector, in the case of a fermion it is a current vector, in the case of a boson it is a vector, for example, of the electromagnetic potential. Each spinor of a field is matched with a spinor of coordinates and a spinor of momentum, which are transformed by the same Lorentz transformations and which have the same structure as their corresponding field spinor, that is, the momentum and coordinates of boson have a bosonic spinor structure, while momentum and coordinates of fermion are a spinor with a fermionic structure. Field, coordinates and momentum vectors of boson automatically have a zero length, while in the case of fermion they all have a nonzero length, so the fermion, in contrast to the boson, has a nonzero mass, nonzero charge and moves with a sub light speed.While quantum mechanics treats probability as a real number, quantum field theory deals with probability as a four-dimensional real vector. The place of the probability amplitude, which in quantum mechanics is a complex number, in quantum field theory is taken by a complex spinor.In the same way as in quantum mechanics the processes of propagation and interaction are described at the level of complex probability amplitudes, and the final result is translated into a real probability value, so in quantum field theory all processes should be described in terms of complex spinor space, and the result is translated into the form of a real vector in Minkowski space.The presented approach, at its proper development, makes it possible to carry out calculations of the interaction of particles in two-dimensional spinor space, and to interpret in terms of the Minkowski vector space only the final results.

Trichothecene mycotoxin T-2 toxin is an important environmental pollutant and poses a global threat to human and animal health. T-2 toxin could induce nephrotoxicity, however, the precise molecular mechanism remains unclear. In this study, the mice were intraperitoneally administrated with a single dose of 2 mg/kg T-2 toxin. The kidney function and ultrastructural observation were also assessed and found T-2 toxin exposure could cause kidney damage. Transmission electron microscopy showed a significant swelling and vacuolization of the mitochondria of renal cell. A total of 1122, 58, and 391 differential expression genes (DEGs) that were predominantly expressed in kidney tissues at 1 d, 3 d, and 7 d after T-2 toxin exposure, respectively. Early transcriptomic changes at 1 d after exposure were down-regulation of DEGs involved in the cell cycle, p53 signaling pathway, and cellular senescence, while up-regulation of DEGs referred to the ribosome pathway. The temporal variations in gene expression pattern in T-2 toxin exposure in mice kidney were presented and cellular metabolism was disturbed at the exposure recovery period with 7 d. In conclusion, this study, for the first time, provided a comprehensive comparative transcriptomic analysis of gene regulation in T-2 toxin exposure-induced nephrotoxicity at different temporal periods and explored the nephrotoxicity mechanism of T-2 toxin at the mRNA level.

Finding a solution for Euler's equations is a classic mechanics problem. This study revisits the problem with numerical approaches. For ease of teaching and research, a Maple code comprising 2 lines is written to find a numerical solution for the problem. The study's results are validated by comparing these with previous studies. Our results confirm the correctness of the principle of maximum moment of inertia of the rotating body, which is verified by thermodynamics. As an essential part of this study, the Maple code is provided.

We prove general stability theorems for $n$-dimensional quartic-cubic-quadratic-additive type functional equations of the form \begin{eqnarray*} \sum_{i=1}^\ell c_i f \big( a_{i1}x_1 + a_{i2}x_2 + \cdots + a_{in}x_n \big) = 0 \end{eqnarray*} by applying the direct method. These stability theorems can save us much trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

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.

In this paper, we study the entire or meromorphic solutions for differential-difference equations in f(z) , its shifts, its derivatives and derivatives of its shifts. and study some Hayman's results for differential-difference polynomials.

The differential gear train and speed regulating motor constitute the variable ratio transmission for grid-connected wind turbine with differential speed regulation. The synchronous generator in the system can accessing the power grid without frequency converter. The transmission can realize the mode of variable speed constant frequency that the wind rotor speed is varying and the generator rotor speed is constant. The power control method is studied under the different wind speed which is lower or higher than rated wind speed with using the relational expression of utilization rate of wind energy Cp, pitch angle β and the tip speed ratio λ. The SIMULINK software is used to build the 1500 kW wind turbine model with differential speed regulation. Some different wind speed is made as input. The feasibility of power control method for grid-connected wind turbine with differential speed regulation is verified by the comparison between the simulation results and the theoretical value of the key parameters.

YH-DIE must have continuity . Given the basic algebraic clusters of homogeneous configurations,we can get the basic three equations: \begin{array}{l} {\mathop{\int}\nolimits_{0}\nolimits^{{x}_{i}}{\frac{{G}\left({{x}_{i}\mathrm{,}s}\right)}{{\left({{x}_{i}\mathrm{{-}}{s}}\right)}^{\mathit{\alpha}}}\mathrm{\varphi}\left({s}\right){ds}}\mathrm{{=}}{f}\left({{x}_{i}}\right)}\ ;\ {\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left({\frac{{\mathrm{\partial}}_{{x}_{i}}G}{\sqrt{{1}\mathrm{{+}}{\left|{\mathrm{\nabla}{G}}\right|}^{2}}}}\right)\mathrm{{=}}{0}}\ ;\ {{i}\mathrm{{=}}\mathop{\sum}\limits_{{x}_{i}\mathrm{{=}}{1}}\limits^{\mathrm{\infty}}{\arccos\hspace{0.33em}\mathrm{\varphi}\left({{x}_{i}}\right)}\mathrm{{=}}{f}\left({\fbox{${Yuh}$}}\right)} \end{array} YH-DIE has become a fusion point and access point in the fields of algebraic geometry and partial differential equations, and its mapping on multidimensional algebraic clusters or manifolds is very special. The minimal surface equation is a special case.

In this article, we introduce a relatively new concept of multi-valued (θ;R)-contractions and utilize the same to prove some xed point results for a new class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

We study the Gaudin models with gl(1|1) symmetry that are twisted by a diagonal matrix and defined on tensor products of polynomial evaluation gl(1|1)[t]-modules, extending all the results of to the twisted case. Namely, we give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation gl(1|1)[t]-modules and show that there exists a bijection between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the highest weights and evaluation parameters. In particular, our result implies that each common eigenspace of the algebra of Hamiltonians has dimension one. We also give dimensions of the generalized eigenspaces.

A diagnosis of typical chronic lymphocytic leukemia (CLL) requires the presence of ≥5000 clonal B-lymphocytes/μL with the coexistence of CD19, CD20, CD5, and CD23 and the restriction of light chain immunoglobulin, and the lack of expression of antigens CD22 and CD79b. Atypical CLL (aCLL) can be distinguished from typical CLL morphologically and immunophenotypically. Atypical CLL cells are defined as prolymphocytes; morphologically, these present as deeply-clefted lymphocytes which are larger than those in typical CLL, with condensed chromatin and without prominent nucleoli. However, current aCLL diagnostics rely more on immunophenotypic characteristics rather than atypical morphology. Immunophenotypically, atypical CLL differs from classic CLL in the lack of expression of one or fewer surface antigens, most commonly CD5 and CD23, and the patient does not meet the criteria for a diagnosis of any other B-cell lymphoid malignancy. Morphologically atypical CLL has more aggressive clinical behavior and worse prognosis than classic CLL. Patients with aCLL are more likely to display markers associated with poor prognosis, including trisomy 12, unmutated IGVH, and CD38 expression compared with classic CLL. However, no standard or commonly-accepted criteria exist for differentiating aCLL from classic CLL and the clinical significance of aCLL is still under debate. This review summarizes the current state of knowledge on the morphological, immunophenotypic and genetic abnormalities of aCLL.

A wide variety of renal neoplasms can have cystic areas. It happens for different reasons: some tumors have an intrinsic cystic architecture, others have a pseudocystic degeneration of necrotic foci or they have cystically dilated renal tubules constrained by stromal neoplastic cells. Clear cell renal cell carcinoma (CCRCC), either solid or cystic, is the most frequent type of renal cancer. While pseudocysts are found in high-grade aggressive CCRCC, cystic growth is associated to low-grade indolent cases. The latter also form through a cyst-dependent molecular pathway and they are more frequent in patients suffering from VHL disease. The differential diagnosis with multilocular cystic renal neoplasm of low malignant potential and clear cell papillary renal cell tumor can be especially hard and it requires a focused macroscopical and microscopical pathological analysis. As every class of renal tumors include cystic forms, a knowledge of criteria for a differential diagnosis is mandatory.

Hessenberg differential algebraic equations (Hessenberg-DAEs) with high index play a critical role in the modeling of mechanical systems and multibody dynamics. Motivated by the widely used Lie Group Differential Algebraic Equation (LGDAE) method which only handles index 2 systems, we propose a Modified Extended Lie Group Differential Algebraic Equation (MELGDAE) method for solving index 3 Hessenberg-DAEs, and provide theoretical analysis to deepen the foundation of the MELGDAE method.The performance of the MELGDAE method is compared with the standard methods RADAU and MEBDF on index 2 and 3 DAE systems, and it is demonstrated that the MELGDAE integrator exhibits competitive performance in terms of high accuracy and the preservation of algebraic constraints. In particular, all differential variables in index 3 Hessenberg DAEs achieve second-order convergence using the MELGDAE method, which suggests potential for extension to Hessenberg-DAEs with an index of 4 or higher.

The study is devoted to the issues of mathematical modeling and simulating the sport differential mechanism (DM) with controllable torque redistribution. The issue is caused by the elaboration of ADAS systems with the automated torque vectoring for transmissions of all-wheel-drive (AWD) vehicles and the inclusion of such devices in the combined autonomous vehicle trajectory control scheme. At the article's beginning, the use of devices for redistributing traction forces is reasoned by analyzing the curvilinear vehicle motion, where they could ensure the accuracy of vehicle steerability. The literature review highlights modern developments in the field of modeling and researching such DMs. Considering the vehicle turn with a minimum radius, the conditions corresponding to passing greater torque over the outrunning rear axle are determined. All the mechanism's components and loads acting between them are described in detail. To form an original method of mathematical description of the mechanism functioning, the system of differential equations, systems of kinematic and force connections are considered separately. The article details the mathematical approach to generalize the way for automating the equation compilation for rotational mechanical systems such as vehicle transmissions. In the simulation section, a Simulink model reflecting the functional components and calculation procedures is presented. A series of testing and simulations on the DM operation with forcible torque distribution is carried out. Modeling data are presented, and the analysis of simulation results is performed. In the completion, conclusions are made regarding the scope and use of this model and the prospects for further developing the method proposed to automate the formation of equation systems.

The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by backpropagating errors through the ODE solver, the neural network weights are adjusted accordingly to minimize the difference between the predicted and actual ODE solutions. It is shown that even when the dimensionality of the thermochemical manifold is trimmed to remove redundant species, the proposed approach accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism.

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

Because only two variables are needed to characterize a simple thermodynamic system in equilibrium, any such system is constrained on a 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since the integral of exact 1-forms is path-independent, a crucial property satisfied by state variables such as internal energy dE and entropy dS. Our prior work [1] shows that given an appropriate language of vector calculus, a machine can re-discover the Maxwell equations and the incompressible Navier-Stokes equations from data. In this paper, We enhance this language by including differential forms and show that machines can re-discover the equation for entropy dS given data. Since entropy appears in various fields of science in different guises, a potential extension of this work is to use the machinery developed in this paper to let machines discover the expressions for entropy from data in fields other than classical thermodynamics.

Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters.

N-maleimide-derivatized phospholipids are often used to facilitate protein anchoring to membranes. In autophagy studies, this is applied to the covalent binding of Atg8, an autophagy protein, to a phosphatidylethanolamine (PE) in the nascent autophagosome. However, the question remains on how closely the N-maleimide PE derivative (PE-mal) mimicks the native PE in the bilayer. In the present paper, spectroscopic and calorimetric techniques have been applied to vesicles containing either PE or PE-mal (together with other phospholipids) to compare the properties of the native and derivatized forms of PE. According to differential scanning calorimetry, and to infrared spectroscopy, the presence of PE-mal did not perturb the fatty acyl chains in the bilayer. Fluorescence spectroscopy and microscopy showed that PE-mal did not alter bilayer permeability either. However, fluorescence emission polarization of Laurdan and DPH probes indicated an increased order, or decreased fluidity, in the bilayers containing PE-mal. In addition, infrared spectral data from the phospholipid phosphate region revealed a PE-mal-induced conformational change of the polar heads, accompanied by an increased hydration. Globally considered, the results suggest that PE-mal would be a reasonable substitute for PE in model membranes containing reconstituted proteins.

Vectorial Boolean functions and codes are closely related, and each corresponding domain gives been to each other. On the one hand, various requirements of binary linear codes are needed for their theatrical interests but, more importantly, for their practical applicants (such as few-weight codes or minimal codes for secret sharing, locally recoverable codes for storage, etc.). On the other hand, various criteria and tables have been introduced to analyse the security of S-boxes that are related to vectorial Boolean functions, such as the Differential Distribution Table (DDT), the Boomerang Connectivity Table (BCT), and the Differential-Linear Connectivity Table (DLCT). In previous years, two new tables have been proposed for which the literature was pretty abundant: the $c$-DDT to extend the DDT and the $c$-BCT to extend the BCT. In the same vein, we propose extended concepts to study further the security of vectorial Boolean functions, especially the $c$-Walsh transform, the $c$-autocorrelation, and the $c$-differential-linear uniformity, and its accompanying table, the $c$-Differential-Linear Connectivity Table ($c$-DLCT). We study these properties of the novel functions at their optimal level concerning these concepts and describe the $c$-DLCT of the crucial inverse vectorial (Boolean) function case. Finally, the derived functions could lead to new families of binary minimal codes, as the recent achievements on minimal codes from low differential uniformity. We draw new avenues for future research toward linear code designs.

Background: While greenness has been associated with lower depression, the generalizability of this association in arid landscapes remains undetermined. We assessed the association between depression and greenness among nursing students living in El Paso, Texas (the Chihuahuan desert). Methods: Depression was measured with the Patient Health Questionnaire-9 scale, and greenness with the normalized difference vegetation index (at buffer sizes =250m, 500m, 1000m). Using data from the National Land Cover Database two additional measures of land patterns were analyzed: grayness and brownness. Structural equation models were used to assess the relationships of these land patterns to depression and quantify the indirect effects of peer alienation. Results: After adjusting for individual characteristics, at buffers 250 m greenness was associated with a decrease in the Incidence Rate Ratios (IRR) of depression by 49% (IRR, 0.51; 95%CI, 0.12-2.10), greyness with increases by 64% (IRR, 1.64; 95%CI, 1.07-2.52) and brownness with decreases by 35% (IRR, 0.65; 95%CI, 0.42-0.99). At buffer 250 m peer alienation explained 17.43% (95% CI, -1.79-36.66) of the association between depression and brownness, suggesting a pathway to depression. Conclusions: We did not observe an association between depression and residential greenness in El Paso, Texas. However, we did observe a protective association between brownness and depression as well as an adverse association with grayness. These results have theoretical implications as based on commonly used frameworks in this literature and adverse association of brownness (and the lack of greenness) and depression was expected.

In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

This paper explores the Wilsonian renormalization group of probe-D-branes, focusing on the Dirac-Born-Infeld (DBI) action. The analysis involves deriving the constant of motion and formulating the Wilsonian renormalization group equation. The study extends to the infrared regime, considering both zero and non-zero temperatures. Additionally, thermodynamic aspects related to the functional form of the grand potential are discussed. The investigation provides insights into the renormalization of probe-D-branes and their thermodynamic properties.

We investigate the determinants of U.S. bilateral imports of olive oil and their dynamics from shocks in foreign supplies and changes in U.S. olive oil demand, using an augmented gravity framework that leads to an equilibrium of bilateral trade flows from olive oil exporters to the U.S. market. The empirical specification is applied at the disaggregated HS-6 level in a panel dataset, and three estimation techniques (truncated OLS, PPML, Heckman), for which the latter two account for zero trade flows, the extensive margin of trade and the potential censored distribution of exports with zero trade flows. We run Reset and HPC tests to qualify our results. On the supply side, exporters’ capacity to exports, multilateral trade resistance, and immigrants’ networks into the US are strong determinants of the bilateral trade flows for both aggregate olive oil exports and for virgin olive oil exports, On the consumer side, U.S. GDP, the import unit value, and immigrant network effects are robust determinants of bilateral flows as well for aggregate and virgin olive oil trade flows. Migrants’ stock, exporters’ GDP and population, and total exports revenues increase the probability of an exporter entering the U.S. market. We could not find robust evidence of consumer behavior being influenced by popular press measures of the emergence of Mediterranean diet and olive oil, or measures of cultural globalization of U.S. consumers.

Observation of parity-violating effects in chiral molecules is a long-standing challenge of the molecular spectroscopy community. In the microwave regime, the difference in transition frequencies between enantiomers is predicted to be below the mHz level, which is considerably beyond current experimental capabilities. The most promising future efforts combine vibrational spectroscopy, buffer gas cooling, and carefully chosen molecular candidates with large predicted parity-violating shifts. Here, we demonstrate for the first time high-precision differential microwave spectroscopy, achieving sub-Hz precision by coupling a cryogenic buffer gas cell with a tunable microwave Fabry-Perot cavity. We report statistically limited sub-Hz precision of (0.08±0.72) Hz, observed between enantiopure samples of (R)-1,2-propanediol and (S)-1,2-propanediol at frequencies near 15 GHz. We confirm highly repeatable spectroscopic measurements compared to traditional pulsed-jet methods, opening up new capabilities in probing subtle molecular structural effects at the 10−10 level and providing a platform for exploring sources of systematic error in parity-violation searches. We discuss dominant systematic effects at this level and propose possible extensions of the technique for higher precision.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

TmMgB5O10 spontaneous crystals were synthesized via flux-growth technique from a K2Mo3O10-based solvent. The crystal structure of the compound was solved and refined within the space group P21/n. The first principles calculations of the electronic structure reveal that TmMg-pentaborate is an insulator with an indirect energy band gap of approximately 6.37 eV. Differential scanning calorimetry measurements and powder X-ray diffraction studies of heat-treated solids show that TmMgB5O10 is an incongruent melting compound. A characteristic band of Tm3+ cation corresponding to the 3H6 → 1D2 transition is observed in the photoluminescence excitation spectra of TmMg-borate. The as-obtained crystals exhibit intense blue emission with the emission peaks centered at 455, 479, 667 and 753 nm. The most intensive band corresponds to the 1D2 3F4 transition.

Sums of M consecutive squared integers (a+i)^2 equaling squared integers (for a<=1, 0<= i<= M-1) yield remarkable regular linear features when plotting values of M in function of a. These features correspond to groupings of pairs of a values for successive same values of M around straight lines of equation mu*M = 2a and are characterized in this paper for rational values of mu.

The well-known equations for the process of powder compaction (PCP) in a rigid die published over the period from the beginning of the last century to the present are considered. Most of the considered equations are converted into the dependence of the densification pressure on the relative density. The equations were analyzed and their ability to describe PCP was assessed by determining the coefficient of determination when approximating experimental data on the compaction of various powders. It is shown that most of the equations contain two constants, the values of which are determined by fitting the mathematical dependence to the experimental curve. Such equations are able to describe PCP with high accuracy in the case of compaction of powders up to a relative density of 0.9-0.95. It is also shown that different equations can describe PCP in the range of density change from the initial to 0.9 with the same and sufficiently high accuracy, but when the process of compaction is extrapolated to higher values of density, the curves diverge. This indicates the importance of equations that can unambiguously describe PCP to a relative density equal to or close to 1.0. For an adequate description of PCP to a relative density greater than 0.95, equations containing three or four constants have proven themselves well.

Micro-expression (ME) is one of the key psychological stress reactions. It is a modest, spontaneous facial mechanism. ME has significant applicability in a variety of psychologically-related sectors because to its precision and unpredictability with regard to psychological manifestations. Nevertheless, the current Micro-expression recognition (MER) algorithms have poor accuracy and a limited quantity of ME data, and this study issue has not been thoroughly investigated. Therefore, we present an approach for deep learning based on a Spatio-temporal capsule network (STCP-Net). STCP-Net has four components: a jitter reduction module, a differential feature extraction module, an STCP module, and a fully linked layer. The first two modules are aimed to extract diversifying differential features more precisely and to limit the influence of head jitter. The STCP module is used to extract Spatio-temporal features layer by layer, taking the temporal and geographical connection between features into account. This research runs sufficient trials using the Leave One Subject Out (LOSO) methodology for cross-validation using the CASMEII dataset. The conclusion and analysis demonstrate that the algorithm is innovative and efficient.

Legendre’s equation is key in various branches of physics. Its general solution is a linear function space, spanned by the Legendre functions of first and second kind. In physics however, commonly the only acceptable members of this set are the Legendre polynomials. Quantization of the eigenvalues of Legendre’s operator is a consequence of this. We present and explain a stand-alone, in-depth argument for rejecting all solutions of Legendre’s equation, but the polynomial ones, in physics. We show that the combination of the linearity, the mirror symmetry and the signature of the regular singular points of Legendre’s equation is quintessential to the argument. We demonstrate that the evenness or oddness of the Legendre polynomials is a consequence of the same ingredients.

Clifford algebra is unified language and efficient tool for geometry and physics. In this paper, we introduce this algebra to derive the integrable conditions for Dirac and Pauli equations. This algebra shows the standard operation procedure and deep insights into the structure of the equations. Usually, the integrable condition is related to the special symmetry of transformation group, which involves some advanced mathematical tools and its availability is limited. In this paper, the integrable conditions are only regarded as algebraic conditions. The commutators expressed by Clifford algebra have a neat and covariant form, which are naturally valid in curvilinear coordinate system and curved space-time. For Pauli and Schr\"odinger equation, many solutions in axisymmetric potential and magnetic field are also integrable. We get the scalar eigen equation in dipole magnetic field. By the virtue of Clifford algebra, the physical researches may be greatly promoted.

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.

In this study the tachyon-like Dirac equation, formulated by Chodos to describe superluminal neutrino, is solved. The analytical solutions are Gaussian wave packets obtained using the envelope method. It is shown that the superluminal neutrino behaves like a pseudo-tachyon, namely a particle with subluminal velocity and pure imaginary mass that fulfils the energy-momentum relation typical of classical tachyons. The obtained results are used to prove that the trembling motion of the particle position around the median, known as Zitterbewegung, also takes place for the superluminal neutrino, even if the oscillation velocity is always lower than the speed of light. Finally, the pseudo-tachyon wave packet is used to calculate the probability of oscillation between mass states, obtaining a formula analogous to the one obtained for the ordinary neutrino. This suggest that in the experiments concerning neutrino oscillation is not possible to distinguish tachyonic neutrinos from ordinary ones.

J. C. Maxwell, B. Riemann and H. Poincaré have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, a generalized Einstein's equation in inertial systems is derived based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some fundamental differences between this theory and Einstein's theory of general relativity.

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

This research explores the depolymerization of waste polymethyl methacrylate (PMMAW) from dental material in fixed-bed semi-batch reactors, focusing on three production scales: laboratory, technical, and pilot. The study investigates the thermal degradation mechanism and kinetics of PMMAW through thermogravimetric (TG) and differential scanning calorimetry (DSC) analyses, revealing a two-step degradation process. The heat flow during PMMAW decomposition is measured by DSC, providing essential parameters for designing pyrolysis processes. The results demonstrate the potential of DSC for energetic analysis and process design, with attention to standardization challenges. Material balance analysis across the production scales reveals a temperature gradient across the fixed bed negatively impacting liquid yield and methyl methacrylate (MMA) concentration. Reactor load and power load variables are introduced, demonstrating decreased temperature with increased process scale. The study identifies the influence of temperature on MMA concentration in the liquid fraction, emphasizing the importance of controlling temperature for efficient depolymerization. Furthermore, the research highlights the formation of aromatic hydrocarbons from the remaining char, indicating a shift in liquid composition during the depolymerization process. The study concludes that lower temperatures below 450 °C favor liquid fractions rich in MMA, suggesting the benefits of lower temperatures and slower heating rates in semi-batch depolymerization. The findings contribute to a novel approach in analyzing pyrolysis processes, emphasizing reactor design and economic considerations for recycling viability. Future research aims to refine and standardize the analysis and design protocols for pyrolysis and similar processes.

The paradigm of molecular communications is applied to the concrete case for delivering electrically charged nanoparticles to tumor. Once them have been injecetd in blood it is expecetd an optimal outcome as to reduce toxicity and minimal dispersion of drugs in the blood stream. With a fraction of nanoparticles arrives to surface of tumor, the scattered part of injected ones can minimize the success of scheme of drug delivery. In this paper is presented a theory based at the sequence electrodynamics-diffusion-Bayes theorem. The resulting probability of Bayes at the end of sequence, might be telling us that dynamical processes based in the injection of electrically charged nanoparticles might be dictated by stochastic formalism more that biochemical approaches by which makes impossible to know the success or fail of drug delivery dynamics. Illustrations demonstrating the transition of a linear to nonlinear scenario are presented

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.

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.

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.

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

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 probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic processes and geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate classical and quantum systems and demonstrate the utility of the information length as a unique Lagrangian diagnostic to quantify the information change as a system continuously evolves in time and to map out attractor structure. We further elucidate quantum effects (uncertainty relation) and the dual role of the width of PDF in quantum systems.

Complex and real valued exact solutions to some reaction-diffusion equations are suggested by using homogeneous balance and Sine-Gordon equation expansion method. The predicted solution of finite series of some hyperbolic functions are determined by using some relations between the hyperbolic functions and trigonometric functions based on Sine-Gordon equation and traveling wave transform. The Newel-Whitehead-Segel and Zeldovich equations are solved explicitly. Some real valued solutions are depicted for some particular choice of parameters.

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time.

In order to sustain the marine environment relationship between the environmental factors and marine biota must be investigated. This study aims to study such a correlation in the adjacent waters of Nan Wan Bay, Kenting, Taiwan, and to explore the covariance of environmental factors on marine life (whether they enhance or diminish it). To achieve these objectives, factor analysis was used to identify potential latent variables that could affect the water quality of the adjacent waters, including phytoplankton (quantity), zooplankton (quantity), and fish (quantity and species). These potential variables were named based on the results of past studies and related literature. Finally, a structural equation model (SEM) was constructed to establish a marine ecological model among the potential variables. The factor analysis results revealed that nutrients, upwelling, and primary productivity are the primary factors affecting the environmental changes in the adjacent waters of Nan Wan Bay. The comprehensive SEM showed that nutrients and primary productivity significantly impact plankton. Path analysis indicated that primary productivity has the highest direct effect on the phytoplankton cluster. However, the upwelling has a low significance in its effect on phytoplankton, zooplankton, and fish clusters. Compared to the results of past related studies, the SEM proposed in this study can reflect a considerable degree of change in the waters.

The main aim of this study is to examine the effects of Total Quality Management (TQM) practices (leadership of management, decision making, continuous improvement, customer focus, employee involvement, process management and relations with suppliers) on the financial and operational performance of hospitals in service industry. The data of the study were collected by the questionnaire prepared in the light of published studies and the suggestions of medical and administrative staff. Medical and administrative staff were chosen as target participants that reflect perspectives of hospitals. 1069 questionnaires were answered in 6 private and 26 public hospitals in the Marmara region in Turkey. The results claim that “customer focus” affects both operational performance as well as the financial performance of hospitals more than other TQM practices. While “process management” and “customer focus” explain the variance of financial performance significantly. “Process management” does not explain variance of operational performance.

In a recent article, the author derived a new generalized Langevin equation and its associated Fokker-Planck equation of a Brownian particle in a parabolic potential where the thermal bath, consisting of $N$ harmonic oscillators, interacts bilinearly with the external field. The time needed for the system to reach a steady state is longer than that for the classical version where such an interaction is off. We find that there is a marked effect of the field-bath interaction on the average heat and entropy production of the bath represented through strong oscillations in such properties. The new theory applied to the system should improve the physical description of previous works done with the classical approach.

Chemotherapy-related deaths, the result of treatment with faulty medications, account for nearly 10% of all breast cancer deaths (Rashbass, 2016). Patient-specific, personalized medicine is evidently required to administer optimized therapeutics and prevent treatment-related mortality. In order to develop a predictive model for breast cancer therapy, the following study analyzed the mRNA data of 4,704 genes derived from 20 breast cancer patients before and after doxorubicin treatment for 16 weeks (O’brien et al., 2006; Perou et al., 2000). The genomic data of each patient was first stratified into 9 groups (corresponding to the 9 Mechanisms defined in Figure 4) based on mRNA expression in response to the tumor and to the doxorubicin treatment. The study then employed the Planckian Distribution Equation (PDE) discovered at Rutgers University to model the stratified samples by transforming each mechanism into a single long-tailed histogram fitted by the PDE. Our PDE model is based on 3 parameters - A, B, and C - of which 2 were extracted from each model to generate the plots seen in figures 5e and 5f. The drug-induced slopes of the A vs C plots were then determined for all 9 mechanisms of each patient. The study observed an increase in post-treatment mRNA levels for longer surviving patients in 6 mechanisms. Further analysis displayed how the drug treatment uniquely altered each of the mechanisms based on the length of patient survival. These results indicate that the PDE-based procedures described herein may provide a novel tool for discovering potential anti-breast cancer pharmaceuticals.

The equation of state of asymmetric nuclear matter as well as the neutron and proton effective masses and their partial-wave and spin-isospin decomposition are analyzed within the Brueckner–Hartree–Fock approach. Theoretical uncertainties for all these quantities are estimated by using several phase-shift-equivalent nucleon-nucleon forces together with two types of three-nucleon forces, phenomenological and microscopic. It is shown that the choice of the three-nucleon force plays an important role above saturation density, leading to different density dependencies of the energy per particle. These results are compared to the standard form of the Skyrme energy-density functional and we find that it is not possible to reproduce the BHF predictions in the (S,T) channels in symmetric and neutron matter above saturation density, already at the level of the two-body interaction, and even more including the three-body interaction.

Pregnancy is a dynamic state with multiple metabolic changes occurring including insulin resistance. Gestational diabetes mellitus (GDM), a form of diabetes that appears during pregnancy, develops if metabolic aberrations occur, in particular, in normal pregnancy-induced insulin resistance. Multi-omics is a powerful approach for uncovering the mechanisms driving metabolic change in different physiologic and pathologic states. A recent study demonstrated that the gestational gut microbiome mediates pregnancy metabolic adaptations through effects on gut indoleamine-2,3 dioxygenase 1 activity and the production of kynurenine. Using the dataset generated from this highly controlled study, we performed a comprehensive analysis of the pregnancy-specific physiological and metabolic profiles, 16S rRNA microbiome, and plasma untargeted LC-MS metabolome data. To facilitate the utilization of these analysis results by other researchers, we developed MOMMI-MP, a database that provides an easy-to-use platform to browse and search differential abundant microbial taxa and metabolites, and to examine metabolic pathways. The datasets consist of data collected from 3 genetically diverse strains of mice (C57BL/6J, CD1, and NIH-Swiss) over 6 time points during the gestational (days 0, 10, 15, and 19 during gestation) and postpartum (days 3 and 20 after delivery) states, totaling 180 samples for each strain. The computational results are presented in various tables and plots, and organized in MOMMI-MP to empower exploratory analyses by other researchers. In conclusion, MOMMI-MP is a resource to facilitate the investigation of novel mechanisms governing metabolic changes during pregnancy.

Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of the stochastic-constrained particles that form ubiquitously within these swarms remain oblivious. This study demonstrates a generalized diffusion equation for stochastic-constrained particles that considers the velocity and location aggregation effects observed from their parent particle swarm (i.e., a completely random particle swarm). This equation can be approximated as the form of Schr\"odinger equation in the microcosmic case (low relative density) and describe the dynamics of the total mass distribution in the macrocosmic case (high relative density). The predicted density distribution of the particle swarm in the stable aggregation state is consistent with the total mass distribution of massive, relaxed galaxy clusters (at least in the range of r < r_s), preventing cuspy problems in the empirical Navarro-Frenk-White (NFW) profile. This study opens a window to observe the dynamics of stochastic-constrained particles from a third perspective, from which the aggregation effect of particles without gravitation can be saw.

For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure.

Background: The reliability of a recent review of meningiomas in the archeologic record was difficult to assess, given the inverted sex ratio of the report and other contents apparently at variance with anatomical/medical findings in scientifically-identified cases. It therefore seemed appropriate to reexamine the nature of meningiomas and derive improve criteria for their recognition in the archeologic record and distinguish them from hemangiomas and bone marrow hyperplasia (recognized in the form of porotic hyperostosis). Methods: Medically-documented cases of meningiomas, hemangiomas and cranial bone marrow hyperplasia were examined to establish a macroscopic standard that distinguishing among them. Alleged cases in the archeologic record were examined for conformity with those criteria. Results: An en face pattern of uniform mesh with contained whorls appears pathognomonic for meningiomas. This contrasts with the non-uniform marrow expansion displacement of trabeculae in porotic hyperostosis and non-uniform vascular displacement of trabeculae in hemangiomas. Reassessment of past attributions revealed few cases of meningiomas that could be confidently diagnosed. Those identified has sex ratios parsimonious with medical literature reports. Conclusions: Criteria suggested for identifying meningiomas permits distinguishing from hemangiomas, bone marrow hyperplasia (porotic hyperostosis) and from the macroscopically-observable surface spicules characteristic of osteosarcomas. Examination for fulfillment of criteria for meningiomas and hemangiomas seems to provide a picture (including sex ratios) more parsimonious with the clinical literature, concluding that Cook and Danforth’s disparate ratios were related to less fastidious case selection. Additionally, confidence in recognizing porotic hyperostosis may be compromised because of apparent similar macroscopic alterations to those seen with hemangiomas.

Conventionally, partial differential equations (PDE) problems are solved numerically through discretization process by using finite difference approximations. The algebraic systems generated by this process are then finalized by using an iterative method. Recently, scientists invented a short cut approach, without discretization process, to solve the PDE problems, namely by using machine learning (ML). This is potential to make scientific machine learning as a new sub-field of research. Thus, given the interest in developing ML for solving PDEs, it makes an abundance of an easy-to-use methods that allows researchers to quickly set up and solve problems. In this review paper, we discussed at least three methods for solving high dimensional of PDEs, namely PyDEns, NeuroDiffEq, and Nangs, which are all based on artificial neural networks (ANNs). ANN is one of the methods under ML which proven to be a universal estimator function. Comparison of numerical results presented in solving the classical PDEs such as heat, wave, and Poisson equations, to look at the accuracy and efficiency of the methods. The results showed that the NeuroDiffEq and Nangs algorithms performed better to solve higher dimensional of PDEs than the PyDEns.

Molybdenum oxides is well-known electro-catalysts in fuel cells systems, they are usually used as anodic materials for the oxidation of low molecular weight alcohols. The utilization of Mo as catalysts in the pharmaceutical analysis is not common yet. In this study, bare glassy carbon electrodes were modified by the oxides by means of electrochemical deposition and the modified electrodes were used as catalysts for the electrochemical oxidation of hydrochlorothiazide (HCT). Well-resolved anodic peaks were reported for the analyzed pharmaceuticals when the Mo/GCE was utilized for the analysis of HCT. Analytical performance of the modified electrodes was evaluated based on the following statistical parameters; linearity ranges, correlation coefficients, limits of detection and quantitation, and recovery values. The prepared electrodes were used for the determination of the active ingredients in their pharmaceutical formulations and the reported activity was correlated to influence of the utilized pH on both structures of the used electrodes and the detected analytes.

We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.

Most of α-thalassemia cases are caused by deletions of the structural α-globin genes. The degree of microcytosis and hypochromia has been correlated with the number of affected α-globin genes, suggesting a promising role of hematologic parameters as predictive diagnostic tools. However, specific cut-off points for these parameters to discriminate between the different subtypes of α-thalassemia remain to be clearly defined. Six hematologic parameters (total number of erythrocytes, hemoglobin concentration, mean corpuscular volume, mean corpuscular hemoglobin, mean corpuscular hemoglobin concentration and red cell distribution width) were evaluated in 174 cases of deletional α-thalassemia (92 heterozygous α+ thalassemia, 39 homozygous α+ thalassemia, 34 heterozygous α0 thalassemia and 9 cases of Hb H disease). A good correlation between the number of deleted alpha genes and MCV (r = -0.672, p<0.001), MCH (r = -0.788, p<0.001) and RDW (r = 0.633, p<0.001) was observed. The deletion of at least two alpha genes in adult individuals with microcytosis without iron deficiency and normal values of Hb A2 and Hb F should be discarded when MCH levels are lower than 23.15 pg. Furthermore, MCH <21.90 pg and/or MCV <70.80 fL are strongly suggestive of the presence of one α0 allele. Finally, an accurate presumptive diagnosis of Hb H disease can be made if both RDW ≥20% and MCH <18.45 pg are seen.

An approach of implementing X-bar and R control charts as a statistical control tool to monitor changes in the melting profile of fresh and stored flaxseed oils by differential scanning calorimetry (DSC) was used. Phase transition melting profiles were collected after 0, 2, 4, 6 months of storing flaxseed oils, originated from five different cultivars. Four peaks at around -36, -30, -25, -12 °C were identified using the deconvolution analysis procedure, which enabled data to be collected on peak temperature (T), peak height (h) and the peak area (A), as well as the ratio calculated from these parameters. Control charts of DSC parameters, linked to the second peak (h2, A2) and calculated ratios of those parameters showed an increasing or decreasing trend within the storage time, thus were considered to be indicators of oil deterioration. Since DSC parameters related to the first peak (h1, A1) and third peak (h3, A3) remained unchanged within storage, they were established as the markers of flaxseed oil authenticity.

This paper applied the space-time generalized finite difference scheme for solving the nonlinear dispersive shallow water waves as the modified Camassa−Holm equation, modified Degasperis-Procesi equation, Fornberg-Whitham equation, and its modified form. The proposed meshless numerical scheme was composed of the space-time generalized finite difference method, the two-step Newton-Raphson method, and the time-marching method. The space-time approach can treat the temporal derivative as one of the spatial derivatives. This numerical technique enables all the partial derivatives in the governing equation can be discretized by a spatial discretization method, and the mixed derivative can efficiently deal with using the proposed meshless numerical scheme. The space-time generalized finite difference method is advanced from the Taylor series expansion and the moving-least square method. The numerical discretization process is only related to functional data and weighting coefficients on the central node and its nearby nodes. Thus, the matrix system composed of nonlinear algebraic equations will be a sparse matrix and can be efficiently solved by the two-step Newton-Raphson method. Furthermore, the time-marching method was utilized to proceed with the space-time domain along the time axis. In this paper, several numerical examples were tested to verify the capability of the proposed space-time generalized finite difference scheme.

We establish certain modular equations of degree three based on some results of Ramanujan's theta functions.

The entropic gravity conception proposes that what has been traditionally interpreted as unobserved dark matter might be merely the product of quantum effects. These effects would produce a novel sort of positive energy that translates into dark matter via $E=mc^2$. In the case of axions, this perspective as been shown to yield quite sensible, encouraging results [DOI:10.13140/RG.2.2.17894.88641] . There, a simple Schrodinger mechanism was utilized, in which his celebrated equation is solved with a potential function based on the microscopic Verlinde's entropic force advanced in [Physica A {\bf 511} (2018) 139]. In this effort we revisit such technique with regards to fermions' behavior (specifically, baryons).

Quaternion algebra is used both for the description of the motion of material objects in 4D space-time and for the representation of the energy-momentum density tensor in the same quaternion basis, accurate to some arbitrary scalar fields. Quaternionic generating operators applied repeatedly to the energy-momentum density tensor lead to the gravitomagnetic equations that are parent equations for the series of physical equations ranging from the wave equations up to the quantum mechanical ones. Before finally deducing the gravitomagnetic equations, it is necessary to use the Lorentz gauge at a certain stage to cut off the arbitrary scalar fields. We declare that these superfluous scalar fields, inaccessible to direct observation, represent dark matter and dark energy. We show in what way the dark matter can provide a flat profile of the orbital speed of the galaxy's arm rotations.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

We carry out in a thin heterogeneous porous layer, the multiscale analysis of Smoluchowski's discrete diffusion-coagulation equations describing the evolution density of diffusing particles that are subject to coagulate in pairs. Assuming that the thin heterogeneous layer is made of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in lower space dimension. We also prove a corrector-type result very useful in numerical computations. In view of the thin structure of the domain, we appeal to a concept of two-scale convergence adapted to thin heterogeneous media to achieve our goal.

The generalized dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac problem. The spectra of one-electron homonuclear quasimolecules are calculated and compared with the previous calculations. The analysis of the monopole approximation with two different choices of the origin is performed. Special attention is paid to the lead and xenon dimers, Pb82+–Pb82+–e− and Xe54+–Xe54+–e−, where the energies of the ground and several excited σ-states are presented in the wide range of internuclear distances. The developed method provides the quasicomplete finite basis set and allows for construction of the perturbation theory, including within the bound-state QED.

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

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.

This study examined injury patterns in fatal falls from heights and pedestrian traffic accidents, aiming to help in differential diagnoses in uncertain and rare cases where it is unclear whether the body may have fallen from nearby buildings or was left on the street after a traffic accident. A retrospective review of autopsy reports from the Institute of Legal Medicine of the University of Rome "Tor Vergata" between 2012 and 2023 was conducted. The analysis encompassed 232 cases, collecting data regarding internal organ injuries, bone fractures, and external skin injuries. Differences were observed in the presence of liver and lung injuries, cranial and forearm fractures, and the total injured skin area, proposing diagnostic markers. Statistical analyses highlighted the discriminative power of the "Total Injured Skin Area (cm²)" with a quantitative approach, potentially providing an optimal cut-off value for distinguishing between the two event types. A comparison with literature highlights the extreme heterogeneity in injuries patterns and highlighted that a spatial approach, considering whether injuries are unilateral or bilateral, may provide more accurate distinctions. The findings suggest the potential for developing a diagnostic algorithm throughout the integration of qualitative, quantitative, and spatial data to improve the objectivity required in medico-legal contexts.

Frontal Temporal Dementia (FTD) is a neurological disorder known to have less therapeutic options. So far only a few biomarkers are available for FTD that can be used as potential comorbidity targets. To this end, in the present study we aim to identify potential biomarkers or susceptible genes for FTD that show comorbidities with diseases such as COVID-19 and Breast Cancer. Gene expression Omnibus datasets containing FTD expression profiles from African American and white ethnicity background were included in our study. In FTD samples of GSE193391 dataset, we identified 305 DEGs with 168 genes being up-regulated and 137 genes being down-regulated. We conducted comorbidity analysis for COVID-19 and Breast cancer followed by analysis of potential drug interactions, pathogenicity, analysis of genetic variants and functional enrichment analysis. Resulting genes AKT3, GFAP, ADCYAP1R1, VDAC1, and C4A showed significant transcriptomic alterations in FTD and significant comorbidity status with COVID-19 and Breast cancer. Functional pathway analysis revealed that these comorbid genes were significantly enriched in the pathways such as glioma, JAK/STAT signaling, systematic lupus erythematosus, neurodegeneration-multiple diseases and neuroactive ligand-receptor interaction. Overall, from these results, we concluded that these genes could be recommended as potential therapeutic targets for the treatment of comorbidities in FTD.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

A scientific investigation into visual preferences of rural recreation path landscapes is crucial for enhancing visual qualities and visitors' experience. Taking Baofeng, a representative traditional village in Yunlong, as an example, this study analyzed the visual preference of three typical linear recreational paths with different landscape attributes. We used eye-tracking technology to collect eye movement data and conducted a subjective semantic differential evaluation. Our findings manifest a general inclination amongst individuals to favor closer views and paths with clear trajectories and rich elevation changes while walking, despite preference differences on different types of paths. Regarding group diversity, more inclusive design should be made to meet the sensory needs of different groups. Moreover, despite the limited level of correlation between subjective and objective evaluation methods, combining these two approaches remains indispensable. This synthesis advances prior quantitative landscape evaluation with a specific focus on rural path landscapes and upholds the integrity of results by combining objectivity with subjectivity. It also provides relevant design suggestions for further rural renewal and path planning of Baofeng village.

Background: Tourism is one of the prominent industry that has a capability to generate handsome income for developed as well as developing countries. However, the study to investigate specifically the perception of local residents towards tourism is still lacking. The perception of the locals is important since it could determine the extent of their support for tourism development. Plus, previous research found that male residents are more support better towards the tourism development. Thus, this factor is adapted as well in this study to examine whether this gender may influence to the tourism industry. 2) Methods: This study used Structural Equation Modeling (SEM) technique for determining the structural estimates between constructs. 3) Results: The respondents agree that positive perception, negative perception and tourism impact has a significant impact on support for tourism development in which has been recognized as Social Exchange Theory model. Moreover, the finding also revealed that gender has a potential to moderates the causal effect of tourism impact on tourism development. 4) Conclusion: The resident understand the tourism sector could strengthen economic nation but they also want the natural resources should be protected.

G protein-coupled receptor 15 (GPR15, also known as BOB) is an extensively studied orphan GPCR involving HIV infection, colonic inflammation and smoking-related diseases. Recently, GPR15 was deorphanized and its corresponding natural ligand demonstrated an ability of inhibiting cancer cell growth. However, no study reported the potential role of GPR15 in a pan-cancer manner. Using large-scale publicly available data from the Cancer Genome Atlas (TCGA) and the Genotype-Tissue Expression (GTEx) databases, we found that GPR15 expression is significantly lower in colon adenocarcinoma (COAD) than in normal tissues. And among 33 cancer types, GPR15 expression is significantly correlated with the prognoses of COAD, neck squamous carcinoma (HNSC), lung adenocarcinoma (LUAD) positively and stomach adenocarcinoma (STAD) negatively. This study also revealed that commonly upregulated gene set in the high GPR15 expression group (stratified via median) of COAD, HNSC, LUAD and STAD are enriched in immune systems, indicating that GPR15 might be considered as a potential target for cancer immunotherapy. Furthermore, we modelled the 3D structure of GPR15 and conducted the structure-based virtual screening. The top 8 hits compounds were screened and then subjected to molecular dynamics (MD) simulation for stability analysis. Our study provided novel insights into the role of GPR15 in a pan-cancer manner and discovered a potential hit compound for GPR15 antagonists.

This paper presents the simplified and quick way to obtain an experimental measure of the modulus of elasticity(E) of a piece of metal rod using the Smartphone microphone and through the experimental configuration in mode of unsupport beam Euler-Bernoulli(E-B). To understand it, it is required to have knowledge about flexural vibration of E-B beams and to know the analysis of the spectogram of the audio signal. The methodology consists in measuring the flexural resonance frequency through an app installed on a Smartphone and using the E formula deduced from the E-B theoretical framework. The results of the experimental measurements have a discrepancy of less than 5% with respect to the factory value, for a carbon steel rod with circular cross section using the impact excitation technique. It describes the precision and accuracy of the experimental measurement. It is useful, because it helps to classify the materials in the Faculty of Engineering and it helps to make a more efficient quality control.

A cuprous oxide (Cu₂O) thin layer served as the base for a non-enzymatic glucose sensor in an alkaline medium, 0.1 NaOH solution, with a linear range of 50-200 mg/dL using differential pulse voltammetry (DPV) measurement. An X-ray photoelectron spectroscopy (XPS) study confirmed the formation of the cuprous oxide layer on the thin gold film sensor prototype. Quantitative detection of glucose in both phosphate-buffered saline (PBS) and undiluted human serum were carried out. Neither ascorbic acid nor uric acid even at a relatively high concentration level of 100mg/dL in serum interfered with the glucose detection, demonstrating the excellent selectivity of this non-enzymatic cuprous oxide thin layer based glucose sensor. Chronoamperometry (CA) and single potential amperometric voltammetry were used to verify the measurements obtained by differential pulse voltammetry (DPV), and the positive results validated that the detection of glucose in a 0.1 M NaOH alkaline medium by DPV measurement was effective. Nickel, platinum and copper are commonly used metals for non-enzymatic glucose detection. The performance of these metal-based sensors for glucose detection using DPV were also evaluated. Cuprous oxide (Cu₂O) thin layer based sensor showed the best sensitivity for glucose detection among the sensors evaluated.

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

This article investigates hydraulic percolation in saturated porous media, focusing on containment systems using sheet pile walls and gravity concrete dams. The Laplace equation, which governs hydraulic flow in porous media, is solved using the Finite Element Method through the ANSYS software. The modeling of the porous media employs a planar quadratic element called Plane 55, originally used for thermal problems, composed of four nodes and one hydraulic degree of freedom per node. The numerical results of the water pressure acting on the hydraulic structure, flow rate, and hydraulic gradient at the outlet of the porous media are compared with results obtained in the technical-scientific literature using flow nets. Two different methodologies are used to obtain the rate of seepage: by using the average hydraulic velocity or by calculating the integral of the hydraulic gradient perpendicular to the flow area. Both methodologies are compared and validated in the numerical simulations. This work also demonstrates the importance of mesh refinement for obtaining the flow rate in the studied hydraulic systems.

ObjectivesThe present study is aimed at characterizing and identifying the important research trends of the application of structural equation modelling (SEM) in nursing research by bibliometric analysis, and further providing reference for nursing researchers to conduct SEM research.MethodsA descriptive bibliometric analysis of publications in the application of SEM in nursing research. Literatures were retrieved from the Web of Science (WoS) core collection database On April 30, 2022. CiteSpace 6.1.R1 and VOSviewer 16 software were used for visualization and bibliometric analysis.ResultsThe annual publication indicated an increasing trend in the future. The intellectual structures of the application of SEM in nursing researches included patient safety, cross-cultural comparison, compassion fatigue, benchmarking, patient discharge, China, psychometrics, and policy. The hotpots and development trends include job satisfaction, nursing home, and nursing student.ConclusionThe hotspots and development trends related to the application of SEM in nursing research mentioned in this study may be helpful for researchers to explore new directions in this field. The intellectual structures and development trends were found in the application of SEM in nursing researches in this study. The awareness of the clusters and bursts in this field can help nursing researchers avoid overlooking some important issues when conducting SEM, and provide nurse researchers with good practice guidelines for conducting SEM.

In this study, we have considered for numerical solution of a Poisson equation in a domain. we have presented a first and second order finite difference method for solving the system of the intial boundary value. We have presented the numerical solution of the Poisson equations in a two-dimensional finite region. Numerical Solution and exact solution for the presented method has been compared and the figures presented. The present error analysis tables demonstrate the efficiency of the method.

In this paper, we consider a pursuit-evasion game of inertial players, where pursuer’s control is subject to integral constraint, and evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit-evasion problems. Also, the main lemma describing the monotonicity of an attainability domain of the evader is proved and an explicit analytical formula for this domain is given. As one of the important results of our paper, the Isaacs Life-line game is solved for a special case.

The present work focuses on developing miniaturized, light weight electrochemical sensors for detection of chemical warfare agents (CWAs) like sarin and tabun simulants, i.e., diisopropyl fluorophosphate (DFP), and O,S-diethyl methyl phosphonothioate (O,S-DEMPT). Differential pulse voltammetry (DPV) was employed to examine the redox properties of capturing molecular probe CE2 with the nerve agent stimulants. Coupling of a portable potentiostat with the drone technology could allow on-situ and remote detection of analytes such CWAs to be realized, which can be crucially important to the national and global securities.