This paper attempts to clarify an long-standing issue about the number of unknowns in the Reynolds-Averaged Navier-Stokes equations (RANS). This study shows that all perspectives regarding the numbers of unknowns in the RANS stem from the misinterpretation of the Reynolds stress tensor. The current literature consider that the Reynolds stress tensor has six unknown components; however, this study shows that the Reynolds stress tensor actually has only three unknown components, namely the three components of fluctuation velocity. This understanding might shed a light to understand the well-known closure problem of turbulence.

The technique of obtaining information or data about any feature or object from afar, called in technical parlance as remote sensing, has proven extremely useful in diverse fields. In the ecological sphere, especially, remote sensing has enabled collection of data or information about large swaths of areas or landscapes. Even then, in remote sensing the task of identifying and monitoring of different water reservoirs has proved a tough one. This is mainly because getting correct appraisals about the spread and boundaries of the area under study and the contours of any water surfaces lodged therein becomes a factor of utmost importance. Identification of water reservoirs is rendered even tougher because of presence of cloud in satellite images, which becomes the largest source of error in identification of water surfaces. To overcome this glitch, the method of the shape matching approach for analysis of cloudy images in reference to cloud-free images of water surfaces with the help of vector data processing, is recommended. It includes the database of water bodies in vector format, which is a complex polygon structure. This analysis highlights three steps: First, the creation of vector database for the analysis; second, simplification of multi-scale vector polygon features; and third, the matching of reference and target water bodies database within defined distance tolerance. This feature matching approach provides matching of one to many and many to many features. It also gives the corrected images that are free of clouds.

This article describes the choice of an optimization algorithm for solving problems and the optimal design of an unmanned aerial vehicle propeller. To solve the problem using evolutionary algorithms, it was transformed into an unconstrained optimization problem using a penalty function. The airfoil contours were constructed using a Bezier curve. Design variables were divided into two types: those that describe in general terms the propeller geometry or operation, such as propeller diameter, number of blades, and rev/min; and those that vary with propeller radius, such as chord length, effective airfoil angle, and airfoil geometry. The objective function is the calculation of the propeller power required to achieve a given thrust. The differential evolution algorithm was used to solve this problem.

Perforating dermatoses are dermatologic disorders with transepidermal elimination (TE) of dermal substances. While TE is typically associated with collagen and elastin, it can also occur as a secondary event in other processes, and it is important to keep a broad differential. We present a case of perforating tophaceous gout, which underscores the need for a thoughtful approach to perforating disorders. An updated review of recent literature is also presented.

Sulfate, the main dissolved contaminant in acid mine drainage (AMD), is ubiquitous in watersheds affected by coal and metal mining operations worldwide. Engineered passive bioremediation systems (PBS) are low-cost technologies that remediate sulfate contamination by promoting (1) precipitation of sulfate-bearing compounds, such as schwertmannite and gypsum; and (2) microbially-mediated sulfate reduction (BSR) to sulfide with subsequent precipitation of sulfide minerals. In this study, chemical and sulfur isotopic data are used to infer multiple pathways for sulfate sequestration in the Tab-Simco PBS. By simultaneously monitoring sulfate concentrations and δ34SSO4 values at four sampling points across the PBS, we (1) identified that the organic layer within the bioreactor was the primary site of BSR processes contributing to sulfate sequestration; (2) observed seasonal variations of BSR processes; (3) estimated that initially the BSR processes contributed up to 30% to sulfate sequestration in the Tab-Simco bioreactor; and (4) determined that BSR contribution to sulfate sequestration continuously declined over the PBS operational lifetime. Together, our results highlight the utility of combining geochemical and microbial fingerprinting techniques to decipher complementary processes involved in sulfur cycling in a PBS as well as the value of adding the sulfur isotope approach as an essential tool to help understand, predict, prevent and mitigate sulfate contamination in AMD-impacted systems.

Solar photovoltaic (PV) generation suffers from multiple serious issues, for example shading effects directly affect the performance of installed PV arrays. By studying these issues, it can play a key role in improving the limitations and performance of PV panels. The study of PV arrays under partial shading conditions is mentioned in many papers as a part of other studies and as an independent phenomenon. Therefore, it is essential to improve these studies and update them with new research and study this problem in detail to know how to limit the effects of partial shading irradiance conditions on PV arrays performances, including economical aspects. This paper proposes to study the effects of different partial shading irradiance conditions for a PV array in various configurations. The analysis is proved in detail through the simulation of the proposed PV array in the Matlab/Simulink environment. The obtained results show the performances of interconnected PV arrays under different partial shading irradiance and temperature conditions, including the solar array I-V and P-V characteristics. In addition, different PV array configurations with and without bypass and blocking protection diodes improve and minimize the effect of partial shading conditions and avoid the reductions in output power.

The aim of this paper is to study a semi-functional partial linear regression model (SFPLR) for spatial data with responses missing at random. The estimators are constructed by the kernel method, and some asymptotic properties such as probability convergence rates of the nonparametric component and asymptotic distribution of the parametric and nonparametric components are established under certain conditions. Next, the performances and the superiority of these estimators are presented and examined using a study on simulated data and on real data by carrying out a comparison between our semi-functional partially linear model with MAR estimator (SFPLRM), the semi-functional partially linear model with the full-case estimator (SFPLRC) and the nonparametric functional model estimator with MAR (FNPM). The results show that the proposed estimators outperform existing estimators as the number of random missing data increases.

Introduction: The aim of the present systematic review was to evaluate the clinical and radiographic success of partial pulpotomies in deep caries processes or post-eruptive defects in young, vital permanent teeth. Methods: Electronic databases, PubMed, Scopus, and Embase, were searched, followed by a manual search. Randomized controlled trials evaluating partial pulpo-tomy with a follow-up period of ≥12 months were included. Meta-analyses using a random effect model were performed. Results: A total of 3.127 articles were retrieved, and after duplicate re-moval, 2.642 were screened by title and abstract; 1 additional article was found during the manual search in the reference lists, and 79 were identified. Finally, 6 papers were included in the review. Regardless of the partial pulpotomy modalities or material used, there were no signifi-cant differences between clinical and radiographic success rates (cumulative success rate 91,8%-92,3%, respectively). Five studies were included in the meta-analysis that did not indicate any statistically significant differences in success rates when Mineral Trioxide Aggregate was compared to other materials (95% CI 0,239 to 1,016 p=0.055). Conclusion: This research system-atically evaluates the evidence and summarises the available data on partial pulpotomy in young permanent teeth. Given its high clinical and radiographic success rate, partial pulpotomy should be considered when vital pulpal therapy needs to be performed in highly damaged young per-manent teeth, as this procedure provides a biological benefit and allows more invasive endodon-tic treatments to be postponed.

With the advancement of photoelectric technology and computer image processing technology, the visual measurement method based on point clouds is gradually applied to the 3D measurement of large workpieces. Point cloud registration is a key step in 3D measurement, and its registration accuracy directly affects the accuracy of 3D measurements. In this study, we designed a novel MPCR-Net for multiple partial point cloud registration networks. First, an ideal point cloud was extracted from the CAD model of the workpiece and was used as the global template. Next, a deep neural network was used to search for the corresponding point groups between each partial point cloud and the global template point cloud. Then, the rigid body transformation matrix was learned according to these correspondence point groups to realize the registration of each partial point cloud. Finally, the iterative closest point algorithm was used to optimize the registration results to obtain a final point cloud model of the workpiece. We conducted point cloud registration experiments on untrained models and actual workpieces, and by comparing them with existing point cloud registration methods, we verified that the MPCR-Net could improve the accuracy and robustness of the 3D point cloud registration.

The comparison of group means in item response models constitutes an important issue in empirical research. The present article discusses an extension of Haebara linking by proposing a flexible class of robust linking functions for comparisons of many groups. These robust linking functions are particularly suited to item response data that are generated under partial invariance. In a simulation study, it is shown that the newly proposed robust Haebara linking approach outperforms existing approaches of Haebara linking. In an empirical application using PISA data, it is illustrated that country means can be sensitive to the choice of linking functions.

With the increasing demand for precise condition monitoring and diagnosis of gas-insulated switchgears (GIS), it has become a challenge to improve the detection sensitivity of partial discharge (PD) induced in the GIS spacer. This paper deals with the elimination of the capacitive component from the phase resolved partial discharge (PRPD) signal generated in GIS spacer based on the discrete wavelet transform. Three types of typical insulation defects were simulated using PD cells. The single PD pulses were detected and were further used to determine the optimal mother wavelet. As a result, the bior6.8 was selected to decompose the PD signal into 8 levels and the signal energy at each level was calculated. The decomposed components related with capacitive disturbance were discarded whereas those associated with PD were de-noised by a threshold and a thresholding function. Finally, the PRPD signals were reconstructed using the de-noised components.

We explore the relationship between the exact renormalization group (RG) equation and quantum mechanics. The central idea is to rewrite the exact Wilsonian RG equation as a Schrödinger-type equation, opening avenues for analysis. By introducing a functional transformation, the RG equation takes on a form analogous to a quantum mechanical Schrödinger equation. The study investigates solutions to this equation and draws parallels with quantum mechanics, paving the way for understanding the infrared behavior of quantum field theories. Furthermore, we extends its insights to a one-dimensional toy model, providing illustrative examples. The discussion encompasses the implications of these findings in multiple dimensions and quantum field theory, with a brief exploration of their relevance in the context of inflationary cosmology.

The research paper provides a mathematical framework for understanding phase shift in wave phenomena, bridging theoretical foundations with real-world applications. It emphasizes the importance of phase shift in physics and engineering, particularly in fields like telecommunications and acoustics. Key equations are introduced to explain phase angle, time delay, frequency, and wavelength relationships. The study also introduces the concept of time distortion due to a 1° phase shift, crucial for precise time measurements in precision instruments. The research also addresses infinitesimal wave energy loss related to phase shift, enriching our understanding of wave behavior, and impacting scientific and engineering disciplines.

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

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

Coronavirus disease 2019 (COVID-19), the emissary behind the worst global pandemic of the 21st century, is primarily a respiratory disease-causing virus called SARS-CoV-2 which is responsible for millions of new cases (incidence) and deaths (mortalities), worldwide. Many factors have played a role in the differential morbidity and mortality experienced by nations and ethnicities against SARS-CoV-2, such as the quality of primary medical health facilities or enabling economies. Nevertheless, the most important variable, i.e., the subsequent ability of individuals to be immunologically sensitive or resistant to the infection, was not properly discussed before. Therefore, an astounding issue arose when some developed countries experienced higher morbidity and mortality, compared with their relatively underdeveloped counterparts, despite having excellent medical health facilities. Hence this investigative review attempts to analyze the issue from an angle of previously undiscussed genetic, epigenetic, and molecular immune resistance mechanisms in correlation with the pathophysiology of SARS-CoV-2 and varied ethnicity-based immunological responses against it. The biological factors discussed here include the overall landscape of human microbiota, endogenous retroviral genes spliced into the human genome, copy number variation, and how they could modulate the innate and adaptive immune systems, which put a particular ethnic genetic architecture at a higher risk of SARS-CoV-2 infection than others. Considering an array of these factors in their entirety may help explain the geographic disparity of disease incidence, severity, and subsequent mortality associated with the disease while at the same time encouraging scientists to design new experimental approaches to investigation.

Fluid flow and chemokine gradients play a large part in not only regulating homeostatic processes in the brain, but also in pathologic conditions by directing cell migration. Tumor cells in particular are superior at invading into the brain resulting in tumor recurrence. One mechanism that governs cellular invasion is autologous chemotaxis, whereby pericellular chemokine gradients form due to interstitial fluid flow (IFF) leading cells to migrate up the gradient. Glioma cells have been shown to specifically use CXCL12 to increase their invasion under heightened interstitial flow. Computational modeling of this gradient offers better insight into the extent of its development around single cells, yet very few conditions have been modelled. In this paper, a computational model is developed to investigate how a CXCL12 gradient may form around a tumor cell and what conditions are necessary to affect its formation. Through finite element analysis using COMSOL and coupled convection-diffusion/mass transport equations, we show that velocity (IFF magnitude) has the largest parametric effect on gradient formation, multidirectional fluid flow causes gradient formation in the direction of the resultant which is governed by IFF magnitude, common treatments and flow patterns have a spatiotemporal effect on pericellular gradients, exogenous background concentrations can abrogate the autologous effect depending on how close the cell is to the source, that there is a minimal distance away from the tumor border required for a single cell to establish an autologous gradient, and finally that the development of a gradient formation is highly dependent on specific cell morphology.

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

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

Estimation and planning play a vital role in the construction of an autonomous navigation framework. However, these problems are often considered separately, while planning gives robot a free-collision path towards the desired goal, estimation algorithm presents the executed trajectory in the sense that it has to be closed to the ground truth path as much as possible. Recently, a unified probabilistic framework, which supports solving these problems simultaneously, dubbed STEAP has been proposed. Nevertheless, its current version is only designated for an omni wheels robot, which allows robot to move and turn in vertical direction. Differential drive robot, on the other hand, though limited to move along only one direction, has been used in various situations due to its flexibility and lower cost in hardware designing. Thus, in this extension, our aim is to control a differential drive robot via STEAP. Moreover, in a more complicated environment such as labyrinth or maze, the original STEAP sometimes fails to find a path. Indeed, this problem is mainly caused by the poor initialization and the non-linearity in optimizer constraints. In our implementation, instead of dealing with these constraints, we employ a global planner algorithm such as Dijkstra or RRT to treat STEAP as an effective local planner module that focus on following the global path. Consequently, the experimental results show that the extended STEAP not only able to navigate a differential drive robot but also in a more complicated and unstructured environment.

We generalize the concept of a fuzzy metric by introducing its approximating counterpart in order to make it more appropriate for the study of some problems related to words combinatorics. We establish close relations between fuzzy approximating metrics in case of special $t$-norms and approximating parametrized metrics, discuss some relations between fuzzy approximating metrics and fuzzy partial metrics as well as show some possible applications of approximating parametrized metrics in the problems of words combinatorics.

Detection of partial discharge (PD) activities in high-voltage equipment can be done according to the several mechanisms of signal detection, which are electromagnetic wave signal detection, acoustic signal detection, chemical reactions, electrical signal detection, or optical emission detection. Recently, multiple methods of detection and localization of partial discharge activities occurred in power transformers and gas-insulated switchgear (GIS) have been proposed to monitor the health condition of high-voltage equipment, especially when the awareness regarding preventive maintenance has been emphasized at the industrial level and electrical providers. In aligning the needs of industrial and the improvement of PD detection methods, this manuscript focused on reviewing the current practice methods for the detection and localization of PD signals in high-voltage equipment and comparing their efficacy, in summarizing the future direction of research work-related methods of PD detection. The comparative reviews are discussed in terms of the mechanism of PD signal detection, indication parameters, calibration technique, advantages, and limitations of each method of PD measurement in detail.

Bohrnstedt’s (1969) attempt to derive a formula to compute the partial correlation coefficient and simultaneously correct for attenuation sought to simplify the process of performing each task separately. He suggested that his formula, developed from algebraic and psychometric manipulations of the partial correlation coefficient, produces a corrected partial correlation value. However, an algebraic error exists within his derivations. Consequently, the formula proposed by Bohrnstedt does not appropriately represent the value he intended it to estimate. By correcting the erroneous step and continuing the derivation based upon his proposed procedure, the steps outlined in this paper ultimately produce the formula that Bohrnstedt desired.

In order to improve the wear resistance of copper contacts in high-voltage switches and improve the abnormal discharge phenomenon caused by wear gaps, laser remelting technology was used to strengthen the surface of copper contacts. The surface morphology, microhardness, and wear resistance of the remelted samples were tested and characterized using scanning electron microscopy (SEM), microhardness tester, and friction and wear tester. The test results indicate that laser frequency, pulse width, and current parameters can directly affect the surface morphology and wear resistance of the sample, but their influencing processes vary. The laser frequency is achieved by the variation of the superposition relationship between the impact points, while the pulse width and current are achieved by the variation of the laser intensity at the impact points. When the pulse frequency is 10Hz, the pulse width is 10ms, and the current is 100A, the sample exhibits a more balanced surface morphology, microhardness, and wear resistance.

We propose a new hierarchy of the vector derivative nonlinear Schr{\"o}dinger equations and consider the simplest multiphase solutions of this hierarchy. The study of the simplest solutions of these equations led to the following results. First, the three-leaf spectral curves $\Gamma=\{(\mu,\lambda)\}$ of the simplest multiphase solutions have a quite simple symmetry. They are invariant with respect to holomorphic involution $\tau$. The type of this involution depends on the genus of the spectral curve. Or the involution has the form $\tau:(\mu,\lambda)\to(\mu,-\lambda)$, or $\tau:(\mu,\lambda)\to(-\mu,-\lambda)$. The presence of symmetry leads to the fact that the dynamics of the solution is determined not by the entire spectral curve $\Gamma$, but by its factor $\Gamma/\tau$, which has a smaller genus. Secondly, it turned out that the dynamics of the two-component vector $\bp=(p_1,p_2)^t$ is determined, first of all, by the dynamics of its length $\abs{\bp}$. Independent equations determine the dependence of the direction of the vector $\bp$ from its length. In cases where the direction of the vector $\bp$ is fixed, the corresponding spectral curve splits into separate components. In conclusion, we note that, as in the case of the Manakov system, the equation of the spectral curve is invariant with respect to the orthogonal transformation of the vector solutions. I.e., the solution can be found from the spectral curve up to the orthogonal transformation. This fact indicates that the spectral curve does not depend on the individual components of the solution, but on their symmetric functions. Thus, the spectral data of multiphase solutions have two symmetries. These symmetries make it difficult to reconstruct signals from their spectral data. The work contains examples illustrating these statements.

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.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

Shown is the derivation of Lorentz-Einstein k-factor in SRT as an amplitude-term of oscillation-differential equations of second order.This case is shown for classical Lorentz-factor as solution of an equation for undamped oscillation as well as the developed theorem as a second solution for advanced SRT of fourth order with an equation for damped oscillation-states.This advanced term allows a calculation for any velocities by real rest mass.Also accelerated coordinate -frames are discussed.

The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincare, Morse-Conley index, power geometry and other methods are employed. Proposed methodology enables justification of the theorems on existence of bifurcation points and bifurcation sets in the nonstandard models. Formulated theorems are constructive. For a certain smoothness of the nonlinear operator, the asymptotic behaviour of the solutions is analysed in the neighbourhood of the branch points and uniformly converging iterative schemes with a choice of the uniformization parameter enables the comprehensive analysis of the problems details. General theorems are illustrated on the nonlinear integral equations.

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.

The exact solutions in the wave form are derived for the time fractional KdV and the time fractional Burgers' equations in conformable fractional derivative sense. The fractional variable change using the fundamental properties of the conformable derivative reduces both equations to some nonlinear ODEs. The predicted solution is assumed to be a finite series form of a function satisfying a particular first-order ODE whose solution contains an exponential function in the denominator. The solutions are represented in the explicit forms and illustrated by some choices of the parameters for various fractional orders of the equations.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

In this work we present some driving strategies for a type of omnidirectional mobile robot, the offset-differential robot. This system presents omnidirectionality while using any type of standard wheels, allowing for applications in all terrain. The work is based on the full kinematic and dynamic analysis of the robot, including the passive elements, to explain some unexpected behaviors that appear during its motion. The stable and unstable behaviors are characterized and some driving strategies are stated in order to achieve the desired performance regarding precise positioning and speed.

Background Polycystic ovary syndrome (PCOS) is a common hormonal disorder worldwide among women of reproductive age. It is characterized by endocrine, reproductive, and metabolic abnormalities. Insulin resistance (IR) is one of its most important clinical features, associated with metabolic disorders and increased risk of type 2 diabetes (T2D). This study aimed to explore the whole blood gene expression profiling related to IR in PCOS patients compared to controls. Methods Blood RNA was extracted from 5 PCOS and 5 non-PCOS women with matched age and BMI. Homeostasis model assessment (HOMA-IR) was used to estimate the IR. The expression of IR genes was analyzed by Profiler PCR array. Results Both groups have similar levels of HOMA-IR (p>0.05). However, differential expression levels were observed between them. Fourteen genes were upregulated and 26 genes were downregulated in PCOS samples. Among the upregulated genes (>2 fold-change, p-value<0.05) are ADIPOQ, ADIPOR1, OLR, IGF-1, and APOE. Downregulated genes (>-2 fold-change, p-value<0.05) include HK-2, IRS1, and SERPINE1. These genes are involved in insulin and adipokines signaling, commonly dysregulated in T2D. They are also involved in innate immunity and inflammatory processes and are essential for lipid and carbohydrate metabolism. Conclusion Our finding suggests that despite both groups having no difference in IR level, there are differentially expressed genes involved in the IR pathway.

Physicists have employed various approaches to solve the “paradox” and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin “paradox” is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter.

Previous studies had shown that mRNA, miRNA and lncRNA were associated with cardiovascular diseases. The study was aimed to explore the differential expressions of mRNA, lncRNA and miRNA between coronary artery disease (CAD) and healthy control, and their interaction in CAD. We investigated the differential expression of ceRNA between CAD and healthy control through data collected from Gene Expression Omnibus (GEO) microarrays. Furthermore, we investigated the biological function of these differential expressions of ceRNAs by Gene Ontology (GO), Kyoto Encyclopedia of Genes and Genomes (KEGG) analyses. Protein-protein interaction (PPI) network was created to identify the hub genes. Biosystems and literature search were performed for signaling pathways and their function of the included differential expression ceRNAs. A total of 456 miRNA expression profiles, 16,325 mRNA expression profiles, and 2,869 lncRNA expression profiles were obtained. Eleven Go and KEGG pathways (count ≥9), top 15 of PPI network node connectivity rank, and top 15 of ceRNA network node degree centrality rank were achieved at the statistical significance level (P<0.05). We further identified that several differential expressions of ceRNAs and their signaling pathways were associated with CAD through biosystems and literature search. Based on eleven Go and KEGG pathways, top 15 of PPI network node connectivity rank, and top 15 of ceRNA network node degree centrality rank in CAD population, our findings would contribute to further exploration for the molecular mechanism of CAD.

An easier method for the calibration of differential drive robots is presented. Most of the calibration is done on-board and it is not necessary to expend too much time taking note of the robot's position. The calibration method does not need a big free space to perform the tests. The bigger space is just in a straight line, which is easy to find. Results with the proposed method are compared with those from UMB as a reference, and they show very little deviation while the proposed calibration is much simpler.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

In the recent years, biochar has emerged as a remarkable biosourced material for addressing global environmental, agricultural, biomedical, and energy challenges. However, the performances of biochar rest in part on finely tuning its surface chemical properties, intended to obtain specific functionalities. In this review, we tackle surface treatment of biochar with silane and other coupling agents such as diazonium salts, titatantes, ionic/non-ionic surfactants, as well as nitrogen-containing (macro)molecules. We summarize the recent progress achieved mostly in the last five years, and correlate the nature and extent of functionalization to eye catchy end applications of the surface engineered biochar.

As society becomes more reliant on Lithium-ion (Li-ion) batteries, state-of-health (SOH) estimation will need to become more accurate and reliable. Therefore, SOH modelling is in the process of shifting from using simple and continuous charge/discharge profiles, to more dynamic profiles constructed to mimic real operation, when ageing the Li-ion batteries. However, in most cases, when ageing the batteries, the same exact profile is just repeated until the battery reaches its end-of-life. Using data from batteries aged in this fashion to build a model, there is a very real possibility that the model will rely on the built-in repetitiveness of the profile. Therefore, this work will examine the dependence of the performance of a multiple linear regression on the number of charges used to train the model, and their location within the profile used to age the batteries. The investigation shows that it is possible to build models using randomly selected partial charges while still reaching errors as low as 0.5%. Furthermore, it shows that only two randomly sampled partial charges are needed to achieve errors of less than 1%. Lastly, as the number of randomly sampled partial charges used to create the model increases, then the dependence on particular partial charges tends to decrease.

The partial discharge (PD) event in high voltage insulation releases energy, exerts mechanical pressure, and generates elastic waves. Detecting and locating these PD events through short-duration acoustic pulses is well-established, particularly in gas-insulated systems and oil-insulated transformers. However, its full potential remains untapped in solid insulation systems, where the propagation capability of acoustic pulse and the acoustic reflections pose fundamental challenges to the Acoustic Emission (AE) detection technique. This study investigates the influence of reflections and multiple paths on the propagating acoustic pulse in polymeric insulating materials using a finite element method (FEM) in COMSOL. It was observed that the reflections from the boundary influence the propagating pulse's shape, peak magnitude, and arrival time. An analytical MATLAB model further quantifies the impact of multiple propagation paths on the shape, magnitude, and arrival time of the pulse travelling in a cylinder. Additionally, a Perfect Matched Layer (PML) was implemented in the COMSOL model to eliminate reflections from the boundary, and it revealed that the acoustic pulse magnitude decreases with distance following the inverse square law. In essence, the models aid in measuring how reflections contribute to the observed signals, facilitating the precise identification of the source of the PD event in the tested system.

Biodiesel is one of the most popular biofuels as it is a promising substitute of the conventional diesel fuel, but for now it cannot be used as a stand-alone fuel due to its low oxidative stability. For this reason, the last years there have been efforts for its upgrading through the partial hydrogenation of the fatty acid methyl esters (FAMEs) that biodiesel consists of. This procedure succeeds in resolving the problem of low oxidative stability, but in some cases a new problem arises as the non-selective hydrogenation is deteriorating the fuel’s cold flow properties, which are crucial for its operation without damaging the vehicle’s engine. More specifically, the problem of deteriorated cold flow properties is caused by the formation of trans-monounsaturated FAMEs and fully saturated FAMEs while the hydrogenation reaction is taking place. The hydrogenated biodiesels are preferred to contain more cis-monounsaturated FAMEs, because these are considered to have the best combination between high oxidative stability and good cold flow properties. As a result, various systems and methods have been tested in order to achieve a selective partial hydrogenation of biodiesel’s FAMEs. In this review article, the catalytic systems and methods that stood out in various researches are presented and the factors that lead to the best possible outcome are investigated and discussed.

This study aims at the sustainable valorization of eggshells (ES) from different countries of origin in cement concrete as a cement replacement for Hong Kong. For this purpose, sixteen different eggs from different regions across the world were selected from the local market. Firstly, the extent of uniformity in the weight and mineral content of sampled eggshells were assessed by a specific gravity test and thermogravimetric analysis (TGA), respectively. It was found that specific gravity varies between 2.02 and 2.39, with an average value of 2.20 ± 0.01, whereas CaCO₃ varies between 94.65% and 97.23%, with an average value of 96.33%. These values were a bit lower than those of extra-pure limestone (LS) because of the organic part and the porous structure of eggshells. Secondly, three different eggshells were selected for cement replacement in cement concrete, both in the uncalcined and calcined states, based on having the highest, medium, and lowest CaCO₃ content, respectively. To get the calcined eggshells, the eggshells were calcined at 800^oC for three hours. It was found that the strength of eggshells varies with CaCO₃, but the variation was acceptable. The calcined eggshells showed comparatively more compressive strength and were close to the LS because of the free CaO and the absence of an organic part. In general, the variation in the basic properties of eggshells from different regions across the world is negligible and suitable to use as a cement replacement with acceptable variation in strength in Hong Kong.

We report on the use of quartz-enhanced photoacoustic spectroscopy (QEPAS) for multi-gas detection. Photo-acoustic (PA) spectra of mixtures of water (H2O), ammonia (NH3) and methane (CH4) were measured in the mid-infrared (MIR) wavelength range using a MIR (mid-infrared) optical parametric oscillator (OPO) light source. Highly overlapping absorption spectra is a common challenge for gas spectroscopy. To mitigate this, we use a partial least-squares regression (PLS) method to estimate the mixing ratio and concentrations of the individual gasses. The concentration range explored in the analysis varies from a few parts-per-million (ppm) to thousands of ppm. Spectra obtained from HITRAN and experimental single-molecule reference spectra of each of the molecular species were acquired and used as training data sets. These spectra were used to generate simulated spectra of the gas mixtures (linear combinations of the reference spectra). Here in this proof-of-concept experiment we demonstrate that after an absolute calibration of the QEPAS cell, the PLS analyses could be used to determine concentrations of single molecular species with a relative accuracy within a few % for mixtures of H2O, NH3 and CH4 and with an absolute sensitivity of approximately 300(±50) ppm/V, 50(±5) ppm/V and 5(±2) ppm/V for water, ammonia and methane, respectively. Thus, demonstrating that QEPAS assisted by PLS is a powerful approach to estimate concentrations of individual gas components with considerable spectral overlap, which is a typical scenario for real-life adoptions and applications.

The use of artificial intelligence in natural language processing (NLP) has significantly contributed to the advancement of natural language applications such as sentimental analysis, topic modeling, text classification, chatbots, and spam filtering. With a large amount of text generated each day from different sources such as webpages, blogs, emails, social media, and articles, one of the most common tasks in natural language processing is the classification of a text corpus. This is important in many institutions for planning, decision-making, and archives of their projects. Many algorithms exist to automate text classification operations but the most intriguing of them is that which also learns these operations automatically. In this study, we present a new model to infer and learn from data using probabilistic logic and apply it to text classification. This model, called GenCo, is a multi-input single-output (MISO) learning model that uses a collaboration of partial classifications to generate the desired output. It provides a heterogeneity measure to explain its classification results and enables the reduction of the curse of dimensionality in text classification. The classification results are compared with those of conventional text classification models, and it shows that our proposed model has a higher classification performance than conventional models.

A common challenge in real-world classification scenarios with sequentially appending target domain data is insufficient training datasets during the training phase. Therefore, conventional deep learning and transfer learning classifiers are not applicable especially when individual classes are not represented or are severely underrepresented at the outset. Domain Generalization approaches reach their limits when domain shifts become too large, making them occasionally unsuitable as well. In many (technical) domains, however, it is only the defect/ worn/ reject classes that are insufficiently represented, while the non-defect class is often available from the beginning. The proposed classification approach addresses such conditions and is based on a CNN encoder. Following a contrastive learning approach, it is trained with a modified triplet loss function using two datasets: Besides the non-defective target domain class (= 1st dataset), a state-of-the-art labeled source domain dataset that contains highly related classes (e.g., a related manufacturing error or wear defect) but originates from a (highly) different domain (e.g., different product, material, or appearance) (= 2nd dataset) is utilized. The approach learns the classification features from the source domain dataset while at the same time learning the differences between the source and the target domain in a single training step, aiming to transfer the relevant features to the target domain. The classifier becomes sensitive to the classification features and – by architecture – robust against the highly domain-specific context. The approach is benchmarked in a technical and a non-technical domain and shows convincing classification results. In particular, it is shown that the domain generalization capabilities and classification results are improved by the proposed architecture, allowing for larger domain shifts between source and target domains.

A partial aperture onboard calibration method can solve the onboard calibration problems of some large aperture remote sensors, which is of great significance for the development trend of increasingly large apertures in optical remote sensors. In this paper, the solar diffuser reflectance degradation monitor (SDRDM) in the onboard calibration assembly (CA) of the FengYun-4 (FY-4) advanced geostationary radiance imager (AGRI) is used as the reference radiometer for measuring the partial aperture factor (PAF) for the AGRI onboard calibration. First, the linear response count variation relationship between the two is established under the same radiance source input. Then, according to the known bidirectional reflection distribution function (BRDF) of the solar diffuser (SD) in the CA, the relative reflectance ratio coefficient between the AGRI observation direction and the SDRDM observation direction is calculated. On this basis, the response count value of the AGRI and the SDRDM is used to realize the high-precision measurement of the PAF of the AGRI B1 ~ B3 bands by simulating the AGRI onboard calibration measurement under the illumination of a solar simulator in the laboratory. According to the determination process of the relevant parameters of the PAF, the measurement uncertainty of the PAF is analyzed; this uncertainty is better than 2.04% and provides an important reference for the evaluation of the onboard absolute radiometric calibration uncertainty after launch.

This paper proposes a solution for the development of microclimate monitoring for Low Voltage / High Voltage switchgear using the PRTG Internet of Things (IoT) platform. This IoT-based real time monitoring system can enable predictive maintenance to reduce the risk of electrical station malfunctions due to unfavorable environmental conditions. The combination of humidity and dust can lead to unplanned electrical discharges along the isolators inside a low or medium voltage electric table. If no predictive measures are taken, the situation may deteriorate and lead to significant damage inside and outside the switchgear cell. Thus, the mentioned situation can lead to unprogrammed maintenance interventions that can conduct to the change of the entire affected switchgear cell. Using a low-cost and efficient system, the climate conditions inside and outside the switchgear is monitored and transmitted remotely to a monitoring center. From the results obtained using a 365-day time interval, we can conclude that the proposed system is integrated successfully in the switchgear maintaining process, having as result the reducing of maintenance costs.

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

Information theory provides robust measures of multivariable interdependence, but classically does little to characterize the multivariable relationships it detects. The Partial Information Decomposition (PID) characterizes the mutual information between variables by decomposing it into unique, redundant, and synergistic components. This has been usefully applied, particularly in neuroscience, but there is currently no generally accepted method for its computation. Independently, the Information Delta framework characterizes non-pairwise dependencies in genetic datasets. This framework has developed an intuitive geometric interpretation for how discrete functions encode information, but lacks some important generalizations. This paper shows that the PID and Delta frameworks are largely equivalent. We equate their key expressions, allowing for results in one framework to apply towards open questions in the other. For example, we find that the approach of Bertschinger et al. is useful for the open Information Delta question of how to deal with linkage disequilibrium. We also show how PID solutions can be mapped onto the space of delta measures. Using Bertschinger et al. as an example solution, we identify a specific plane in delta-space on which this approach’s optimization is constrained, and compute it for all possible three-variable discrete functions of a three-letter alphabet. This yields a clear geometric picture of how a given solution decomposes information

Background: A large percentage of deaths in an epidemic or pandemic can be due to overshoot of population (herd) immunity, either from the initial peak or from planned or unplanned exit from lockdown or social distancing conditions. Objectives: We study partial unlock or reopening interaction with seasonal effects in a managed epidemic to quantify overshoot effects on small and large unlock steps and discover robust strategies for reducing overshoot. Methods: We simulate partial unlock of social distancing for epidemics over a range of replication factor, immunity duration and seasonality factor for strategies targeting immunity thresholds using overshoot optimization. Results: Seasonality change must be taken into account as one of the steps in an easing sequence, and a two step unlock, including seasonal effects, minimizes overshoot and deaths. It may cause undershoot, which causes rebounds and assists survival of the pathogen. Conclusions: Partial easing levels, even low levels for economic relief while waiting on a vaccine, have population immunity thresholds based on the reduced replication rates and may experience overshoot as well. We further find a two step strategy remains highly sensitive to variations in case ratio, replication factor, seasonality and timing. We demonstrate a three or more step strategy is more robust, and conclude that the best possible approach minimizes deaths under a range of likely actual conditions which include public response.

In this paper, we proposed a novel saddle type FinFET (S-FinFET) to effectively solve problems occurring under the capacitor node of dynamic random-access memory (DRAM) cell and showed how its structure was superior to conventional S-FinFETs in terms of short channel effect (SCE), subthreshold slope (SS), and gate-induced drain leakage (GIDL). The proposed FinFET exhibited 4 times lower Ioff than modified S-FinFET called RFinFET with more improved DIBL characteristics while minimizing Ion reduction compared to RFinFET. Our results also confirmed that the proposed device showed improved DIBL and Ioff characteristics as gate channel length decreased.

Maxwell equations governing electromagnetic effects are being shown to be equivalent to the compressible inviscid Navier-Stokes equations applicable in fluid dynamics and representing conservation of mass and linear momentum. The latter applies subject to a generalized Beltrami condition to be satisfied by the magnetic field. This equivalence indicates that the compressible inviscid Navier-Stokes equations are Lorentz invariant as they derive directly from the Lorentz invariant Maxwell equations subject to the same Beltrami condition. In addition, the derivation results provide support for the claim that electromagnetic potentials have physical significance as demonstrated by Aharonov-Bohm effect, and are not only a convenient mathematical formulation.

We present three reduced integrable hierarchies of nonlocal integrable NLS type equations from a vector integrable hierarchy associated with a matrix Lie algebra, not being A type. Three similarity transformations are taken to keep the invariance of the transformed zero curvature equations. The key step is to formulate a solution to a reduced stationary zero curvature equation so that the zero curvature formulation works for a reduced case.

In this paper, we consider the fourth-order parabolic equations with integer and fractional order time derivatives with Neumann boundary conditions. The integer order time derivatives are approximated by backward Euler difference quotients, and the fractional order time derivatives are approximated by L1 interpolation. We propose the block-centered finite difference scheme for fourth-order parabolic equations of integer and fractional order time derivatives. We prove the stability of the block-centered finite difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are given to verify the effectiveness of the block-centered finite difference scheme.

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

The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system with an electromagnetic field, leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress-energy tensor expresses relativistic Cauchy's momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.

We point out that field equations of general relativity are implied by a maximal force given by c⁴/4G, analogous to the way that special relativity is implied by a maximal speed given by c. We present some of the arguments for this equivalence. The maxi-mal force naturally plays the role of an elastic constant for space-time. Implications of the maximal force for gravitational wave measurements, cosmology and black holes are highlighted. Quantum aspects of the maximal force are discussed.

Up to now, Schrödinger equation, Klein-Gordon equation (KGE) and Dirac equation are believed the fundamental equations of quantum mechanics. Schrödinger equation has a defect that there is no NKE solutions. Dirac equation has positive kinetic energy (PKE) and negative kinetic energy (NKE) branches. Both branches should have low momentum, or nonrelativistic, approximations: one is Schrödinger equation and the other is NKE Schrödinger equation. KGE has two problems: it is an equation of second time derivative, and calculated density is not definitely positive. To overcome the problems, it should be revised as PKE and NKE decoupled KGEs. The fundamental equations of quantum mechanics after the modification have at least two merits. They are of unitary in that everyone contains the first time derivative and are symmetric with respect to PKE and NKE. This reflects the symmetry of the PKE and NKE matters, as well as matter and dark matter, of our universe. The problems of one-dimensional step potentials are resolved by means of the modified fundamental equations for a nonrelativistic particle.

The current health crisis derived from COVID 19 has become a serious threat to humanity. The collateral effects related to economic aspects are affecting companies, workers and, of course, families in general. The problems of financial insolvency are frequently present in debtors who have contracted a debt with their creditor. Therefore, the objective of the study is focused on modeling a debt restructuring proposal, through three hypothetical scenarios in which the debt is reconvened when some documents have expired and others are yet to expire. In each of the scenarios, the mathematical model is designed and subsequently corroborated in an Excel spreadsheet. The predominant variables in the restructuring are the adjustment rates used to update the past due promissory notes and the discount rates of those promissory notes that have not yet expired, capitalizations, transaction costs and, if applicable, whether the debt is in foreign currency. In this case, it is converted to the local currency, then the spot exchange rate is used.

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

In this paper, we investigate the equilibrium points, stability of two equilibrium points, convergences of negative equilibrium point, periodic solutions, and existence of bounded or unbounded solutions of a system of nonlinear difference equations x_n+1 =x_n-1y_n - 1, y_n+1 = y_n-1x_n - 1 n = 0,1,..., where the initial values are real numbers. Additionally we present some numerical examples to verify our theoretical results.

In this paper, we investigate the equilibrium points of following a system of difference equations x_n+1 = x_n 2y_n−1, y _n+1 = y_n 2x_n−1. We also study the asymptotic stability of related system of difference equations. Further we examine the periodic solutions of related system with period two. Additionally, we find out the invariant interval and periodic cycles of related system of difference equations.

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

We have shown that the use of evolutionary gravitational constants G, the speed of light c, and cosmological constant Λ in the Einstein’s field equations leads to a very simple model that fits the supernovae Ia data with a single parameter as well as the standard ΛCDM model with two parameters, and has the predictive capability superior to the latter. We have shown that at the current time G and c both increase as dG/dt = 5.4GH₀ and dc/dt = 1.8cH₀ with H₀ as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH₀. Negative finding on the variation of G with time derived from the analysis of lunar laser ranging data in several studies has been attributed to the fact that these studies did not consider the variation of c simultaneously with G.

Different bacterial species have dramatically different generation times, from 20-30 minutes in Escherichia coli to about two weeks in Mycobacterium leprae. The translation machinery in a cell needs to synthesize all proteins for a new cell in each generation. The three subprocesses of translation, i.e., initiation, elongation, and termination, are expected to be under stronger selection pressure to optimize in short-generation bacteria (SGB) such as Vibrio natriegens than in the long-generation Mycobacterium leprae. The initiation efficiency depends on the start codon decoded by the initiation tRNA, the optimal Shine-Dalgarno (SD) decoded by the anti-SD (aSD) sequence on small subunit rRNA, and the secondary structure that may embed the initiation signals and prevent them from being decoded. The elongation efficiency depends on the tRNA pool and codon usage. The termination efficiency in bacteria depends mainly on the nature of the stop codon and the nucleotide immediately downstream of the stop codon. By contrasting SGB with long-generation bacteria (LGB), we predict that 1) SGB to have more ribosome RNA operons to produce ribosomes, and more tRNA genes for carrying amino acid to ribosomes, 2) SGB to have a higher percentage of genes using AUG as start codon and UAA as stop codon than LGB, 3) SGB to exhibit better codon and anticodon adaptation than LGB, and 4) SGB to have weaker secondary structure near translation initiation signals than LGB. These differences between SGB and LGB should be more pronounced in highly expressed genes than lowly expressed genes. We present empirical evidence in support of these predictions.

The Standard Model is not a complete description of reality; it omits the existence of dark matter, dark energy, and an explanation as to why no CP violation has been observed. However, some of these phenomena could be explained through a new force mediated by a new boson. If such a boson were massless it would result in a power law potential and if massive the interaction would be Yukawa-like. A previous experiment employing a micro-mechanical oscillator and a spherical test mass interactions was successful in placing the best limits on a mass-mass Yukawa-like interaction, but the data was never analyzed in the context of a power law. Here that data is analyzed considering a power law for powers n = 1-5 where n is the number of boson exchanges. The results show that the limits obtained through power law analysis of this data are not better than the currently accepted limits. A discussion of an experiment design capable of producing better limits on power law extensions to the Standard Model is presented, and suggests micro mechanical oscillators based experiment remains capable of improving the limits by at least one order of magnitude.

Using the World Bank Global Findex Database for 91 countries in 2014, 2017, and 2021, we examine whether fintech levels influence bank performance and whether fintech’s interaction with GDP per capita causes differential effects on bank performance globally. Since fintech levels were already very high for rich countries when the World Bank started providing fintech development statistics in 2014, we estimate AbFintech by regressing fintech levels on GDP per capita by year. AbFintech is the difference between the fintech level and its fitted values. Then, using multiple regression analyses, we investigate the impact of AbFintech on bank performance worldwide, focusing on the differential effects of AbFintech and GDP levels on bank performance. We find AbFintech significantly increases bank performance, primarily in less developed countries. Specifically, AbFintech increases banks’ ROA in the least developed countries and net interest margin in the 75th percentile countries. Also, AbFintech decreases the cost-to-income ratio in the 75th percentile countries, while it increases the ratio in the most developed countries. AbFintech does not affect the ratio of noninterest income to total income, regardless of the level of economic development.

The triple-negative breast cancer (TNBC) subtype is one of the most aggressive forms of breast cancer that has poor clinical outcome and still remains as an unmet clinical challenge. Accumulating evidence suggests that intratumoral heterogeneity or the presence of phenotypically heterogeneous cell populations within a tumor plays a crucial role in chemoresistance, tumor progression and metastasis. Increased understanding of the molecular regulators of intratumoral heterogeneity will enable the development of effective therapeutic strategies in TNBC. We have identified a molecular mediator involved in intratumoral heterogeneity in breast cancer using an unbiased approach. We isolated two heterogeneous tumor cell populations from the 4T1 TNBC tumor model and phenotypic characterization revealed that the cells are distinct in terms of their morphology, proliferation and self-renewal ability in vitro; as well as primary tumor formation and metastatic potential in vivo. Further, RNA sequencing on both cell populations was performed to identify the molecular mediators underlying this heterogeneity. Bioinformatic analysis performed on the differentially expressed genes along with the Kaplan-Meier survival analysis in TNBC patients identified Metastasis associated colon cancer 1 (Macc1) as the top candidate gene mediating the aggressive phenotype. The role of Macc1 in regulating the proliferative phenotype was validated using siRNA mediated gene knockdown. The role of Macc1 in the aggressive cancer cell phenotypes and disease progression is being studied further using a small molecule transcriptional inhibitor of Macc1 in cell line and animal models, thus increasing our understanding of the molecular underpinnings of intratumoral heterogeneity in breast cancer that is critical to the improvement in the treatment of women currently living with the highly aggressive TNBC subtype.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

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

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 study, we investigated the effects of three surface treatment techniques on 316L stainless steel, low-temperature immersion corrosion, shot peening followed by immersion corrosion, and electrochemical corrosion. Surface alterations were analyzed using scanning electron microscopy, Raman spectroscopy, and α-step thin-film thickness profiling. Human osteoblast adhesion was evaluated using Liu’s stain and metallographic optical microscopy. The results revealed weak cell adhesion after low-temperature immersion and shot peening followed by immersion corrosion. By contrast, electrochemical corrosion, particularly with a high current density and low corrosive solution concentration, resulted in a uniformly corroded surface, thus promoting dense cell adhesion. All three techniques resulted in porous oxide layers. Overall, our experimental findings highlighted shot peening (1 kg/cm2 for 20 s) and electrochemical corrosion (0.5 M HCl) as effective processes. Electrochemical corrosion produced uniformly dense corrosion pits, whereas shot peening produced semicircular grooves with small corrosion pits, both favorable for cell adhesion. Electrochemical corrosion also yielded excellent cell adhesion, emphasizing its suitability for biomedical activity. We developed a process for creating a porous surface layer and thereby enhancing the cell adhesion to 316L stainless steel for potential biomedical implant applications.

Surfaces of additively manufactured metal parts from powder-based processes typically show powder particle agglomerations and other features, resulting in high surface roughness. Proper characterization of those surfaces is necessary in order to assess part quality with respect to coatability, mechanical performance or corrosion resistance for use in aerospace, automotive, medical and more industrial applications. Optical surface texture measurement allows for collection of areal surface data, while the established contact stylus method only captures line profile data. When applying optical methods for surface topography measurements, proper data acquisition and post-processing in order to assess surface texture may be complex. A number of variables can be adjusted, such as different measurement settings, approaches to outlier removal, evaluated area size or form removal. This work shows the influence of selected z-range prior to measurement and the influence of choosing pre-defined outlier removal settings in MountainsMap 9.2 on selected ISO 25178-2:2022 parameters calculated from data obtained from confocal microscopy for as-built Ti6Al4V from laser powder bed fusion. The aim is to show the influence of variation in measurement and post-processing on calculated surface texture parameters and stress the importance of proper documentation in order to achieve reproducibility of data for quality management.

Background. Gene rearrangements affecting KMT2A are frequent in acute myeloid leukemia (AML) and are often associated with a poor prognosis. KMT2A gene fusions are often detected by chromosome banding analysis and confirmed by fluorescence in-situ hybridization. However, small intragenic insertions, termed KMT2A partial tandem duplication (PTD), are particularly challenging to detect using standard molecular and cytogenetic approaches. Methods. We have validated the use of a custom hybrid capture based next-generation sequencing (NGS) panel for comprehensive profiling of AML patients seen at our institution. This NGS panel targets the entire consensus coding DNA sequence of KMT2A; to deduce the presence of a PTD we used the relative ratio of KMT2A exons coverage. We sought to corroborate the KMT2A-PTD NGS results using (1) multiplex-ligation probe amplification (MLPA) and (2) optical genome mapping (OGM). Results. We analyzed 932 AML cases and identified 41 individuals harboring a KMT2A-PTD. MLPA, NGS and OGM confirmed the presence of a KMT2A-PTD in 22 of the cases analyzed where orthogonal testing was possible. Two false positive PTD calls by NGS could be explained by the presence of cryptic structural variants impacting KMT2A and interfering with PTD analysis. OGM revealed the nature of these previously undetected gene rearrangements in KMT2A, while MLPA yielded in-conclusive results. MLPA analysis for KMT2A-PTD is limited to exon 4, whereas NGS and OGM resolved KMT2A-PTD sizes and copy number levels. Conclusion. KMT2A-PTDs are complex gene rearrangements that cannot be fully ascertained using a single genomic platform. MLPA, NGS panels and OGM are complementary technologies applied in standard of care testing for AML patients. MLPA and NGS panels are designed for targeted copy number analysis; however, our results show that integration of concurrent genomic alterations is needed for accurate KMT2A-PTD identification. Unbalanced chromosomal rearrangements overlapping with KMT2A can interfere with the diagnostic sensitivity and specificity of copy number based KMT2A-PTD detection methodologies.

This paper aims to propose improvements for plastic waste management in Salvador – the Brazilian third most populated metropolis – via Partial Least Squares Structural Equation Modeling (PLS-SEM). All indicators, constructs, and hypotheses regarding collection, sorting, recycling, and disposal in the proposed PLS model were derived from the literature review, and the dependence of the performance construct on efficiency, effectiveness, municipality's socioeconomic aspects and municipality infrastructure is evaluated. Academic and practitioner publics were surveyed, and after analysis in both SmartPLS and RStudio software, suggestions for improvement regarding plastics recycling rate, market maturity, and infrastructural aspects for optimized reverse logistics were made. Since almost double the minimum number of respondents answered the survey questionnaire and the PLS-SEM statistics showed that the modeling presents consistency, the discussion is relevant. The model can and will evolve, but examples of suggested improvement are the installation of Deposit-Return Systems (DRS) in parks, streets, and avenues for increasing selective collection and the direct purchasing of waste from residents by municipal administration, compensating them with vouchers for food. The model can be a basis for other cities worldwide sharing analogous characteristics. By considering it, organizations can contribute to both reduced Greenhouse Gas (GHG) emissions and reduced terrestrial pollution.

Coral reefs are one of the most productive yet vulnerable ecosystems on Earth. An important step in understanding the functioning of coral communities is studying the environmental impact on the state of reefs. The present study aimed to assess the impacts of the water temperature, precipitation, wave action and population density on the seasonal bleaching, partial and complete mortality of shallow-water branching corals of Pocillopora verrucosa species complex. The present study was conducted at the Dam Bay research station (Nha Trang Bay) from 26 April 2020 to 2 April 2021. Throughout the study the percentage of bleached coral colonies varied from 1 to 41.5% with two peaks, in autumn (October) and spring (April). Rates of the development of partial mortality varied from 0 to 10%, with a pronounced peak in December. At the end of the experiment, the percentage of coral colonies suffering from partial mortality reached 47%. Only 4,5% of experimental colonies died by the end of the study. Analysis revealed that water temperature and partial mortality are the drivers of bleaching, while wave action, temperature and bleaching are the factors with a significant impact on partial mortality. In the present study, the main cause of coral death was the development of algal fouling at the sites of colony lesions, which gradually spread over the entire surface of the colony. We showed also that the impact of individual stress on mortality prevailed over the impact of seasonal bleaching and partial mortality events.

Partial least square (PLS) regression is a well-known chemometric method used for predictive modelling, especially in the presence of many variables. Although PLS was not initially developed as a technique for classification tasks, scientists have reportedly used this approach successfully for discrimination purposes. Whereas some non-supervised learning approaches including but not limited to PCA, and k-means clustering do well in identifying/understanding grouping and clustering patterns in multidimensional data, they are limited when the end target is discrimination, making PLS a preferable alternative. A total of fertilized 672 chicken egg hyperspectral imaging data, consisting of 336 white eggs and 336 brown eggs were used in this study. Hyperspectral images in the NIR region of 900-1700 nm wavelength range were captured prior to incubation on day 0 and on days 1-4 after incubation. Eggs were candled on incubation day 5 and broken out on day 10 to confirm fertility. While a total number of 312 and 314 eggs were found to be fertile in the brown and white egg batches respectively, total numbers of non-fertile eggs in the same set of batches were 23 and 21 respectively. Spectral information was extracted from a segmented region of interest (ROI) of each hyperspectral image and spectral transmission characteristics were obtained by averaging the spectral information. A moving-thresholding technique was implemented for discrimination based on PLS regression results on the calibration set. With true positive rates (TPR) of up to 100% obtained at selected threshold values of between 0.50-0.85 and on different days of incubation, the results indicated that the proposed PLS technique can accurately discriminate between fertile and non-fertile eggs. The adaptive PLS approach was thereby presented as suitable for handling hyperspectral imaging-based chicken egg fertility data

Objective: One of the major causes of cerebral ventricular shunt failure is proximal catheter occlusion. We describe a novel ventricular cerebrospinal fluid (CSF) flow replicating system that assesses pressure and flow responses to varied degrees of catheter occlusion. Methods: Ventricular catheter performance was assessed during conditions of partial and complete occlusion. The catheters were placed into a three-dimensionally printed phantom ventricular replicating system. Artificial CSF was pumped through the ventricular system at a constant rate of 1 ml/min to mimic CSF flow, with the proximal end of the catheter in the phantom ventricle. Pressure transducer and flow rate sensors were used to measure intra-phantom pressure, outflow pressure and CSF flow rates. The catheters were also inserted into silicone tubing and pressure was measured in the same manner for comparison with the phantom. Results: Pressure measured in the phantom ventricle did not change when the outflow of the ventricular catheter was partially occluded. However, the intraventricular phantom pressure significantly increased when the outflow catheter was 100% occluded. Flow through the catheter showed no significant difference in rate with any degree of partial occlusion of the catheter. At the distal end of the partially occluded catheters, there was less pressure compared with the nonoccluded catheters. This difference in pressure in partially occluded catheters correlated with the percentage of catheter hole occlusion. Conclusions: Our model mimics physiological dynamics of the CSF flow in partially and completely obstructed ventricular catheters. We found that partial occlusion of the catheter had no effect on CSF flow rate, but did reduce outflow pressure of the catheter.

The conversion of methane into chemicals is of interest to achieve a decarbonized future. Fuel cells are electrochemical devices commonly used to obtain electrical energy, but can be utilized either for chemicals production or both energy and chemicals cogeneration. In this work, the partial oxidation of methane in fuel cells for electricity generation and valuable chemicals production at the same time is reviewed. For this purpose, different types of methane-fed fuel cells, both low temperature fuel cells, such as PEMFCs and AAEMFCs, and high temperature fuel cells, such as SOFCs, have been used. Also if few works have been devoted to this topic, the promising results drive the development of fuel cells using methane as the source for the cogeneration of power and valuable chemicals.

Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of the solution, without calculating the full inversion operator and the complete solution. It is a well-known fact about partial differential equations that the solution at each discretisation point depends on the solutions at all other discretisation points. Therefore, it is impossible to compute the solution only at one point, without calculating the solution at all other points. The standard numerical methods like a conjugate gradient or Gauss elimination compute the whole solution and/or the complete inverse operator. We suggest a method which can compute the solution of the given partial differential equation 1) at a point; 2) at few points; 3) on an interface; or a functional of the solution, without computing the solution at all points. The required storage cost and computational resources will be lower as in the standard approach. With this new method, we can speed up, for instance, computation of the innovation in filtering or the likelihood distribution, which measures the data misfit (mismatch). Further, we can speed up the solution of the regression, Bayesian inversion, data assimilation, and Kalman filter update problems. Applying additionally the hierarchical matrix approximation, we reduce the cubic computational cost to almost linear $\mathcal{O}(k^2n \log^2 n)$, where $k\ll n$ and $n$ is the number of degrees of freedom. Up to the hierarchical matrix approximation error, the computed solution is exact. One of the disadvantages of this method is the need to modify the existing deterministic solver.

Researchers in different disciplines studied liver’s genetic expression of organogenesis in embryogenesis; however, organogenesis has not been studied as an independent and a complementary process during adult liver regeneration. This paper reviewed studies and extracted information related to organogenesis in adult liver regeneration because of organogenesis’ important role in cancer and tissue regeneration.

The purpose of the review is to provide new insight into the potential of surface modification of carbon fibers for enhancing the application of the carbon fibers many a fold. To this end a total of 429 papers on the subject of surface modication of carbon fibers by a variety of chemical and electrochemical methods published during the period from 2010-2022 have been reviewed. Astounding results of surface funcationalization of carbon fibers by a variety of state of the art methods resulting in the unconventional applications of the resulting modified carbon fibers are summarized in a nut-shell in schemes from 1-6 towards the end of the review. Surface modifica-tion induces functionality to carbon fibers (CFs). The vitality of CF surface modification reac-tions could only be compared to the life process of respiration that sustains the multi functional-ity of living cells. Applicability of CFs can be drastically enhanced in incomprehensible ways by surface modification. Upon surface modification, inert and non-reactive CF surface becomes chemically active and functional with utility in diverse fields, namely, health, energy, environ-ment, defense, catalysis, smart materials and many others. Surface modification methods can be broadly classified into chemical, electrochemical and physical methods. By these surface modi-fication methods, the inert FC surface becomes polar. Surface properties like roughness, wetta-bility and energy are enhanced. Modification processes like sizing, oxidation, amination, si-lanization, polymerization, nanoarchitecture induces multifunctionality on CF surface. Modi-fied CFs when used as reinforcing material in carbon fiber reinforced plastics (CFRPs), im-proved bonding at the interface with resin matrices is observed with enhanced and outstanding mechanical properties (flexural strength, flexural modulus, IFSS, ILSS, hardness, elastic modulus, bending strength and compression strength).

For distances less 10 nm, a total energy transfer occurs from a quantum emitter to a nearby metallic surface, producing evanescent surface waves that are plasmonic in nature. When investigating a metallic nanohole supported on an optically dense substrate (such as diamond with NV-), the scattering occurred preferentially from the diamond substrate towards the air for dipole distances less 10 nm from the aperture. In addition, an enhancement to the dipole's radiative decay rate was observed when resonance of the aperture matched the emitters wavelength. The relationship between an emitter and a nearby resonant aperture is shown to be that of the resonance energy transfer where the emitter acts as a donor and the hole as an acceptor. In conjunction with the preferential scattering behavior, this has led to the proposed device that operates in transmission mode, eliminating the need for epi-illumination techniques and optically denser than air superstrates in the collection cycle, hence making the design simpler and more suitable for miniaturization. A design criterion for the surface grating is also proposed to improve the performance, where the period of the grating differs significantly from the wavelength of the surface plasmon polaritons. Response of the proposed device is further studied with respect to changes in NV's position and its dipolar orientation to identify the crystallographic planes of diamond over which the performance of the device is maximized.

Axial resolution is one of the most important characteristics of a microscope. In all microscopes, a high axial resolution is desired in order to discriminate information efficiently along the longitudinal direction. However, when studying thick samples that do not contain laterally overlapping information, a low axial resolution is desirable as information from multiple planes can be recorded simultaneously from a single camera shot instead of plane-by-plane mechanical refocusing. In this study, we increased the focal depth of an infrared microscope non-invasively by introducing a binary axicon fabricated on barium fluoride substrate close to the sample. Preliminary results of imaging thick and sparse silk fibers showed an improved focal depth with a slight decrease in lateral resolution and increase in background noise.

When discussing the Diophantine quintic equation $p(a^5 + b^5) = q(c^5 + d^5)$ where p is a prime and q is an integer, there is a clear gap between the mathematical literature and online forums. Because of the intrinsic complexity of parameterizing fifth-degree equations, this equation re- mains largely unexplored. In this work, we approach this quintic problem through algebraic methods with the goal of providing numerical solutions that illuminate its properties and behaviors.Our research uncovers in- triguing patterns and connections that shed light on the enigmatic nature of Diophantine quintic equations in this particular form.

Studies involving vortex in hybrid superconducting devices and their interaction with different components inside the sample are an important issue to reach higher values of their critical parameters in superconducting materials. The vortex distribution on each side of sample with different fundamental parameters, such as temperature T, penetration depth λ, coherence length ξ, electron mass m and the order parameter Ψ, may help to improve the superconducting properties. Thus, in this work, we used the modified Ginzburg-Landau theory to investigate hybrid superconductor (HS), but also to provide a highly tunable and adjustable theoretical tool to theoretically explain the experimental results involving HS, in order to study the vortex behaviour in superconductors of mesoscopic dimensions with extremely differences among their fundamentals parameters. Therefore, we evaluated the influence of HS on vortex configuration and their effects in the field-dependent magnetization. The results show that the during the increment of applied magnetic field H the diamagnetic response of HS, Meissner effect, include additional jumps of magnetization while diamagnetism continues its increase in the sample. In addition, the differences among parameters, create an interface between both components, two different magnitudes of supercurrent and vortex sizes producing a lower degradation of local superconductivity, which increase the upper critical field. On the other hand, this type HS with differences of parameters on both sides can be used to control the vortex movement in the selected superconducting region sample with more accuracy.

Recently, Li et al [1] investigated the nonlinear Langevin equations existence including two fractional orders with infinite-point boundary conditions. It has shown that the outcomes given it does count on the solution form for which it has boundary values. It means that their solution needs more to be in the final step. In current work, we will have discussion about the existence and uniqueness for the same boundary conditions by investigating the closely explicit solution form that has no boundary values. Numerical example is supported to have more vision to compare the between new and previous results. It turns out that our results are superior.

This study delves into the intricate dynamics of sustainable fisheries through the lens of mathematical modeling, specifically employing the Lotka-Volterra equations. The Lotka-Volterra equations, originally conceived to understand predator-prey interactions, offer a potent framework to model and predict fish population dynamics within aquatic ecosystems. The aim of this research is to demonstrate the applicability and efficacy of the Lotka-Volterra equations in understanding the delicate balance of fish populations and aiding sustainable fisheries management. Through this mathematical approach, we seek to provide a structured methodology and present results that showcase the potential of this model in predicting and managing fish populations. In our analysis, we adjust the parameters of the Lotka-Volterra equations to simulate various scenarios, enabling a comprehensive understanding of sustainable fishing practices. Our findings underscore the significance of mathematical models, particularly the Lotka-Volterra equations, in informing strategies to maintain fish populations in a sustainable and ecologically balanced manner, thereby ensuring the longevity of marine ecosystems and the fisheries thatrely upon them.

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

The nonlocal boundary value problem, dtρu(t)+Au(t)=f(t) (0&lt;ρ&lt;1, 0&lt;t≤T), u(ξ)=αu(0)+φ (α is a constant and 0&lt;ξ≤T), in an arbitrary separable Hilbert space H with the strongly positive selfadjoint operator A, is considered. The operator dt on the left hand side of the equation expresses either the Caputo derivative or the Riemann-Liouville derivative; naturally, in the case of the Riemann - Liouville derivatives, the nonlocal boundary condition should be slightly changed. Existence and uniqueness theorems for solutions of the problems under consideration are proved. The influence of the constant α on the existence of a solution to problems is investigated. Inequalities of coercivity type are obtained and it is shown that these inequalities differ depending on the considered type of fractional derivatives. The inverse problems of determining the right-hand side of the equation and the function φ in the boundary conditions are investigated.

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

For the KdV-Burgers equations on cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is studied. The equations describe a medium which is both dissipative and dispersive. Symmetries, invariant solutions and conservation laws are investigated. For an appropriate combination of dispersion and dissipation the asymptotic profile looks like a periodical chain of shock fronts with a decreasing amplitude (sawtooth waves). The development of such a profile is preceded by a head shock of a constant height and equal velocity which depends on spatial dimension as well as on integral characteristics of boundary condition; an explicit asymptotic for this head shock and a median of the oscillating part is found.

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system in case of few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes interactions. In this case, the non-linear coupled Schrödinger equation system solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails, due to the non-stability of the computing scheme. Due to this fact, the combined explicit/implicit finite-difference integration scheme, based on the implicit Crank–Nicolson finite-difference scheme, is used. It allows ensuring the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has performance gains (or resolutions) up to three or more orders of magnitude in comparison with the split-step Fourier method due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step. The main advantage of the proposed method is the ability to calculate the propagation of an arbitrary number of modes in the fiber.

This paper aims to investigate the global asymptotic stability of following system of higher order difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-m}²)),y_{n+1}=A+B((x_{n})/(x_{n-m}²)) where A and B are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system.

The storm of November 12th-13th, 2019 provoked the displacements of boulders in a central Mediterranean rocky coast; with reference to a selected area, prone to the boulder production and geomorphologically monitored for years, a field-oriented study approach was applied for the phenomenon, by collating data concerning pre-storm locations and kinematics of these boulders. The number of displaced boulders is 11, that is, in terms of morphological imprint of a specific storm, one of the major study cases for the Mediterranean. In addition, based on widely used hydrodynamic equations, the minimum wave height required to displace the boulders is assessed. The values conform with the expected values for the wave climate dominating during the causative meteorological event and give a measure of the energy of the storm slamming the coast. Boulder dislodgements usually have plays a key role in determining the rate of the coastal recession, likely also in the investigated area. In view of an adverse climate evolution with a possible increase of energy and frequency of severe storms, the results deriving from the study of this morphodynamics should be considered for the hazard assessment and coastal management.

Electrodynamics is usually written using polarization fields to describe changes in distribution of charge as electric fields change. This approach does not specify polarization fields uniquely from electrical measurements. Many polarization fields will produce the same electrodynamic forces and flows because only divergence of polarization enters Maxwell’s first equation, relating charge and electric field. The curl of any function can be added to a polarization field without changing the electric field at all. The divergence of the curl is always zero. To be unique, models must describe the charge distribution and how it varies. I propose a different paradigm to describe field dependent charge, i.e., the phenomenon of polarization. This operational definition of polarization has worked well in biophysics for fifty years, where a field dependent, time dependent polarization provides gating current that makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that operational definition be used to define polarization charge in general. Charge movement needs to be computed from a combination of electrodynamics and mechanics because ‘everything interacts with everything else’. The classical polarization field need not enter into that treatment at all. When nothing is known about polarization, it is necessary to use an approximate representation with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.