For many disciplines of science, all conceivable collisional cross sections and reactions must be precisely known. Although the recent decades were a trial of large-scale research to give these data, many essential atomic and molecular cross section data still missing, and the reliability of the existing cross sections has to be validated. In this paper, we present electron stripping, electron capture, and system breakdown cross sections in carbon (C5+) ions and lithium (Li2+) ions collisions with atomic hydrogen based on the Monte Carlo models of classical and quasi-classical trajectories. According to our expectation, the QCTMC results show higher results in comparison to standard CTMC data, emphasizing the role of Heisenberg correction constraint, especially in the low energy regime. On the Other hand, at high energy, the Heisenberg correction term has less influence as a projectile momentum increase. We present the total cross sections of electron stripping, electron capture, and system breakdown in C5+ ions and Li2+ ions collisions with atomic hydrogen in the impact energy range from 10 keV to 160 keV, which is of interest in astrophysical plasmas, atmospheric sciences, plasma laboratories, and fusion research.

According to the requirement of 20kg load of casting barrel, we design a three-dimensional model of the robot and analyze the three stages of liquid level change in the casting barrel during the casting process. Through the analysis, it is determined that the time and angle function is an implicit function, and it is impossible to find the analytical expression of time about angle. The kinetic function of the casting barrel is simulated by MATLAB, and it is found that the function image has mutation points, and when the original function is fitted and approximated by fifth-degree polynomial interpolation, the fifth-degree polynomial function image of the time versus the angular acceleration has a large amplitude of oscillation, especially the mutation points. A PID algorithm based on the discretization of the time and acceleration function is introduced for correction, and the results show that this method effectively reduces the oscillation amplitude of the image and improves the coincidence with the original function.

Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernels on compact intervals can have significant errors near the boundaries. This paper proposes a quasi-interpolation method with Gaussian kernels using Chebyshev points and boundary corrections to improve the approximation near the boundaries. The boundary corrections use a linear approximation of the function beyond the interval to estimate the truncation error and add correction terms. Numerical studies on test functions show that the proposed method reduces errors significantly near boundaries compared to quasi-interpolation without corrections, for both equally spaced and Chebyshev points. The convergence and accuracy with the boundary corrections are generally better with Chebyshev points compared to equally spaced points. The proposed method provides an efficient way to perform quasi-interpolation on compact intervals while controlling the boundary errors.

P versus NP is considered as one of the most fundamental open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is NP-complete. It is well-known that P is equal to NP under the assumption of the existence of a polynomial time algorithm for some NP-complete. We show that the Monotone Weighted Xor 2-satisfiability problem (MWX2SAT) is NP-complete and P at the same time. Certainly, we make a polynomial time reduction from every directed graph and positive integer k in the K-CLOSURE problem to an instance of MWX2SAT. In this way, we show that MWX2SAT is also an NP-complete problem. Moreover, we create and implement a polynomial time algorithm which decides the instances of MWX2SAT. Consequently, we prove that P = NP.

In this paper, we consider a class of bilevel programming problems (abbreviated as, BLPP). Exploiting the generalized approximate convexity assumptions, we investigate the relations among the solutions of approximate Minty (respectively, Stampacchia) type variational inequalities (abbreviated as, AMTVI (respectively, ASTVI)), and the local ϵ-quasi solutions of the BLPP. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (abbreviated as, KKM)-Fan’s lemma, we derive some existence results for the solutions of approximate variational inequalities (abbreviated as, AVI), namely, AMTVI and ASTVI. A non-trivial example is given to highlight the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that establishes relationships between the AVI and the BLPP under the assumptions of generalized approximate convexity in terms of limiting subdifferentials.

In the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging tropical semirings’ computational prowess and block matrices’ structural resilience. Moving away from the conventional use of finite fields, these protocols deliver markedly faster processing speeds and heightened security. We present two implementations of our concept, each utilizing a different platform for the set of commuting matrices: one employing tropical polynomials of matrices and the other employing Linde-de la Puente matrices. The inherent simplicity of tropical semirings leads to a decrease in operational complexity, and using block matrices enhances our protocols’ security profile. The security of these protocols relies on the Matrix Decomposition Problem. We also provide a comparative analysis of our protocols against existing matrix block-based protocols in finite fields. This research marks a significant shift in cryptographic protocol design, specifically tailored for demanding engineering applications, and sets a new standard in secure and efficient digital communication.

This paper introduces an innovative Particle Swarm Optimization (PSO) Algorithm in-corporating Sobol and Halton Random number samplings. It evaluates the enhanced PSO's performance against conventional PSO employing Monte Carlo Random Number Samplings. The comparison involves assessing the algorithms across nine benchmark problems and the renowned Travelling Salesman Problem (TSP). The re-sults reveal consistent enhancements achieved by the enhanced PSO utilizing Sob-ol/Halton samplings across the benchmark problems. Particularly noteworthy are the substantial improvements demonstrated by the enhanced PSO in solving the Travel-ling Salesman Problem. These findings underscore the efficacy of employing Sobol and Halton random number generation methods in enhancing algorithm efficiency.

Keywords: liquid alloys, microstratification, dispersed particles, spontaneous dispersion, criteria for true (entropic) spontaneous dispersion, mechanisms of quasi-spontaneous dispersion, methods and results for assessing size of dispersed particles.

In this paper we present two ways to solve the Jacobian conjecture. The first way is an equivalent statement to the Jacobian conjecture using idempotent ideals. The second way is to use an equivalent thesis to the thesis of the Jacobian conjecture. In both cases we will show that the Jacobian conjecture is true.

Polymer-based composites are widely used in the automotive, security, aeronautical and space industries, to mention a few. This is because of their good mechanical properties, which are similar to those of metals but with the attraction of being lightweight. Kevlar® as a reinforcement is extensively used in the security industry owing to its good ballistic properties. This investigation presents the mechanical characterization based on in-plane quasi-static tensile testing of Kevlar® composite using a universal testing system. The methodology developed for the preparation of coupons is based on pressure, temperature and time. As a result of this work, elastic moduli (EL and ET), Poisson’s ratio (νLT), shear modulus (GLT) and strengths (XT, YT, S) were obtained. It is worth mentioning that there is scarce or no characterization of this material in the literature, and those studies that do characterize it do not present the coupon thermoforming conditions or the reasons of the specimen dimensions (width, length and thickness).

The technology for determining the point’s coordinates on the earth’s surface using the global navigation satellite system (GNSS) is becoming the norm along with ground-based methods. In this case, determining coordinates does not cause any particular difficulties. However, to identify normal heights using this technology with a given accuracy, special research is required. The fact is that satellite determinations of geodetic heights (h) over an ellipsoid surface differ from ground-based measurements of normal height (HN) over a quasi-geoid surface by a certain value called quasi-geoid height or height anomaly (ζ). In relation to determining heights of a certain territory, the concept of geoid height (N) is usually operated when dealing with a geoid model. In this work, geodetic and normal heights are determined for 5 control points in three different regions in Lebanon, where measurements are carried out using GNSS technology and geometric levelling. The obtained quasi-geoid heights are compared with geoid heights derived from the global Earth model EGM2008. The results obtained showed that, in the absence of gravimetric data, the combination of global Earth model data, geometric levelling for selected areas and satellite determinations allows the creation of a high accurate altitude network for mountainous areas.

Layered halide perovskites have emerged as a promising contender in solid-state lighting thanks to their tunable bandgap, high luminescence quantum yield, and high color purity. However, the fabrication of perovskite light-emitting devices in laboratories usually experiences low de-vice-to-device reproducibility since perovskite crystallization is highly sensitive to ambient condi-tions, such as humidity and temperature. Although device processing inside gloveboxes is primarily used to reduce the influence of oxygen and moisture, several extraneous variables, including gas-eous pollution traces and thermal fluctuations in the inert atmosphere or contaminations from re-sidual solvents confined in the enclosed environment, can destabilize the crystallization process and alter the properties of the emissive layers. Here, we examine different experimental set-ups for spin-coating deposition of layered perovskites in inert atmospheres and their influences on the formation of polycrystalline thin films. Our results demonstrate that fluctuations in the glovebox properties (concentrations of residual O2 and H2O or solvent traces), even in very short timescales, can negatively impact the consistency of the perovskite film formation, while thermal variation plays a relatively minor role in this phenomenon. Furthermore, careful storage of chemical species inside the workstation is critical for reproducing high-quality perovskite layers. Consequently, when applying our most controlled environment for perovskite deposition, the photoluminescence life-time of perovskite thin films shows a standard deviation of only 3%, whereas the reference set-up yields a 15% standard deviation. Regarding complete perovskite light-emitting diodes, the uncer-tainties in statistical luminance and EQE data are significantly reduced from 230% and 140% to 38% and 42%, respectively.

This article studies electrostatic fields and potentials in the presence of conductors and point charges under the framework of solving Laplace’s equation with specifi ed boundary conditions. The results demonstrate that many problems posed and solved in elementary electrostatics through various heuristics such as the method of images, can be more rigorously treated under the solution framework of Laplace’s equation.

In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.

In this paper, a class of coupled competitive neural networks, which subject to disturbance and discontinuous activation functions, is concerned. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results.

This work presents a new type of chaotic dynamical system originated from Dirichlet Eta function. Although the exposition describes only a bidimensional instance, it is certainly possible to construct higher dimensional such models. The novelty resides in the multitude of interesting characteristics concentrated in only one kind of dynamical system, mainly because of its simple abstract definition - it provokes dissipative, chaotic and itinerant behavior, and its paths typically display nonrecurring quasi-attractors and associate regions of ruin. In addition, it is discrete and nonautonomous, being additively driven by a simple real vector sequence. Also, the defining formulas have parameters which permit to activate bifurcatory effects, mainly related to setting the number of quasi-attractors and overall geometric complexity and diversity. In this fashion, it holds a certain similarity with classical itinerant chaotic systems, but it is a completely different object. One of its parameters is very influential and may be intuitively compared to a type of "potential energy", capable of changing the duration of sojourns etc. In this fashion, there is a potential opportunity to employ artificial inference techniques for designing specific structures on paths. Of course, the other parameters are also relevant, but not necessarily in the control of the number of quasi-attractors and the permanence periods near them. It is important to state that the described system was found during a previous investigation about certain features of the Riemann hypothesis, using the Dirichlet Eta function instead of the Riemann Zeta function - the components of the system under study here were part of certain series whose convergence had to be established, and that scenario produced this very positive side effect. The text also suggests an atypical, but important, potential application in philosophy: the representation of the Hindu concepts of Samsara and Moksha.

Background: Pediatric Rapid Response Teams (RRTs) are expected to significantly lower pediatric mortality in healthcare settings. This study evaluates RRTs' effectiveness in decreasing cardiac arrests and unexpected Pediatric Intensive Care Unit (PICU) admissions. Methods: A quasi-experimental study (2014-2017) at King Abdulaziz University Hospital, Jeddah, Saudi Arabia, involved 3,261 pediatric inpatients, split into pre-intervention (1,604) and post-intervention (1,657) groups. The intervention entailed pediatric specialists collaboratively managing acute decompensations following set protocols. Results: RRT was activated 471 times, primarily for respiratory distress (29.30%), sepsis (22.30%), clinical anxiety (13.80%), and hematological abnormalities (6.7%). Family concerns triggered 0.1% of activations. Post-RRT implementation, unplanned PICU admissions significantly reduced (RR = 0.552, 95% CI 0.485-0.628, P < 0.0001), and non-ICU cardiac arrests were eliminated (RR = 0). Patient care improvement was notable, with a -9.61 coefficient for PICU admissions (95% CI: -12.65 to -6.57, P < 0.001) and a -1.641 coefficient for non-ICU cardiac arrests (95% CI: -2.22 to -1.06, P < 0.001). Sensitivity analysis showed mixed results for PICU admissions, while zero-inflation Poisson analysis confirmed a reduction in non-ICU arrests. Conclusions: The deployment of pediatric RRTs is associated with fewer unexpected PICU admissions and non-ICU cardiopulmonary arrests, indicating improved PICU management. Further research using robust scientific methods is necessary to conclusively determine RRTs' clinical benefits.

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

We prove a quasi-pseudometric version of the strong Ekeland principle proved by P. Georgiev and T. Suzuki.

Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.

Nuclear fusion reactors are composed by several complex components whose behaviour may be not certain a priori. This uncertainty may have a significant importance in the evolution of fault transients in the machine, causing unexpected damages to its components. For this reason a suitable method for the uncertainty propagation during those transient is required. The Monte Carlo method would be the reference option, but it is, in most of the cases, not applicable due to the large amount of required simulations to be repeated. In this context the Polynomial Chaos Expansion has been considered as a valuable alternative. It allows to create a surrogate model of the original one in terms of orthogonal polynomials. Then, the uncertainty quantification is performed repeatedly calling this much simpler and faster model. Using the fast current discharge in the Divertor Tokamak Test Toroidal Field (DTT TF) coils as a reference scenario, this method has been applied: the uncertainty on the parameters of the Fast Discharge Unit (FDU) varistor disks is propagated to the simulated electrical and electro-magnetic relevant effects. Eventually two worst case scenarios have been analyzed from the thermal-hydraulic point of view with the 4C code, simulating a fast current discharge as a consequence of a coil quench. Eventually it has been demonstrated that the uncertainty on the inputs (varistor parameters) strongly propagates obtaining a wide range of possible scenarios in case of accidental transients. This result underlines the necessity to take into account and propagate all possible uncertainties in the design of a fusion reactor, according to the Best Estimate Plus Uncertainty approach.

The fundamental theory of nuclear interactions, Quantum Chromodynamics (QCD), operates in terms of quarks and gluons at higher resolution. At low resolution the relevant degrees of freedom are nucleons. Two-nucleon Short-Range Correlations (SRC) help to interconnect these two descriptions. SRCs are temporary fluctuations of strongly interacting close pairs of nucleons. The distance between the two nucleons is comparable to their radii and their relative momenta are larger than the fermi sea level. According to the electron scattering experiments held in the last decade, SRCs have far-reaching impacts on many-body systems, the nucleon-nucleon interactions, and nuclear substructure. The modern experiments with ion beams and cryogenic liquid hydrogen target make it possible to study properties of the nuclear fragments after quasi-elastic knockout of a single nucleon or an SRC pair. The first SRC experiment at BM@N (2018) with a carbon beam has shown that detection of an intact 11B nucleus after interaction selects out the quasi-elastic knockout reaction with minimal contribution of initial- and final-state interactions. Also, 25 events of SRC-breakups showed agreement in SRC properties as knows from electron beam experiments. The analysis of the second measurement of SRC at BM@N held in 2022 with an improved setup is currently ongoing. The SRC project at JINR moved to a new experimental area in 2023, where the next measurement is being planned in terms of experimental setup and physics goals.

Crop digital twin is redefining traditional farming practices, offering unprecedented opportunities for real-time monitoring, predictive and simulation analysis, and optimization. This research embarks on an exploration of the synergy between precision agriculture, crop modeling, and regression algorithms to create a digital twin for augmenting farmers the concentration and composition prediction-based crop nutrient recovery. This captures the holistic representation of crop characteristics, considering the intricate relationships between environmental factors, nutrient concentrations, and crop compositions. However, the complexity arising from diverse soil and environmental conditions makes nutrient content analysis expensive and time-consuming. This paper presents the result of a predictive digital twin case study that employs six regression algorithms namely Elastic Net, Polynomial, Stepwise, Ridge, Lasso, and Linear Regression to predict rice nutrient content efficiently, particularly considering the coexistence and composition of multiple nutrients. Our research findings highlight the superiority of the Polynomial Regression model in predicting nutrient content, with a specific focus on accurate nitrogen percentage prediction. This insight can be used for nutrient recovery intervention by knowing the precise amount of nutrient to be added into the crop medium. The adoption of the Polynomial Regression model offers a valuable tool for nutrient management practices in the crop digital twin, potentially resulting in higher-quality rice production and a reduced environmental impact. The proposed method can be replicable in other low-resourced crop digital twin system.

A system of simultaneous multi-variable nonlinear equations can be solved by the Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in some way. Unfortunately, the quasi-Newton condition (secant equation) doesn’t completely specify the Jacobian approximate in multi-dimensional case, so its full-rank update is not possible with classic variants of methods. The suggested new iteration strategy (“T-Secant”) allows full-rank update of the Jacobian approximate in each iteration by determining two independent approximates for the solution. They are used to generate a set of new independent trial approximates, then the Jacobian approximate can fully be updated. It is shown, that the T-Secant approximate is in the vicinity of the classic quasi-Newton approximate, providing that the solution is evenly surrounded by the new trial approximates. The suggested procedure increases the super-linear convergence of the secant method (φS = 1.618...) to super-quadratic (φT = φS + 1 = 2.618...) and the quadratic convergence of the Newton-method (φN = 2) to cubic (φT = φN + 1 = 3) in one dimensional case. The Broyden-type efficiency (mean convergence rate) of the suggested method in multi-dimensional case is an order higher than the efficiency of other classic low-rank update quasi-Newton methods as shown by numerical examples on a Rosenbrock-type test-function with up to 1000 variables. The geometrical representation (hyperbolic approximation) in single variable case helps explaining the basic operations and a vector-space description is also given in multi-variable case.

Using the method of the beta function, Sun has recently evaluated some series of the type $\sum_{k=0}^{\infty}(ak+b)x^k/\binom{mk}{nk}$. By factorization of the polynomial $t^{m-n}(1-t)^n-x$, we will give a general method to find new $\pi$-series.

Many probability-based uncertainty quantification (UQ) schemes require a large amount of sampled data to build credible probability density function (PDF) models for uncertain parameters. Unfortunately, the data collected in compressor blades of aero-engine are mostly limited due to expensive and time-consuming tests. In this paper, we develop a preconditioner-based data-driven polynomial chaos (PDDPC) method that can efficiently deal with uncertainty propagation of limited sampled data. The calculation accuracy of PDDPC method is closely related to the sample size of collected data. Therefore, the influence of sample size on PDDPC method is investigated using a nonlinear test function. Subsequently, we consider the real manufacturing errors of stagger angle for compressor blades. Under three different operating conditions, PDDPC method is applied to investigate the effect of stagger angle error on UQ results of multiple aerodynamic parameters of a two-dimensional compressor blade. The results show that as the sample size of measured data increases, UQ results of aerodynamic performance obtained by PDDPC method gradually converge. There exists a critical sample size that ensures accurate UQ analysis of compressor blades. The probability information contained in the machining error data is analyzed through Kullback-Leibler divergence, and the critical sample size is determined. The research results can make a valuable reference for the fast and cheap UQ analysis of compressor blades in practical engineering.

In this paper we provide some important and significant observations on invo-regular rings appeared in Ann. Univ. Mariae Curie-Sklodowska Sect. A Mathematica (2018). In addition we exhibit that strongly invo-regular rings, invo-regular rings and quasi invo-regular rings all coincide with the well known and well characterized tripotent rings and all these rings further coincide with the well known unit regular rings.

A simple bounded stochastic motion is employed for modelling equity price dynamics under shocks, where the prices are constrained to lie between two positive bounds. While the stochastic process has an inaccessible boundary, the other boundary is quasi-bounded, implying that the boundary can be breached if the probability leakage condition is met. The quasi-boundedness of the process at the boundary can thus provide an indicator of possible risk of equities under price shocks. Empirical calibration of model parameters of the proposed process for equities can be performed easily due to the availability of an analytically tractable probability density function which generates fat-tailed distributions consistent with empirical observations. The volatility and mean-reversion of the S&P500 dynamics calibrated by the process is positively and negatively co-integrated respectively with the VIX index representing the level of market distress. The process captures the high likelihood of Hertz’s default about two months earlier, using only information until that point, and before the firm filed for Chapter 11 bankruptcy in May 2020 as a result of the Covid-19 pandemic. Empirical calibration of the process for GameStop’s stock price shows that the short squeeze of the stock occurred when the condition for breaching an upper boundary was met on 14 January 2021, i.e., about two weeks before major short sellers closed out their positions with significant losses. The trading volume of the stock was positively co-integrated with the probability leakage ratio.

The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi univalent function defined in open unit disk connected with a linear q-convolution operator, which are associated with the quasi-subordination. We find coefficients estimate |h_2 |,|h_3 | for functions in these subclasses. Several known and new consequences of these results are also pointed out.

The behaviour and bifurcations of solutions to three-dimensional (three-phase) quadratic polynomial dynamical systems (DSs) are considered. The integrability in elementary functions is proved for a class of autonomous polynomial DSs. The occurrence of bifurcations of the type twisted fold is discovered on the basis and within the frames of the elements of the developed DS qualitative theory. The discriminant criterion applied originally to two-phase quadratic polynomial DSs is extended to three-phase DSs investigated in terms of their coefficient matrices. Specific classes of D- and S-vectors are introduced and complete description of the symmetry relations inherent to the DS coefficient matrices is performed using the discriminant criterion.

We classify all the topologically non-equivalent phase portraits of the quadratic polynomial differential system dx/dt = (1-2x)(y-x), dy/dt =y (2-g y-(5g-4)x/(g-1)), in the Poincaré disc for all the values of the parameter g in R\{1}. The differential system dx/dt = y-x, dy/dt =y (2-g y-(5g-4)x/(g-1))/(1-2x), when the parameter g in (1,2] models the structure equations of a static star in general relativity in the case of the existence of a homologous family of solutions, being x = m(r)/r where m(r)>= 0 is the mass inside the sphere of radius r of the star, y = 4pi r^2 rho where rho is the density of the star, and t = ln (r/R) where R is the radius of the star. We classify the possible values of m(r)/r and 4pi r^2 rho when r-->0.

Analyzing network robustness against random failures or malicious attacks is a critical research issue in network science as it helps to enhance the robustness of beneficial networks or efficiently disintegrate harmful networks. Most studies commonly neglect the impact of the attack success rate (ASR) and assume that attacks on the network will always be successful. However, in real-world scenarios, an attack may not always succeed. This paper proposes a novel robustness measure called Robustness-ASR (RASR), which utilizes mathematical expectations to assess network robustness when considering the ASR of each node. To efficiently compute the RASR for large-scale networks, a parallel algorithm named PRQMC is presented, which leverages randomized quasi-Monte Carlo integration to approximate the RASR with a faster convergence rate. Additionally, a new attack strategy named HBnnsAGP is introduced to better assess the lower bound of network RASR. Finally, the experimental results on 6 representative real-world complex networks demonstrate the effectiveness of the proposed methods compared with the state-of-the-art baselines.

Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. In addition to computation, it is also a powerful tool for analysis, allowing one to study various numbers in a unified way. This article contains many results of two types of Stirling numbers, associated Stirling numbers, and Eulerian numbers, making a great generalization of Euler polynomials, Wilson's theorem, and Wolstenholme's theorem, showing that they are just special cases. Formal Calculation provides a novel method for obtaining combinatorial identities and analyzing q-binomial.This article has obtained a large number of results in q-analogues, including inversion formulas for q-binomial coefficients. This article also introduces a theorem on symmetry.

The fatigue crack growth rate (FCGR) of aluminium alloys under the combined influence of temperature and humidity remains a relatively unexplored area, receiving limited attention due to its intricate nature and challenges in predicting the combined impact of these factors. The challenge was to investigate and address the specific mechanisms and interactions between temperature and humidity, as in coastal environment conditions, on the FCGR of aluminium alloy. The present study conducts a comprehensive investigation on the combined influence of temperature and humidity on the FCGR of Al6082 alloy. The fatigue pre-cracked compact tension specimens were corroded for 7 days and then subjected to various temperature and humidity conditions in a thermal chamber for 3 days to simulate coastal environments. The obtained data were analysed to determine the influence of temperature and humidity on the FCGR of Al6082 alloy. An empirical model was also established to predict fatigue life cycle values under these environmental conditions precisely. The correlation between FCGR and fracture toughness models was also examined. The Al6082 alloy exhibits a 34% increase in the Paris constant C, indicating reduced FCGR resistance due to elevated temperature and humidity levels. At the same time, fatigue, corrosion, moisture-assisted crack propagation, and hydrogen embrittlement lead to a 27% decrease in threshold fracture toughness. The developed model exhibited accurate predictions for fatigue life cycles, and the correlation between fracture toughness and FCGR showed less than 10% error, indicating a strong relationship between these parameters.

The paper proposes an approach to determine the optimal number of medical specialists in the region. According to the author's theoretical model, in order to maximize public welfare, the marginal contribution of the last physician recruited to the growth of the public utility function should be equal to the marginal cost of attracting him and providing conditions for his work. To empirically assess the contribution of physicians to the number of lives saved, the CVD mortality rate is modeled using the instrumental variable method. On average, a 1% increase in the number of cardiologists is associated with a 0.6% decrease in cardiovascular mortality. At the level of provision with cardiologists in the amount of 1 per 100 thousand people, their marginal contribution to the number of lives saved is not less than 129 per 100 thousand people, with a further decrease by 5 people with the increase in the level of provision by 1 unit. The use of the obtained results will increase the validity of managerial decisions and in determining the optimal level of doctors when choosing between alternative possibilities of spending money on hiring doctors of different profiles or other expenses, especially in the case of limited resources.

A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi bound (or resonance) states. When the system is prepared in one of such quasi bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and because of quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers.

Log collection and storage is a crucial process for enterprises around the globe. Log analysis helps identify potential security breaches and, in some cases, is required by law for compliance. However, enterprises often delegate these responsibilities to third-party Cloud Service Providers (CSPs), where the logs are collected and processed for anomaly detection and stored in a data warehouse for archiving. Prevalent schemes rely on plain (unencrypted) data for anomaly detection. More often, these logs can reveal sensitive information about an organization or the customers of that organization. Hence, it is best to keep it encrypted at all times. This paper presents "SigML++," an extension of work done in "SigML." We utilize Fully Homomorphic Encryption (FHE) with the Cheon-Kim-Kim-Song (CKKS) scheme for supervised log anomaly detection on encrypted data. We use an Artificial Neural Network (ANN) based probabilistic polynomial approximations using a Perceptron with linear activation. We probabilistically approximate the Sigmoid activation function (σ(x)) in the encrypted domain for the intervals [−10,10] and [−50,50]. Experiments show better approximations for Logistic Regression (LR) and Support Vector Machine (SVM) for low-order polynomials.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

Currently, efficient utilization of low-grade thermal energy is a great challenge. Thermoelectricity is an extremely promising method of generating electrical energy from temperature differences. As a promising energy conversion technology, thermo-electrochemical cells (TECs) have attracted much attention in recent years for their ability to convert thermal energy directly into electricity with high thermal power. Within TECs, anions and cations gain and lose electrons, respectively at the electrodes using the potential difference between the hot and cold terminals of the electrodes by redox couples. Additionally, the anions and cations therein are constantly circulating and mobile via concentration diffusion and thermal diffusion, providing an uninterrupted supply of power to the exterior. This review article focuses mainly on the operation of TECs, recent ad-vances in redox couples, electrolytes, and electrodes. The outlook for optimization strategies re-garding TECs is also presented in this paper.

The degradation of Proton-exchange membrane fuel cell (PEMFC) gasket materials is crucial in electric vehicles as it can cause hazardous hydrogen fuel leaks, which are usually due to high temperatures, pressures, and hydrogen fuel exposure. Degradation of gasket materials in PEMFC presents a critical concern for electric vehicle safety due to potential hydrogen fuel leaks. This study utilizes finite element analysis (FEA) to assess the suitability of gasket materials for PEMFC applications, focusing on aging and tensile conditions. The dual degradation framework, incorporating contact pressure and von Mises stress, is employed to evaluate Liquid Silicon Rubber (LSR) and Ethylene Propylene Diene Monomer (EPDM) materials. Under aging techniques, the Yeoh model exhibits the least Mean Absolute Percentage Error (MAPE) and computational cost of 0.27 seconds, while the Ogden model records the highest computational cost of 0.89 seconds. In evaluating MAE, Root Mean Square Error (RMSE), and R-squared metrics, LSR and EPDM materials demonstrate respective averages of 0.25%, 0.275%, 0.945%, and 0.815%, 0.685%, 0.77%. Tensile testing (Uniaxial) reveals RMSE and MAE values of 0.30%, 0.40%, and 0.50%, 0.40%, respectively. FEA proves instrumental in identifying suitable gasket materials for PEMFC applications. LSR emerges as the superior choice, demonstrating enhanced FEA modelling performance under aging and tensile conditions. These findings contribute valuable insights to the design and development of improved gasket materials, bolstering the safety and reliability of electric vehicles.

Induction heating (IH) technology is widely recognized and utilized in residential applications due to its high efficiency and safe operating characteristics. Resonant inverter circuits are widely used in IH systems because of their high efficiency and ability to perform soft-switching. Among the various resonant inverters used in IH systems, the single-switch quasi-resonant (SSQR) inverter topology is typically preferred for low-cost and low-output-power applications. Despite its cost advantage, the SSQR topology has a relatively narrow soft-switching range, which can be unstable depending on the electrical parameters of the load and the resonant converter circuit. Accurately determining the capacitance value of the resonant capacitor and the inductance value of the induction coil, which are the key circuit elements of the SSQR induction cooker, is crucial for designing a reliable, efficient, and durable cooking system. In other words, there exists a critical relationship between the resonant converter circuit parameters, load characteristics, and safe operating conditions. Additionally, when considering closed-loop control methods used for power control and safety, selecting appropriate resonant circuit elements becomes vital in ensuring both reliable and efficient operation. This paper focuses on a novel and simplified design method for the SSQR inverter utilized in household appliances. The proposed method and its advantages in terms of the safe operating area of the switch are theoretically investigated and verified through simulations and prototype circuits.

The inherent non-smoothness of vibroimpact system leads to complex behaviors as well as strong sensitive dependence on parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, the investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form by the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed by the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point.

The objective of this study is to examine a nonparametric estimate , using the kernel approach, of the conditional distribution function of a scalar response variable that is given a random variable whose values take place in a separable real Hilbert space. The observations will be dependent on one another in a quasi-associated fashion. The pointwise practically perfect consistencies with rates of this estimator are established by us under some broad conditions. The study’s major objective is to investigate the convergence rate of the proposed estimator and its application in the convergence rate and asymptotic normality of the hazard function. The asymptotic normality of the developed estimator is established precisely. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data.

In this paper, a short survey of the existed results concerning the Jacobian Conjecture is first given. Then the 3-fold linear type polynomial map will be analyzed in detail. The expansion of the Jacobian condition is deduced to obtain its equivalent algebraic equations, and the Jacobian condition will be analyzed to derive two coordinate transformations that can maintain the invariance of the Jacobian condition. Finally, it is proved by mathematical induction method that one general chain expression presented in this paper is just the inverse polynomial map of 3-fold linear type polynomial map, i.e. LJC(n,[3]) holds such that the Jacobian Conjecture holds.

This study investigates the application of Unmanned Aerial Vehicles (UAVs) equipped with a Micasense RedEdge-MX multispectral camera for the estimation of Secchi Depth (SD) in inland water bodies. The research analyzed and compared five sun-glint correction methodologies — Hedley, Goodman, Lyzenga, Joyce, and threshold removed glint to model the SD values derived from UAV multispectral imagery, highlighting the role of reflectance accuracy and algorithmic precision in SD modeling. While Goodman's method showed a higher correlation (0.92) with in situ SD measurements, Hedley's method exhibited the smallest average deviation (0.65 m), suggesting its potential in water resource management, environmental monitoring, and ecological modeling. The study also underscored the Quasi-Analytical Algorithm (QAA) potential in estimating SD due to its flexibility to process data from various sensors without requiring in situ measurements, offering scalability for large-scale water quality surveys. The accuracy of SD measures, calculated using QAA, was related to variability in water constituents of coloured dissolved organic matter and the solar zenith angle. A practical workflow for SD acquisition using UAVs and multispectral data was proposed for monitoring inland water bodies.

In many research fields, statistical probability models are often used to analyze real-world data. However, data from many fields, such as the environment, economics, and health care, do not necessarily fit traditional models. New empirical models need to be developed to improve their fit. In this paper, we explore a further extension of the quasi-Lindley model. Maximum likelihood, least square error, Anderson-Darling algorithm, and expectation-maximization algorithm are four techniques for estimating the parameters under study. All techniques provide accurate and reliable estimates of the parameters. However, the mean square error of the expectation maximization approach was lower. The usefulness of the proposed model was demonstrated by analyzing a dynamical systems data set, and the analysis shows that it outperforms the other models in all statistical models considered.

We present evidence of the anchoring bias and disposition effect (DE) in investor trading decisions across different asset markets (stable and volatile assets) and market scenarios (stable and volatile markets), as well as how these biases affect investors' portfolio performance. The study employs a quasi-experimental design, allowing subjects to engage in interactive trading with four securities, two with potential negative returns and two with potential positive returns, within a simulated asset market. Our findings reveal the presence of the disposition effect and anchoring bias among individual investors in India. Second, market scenarios or volatility can influence the investors’ behavioral biases. The disposition effect was more prominent in volatile markets and the total market, while the anchoring bias was significant in stable and total markets. Additionally, investors exhibiting the disposition effect exhibit lower portfolio performance, while those demonstrating anchoring bias perform relatively better. The study's findings can help individual investors understand their behavioral biases, avoid them in future trading decisions, and improve portfolio performance. Financial institutions and regulatory agencies could identify investment products and supportive investor interactions towards better market trade decisions.

To improve the understanding of soil–pile interaction of laterally loaded piles, the quasi-static test of pile group foundation in silty clay with 5 foundation piles arranged in cross shape is carried out. The direct measurement-based p–y curves at different depths showed nonlinear behavior, in which the initial stiffness and ultimate soil reaction increased as the depth increased. The loading displacement amplitude corresponding to the failure of each foundation pile in the high axial compression reinforced concrete pile group foundation is given as follows: the front-end nappe foundation pile (#3 pile) is 6mm, the middle pile is 16mm, the front-end nappe foundation pile is 20mm, and the loading displacement amplitude of side pile is 24mm. In silty clay, due to the existence of pile group effect, the edge effect has little effect on the horizontal foundation bed coefficient of foundation pile in pile group, while the influence of masking effect on the horizontal foundation bed coefficient of each foundation pile in pile group is not related to the position of pile, but only to the existence of masking effect, and the influence of different columns of masking effect on the horizontal foundation bed coefficient is the same.

Quantum theory is the land of indiscernible things, of things that in some situations cannot be put apart. This contrasts in much with standard mathematics and classical logic, which were elaborated to deal with \textit{individuals}, discernible things. Many thinkers, among them the mathematician Yuri Manin, have proposed that a more general theory of `sets' than standard set theories (where sets are collections of discernible elements) should be elaborated to cope with quantum physics. Quasi-set theory was proposed with such an aim. In this paper, we consider some aspects of this theory and discuss the way we can use such a theory as a framework for constructing deformable (not rigid) structures where indiscernible things can be considered but with one additional and fundamental detail: these structures cannot be extended to rigid structures as it happens in the standard frameworks. Really, the way of dealing with indiscernible (or indistinguishable) elements within a `standard' framework such as a `classical' set theory (like the ZFC system) requires the confinement of the discussion to deformable (non-rigid) structures. But in ZFC every structure can be extended to a rigid structure (encompassing only the trivial automorphism -- the identity function), so that in the extended structure (or in the whole universe) one can realize that the supposed indiscernible objects are not indiscernible at all. Quasi-set theory is such that the universe of quasi-sets is deformable and in such a theory one can construct deformable structures which cannot be extended to rigid ones. The aim of this paper is to put these things in a clear way.

The paper analyzes the phenomenon that condition the durability and reliability of a type of dental bur based on the wear of the active part and with effect on its quality. For the experimental study, a conical-cylindrical dental bur and a sample dental material in cobalt-chromium alloy, cylindrical shape, tested on a specially made experimental installation were used. The paper was limited to the consideration of a single parameter (loss of mass, mw by wear of the active part of the dental bur tested) for the establishment the durability and reliability, useful for the extension of the lifetime or even optimization of its operation. The wear phenomenon of the active part of dental bur is studied based on the results and experimental data obtained in the work process that was validated by interpolation and led to polynomial functions which approximate very well the dependent parameter, mw, considered in the experimental program. The results of the interpolation showed that in the first 11 h of work, the dental bur works with high efficiency, after which it can be easily decommissioned (optimizing operation, possibly constructive solutions); i.e., it should be replaced with a new one (criterion for replacing of worn dental bur).

The pore-throat radius of shale oil reservoir is extremely small, and it is difficult to accurately obtain the absolute permeability and oil-water two-phase relative permeability of actual oil reservoir through conventional core experiments. However, these parameters are very important for reservoir numerical simulation. In this paper, a method for characterizing flow parameters based on pore network model that considers differential pressure flow and diffusion flow is proposed. Firstly, a digital core was reconstructed using focused ion beam scanning electron microscopy (FIB-SEM) from the Gulong shale reservoir in the Songliao Basin, China, and a pore network model was extracted. Secondly, quasi-static single-phase flow and two-phase flow equations considering diffusion were established in the pore network model. Finally, pore throat parameters, absolute permeability, and oil-water two-phase permeability curves were calculated, respectively. The results show that the pore throat distribution of Gulong shale reservoir is mainly concentrated in the nanometer scale, the mean pore radius is 87 nm, the mean throat radius is 41 nm, and the mean coordination number is 3.97; The calculated permeability considering diffusion is 0.000124mD, which is approximately twice the permeability calculated without considering diffusion; The irreducible water saturation of the Gulong shale reservoir is approximately 0.26, and the residual oil saturation is approximately 0.73. The method proposed in this paper can provide an important approach for characterizing the flow parameters of similar shale oil reservoirs.

The paper examines common elements between Lévai’s and Milson’s potentials obtained by Liouville transformations of two rational canonical Sturm-Liouville equations (RCSLEs) with even density functions which are exactly solvable via Jacobi polynomials in a real or accordingly imaginary argument. We refer to the polynomial numerators of the given rational density function as ‘tangent polynomial’ (TP) and thereby term the aforementioned potentials as ‘e-TP’ A special attention is given to the overlap between the two potentials along symmetric curves which represent two different forms of the Ginocchio potential exactly quantized via Gegenbauer and Masjed-Jamei polynomials respectively. Our analysis reveals that the actual interconnection between Lévai’s parameters for these two rational realizations of the Ginocchio potential is much more complicated than one could expect based on the striking resemblance between two quartic equations derived by Lévai for ‘averaged’ Jacobi indexes.

A structural study of the 6√3 reconstruction conversion on 4H-SiC substrate surface in an Ar medium with a short sublimation annealing time into quasi-free epitaxial graphene by means of hydrogen intercalation between the upper layer of SiC and the adjacent reconstructed layer was carried out using the technique of reflection high-energy electron diffraction (RHEED) characterizing the surface of a crystalline material. A slight violation of the 6√3 reconstruction layer formation uniformity was found. The results of the study of the crystal structure of quasi-free graphene and single-layer graphene comprising a buffer layer formed on 4H-SiC in the traditional way in an Ar atmosphere without intercalation were compared.

Polynomial recurrence bounds for a class of stochastic differential equations with a gradient type drift and an additive Wiener process are studied without Lyapunov functions.

In response to the fire protection design challenges faced by the integrated station-city engineering under the new model of station-city fusion, such as large building volume, diverse traffic types, functional integration, spatial complexity, and inapplicable standards, this paper selects Chongqing East Station as a typical engineering case. The fire safety engineering methods and performance-based fire protection design ideas were used. The paper summarized the fire protection difficulties, such as multifunctional combination construction, large fire protection distance, large fire protection zoning area, long evacuation distance, and design of evacuation (quasi) safety zones. Combining with the actual situation of the engineering, this paper analyzed the basic technical measures taken to address these design challenges. By adopting the method of fire safety engineering, the safety of the design scheme is verified, which can provide a solution approach for the current fire protection design challenges in the integrated station-city engineering.

In this paper, a fuzzy logic-based energy management system and multi-port quasi-z-source converter are proposed that utilizes hybrid renewable energy sources. The system ensures that each energy source module can be used individually by employing fuzzy logic to define power modes. This approach also helps prevent switching losses resulting from extra switching of the source modules. Also, the proposed energy management does not have a mathematical model, so applicability is simple and it is suitable for different multiple input topologies. The Mamdani fuzzy inference system can be designed to capture the nonlinear behavior of the system because of the linguistic rules. Moreover, by adopting the quasi-z-source network to the end of the multi-port converter, the switching losses of the multi-port modules have been significantly reduced. The simulation results are obtained using MATLAB Simulink, and the experimental results are obtained by connecting the circuit to MATLAB Simulink via an Arduino Due.

Suppose G is a graph with vertex-orbits O1,1 O2, . . . ,Ot, and jOi j denotes the cardinallity of Oi. Then OG (x) = åt 2 i=1 xjOi j is called as orbit polynomial. It is well-known that this polynomial 3 has a unique positive zero d in the interval [0, 1]. The aim of this paper is to study the specific 4 properties of this polynomial and then we determine the location of this root for several classes of 5 complex networks to compare with other graphical measures. Besides, we compare the unique 6 positive zero measure with several well-known centrality graph measures.

This paper discusses a passive control issue for Nonlinear Time-Varying (NTV) systems subject to stability and attenuation performance. Based on the modeling approaches of Takagi-Sugeno (T-S) fuzzy model and the Linear Parameter-Varying (LPV) model, a Parameter-Dependent Polynomial Fuzzy (PDPF) model is constructed to represent the NTV systems. According to Parallel Distributed Compensation (PDC) concept, a parameter-dependent polynomial fuzzy controller is built to achieve robust stability and passivity of PDPF model. Furthermore, the passive theory is applied to achieve the performance constraining the disturbance effect on the PDPF systems. To develop the stability criteria, by introducing a parameter-dependent polynomial Lyapunov function, one can derive some stability conditions which belong to the term of Sum-Of-Squares (SOS) form. Based on the Lyapunov function, two stability criteria are proposed to design the corresponding PDPF controller such that the NTV system is robustly stable and passive. Finally, a numerical example is applied to demonstrate the effectiveness of the proposed stability criterion.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.

Exact sequential state estimation of orbiting objects in space can be found by predicting the state using Fokker Planck Kolmogorov Equation (FPKE) and measurement correction using Bayes’ conditional/posterior Probability Density Function (PDF). Posterior PDF can be expressed as Gaussian density expanded in terms of Hermite polynomials named as Gram Charlier Series (GCS). This research is an extension of an earlier work on second order linearized solution to nonlinear Bayesian filtering using Taylor series and third order GCS expansion of posterior PDF. In this new extension, Bayes’ posterior PDF is approximated by a mixture of GCS functions for which the parameters are propagated using linear propagation theory. The update of weights of different components of GCS mixture model uses the FPKE error as feedback to adapt for the amplitude of different GCS components while solving a quadratic programming problem earlier used for Gaussian Mixture Model (GMM) PDF. Proposed filtering method is applied on tracking of space debris. The simulation results for the filter shows performance is moderately better than single GCS filter, Extended Kalman Filter (EKF) and Gaussian Sum Filter (GSF) under space debris’ highly uncertain initial conditions and sparse measurement availability.

In this article, we analyze the thermodynamics, thermal fluctuations and quasi-normal modes of a torus-like charge AdS black hole. The parameters of a torus-like charged AdS black hole are its mass, electric charge, and cosmological constant. We used a torus-like charge AdS black hole to evaluate thermodynamics through thermal fluctuations and found that it significantly affected the corrected thermodynamic potentials. Black holes of larger radii are more stable and significant. The effect of thermal fluctuation has been investigated on the other thermodynamic potentials such as the Hemohltz free energy, Gibbs free energy, enthalpy, and specific heat, using the concept of corrected entropy. Finally, we use null geodesics to deal with quasi-normal modes. The null geodesics provide the photon sphere angular velocity and Lyapunov exponent, which are the real and imaginary components of the quasi-normal modes in the eikonal limit. With inceasing charge and photon radius, angular velocity reaches its maximum, similar to Lyapunov's exponent.

This paper presents the symmetries of differential equations associated with one-variable and Bivariate Hermite polynomials by proposing a representation of Lie algebra for these differential operators. Applying the Baker-Campbell-Hausdorff formula to these algebras, results in new relations and generating functions in one-variable and Bivariate Hermite polynomials. A general form of representation for other orthogonal polynomials such as Laguerre polynomials is introduced.

In present paper, spatial Minkowski Pythagorean Hodograph (MPH) curves are characterized with Rational Rotation Minimizing Frames (RRMFs). We define Euler-Rodrigues Frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type (n, m). Expressing the conditions provided by these curves in the form of Minkowski-Hopf map that we define, it is aimed to establish a connection with the Lorentz force which occurs during the process of Computer Numerical Control (CNC) type sinker Electronic Discharge Machines (EDMs). This approach is reinforced by split quaternion polynomials. Finally, we give conditons satisfied by MPH curves of low degree to be type (n, m) and construct illustrative examples.

In this study, we present more than 8 years of observations of the quasi-16-day wave (Q16DW) in the mesosphere and lower thermosphere (MLT) wind at middle latitudes observed by the Mengcheng (33.4°N, 116.5°E) meteor radar. The long-term variation in amplitudes calculated from the data between April 2014 and December 2022 shows enhanced wave activity during winter and early spring (near equinox) and suppressed wave activity during the summer. The Q16DWs are relatively weak in the meridional wind. During the winter months, the Q16DWs in the zonal component exhibit a burst below 85 km, and their amplitudes reach up to 10 m/s. In the early spring, the Q16DWs strengthen above 90 km with amplitudes in excess of 12 m/s. The phase differences between the zonal and meridional components of the Q16DW are, on average, slightly smaller than 90°, suggesting the existence of orthogonal relationships between them. During strong bursts, the periods of the Q16DW in winter range between 15 and 18 d, whereas in winter, the periods tend to be more diffuse. The wintertime Q16DW is amplified, on average, when the zonal wind shear peaks, suggesting that barotropic instability may be one source of Q16DW. Q16DW amplitudes exhibit considerable interannual variability; however, a relationship between the 11-year solar cycle and the Q16DW is not found.

The paper presents a new conception of quasi-distributed sensor for simultaneous measurement of several physical fields and the results of an experimental study of this sensor. A distinctive feature of the sensor defined by the sensitive RC elements connected in the original tree-like structure. The proposed is the structure of the sensor and measurement system as well as corresponding measurement algorithm. The high accuracy demonstrated by the sensor’s prototype gives possibility to effective use the proposed sensors in many technical and scientific applications.

This paper proposes a parameter coordination optimization design of Power System Stabilizer (PSS) based on an improved Quasi-Affine Transformation Evolutionary (QUATRE) algorithm to suppress low-frequency oscillation and improve the dynamic stability of power system. To begin, the Simulated Annealing (SA) algorithm randomly updates the globally optimal solution of each QUATRE iteration and matches the inferior solution with a certain probability to escape the local extreme point. This new algorithm is first applied to power system. Second, Since damping ratio is one of the criteria to measure the dynamic stability of power system, this paper sets the objective function according to the principle of maximization of damping coefficient of electromechanical mode, and uses SA-QUATRE to search a group of global optimal PSS parameter combinations to improve the stability margin of the system as much as possible. Finally, the method's rationality and validity were validated by applying it to the simulation examples of IEEE 4-machine 2-area system with different operation states. The comparison with the traditional optimization algorithm shows that the proposed method has more advantages for multi-machine PSS parameter coordination optimization, and can restrain the low-frequency oscillation of power system more effectively and enhance the system stability.

Abstract: A new method for constructing exact solutions of the General Relativity equations for a dusty matter with fractal property is proposed. This method allows to find the solution of the GR-equations in terms of matter velocities : the connection coefficients and the Ricci tensor of space-time are expressed in terms of matter velocities; the metric tensor and the matter density are found as functions of velocity from the GR-equations. The connection coefficients and the Ricci tensor are invariant with respect to the discrete scaling transformation of velocity , where is constant. Therefore, the found solution can be used to simulate the fractal properties of the cosmic web in terms of matter velocities. This solution includes isotropic and anisotropic distributions of matter density. In an isotropic case, there is a class of exact solutions including both the well-known Friedmann’s solution and a solution with a periodic distribution of the matter density in space. This last solution may be used to simulate the quasi-periodic distribution of matter in the cosmic web. It is possible that, the cosmic web and its fractal properties are the space-time primary properties. These properties are described with a deformation tensor of the space-time.

Tick-borne encephalitis virus (TBEV) is a pathogenic, enveloped, positive-stranded RNA virus in the family Flaviviridae. Structural studies of flavivirus virions have primarily focused on mosquito-borne species with only one cryo-electron microscopy (cryo-EM) structure of a tick-borne species published. Here, we present a 3.3 Å cryo-EM structure of the TBEV virion of the Kuutsalo-14 isolate, confirming the overall organisation of the virus. We observe conformational switching of the peripheral and transmembrane helices of M protein, which can explain the quasi-equivalent packing of the viral proteins and highlights their importance in stabilizing the membrane protein arrangement in the virion. The residues responsible for the M protein inter-actions are highly conserved in TBEV but not in the structurally studied Hypr strain, nor in mosquito-borne flaviviruses. These interactions may compensate for the lower number of hydrogen bonds between E proteins in TBEV compared to the mosquito-borne flaviviruses. The structure reveals two lipids bound in the E protein, which are important for virus assembly. The lipid pockets are comparable to those recently described in mosquito-borne Zika, Spondweni, Dengue, and Usutu viruses. Our results thus advance the understanding of tick-borne flavivirus architecture and virion-stabilising interactions.

The purpose of this work is to study Rossby wave parameters in total ozone over Arctic in 2000–2021. We consider the averages in the January–March period, when stratospheric trace gases (including ozone) in sudden stratospheric warming events are strongly disturbed by planetary waves. To characterize the wave parameters, we analyzed ozone data at the latitudes of 50° N (the sub-vortex area), 60° N (the polar vortex edge) and 70° N (inner region of the polar vortex). Total ozone column (TOC) measurements during 22-year time interval were used from Total Ozone Mapping Spectrometer (TOMS) / Earth Probe and Ozone Mapping Instrument (OMI) / Aura satellite observations. The total ozone zonal distribution and variations in the parameters of the Fourier spectral components with zonal wave numbers m = 1–5 are presented. Daily and interannual variations in TOC, amplitudes and phases of spectral wave components, and linear trends of the quasi-stationary wave 1 (QSW1) amplitudes are discussed. The positive TOC peaks inside the vortex in 2010 and 2018 alternate with negative ones in 2011 and 2020. The latter TOC anomalies correspond to severe depletion of stratospheric ozone over the Arctic in the strong vortex conditions due to anomalously low activity of planetary waves. Variations in TOC in sub-vortex region exhibit the statistically significant negative trend –4.8±5.4 DU decade–1 in QSW1 amplitude, while the trend is statistically insignificant at the vortex edge region due to increased TOC variability. Processes associated with polar vortex dynamics are discussed, including quasi-stationary vortex asymmetry and quasi-circumpolar migration of the wave-1 phase at the vortex edge.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

The aim of this work is to study the zonally asymmetric stratopause that occurred in the Arctic winter of 2019/2020, when the polar vortex was particularly strong and there was no sudden stratospheric warming. Aura Microwave Limb Sounder temperature data were used to analyze the evolution of the stratopause with a particular focus on its zonally asymmetric wave 1 pattern. There was a rapid descent of the stratopause height below 50 km in the anticyclone region in mid-December 2019. The descended stratopause persisted until mid-January 2020 and was accompanied by a slow descent of the higher stratopause in the vortex region. The results show that the stratopause in this event was inclined and lowered from the mesosphere in the polar vortex to the stratosphere in the anticyclone. It was found that the vertical amplification of wave 1 between 50 km and 60 km closely coincides in time with the rapid stratopause descent in the anticyclone. Overall, the behavior contrasts with the situation during sudden stratospheric warmings when the stratopause reforms at higher altitudes following wave amplification events. We link the mechanism responsible for coupling between the vertical wave 1 amplification and this form of zonally asymmetric stratopause descent to the unusual disruption of the quasi-biennial oscillation that occurred in late 2019.

The purpose of this work is to study quasi-stationary wave structure in the mid-latitude stratosphere and mesosphere (40–50°N) and its role in the formation of the annual ozone cycle. Geopotential height and ozone from Aura MLS data are used and winter climatology for January–February 2011–2020 is considered. More closely examined is the 10-degree longitude segment centered on Longfengshan Brewer station, China, and located in the region of the Aleutian Low influence associated with the quasi-stationary zonal maximum of total ozone. Annual and semi-annual oscillations in ozone were compared using units of ozone volume mixing ratio and concentration, as well as changes in ozone peak altitude and in time series of ozone at individual pressure levels between 316 hPa (9 km) and 0.001 hPa (96 km). The ozone maximum in the vertical profile is higher in volume mixing ratio (VMR) values than in concentration by about 15 km (5 km) in the stratosphere (mesosphere), in consistency with some previous studies. We found that the properties of the annual cycle are better resolved in the altitude range of the main ozone maximum: middle–upper stratosphere in VMR and lower stratosphere in concentration. Both approaches reveal SAO/AO-related changes in the of ozone peak altitudes in a range of 4–6 km during the year. In the lower-stratospheric ozone of the Longfengshan domain, an earlier development of the annual cycle takes place with a maximum in February and a minimum in August compared to spring and autumn, respectively, in zonal means. This is presumably due to the higher rate of dynamical ozone accumulation in the region of the quasi-stationary zonal ozone maximum. The “no-annual-cycle” transition layers are found in the stratosphere and mesosphere. These layers with undisturbed ozone volume mixing ratio throughout the year are of interest for more detailed future study.

New setting is introduced to study quasi-degree and quasi-co-degree arising from co-neighborhood. quasi-degree and quasi-co-degree is about a vertex which are applied into the setting of neutrosophic graphs. . The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs and star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-multipartite-neutrosophic graphs are investigated in the terms of a vertex which is called either quasi-degree or quasi-co-degree. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form quasi-degree and quasi-co-degree. Quasi-degree is a value of a vertex which is maximum amid all values of vertices which are neighbors to a fixed vertex. Quasi-co-degree is a value of an edge which is maximum amid all values of edges which are neighbors to a fixed vertex but corresponded vertex is representative for this notion. Using different values which are related to a vertex inspire us to focus on edge and vertices which are corresponded to a fixed vertex. The notion of neighborhood is used to collect either vertices are titled neighbors or edges are incident to fixed vertex. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definitions are provided. Using fixed vertex has key role to have these notions in the form of vertex or edge. The value of an edge has eligibility to call quasi-co-degree but the value of a vertex has eligibility to call quasi-degree. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connection together, open the way to define neighborhood and co-neighborhood. The maximum values in neighborhood and co-neighborhood introduces quasi-degree and quasi-co-degree, respectively. New name is chosen from degree. Since amid all vertices with different degrees, one vertex is chosen. In other words, one vertex is fixed and its degree turns out quasi-degree where two degrees could be assigned to a vertex. Degree of edges and degree of vertices. The number of edges which are incident to the vertex and the number of vertices which are neighbors to the vertex. Degree and co-degree are the notions which are transformed to use in quasi-style. Two neutrosophic values introduce two neutrosophic vertices separately in each settings. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to purse this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

In this note we study the computation of the minimum polynomial of a matrix $A$ and how we can use it for the computation of the matrix $A^n$. We also describe the form of the elements of the matrix $A^{-n}$ and we will see that it is closely related with the computation of the Drazin generalized inverse of $A$. Next we study the computation of the exponential matrix and finally we give a simple proof of the Leverrier - Faddeev algorithm for the computation of the characteristic polynomial.

Gradient based methods are popularly used in training neural networks and can be broadly categorized into first and second order methods. Second order methods have shown to have better convergence compared to first order methods, especially in solving highly nonlinear problems. The BFGS quasi-Newton method is the most commonly studied second order method for neural network training. Recent methods have shown to speed up the convergence of the BFGS method using the Nesterov’s acclerated gradient and momentum terms. The SR1 quasi-Newton method though less commonly used in training neural networks, are known to have interesting properties and provide good Hessian approximations when used with a trust-region approach. Thus, this paper aims to investigate accelerating the Symmetric Rank-1 (SR1) quasi-Newton method with the Nesterov’s gradient for training neural networks and briefly discuss its convergence. The performance of the proposed method is evaluated on a function approximation and image classification problem.

The main idea of this paper is to investigate the exact solutions and dynamic properties in optical nanofibers, which is modeled by space-time fractional perturbed nonlinear schr\"odinger equation involving Kerr law nonlinearity with conformal fractional derivative. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely the Hamiltonian is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the prior estimate of the existence of the soliton and periodic solution is established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for polynomial method.

A quasi-two-dimensional (quasi-2D) modelling approach is introduced to mimic transverse mixing of an inflow into a river from one of its banks, either an industrial outfall or a tributary. The concentrations of determinands in the inflow vary greatly from those in the river, leading to very long mixing lengths in the river downstream of the inflow location. Ideally, a two-dimensional (2D) model would be used on a small scale to capture the mixing of the two flow streams. However, for large-scale applications of several hundreds of kilometres of river length, such an approach demands too many computational resources and too much computational time, especially if the application will at some point require ensemble input from climate-change scenario data. However, a one-dimensional (1D) model with variables varying in the longitudinal flow direction but averaged across the cross-sections is too simple of an approach to capture the lateral mixing between different flow streams within the river. Hence, a quasi-2D method is proposed in which a simplified 1D solver is still applied but the discretisation of the model setup can be carried out in such a way as to enable a 2D representation of the model domain. The quasi-2D model setup also allows secondary channels and side lakes in floodplains to be incorporated into the discretisation. To show proof-of-concept, the approach has been tested on a stretch of the lower Athabasca River in Canada flowing through the oil sands region between Fort McMurray and Fort MacKay. A dye tracer and suspended sediments are the constituents modelled in this test case.

Variations in the implant thread shape and occlusal load behavior may result in significant changes in the biological and mechanical properties of dental implants and surrounding bone tissue. Most previous studies consider a single implant thread design, an isotropic bone structure, and a static occlusal load. However, the effects of different thread designs, bone material properties, and loading conditions are important concerns in clinical practice. Accordingly, the present study performs Finite Element Analysis (FEA) simulations to investigate the static, quasi-static and dynamic response of the implant and implanted bone material under various thread designs and occlusal loading directions (buccal-lingual, mesiodistal and apical). The simulations focus specifically on the von Mises stress, displacement, shear stress, compressive stress and tensile stress within the implant and the surrounding bone. The results show that the thread design and occlusal loading rate have a significant effect on the stress distribution and deformation of the implant and bone structure during clinical applications. Overall, the results provide a useful insight into the design of enhanced dental implants for an improved load transfer efficiency and success rate.

The process of senescence (aging) is largely determined by the action of wild-type genes. For most organisms, this does not reflect any adaptive function of senescence, but rather evolutionary effects of declining selection against genes with deleterious effects later in life. To understand aging requires an account of how evolutionary mechanisms give rise to pathogenic gene action and late-life disease, that integrates evolutionary (ultimate) and mechanistic (proximate) causes into a single explanation. A well-supported evolutionary explanation by G.C. Williams argues that senescence can evolve due to pleiotropic effects of alleles with antagonistic effects on fitness and late-life health (antagonistic pleiotropy, AP). What has remained unclear is how gene action gives rise to late-life disease pathophysiology. One ultimate-proximate account is T.B.L. Kirkwood’s disposable soma theory. Based on the hypothesis that stochastic molecular damage causes senescence, this reasons that aging is coupled to reproductive fitness due to preferential investment of resources into reproduction, rather than somatic maintenance. An alternative and more recent ultimate-proximate theory argues that aging is largely caused by programmatic, developmental-type mechanisms. Here ideas about AP and programmatic aging are reviewed, particularly those of M.V. Blagosklonny (the hyperfunction theory) and J.P. de Magalhães (the developmental theory), and their capacity to make sense of diverse experimental findings is described.

The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e. stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T–S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T–S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

A method for noise reduction of spectra based on fitting a multi-window model is presented. The spectrum is modeled as the sum of the polynomial background and Lorentzian peaks. This model applies to all points in the spectrum and to all window sizes. An iterative algorithm is used for fitting. Based on the initial data, the background calculated by the direct least squares method is subtracted. Positive data values ​​are inverted using the 1/x function and the same procedure is used to fit the Lorentzian peaks. The weighted sum of all windows fit containing the point to be processed is used as the result. The weighting factors are calculated by evaluating the quality of the fit. The performance of the presented method is compared with the Savitsky-Golay method and the wavelet noise reduction method. The proposed approach provides good noise reduction performance without using user-entered parameters.

A method for noise reduction of spectra based on the adaptive application of the Savitsky-Golay polynomial filter is presented. A polynomial approximation is calculated at all points of the spectrum and for all window sizes. The weighted sum of all polynomials containing the point to be processed is used as the result. The weighting factors are calculated by evaluating the quality of the fit. This paper proposes two evaluation functions. The performance of the presented method is compared with the Savitsky-Golay method and the wavelet noise reduction method. The proposed approach provides good noise reduction performance without using user-entered parameters.

Using the orbit decomposition, a new enumerative polynomial P(x) is introduced for abstract (simplicial) complexes of a given type, e.g., trees with a fixed number of vertices or triangulations of the torus with a fixed graph. The polynomial has the following three useful properties. (I) The value P(1) is equal to the total number of unlabeled complexes (of a given type). (II) The value of the derivative P'(1) is equal to the total number of nontrivial automorphisms when counted across all unlabeled complexes. (III) The integral of P(x) from 0 to 1 is equal to the total number of vertex-labeled complexes, divided by the order of the acting group. The enumerative polynomial P(x) is demonstrated for trees and then is applied to the triangulations of the torus with the vertex-labeled complete four-partite graph G = K_{2,2,2,2}, in which specific case P(x) = x^{31}. The graph G embeds in the torus as a triangulation, T(G). The automorphism group of G naturally acts on the set of triangulations of the torus with the vertex-labeled graph G. For the first time, by a combination of algebraic and symmetry techniques, all vertex-labeled triangulations of the torus (twelve in number) with the graph G are classified intelligently without using computing technology, in a uniform and systematic way. It is helpful to notice that the graph G can be converted to the Cayley graph of the quaternion group Q_8 with the three imaginary quaternions i, j, k as generators.

With the advent of submesoscale O(1km) permitting basin-scale ocean simulations, the seasonality in the mesoscale O(50km) eddies with kinetic energies peaking in summer has been commonly attributed to submesoscale eddies feeding back onto the mesoscale via an inverse energy cascade under the constraint of stratification and Earth’s rotation. In contrast, by running a 101-member, seasonally forced, three-layer quasi-geostrophic (QG) ensemble configured to represent an idealized double-gyre system of the subtropical and subpolar basin, we find that the mesoscale kinetic energy shows a seasonality consistent with the summer peak without resolving the submesoscales; by definition, a QG model only resolves small Rossby number dynamics (O(Ro)≪1) while as submesoscale dynamics are associated with O(Ro)∼1. Here, by quantifying the Lorenz cycle of the mean and eddy energy, defined as the ensemble mean and fluctuations about the mean respectively, we propose a different mechanism from the inverse energy cascade by which the stabilization and strengthening of the western-boundary current during summer due to increased stratification leads to a shedding of stronger mesoscale eddies from the separated jet. Conversely, the opposite occurs during the winter; the separated jet destablizes and results in overall lower mean and eddy kinetic energies despite the domain being more susceptible to baroclinic instability from weaker stratification.

Mesoscale eddies, the weather system of the oceans, although being on the scales of O(20-100km), have a disproportionate role in shaping the mean jets such as the separated Gulf Stream in the North Atlantic Ocean, which is on the scale of O(1000km) in the along-jet direction. With the increase in computational power, we are now able to partially resolve the eddies in basin-scale and global ocean simulations, a model resolution often referred to as mesoscale permitting. It is well known, however, that due to grid-scale numerical viscosity, mesoscale permitting simulations have less energetic eddies and consequently weaker eddy feedback onto the mean flow. In this study, we run a quasi-geostrophic model at mesoscale resolving resolution in a double gyre configuration and formulate a deterministic parametrization for the eddy rectification term of potential vorticity (PV), namely, the eddy PV flux divergence. We have moderate success in reproducing the spatial patterns and magnitude of eddy kinetic and potential energy diagnosed from the model. One novel point about our approach is that we account for non-local eddy feedbacks onto the mean flow by solving the eddy PV equation prognostically in addition to the mean flow. In return, we are able to parametrize the variability in total (mean+eddy) PV at each time step instead of solely the mean PV. A closure for the total PV is beneficial as we are able to account for both the mean state and extreme events.

The paper describes a method of solving some stochastic processes using generating functions. A general theorem of generating functions of a particular type is derived. A generating function of this type is applied to a stochastic process yielding polynomial time algorithms for certain partitions. The method is generalized to a stochastic process describing a rather general linear transform. Finally, the main idea of the method is used in deriving a theoretical polynomial time algorithm to the knapsack problem.

Current industrial trends bring new challenges in energy absorbing systems. Polymer materials as the traditional packaging material seem to be promising due to their low weight, structure and production price. Based on the review, the linear low-density polyethylene material was identified as the most promising material for absorbing impact energy. The current paper addresses the identification of the material parameters and the development of a Constitutive material model to be used in future design by virtual prototyping. The paper deals with the experimental measurement of the stress-strain relations of the linear low-density polyethylene under static and dynamic loading. The quasi-static measurement is realized in two perpendicular principal directions and is supplemented by a test measurement in the 45 degrees direction, i.e. exactly between the principal directions. The quasi-static stress-strain curves are analyzed as an initial step for dynamic strain rate dependent material behavior. The dynamic response is tested in the drop tower using a spherical impactor hitting the flat material multi-layered specimen at two different energy levels. The strain rate dependent material model is identified by optimizing the static material response obtained in the dynamic experiments. The material model is validated by the virtual reconstruction of the experiments and by comparing the numerical results to the experimental ones.

Solidification microstructure is formed under high cooling rates and temperature gradients in powder-based additive manufacturing. In this study, a non-equilibrium multi-phase field method (MPFM), which was based on a finite interface dissipation model proposed by Steinbach et. al., coupled with a CALPHAD database was developed for a multicomponent Ni alloy. A qua-si-equilibrium MPFM was also developed for comparison. Two-dimensional equiaxed micro-structural evolution for the Ni (Bal.)–Al–Co–Cr–Mo–Ta–Ti–W–C alloy was performed at various cooling rates. The temperature–γ fraction profiles obtained under 10^5 K/s using non- and qua-si-equilibrium MPFMs were in good agreement with each other. Over 10^6 K/s, the differences between non- and quasi-equilibrium methods grew as the cooling rate increased. The non-equilibrium solidification was strengthened over a cooling rate of 10^6 K/s. Colum-nar-solidification microstructural evolution was performed under cooling rates from 5×10^5 K/s to 1×10^7 K/s at various temperature gradient values under the constant interface velocity (0.1 m/s). The results showed that as the cooling rate increased, the cell space decreased in both methods, and the non-equilibrium MPFM agreed well with experimental measurements. Our results show that the non-equilibrium MPFM can simulate solidification microstructure in powder bed fusion additive manufacturing.

This is the first study to comprehensively evaluate the benefit of urban open spaces and cropland with different adjacent public facilities seen as locally undesirable (“not in my backyard,” NIMBY) or desirable (“yes in my backyard,” YIMBY). The total benefit increases or decreases for urban open space and cropland with adjacent NIMBY or YIMBY facilities in a municipality in Taiwan. The results show that for the city as a whole, the current arrangement of NIMBY and YIMBY in different zones decreases the total benefit of urban open spaces in highly urbanized zones and increases the total damage to cropland in extremely rural zones. This indicates a need to avoid further installing NIMBY or YIMBY facilities in already occupied urban open spaces. The results also demonstrate that locating NIMBY or YIMBY facilities near cropland fails to highlight the benefit of YIMBY facilities and magnifies opposition to NIMBY facilities. For individual housing units, the total damage is 1.87% of the average housing price for cropland-type open space with adjacent NIMBY or YIMBY facilities, and the total benefit is 7.43% of the average housing price for urban-type open space in a highly urbanized area. In contrast, the total benefit for open space with adjacent NIMBY or YIMBY facilities is a 2.95%-13.80% increase in the average housing price for areas with mixed urban open space and cropland.

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

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

This paper deals with a non-standard finite difference scheme defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z^(-1) which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z^(- i) by time functions which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of z^(i) at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

Waterbomb structures are origami-inspired deformable structural components used in new types of robots. They have a unique radially deployable ability that enables robots to better adapt to their environment. In this paper, we propose a series of new waterbomb structures with square, rectangle, and parallelogram base units. Through quasi-static axial and radial compression experiments and numerical simulations, we prove that the parallelogram waterbomb structure has a twist displacement mode along the axial direction. Compared with the square waterbomb structure, the proposed optimal design of the parallelogram waterbomb structure reduces the critical axial buckling load-to-weight ratio by 55.4% and increases the radial stiffness-to-weight ratio by 67.6%. The significant increase in the radial stiffness-to-weight ratio of the waterbomb structure and decrease in the critical axial buckling load-to-weight ratio make the proposed origami pattern attractive for practical robotics applications.

In this work we have critically reviewed the processes in high-temperature sublimation growth of graphene in Ar atmosphere using enclosed graphite crucible. Special focus is put on buffer layer formation and free charge carrier properties of monolayer graphene and quasi-freestanding monolayer garphene on 4H-SiC. We show that by introducing Ar at different temperatures, TAr one can shift to higher temperatures the formation of the buffer layer for both n-type and semi-insulating substrates. A scenario explaining the observed suppresed formation of buffer layer at higher TAr is proposed and discussed. Increased TAr is also shown to reduce the sp3 hybridization content and defect densities in the buffer layer on n-type conductive substrates. Growth on semi-insulating substrates results in ordered buffer layer with significantly improved structural properties, for which TAr plays only a minor role. The free charge density and mobility parameters of monolayer graphene and quasi-freestanding monolayer graphene with different TAr and different environmental treatment conditions are determined by contactless terahertz optical Hall effect. An efficient annealing of donors on and near the SiC surface takes place in intrinsic monolayer graphene grown at 2000∘C, and which is found to be independent of TAr. Higher TAr leads to higher free charge carrier mobility parameters in both intrinsically n-type and ambient p-type doped monolayer graphene. TAr is also found to have a profound effect on the free hole parameters of quasi-freestanding monolayer graphene. These findings are discussed in view of interface and buffer layer properties in order to construct a comprehensive picture of high-temperature sublimation growth and provide guidance for growth parameters optimization depending on the targeted graphene application.

Graph entropies have been used to interpret the complexity of the networks. There are various graph entropies in the literature. In this note a new graph entropy is defined which is based on the dominating sets of the graphs. Moreover the entropy of some classes of the graphs is obtained

Previous studies generally reckon that the full converter-base wind power generation (FCWG) is a ’decoupled’ power source from the grid, which hardly participates in electromechanical oscillations. However, it is found recently that strong interaction could be induced which might incur severe resonance incidents in electromechanical dynamic timescale. In this paper, the participation of FCWG in electromechanical dynamics is extensively investigated, and particularly, an unusual transition of electromechanical oscillation mode (EOM) is uncovered for the first time. The detailed mathematical models of open-loop and closed-loop power systems are firstly established, and modal analysis is employed to quantify the FCWG participation in electromechanical dynamics, with two new mode identification criteria, i.e., FCWG dynamics correlation ratio (FDCR) and quasi-electromechanical loop correlation ratio (QELCR). On this basis, the impact of different wind penetration levels and controller parameter settings on the participation of FCWG is investigated. It is revealed that if an FOM has a similar oscillation frequency to the system EOMs, there is a high possibility to induce strong interactions between FCWG dynamics and system electromechanical dynamics of the external power systems. In this circumstance, an interesting phenomenon may occur that an EOM may be dominated by FCWG dynamics, and hence is transformed into a quasi-EOM, which actively involves the participation of FCWG quasi-electromechanical state variables.

In this work, the recently proposed cracking elements method (CEM) is used for simulating the damaging processes of structures with initial imperfections. CEM is built in the framework of conventional FEM which is formally like a special type of finite element. The disconnected piecewise cracks are used for representing crack paths. Taking the advantages of CEM that both the initiations and propagations of cracks can be naturally captured, we numerically study the uni-axial compression tests of specimens with multiple joints and fissures, where the cracks may propagate from the tips, or from some other unexpected positions. Though uni-axial compression tests are considered, mainly tensile damage criteria are used in the numerical model. On one hand, the results demonstrate the robustness and effectiveness of the CEM while on the other hand, some drawbacks of the present model are demonstrated, showing the future work.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem