We apply Geometric Arbitrage Theory (GAT) to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. The remarkable aspect of the GAT is the gauge symmetry, which can be translated to the financial context, by packaging all of the asset model information into a (stochastic) principal fiber bundle. We obtain closed-form equations involving default intensities and loss-given defaults characterizing the no-free-lunch-with-vanishing-risk condition for government and corporate bond markets while relying on the spread-term structure with default intensity and loss-given default. Moreover, we provide a sufficient condition equivalent to the Novikov condition implying the absence of arbitrage. Furthermore, the generic dynamics for an isolated credit market allowing for arbitrage possibilities (and minimizing the total quantity of potential arbitrage) are derived, and arbitrage credit bubbles for both base credit assets and credit derivatives are explicitly computed. The existence of an approximated risk-neutral measure allowing the definition of fundamental values for the assets is inferred through spectral theory. We show that instantaneous bond returns are serially uncorrelated and centered, that the expected value of credit bubbles remains constant for future times where no coupons are paid, and that the variance of the market portfolio nominals is concurrent with that of the corresponding bond deflators. Full article

The extrastriate visual cortex is activated by visual regularity and generates an ERP known as the sustained posterior negativity (SPN). Spatial filter models offer a biologically plausible account of regularity detection based on the spectral properties of an image. These models are specific to reflection and therefore imply that reflectional symmetry and Glass patterns are coded by different neural populations. We utilised the SPN priming effect to probe representational overlap between reflection and Glass patterns. For each trial, participants were presented with a rapid succession of three patterns. In the Repeated condition, three reflections or three Glass patterns were presented. In the Changing condition, patterns alternated between reflection and Glass patterns. An increase in SPN amplitude (priming) was observed in both the Repeated and Changing conditions. Results indicate a greater representational overlap in the brain between reflection and Glass patterns than predicted by spatial filter models. Full article

The purpose of this article is to introduce an ordered implicit relation that can be used for the existence of fixed points of new contractions defined in cone A-metric spaces. We investigate a fixed-point method for proving the existence of Urysohn integral equation solutions. We prove an homotopy result by the application of obtained fixed-point theorem. The hypothesis is demonstrated with examples. Full article

Erdős–Faber–Lovász conjecture states that if a graph G is a union of the n edge-disjoint copies of complete graph $K_n$, that is, each pair of complete graphs has at most one shared vertex, then the chromatic number of graph G is n. In fact, we only need to consider the graphs where each pair of complete graphs has exactly one shared vertex. However, each shared vertex may be shared by more than two complete graphs. Therefore, this paper first considers the graphs where each shared vertex happens to be shared by two complete graphs, and then discusses the graphs with only one shared vertex shared by more than two complete graphs. The conjecture is correct for these two kinds of graphs in this work. Finally, the graph where each shared vertex happens to be shared by three complete graphs has been studied, and the conjecture also holds for such graphs when $n=13$. The graphs discussed in this paper have certain symmetric properties. The symmetry of graphs plays an important role in coloring. This work is an attempt to combine the symmetry of graphs with the coloring of graphs. Full article

We review the peculiarities that make neutrinos very special cosmic messengers in high-energy astrophysics, and, in particular, to provide possible indications of deviations from special relativity, as it is suggested theoretically by quantum gravity models. In this respect, we examine the effects that one could expect in the production, propagation, and detection of neutrinos, not only in the well-studied scenario of Lorentz Invariance Violation, but also in models which maintain, but deform, the relativity principle, such as those considered in the framework of Doubly Special Relativity. We discuss the challenges and the promising future prospects offered by this phenomenological window to physics beyond special relativity. Full article

Digital image steganography is the process of embedding information within a cover image in a secure, imperceptible, and recoverable way. This research extends a symmetry-adapted deep-learning approach to identify hidden patterns of images using two-dimensional convolutional neural networks (CNN). The proposed method (SteGuz) uses three CNNs to implement the different phases of the steganography process on digital image covers. SteGuz introduced a gain function, based on several image similarity metrics, to maximize the imperceptibility of the hiding process. Using 10 different pairs of cover-secret images, the performance of the proposed method was measured in terms of standard metrics such as peak signal to noise ratio (PSNR) and structured similarity index measurement (SSIM). The results showed that the proposed methodology outperformed the original method in terms of both imperceptibility and recoverability. In addition, when compared with some existing methods, SteGuz proved the outstanding performance of achieving a very high PSNR value while maintaining high accuracy of the extracted image. Full article

In this paper, we present an iteration algorithm for the pricing of American options based on reinforcement learning. At each iteration, the method approximates the expected discounted payoff of stopping times and produces those closer to optimal. In the convergence analysis, a finite sample bound of the algorithm is derived. The algorithm is evaluated on a multi-dimensional Black-Scholes model and a symmetric stochastic volatility model, the numerical results implied that our algorithm is accurate and efficient for pricing high-dimensional American options. Full article

This paper investigates the fractional local Poisson equation using the homotopy perturbation transformation method. The Poisson equation discusses the potential area due to a provided charge with the possibility of area identified, and one can then determine the electrostatic or gravitational area in the fractal domain. Elliptic partial differential equations are frequently used in the modeling of electromagnetic mechanisms. The Poisson equation is investigated in this work in the context of a fractional local derivative. To deal with the fractional local Poisson equation, some illustrative problems are discussed. The solution shows the well-organized and straightforward nature of the homotopy perturbation transformation method to handle partial differential equations having fractional derivatives in the presence of a fractional local derivative. The solutions obtained by the defined methods reveal that the proposed system is simple to apply, and the computational cost is very reliable. The result of the fractional local Poisson equation yields attractive outcomes, and the Poisson equation with a fractional local derivative yields improved physical consequences. Full article

The challenge in the field of inertial confinement fusion (ICF) research is related to the study of alternative schemes for fuel ignition on laser systems of medium and megajoule scales. At the moment, it is considered promising to use the method of shock ignition of fuel in a pre-compressed cryogenic target using a focused shock wave (shock- or self-ignition (SI) mode). To confirm the applicability of this scheme to ICF, it is necessary to develop technologies for mass-fabrication of the corresponding targets with a spherically symmetric cryogenic layer (hereinafter referred to as SI-targets). These targets have a low initial aspect ratio A_cl (A_cl = 3 and A_cl = 5) because they are expected to be more hydrodynamically stable during implosion. The paper discusses the preparation of SI-targets for laser experiments using the free-standing target (FST) layering method developed at the Lebedev Physical Institute (LPI). It is shown that, based on FST, it is possible to build a prototype layering module for in-line production of free-standing SI-targets, and the layering time, τ_form, does not exceed 30 s both for deuterium and deuterium-tritium fuel. Very short values of τ_form make it possible to obtain layers with a stable isotropic fuel structure to meet the requirements of implosion physics. Full article

In this paper, an analytical method is implemented to solve fractional-order Keller–Segel equations. The Yang transformation along with the Adomian decomposition method is implemented to obtain the solution of the given problems. The present method has an edge over other techniques as it does not need extra calculations and materials. The validity of the suggested technique is verified by considering some numerical problems. The results obtained confirm the better accuracy of the current technique. The suggested technique has a lesser number of calculations and is straightforward to apply and therefore can be applied to other fractional-order partial differential equations. Full article

A bent line expectile regression model can describe the effect of a covariate on the response variable with two different straight lines, which intersect at an unknown change-point. Due to the existence of the change-point, the objective function of the model is not differentiable with respect to the change-point, so it cannot be solved by the method of the traditional linear expectile regression model. For this model, a new estimation method is proposed by a smoothing technique, that is, using Gaussian kernel function to approximate the indicator function in the objective function. It can not only estimate the regression coefficients and change-point location simultaneously, but also have better estimation effect, which compensates for the insufficiency of the previous estimation methods. Under the given regularity conditions, the theoretical proofs of the consistency and asymptotic normality of the proposed estimators are derived. There are two parts of numerical simulations in this paper. Simulation 1 discusses various error distributions at different expectile levels under different conditions, the results show that the mean values of the biases of the estimation method in this paper, and other indicators, are very small, which indicates the robust property of the new method. Simulation 2 considers the symmetric and asymmetric bent lien expectile regression models, the results show that the estimated values of the estimation method in this paper are similar to the true values, which indicates the estimation effect and large sample performance of the proposed method are excellent. In the application research, the method in this paper is applied to the Arctic annual average temperature data and the Nile annual average flow data. The research shows that the standard errors of the estimation method in this paper are very similar to 0, indicating that the parameter estimation accuracy of the new method is very high, and the location of the change-point can be accurately estimated, which further confirms that the new method is effective and feasible. Full article

Unsteady axial symmetric flows of an incompressible and electrically conducting Casson fluid over a vertical cylinder with time-variable temperature under the influence of an external transversely magnetic field are studied. The thermal transport is described by a generalized mathematical model based on the time-fractional differential equation of Cattaneo’s law with the Caputo derivative. In this way, our model is able to highlight the effect of the temperature gradient history on heat transport and fluid motion. The generalized mathematical model of thermal transport can be particularized to obtain the classical Cattaneo’s law and the classical Fourier’s law. The comparison of the three models could offer the optimal model of heat transport. The problem solution has been determined in the general case when cylinder surface temperature is described by a function f(t); therefore, the obtained solutions can be used to study different convective flows over a cylinder. In the particular case of surface temperature varying exponentially in time, it is found that fractional models lead to a small temperature rise according to the Cattaneo model. Full article

In this paper, we consider a class of jerk equations which are invariant to inversion. We discuss the stability and some bifurcations of the considered equation. In addition, we construct integrable deformations in order to stabilize some equilibrium points. Finally, we introduce a piecewise chaotic system which belongs to the considered class of jerk equations. Full article

The main focus of this paper is to develop certain types of fundamental theorems using q, $q(\alpha )$, and h difference operators. For several higher order difference equations, we get two forms of solutions: one is closed form and another is summation form. However, most authors concentrate only on the summation part. This motivates us to develop closed-form solutions, and we succeed. The key benefit of this research is finding the closed-form solutions for getting better results when compared to the summation form. The symmetric difference operator is the combination of forward and backward difference symmetric operators. Using this concept, we employ the closed and summation form for q, $q(\alpha )$, and h difference symmetric operators on polynomials, polynomial factorials, logarithmic functions, and products of two functions that act as a solution for symmetric difference equations. The higher order fundamental theorems of q and $q(\alpha )$ are difficult to find when the order becomes high. Hence, by inducing the h difference symmetric operator in q and $q(\alpha )$ symmetric operators, we find the solution easily and quickly. Suitable examples are given to validate our findings. In addition, we plot the figures to examine the value stability of q and $q(\alpha )$ difference equations. Full article

The results of the model analysis of hadron femtoscopic correlations and factorial moments of particle multiplicity in heavy ion collisions for the energy range of the Beam Energy Scan (BES) program at RHIC and future NICA collider are presented. For this purpose, the simulation of Au+Au collisions at center-of-mass energies 7.7 and 11.5 GeV per nucleon pair using the UrQMD, vHLLE+UrQMD (with the crossover and first-order equation of states), and HYDJET++ event generators was performed. The sensitivity of pion and kaon correlation radii and the dependence of the factorial moments on heavy ion beam energy to quark–hadron phase transition details was studied. In addition, the possible influence of some relevant detector effects on the corresponding experimental observables is discussed. Full article

In this paper, by applying the Lie group method and the direct symmetry method, Lie algebras of the Benjiamin Ono equation are obtained, and we find that results of the two methods are same. Based on the Lie algebra, Lie symmetry groups, relationships between new solutions and old solutions, two kinds of ODEs as symmetry reductions are obtained. Making use of the power series method, the exact power series solution of the Benjiamin Ono equation has been derived. We also give the conservation laws of Benjiamin Ono equation by means of Ibragimovs new conservation Theorem. Full article

In a previous paper, we used a classification of the self adjoint extensions, also called self-adjoint determinations, of the differential operator $-d^2/d{x}^2$ in order to obtain the whole list of Supersymmetric (SUSY) partners of those selfadjoint determinations for which the ground state has strictly positive energy. The existence of self adjoint determinations with a ground state of zero or even negative energy is a proved fact. In this paper, we analyze the possibility of constructing SUSY partners for those determinations. We also study those cases for which the ground state has a degeneracy, the study of their SUSY partners should be analyzed separately. So far, we have studied those determinations having an exactly solvable eigenvalue problem. On the present study, we also included some comments in relation to determinations not exactly solvable from this point of view. In addition, the use of self adjoint determinations for which the ground state wave function has nodes (zeroes) produces formal SUSY partners with a finite number of eigenvalues or even with a purely continuous spectrum. We give some worked examples of these situations. Full article

In the paper, we determine the period of an n-dimensional nonlinear dynamical system by using a derived formula in an (n + 1)-dimensional augmented space. To form a periodic motion, the periodic conditions in the state space and nonlinear first-order differential equations constitute a special periodic problem within a time interval with an unknown length. Two periodic problems are considered: (a) boundary values are given and (b) boundary values are unknown. By using the shape functions, a boundary shape function method (BSFM) is devised to obtain an initial value problem with the initial values of the new variables given. The unknown terminal values of the new variables and period are determined by two iterative algorithms for the case (a) and one iterative algorithm for the case (b). The periodic solutions obtained from the BSFM satisfy the periodic conditions automatically. For the numerical example, the computed order of convergence displays the merit of the BSFM. For the sake of comparison, the iterative algorithms based on the shooting method for cases (a) and (b) were developed by directly implementing the Poincaré map into the fictitious time-integration method to determine the period. The BSFM is better than the shooting method in terms of convergence speed, accuracy, and stability. Full article

Riga surface can be utilized to reduce the pressure drag and the friction of the submarine by stopping the separation of the boundary layer as well as by moderating turbulence production. Therefore, the current symmetry of the work investigates the slip impacts on mixed convection flow containing water-based hybrid Ag-MgO nanoparticles over a vertical expanding/contracting Riga wedge. In this analysis, a flat surface, wedge, and stagnation point are also discussed. A Riga surface is an actuator that contains electromagnetic where a span-wise array associated with the permanent magnets and irregular electrodes accumulated on a smooth surface. A Lorentz force is incorporated parallel to the surface produced by this array which eases exponentially normal to the surface. Based on the considered flow symmetry, the physical scenario is initially modeled in the appearance of partial differential equations which are then rehabilitated into a system of ordinary differential equations by utilizing the pertinent similarity variables. A bvp4c solver is engaged to acquire the numerical solution. The flow symmetry and the influences of pertaining parameters involved in the problem are investigated and are enclosed in graphical form. The findings confirm that the velocity reduces, and temperature enhances due to nanoparticle volume fraction. A modified Hartmann number increases the velocity and diminishes the temperature. Moreover, the suction parameter enhances the velocity profiles and reduces the dimensionless temperature profiles. The heat transfer gradually increases by diminishing the contracting parameter and increasing the expanding parameter. Full article

By using the symmetry of the Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and a logarithmic Sobolev inequality for the Dunkl transform. Combining these inequalities, we obtain a new, short proof for Heisenberg-type uncertainty principles in the Dunkl setting. Moreover, by combining Nash’s inequality, Carlson’s inequality and Sobolev’s embedding theorems for the Dunkl transform, we prove new uncertainty inequalities involving the $L^{\infty }$-norm. Finally, we obtain a logarithmic Sobolev inequality in $L^p$-spaces, from which we derive an $L^p$-Heisenberg-type uncertainty inequality and an $L^p$-Nash-type inequality for the Dunkl transform. Full article

Coronavirus disease (COVID-19), which affects the whole world, continues to spread. This disease has infected and killed millions of people worldwide. To limit the rate of spread of the disease, early detection should be provided and then the infected person should be quarantined. This paper proposes a Deep Learning-based application for early and accurate diagnosis of COVID-19. Compared to other studies, this application’s biggest difference and contribution are that it uses Tree Seed Algorithm (TSA)-optimized Artificial Neural Networks (ANN) to classify deep architectural features. Previous studies generally use fully connected layers for end-to-end learning classification. However, this study proves that even relatively simple AlexNet features can be classified more accurately with the TSA-ANN structure. The proposed hybrid model provides diagnosis with 98.54% accuracy for COVID-19 disease, which shows asymmetric distribution on Computed Tomography (CT) images. As a result, it is shown that using the proposed classification strategy, the features of end-to-end architectures can be classified more accurately. Full article

Etoposide is a widely used anticancer drug that targets type II topoisomerases, including topoisomerase IIα (TOP2A). TOP2A is a nuclear enzyme involved in regulating DNA topology through a double-strand passage mechanism. TOP2A is a homodimeric enzyme with two symmetrical active sites formed by residues from either half of the dimer. Both active sites cleave DNA, forming an enzyme-bound, double-stranded DNA break. Etoposide acts by binding in the active site between the ends of cleaved DNA, preventing the enzyme from ligating the DNA. In the present study, biochemical and structural data are used to examine the mechanism of etoposide resistance found with specific point mutations in TOP2A. Mutations near the active site (D463A, G534R, R487K), along with some outside of the active site (ΔA429 and P716L), are examined. We hypothesize that changes in the coordination of DNA cleavage results from mutations that impact symmetrical relationships in the active site and surrounding regions. In some cases, we report the first data on purified versions of these enzymes. Based upon our results, both local and long-distance factors can impact etoposide action and may indicate interdependent relationships in structure and function. Full article

The E-Bayesian estimation approach has been presented for estimating the parameter and/or reliability characteristics of various models. Several investigations in the literature have considered this method under the assumption that just one parameter is unknown. So, based on Type-II censoring, this study proposes for the first time an effort to use the E-Bayesian estimation approach to estimate the full model parameters as well as certain related functions such as the reliability and hazard rate functions. To illustrate this purpose, we apply the proposed technique to the two-parameter generalized inverted exponential distribution which can be considered to be one of the most flexible asymmetrical probability distributions. Moreover, the E-Bayesian method, maximum likelihood, and Bayesian estimation approaches are also considered for comparison purposes. Under the assumption of independent gamma priors, the Bayes and E-Bayes estimators are developed using the symmetrical squared error loss function. Due to the complex form of the joint posterior density, two approximation techniques, namely the Lindley and Markov chain Monte Carlo methods, are considered to carry out the Bayes and E-Bayes estimates and also to construct the associate credible intervals. Monte Carlo simulations are performed to assess the performance of the proposed estimators. To demonstrate the applicability of the proposed methods in real phenomenon, one real data set is analyzed and it shows that the proposed method is effective and easy to operate in a real-life scenario. Full article

Automatic control of intelligent vehicles depends heavily on accurate lane-level location information. The traditional digital map cannot meet the automatic driving requirements, and it is very difficult for lane-level road maps (LRMs) to achieve a good balance between the representation accuracy and data storage volume. To tackle this problem, we obtain the recursive definition of a lane line by analyzing road lanes using the fractal geometry theory. Subsequently, we construct a recursive feedback system and model it. On this basis, an autonomous storage optimization LRM generation strategy based on cascaded NURBS is devised. According to the input data density, this framework generates an LRM with the minimum data storage volume within the error constraint. It is mainly composed of two modules: (1) a random fractal and (2) an adaptive iteration memory optimizer, based on cascaded NURBS error feedback. First, the whole lane is divided into several meta lane line modules. Second, data sampling/interpolation is carried out iteratively according to the NURBS fitting error and symmetry of road geometry. In this way, the storage space used to store lane lines and other information is automatically optimized. Last, a simulation experiment is carried out by using a dataset obtained from a park. The simulation results show that the proposed method can achieve high accuracy and high storage efficiency. Under the constraint of a 0.1 m curve fitting error, the average memory demand of the lane line elements is less than 2.4 bytes/m. Full article

It is extremely frequent for systems to fail in their demanding operating environments in many real-world contexts. When systems reach their lowest, highest, or both extreme operating conditions, they usually fail to perform their intended functions, which is something that researchers pay little attention to. The goal of this paper is to develop inference for multi-reliability using unit alpha power exponential distributions for stress–strength variables based on the progressive first failure. As a result, the problem of estimating the stress–strength function R, where X, Y, and Z come from three separate alpha power exponential distributions, is addressed in this paper. The conventional methods, such as maximum likelihood for point estimation, Bayesian and asymptotic confidence, boot-p, and boot-t methods for interval estimation, are also examined. Various confidence intervals have been obtained. Monte Carlo simulations and real-world application examples are used to evaluate and compare the performance of the various proposed estimators. Full article

A method is proposed for determining the number of damaged stator windings in the presence of an asymmetric power supply system for an induction electric motor based on the Park vector hodograph. As a result of the experiments on the simulation model, it was found that with the symmetry of the system of supply voltages and stator windings, the hodograph of the Park vector describes a circle; in all other cases it is an ellipse. It has been established that the presence of asymmetry in the supply voltage system is indicated by the angle of inclination of the ellipse, and the indicator of the presence of the asymmetry of the stator windings is the angle of ellipticity. In order to identify the presence of asymmetry of the stator windings in the conditions of asymmetry of the supply voltage system, an algorithm for recalculating the ellipse parameters for the condition of the symmetry of the supply voltage system was proposed. Recalculation errors did not exceed 6%. It has been established that the dependence of the increment of the amplitudes of the phase and angles of the phase currents of the stator on the number of damaged turns of the stator winding is linear. Based on this fact, an algorithm for determining the number of damaged turns was proposed. The results of this work can be used to build systems for diagnosing the interturn short circuit of the stator of an induction electric motor built into the drive. Full article

An investigation on the flutter derivative prediction of flat steel box girders is carried out based on CFD simulations. Firstly, by taking the flat steel girder section of Qingshan Yangtze River Bridge as the basic section and considering its width and height as the design variables of cross-section shape, the design domain of cross-section shape is defined by controlling the possible variation range of cross-section design variables. A small number of cross-sections are selected for the calculation of aerodynamic forces by CFD simulations. Secondly, according to the aerodynamic lift and moment time-histories of these steel box girders, of which the flutter derivatives are identified by the least square method. Next, these selected cross-section shape design parameters are used as the inputs, and the flutter derivatives obtained from CFD simulations are used as the outputs to train Kriging models. To improve the prediction accuracy of Kriging models, a modified method of model training is presented. Finally, the flutter derivatives of other cross-sections in the design domain are predicted by using the trained Kriging models, and the predicted flutter derivatives are verified by CFD simulations. It is feasible to directly predict the flutter derivatives of steel box girders by Kriging models. Full article

The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform (QFT), we first derive a variation on the Heisenberg-type uncertainty principle related to this transformation. We then consider the general two-sided quaternion linear canonical transform. It may be considered as an extension of the two-sided quaternion linear canonical transform. Based on an orthogonal plane split, we develop the convolution theorem that associated with the general two-sided quaternion linear canonical transform and then derive its correlation theorem. We finally discuss how to apply general two-sided quaternion linear canonical transform to study the generalized swept-frequency filters. Full article

Genetic regulation of organisms involves complicated RNA–RNA interactions (RRIs) among messenger RNA (mRNA), microRNA (miRNA), and long non-coding RNA (lncRNA). Detecting RRIs is beneficial for discovering biological mechanisms as well as designing new drugs. In recent years, with more and more experimentally verified RNA–RNA interactions being deposited into databases, statistical machine learning, especially recent deep-learning-based automatic algorithms, have been widely applied to RRI prediction with remarkable success. This paper first gives a brief introduction to the traditional machine learning methods applied on RRI prediction and benchmark databases for training the models, and then provides a recent methodology overview of deep learning models in the prediction of microRNA (miRNA)–mRNA interactions and long non-coding RNA (lncRNA)–miRNA interactions. Full article

Bin packing is a typical optimization problem with many real-world application scenarios. In the online bin packing problem, a sequence of items is revealed one at a time, and each item must be packed into a bin immediately after its arrival. Inspired by duality in optimization, we proposed pattern-based adaptive heuristics for the online bin packing problem. The idea is to predict the distribution of items based on packed items, and to apply this information in packing future arrival items in order to handle uncertainty in online bin packing. A pattern in bin packing is a combination of items that can be packed into a single bin. Patterns selected according to past items are adopted and periodically updated in scheduling future items in the algorithm. Symmetry in patterns and the stability of patterns in the online bin packing problem are discussed. We have implemented the algorithm and compared it with the Best-Fit in a series of experiments with various distribution of items to show its effectiveness. Full article

For now, the open humidification method is applied in the tobacco bulk curing barn, which has some disadvantages, such as the loss of the oil content and aroma components of the tobacco leaves and the waste heat loss of the exhaust air flow. In this context, a tobacco bulk curing barn with totally closed hot air circulation is designed to perfect the curing quality of tobacco and avoid the loss of residual heat in the bulk curing barn. Meanwhile, due to the balance and symmetry of input and output of the curing barn temperature, according to the law of conservation of energy, a mathematical model of the temperature control system of the closed hot air circulation tobacco bulk curing barn is established, and the temperature transfer function of the system is obtained. On this basis, 10 algorithms are used to optimize the full closed hot air circulation tobacco bulk curing barn temperature control system PID parameters. The result of the sobol sequence seeker optimization algorithm (SSOA) is better than the other algorithms. So, the PID control strategy based on the SSOA is used to simulate and experiment the temperature control system of tobacco bulk curing barn. The simulation and experimental results show that for the tobacco bulk curing barn temperature control system, the sobol sequence seeker optimization algorithm PID control has better dynamic characteristics compared with fuzzy PID control, and the temperature control system of tobacco bulk curing barn has fast adjustment and small overshoot. Therefore, the new baking barn with proper PID parameters can improve the tobacco’s curing quality and save energy by reducing the residual heat. Full article

The presence of a hidden or dark sector of phenomena that relates either weakly or in a particular way to Standard Model (SM) fields has theoretical as well as experimental support. Many extensions of SM use hidden or dark sector states to propose a specific candidate for dark matter (DM) in the universe or to explain astrophysical findings. If such a family of Beyond the Standard Model (BSM) particles and interactions exists, it is possible that they will be discovered experimentally at CERN’s Large Hadron Collider (LHC, $\sqrt{s}\cong$ 14 TeV) and future High Energy Colliders. The primary emphasis is on a few examples of searches undertaken at the LHC that are relevant to Higgs Hidden–Dark Sector Physics. These studies’ existing constraints and prospects are also reported. Full article

Modeling competing failure modes is an important problem in engineering and survival analyses. Competing failure modes are partially observed in many applications and often pose a modeling challenge. This study discusses the inference for partially observed failure modes assuming a Burr XII distribution. In particular, we consider two failure modes, and the failure time data are collected under a hybrid type I censoring scheme. The model parameters are estimated using maximum likelihood and Bayesian methods under a symmetric squared error loss function, whereas the intervals estimation is done with three methods: asymptotic and credible confidence intervals. Besides a simulation study, a real-life data set is taken from individuals who live in an environment with several diseases to present the utility of the work. Additionally, a simulation study is constructed to measure and compare different estimation methods. Full article

We show that the results we had previously obtained on diagonals of 9- and 10-parameter families of rational functions in three variables $x$, $y$, and $z$, using creative telescoping, yielding modular forms expressed as pullbacked ${}_2{F}_1$ hypergeometric functions, can be obtained much more efficiently by calculating the $j$-invariant of an elliptic curve canonically associated with the denominator of the rational functions. These results can be drastically generalized by changing the parameters into arbitrary rational functions of the product $p=xyz$. In other cases where creative telescoping yields pullbacked ${}_2{F}_1$ hypergeometric functions, we extend this algebraic geometry approach to other families of rational functions in three or more variables. In particular, we generalize this approach to rational functions in more than three variables when the denominator can be associated to an algebraic variety corresponding to products of elliptic curves, or foliations in elliptic curves. We also extend this approach to rational functions in three variables when the denominator is associated with a genus-two curve such that its Jacobian is a split Jacobian, corresponding to the product of two elliptic curves. We sketch the situation where the denominator of the rational function is associated with algebraic varieties that are not of the general type, having an infinite set of birational automorphisms. We finally provide some examples of rational functions in more than three variables, where the telescopers have pullbacked ${}_2{F}_1$ hypergeometric solutions, because the denominator corresponds to an algebraic variety that has a selected elliptic curve. Full article

We study a D-dimensional Einstein–Gauss–Bonnet model which includes the Gauss–Bonnet term, the cosmological term $\Lambda$ and two non-zero constants: ${\alpha }_1$ and ${\alpha }_2$. Under imposing the metric to be diagonal one, we find cosmological type solutions with exponential dependence of three scale factors in a variable u, governed by three non-coinciding Hubble-like parameters: $H\ne 0$, $h_1$ and $h_2$, obeying $mH+k_1{h}_1+k_2{h}_2\ne 0$, corresponding to factor spaces of dimensions $m>1$, $k_1>1$ and $k_2>1$, respectively, and depending upon sign parameter $\epsilon =\pm 1$, where $\epsilon =1$ corresponds to cosmological case and $\epsilon =-1$—to static one). We deal with two cases: (i) $m<k_1<k_2$ and (ii) $1<k_1=k_2=k$, $k\ne m$. We show that in both cases the solutions exist if $\epsilon \alpha =\epsilon {\alpha }_2/{\alpha }_1>0$ and $\alpha \Lambda >0$ satisfy certain (upper and lower) bounds. The solutions are defined up to solutions of a certain polynomial master equation of order four (or less), which may be solved in radicals. In case (ii), explicit solutions are presented. In both cases we single out stable and non-stable solutions as $u\to \pm \infty$. The case $H=0$ is also considered. Full article

Based on the design of a prefabricated pervious composite cement concrete pavement slab, the interface properties and bending deformation properties of basalt pervious concrete (BPC) and PVA fiber base impervious concrete (PFBIC) composite specimens were studied. The effects of the different interfacial agents on the interfacial bonding performance were compared using a splitting tensile strength test and interfacial shear test. The deformation capacity of the composite specimens under bending load was tested using a three-point bending test, with the symmetry of the model considered and compared with the deformation capacity of the BPC specimen and PFBIC specimen. The results showed that the compressive strength of the BPC prepared using an orthogonal test reached 40.30 MPa, while the permeability coefficient was 2.41 mm/s. Different interface treatment processes determine the interface bonding properties. The best interface treatment method can induce the interface bonding strength to be higher than the strength of the BPC matrix itself, while the interface transition zone matrix will be denser without obvious microscopic defects. Under the bending tensile load, the ultimate bending stress reached 6.58 MPa and the maximum deflection in the midspan was 0.81 mm. As a protective layer, the PFBIC can alleviate the disadvantage of the insufficient strength of the BPC and can improve the bending ultimate bearing capacity of the BPC-PFBIC through its own stiffness. Full article

The calculus in the absence of limits is known as quantum calculus. With a difference operator, it substitutes the classical derivative, which permits dealing with sets of functions that are non-differentiations. The theory of integral inequality in quantum calculus is a field of mathematics that has been gaining considerable attention recently. Despite the fact of its application in discrete calculus, it can be applied in fractional calculus as well. In this paper, some new Anderson type q-integral and h-integral inequalities are given using a Feng Qi integral inequality in quantum calculus. These findings are highly beneficial for basic frontier theories, and the techniques offered by technology are extremely useful for those who can stimulate research interest in exploring mathematical applications. Due to the interesting properties in the field of mathematics, integral inequalities have a tied correlation with symmetric convex and convex functions. There exist strong correlations and expansive properties between the different fields of convexity and symmetric function, including probability theory, convex functions, and the geometry of convex functions on convex sets. The main advantage of these essential inequalities is that they can be converted into time-scale calculus. This kind of inevitable inequality can be very helpful in various fields where coordination plays an important role. Full article

Hyperspectral image (HSI) analysis has become one of the most active topics in the field of remote sensing, which could provide powerful assistance for sensing a larger-scale environment. Nevertheless, a large number of high-correlation and redundancy bands in HSI data provide a massive challenge for image recognition and classification. Hybrid Rice Optimization (HRO) is a novel meta-heuristic, and its population is approximately divided into three groups with an equal number of individuals according to self-equilibrium and symmetry, which has been successfully applied in band selection. However, there are some limitations of primary HRO with respect to the local search for better solutions and this may result in overlooking a promising solution. Therefore, a modified HRO (MHRO) based on an opposition-based-learning (OBL) strategy and differential evolution (DE) operators is proposed for band selection in this paper. Firstly, OBL is adopted in the initialization phase of MHRO to increase the diversity of the population. Then, the exploitation ability is enhanced by embedding DE operators into the search process at each iteration. Experimental results verify that the proposed method shows superiority in both the classification accuracy and selected number of bands compared to other algorithms involved in the paper. Full article

We provide arguments for the use of the rational form of unitarization, its relation with the diffraction peak shrinkage and asymptotics of the inelastic cross-section. The particular problems of the Regge model and the exponential form of unitarization with a factorized eikonal are discussed as well. A central role belongs to the asymptotic amplitude factorization resulting from Mandelstam analyticity and its symmetry over the scattering variables. Full article

Metal rolls in a non-ferrous-metal manufacturing workshop manifest the characteristics of symmetry, multiple scales and mutual covering, which poses great challenges for metal roll detection. To solve this problem, firstly, an efficient attention mechanism algorithm named ECLAM (efficient capture location attendant model) is proposed for capturing spatial position features efficiently, to obtain complete location information for metal rolls in a complex environment. ECLAM can improve the ability to extract the spatial features of backbone networks and reduce the influence of the non-critical background. In addition, in order to give feature maps a larger receptive field and improve the weight of location information in multi-scale feature maps, a nonlinear feature fusion module named LFFM (location feature fusion module) is used to fuse two adjacent feature images. Finally, a multi-scale object detection network named L-MSNet (location-based multi-scale object detection network) based on the combination of ECLAM and LFFM is proposed and used to accurately detect multi-scale metal rolls. In the experiments, multi-scale metal roll images are collected from an actual non-ferrous-metal manufacturing workshop. On this basis, a pixel-level image dataset is constructed. Comparative experiments show that, compared with other object detection methods, L-MSNet can detect multi-scale metal rolls more accurately. The average accuracy is improved by 2% to 5%, and the average accuracy of small and medium-sized objects is also significantly improved by 3% to 6%. Full article

We perform a Lie analysis of $(2k+2)$th-order difference equations and obtain $k+1$ non-trivial symmetries. We utilize these symmetries to obtain their exact solutions. Sufficient conditions for convergence of solutions are provided for some specific cases. We exemplify our theoretical analysis with some numerical examples. The results in this paper extend to some work in the recent literature. Full article

Symmetry, such as structural symmetry, color symmetry and so on, plays an important role in graph coloring. In this paper, we use structural symmetry and color symmetry to study the characterization for the neighbor-distinguishing index of planar graphs. Let G be a simple graph with no isolated edges. The neighbor-distinguishing edge coloring of G is a proper edge coloring of G such that any two adjacent vertices admit different sets consisting of the colors of their incident edges. The neighbor-distinguishing index ${\chi }_a^{\prime }\left(G\right)$ of G is the smallest number of colors in such an edge coloring of G. It was conjectured that if G is a connected graph with at least three vertices and $G\ne C_5$, then ${\chi }_a^{\prime }\left(G\right)\le \Delta +2$. In this paper, we show that if G is a planar graph with maximum degree $\Delta \ge 13$, then $\Delta \le {\chi }_a^{\prime }\left(G\right)\le \Delta +1$, and, further, ${\chi }_a^{\prime }\left(G\right)=\Delta +1$ if and only if G contains two adjacent vertices of maximum degree. Full article

Ceratophyllum is an ancient and phylogenetically isolated angiosperm lineage. Comparisons between Ceratophyllum and other angiosperms are hampered by uncertainty in inferring organ homologies in this genus of specialized aquatics. Interpretation of shoot morphology is especially problematic in Ceratophyllum. Each node has several leaf-like appendages interpreted as verticillate leaves, modified parts of one and the same leaf or parts of two leaves under decussate phyllotaxis. Vegetative branches are axillary, but reproductive units (interpreted as flowers or inflorescences) are commonly viewed as developing from collateral accessory buds. We studied shoot development in Ceratophyllum submersum, C. tanaiticum, and C. demersum using scanning electron microscopy to clarify shoot morphology and branching patterns. Our data support the idea that the phyllotaxis is essentially decussate with appendages of stipular origin resembling leaf blades. We conclude that a leaf axil of Ceratophyllum possesses a complex of two serial buds, the lower one producing a vegetative branch and the upper one developing a reproductive unit. The reproductive unit is congenitally displaced to the subsequent node, a phenomenon known as concaulescence. Either member of the serial bud complex may be absent. There is a theory based on a synthesis of molecular and morphological data that Chloranthaceae are the closest extant relatives of Ceratophyllum. Serial buds and concaulescence are known in Hedyosmum (Chloranthaceae). Our new interpretation facilitates morphological comparisons between Hedyosmum and Ceratophyllum. Full article

Hemimandibular hyperplasia (HH) and elongation (HE) are the most common pathologies present in the mandible. Presented condylar hyperplasias have their own radiological and clinical features. In most cases, patients suffer from various forms of malocclusion. From a total of 150 asymmetrical jaw radiographs evaluated, 46 were evaluated and included in this study. A retrospective study on the data of 46 selected patients treated, diagnosed, and consulted from various forms of mandibular and skeletal asymmetry based on routine diagnostic panoramic radiographs evaluated typical and atypical radiological and anatomical symptoms of condylar hyperplasia. The presented evaluation focused on mandibular, maxillary, and other bones, in order to distinguish condylar hyperplasia from other forms of mandibular asymmetry. The degree of maxillary downward growth followed by the occurrence of an open bite on the affected side estimate the degree/presence or cessation of growth in the affected condyle. Mandibular asymmetry with incisor teeth inclination remains the most typical characteristic of condylar hyperplasia. Increased height of mandibular ramus differentiates between condylar hyperplasia and elongation, which also influences the position of the inferior alveolar nerve. Mentioned symptoms, described as the acronym “Go Moira!”, are useful in a quick and simple “glimpse of an eye” differential diagnostic approach. It is possible to quickly and accurately establish the first diagnosis simply by a careful evaluation of patients’ panoramic radiographs. Full article

Quantum Gaussian states play a fundamental role in quantum communications and in quantum information. This paper deals with the implementation of multimode, and particularly of two-mode Gaussian unitaries and Gaussian states with primitive components (phase shifters, single-mode real squeezers, displacements, and beam splitters). The architecture thus obtained allows one to obtain an insight into the physical meaning of each variable involved. Moreover, following the implementation architecture, it is possible to formulate an easy algebra (radical free) for the main operations and transformations of Gaussian states. Full article

In a foregoing paper, the author reported evidence that the multi-spin-axis magnetic structure proposed in 1964 by van Laar is realized in antiferromagnetic CoO. Within the nonadiabatic Heisenberg model, this tetragonal body-centered structure is generated by atomic-like electrons in a special magnetic band of CoO, a mechanism that may emerge only because the nonadiabatic Heisenberg model goes beyond the adiabatic approximation. The present paper compares the band structures of the transition-metal monoxides NiO, CoO, FeO, and MnO, and shows that only CoO possesses a magnetic band which may produce the tetragonal magnetic structure proposed by van Laar. The magnetic bands of the other monoxides, NiO, FeO, and MnO, are clearly related to the monoclinic base-centered magnetic structure experimentally observed in these materials. Full article

The energy harvested by an ocean wave energy converter (WEC) can be enhanced by a well-designed wave-by-wave control strategy. One of such superior control methods is model predictive control (MPC), which is a nonlinear constrained optimization control strategy. A limitation of the classical MPC algorithm is its requirement of an accurate WEC dynamic model for real-time implementation. This article overcomes this challenge by proposing a data-driven MPC scheme for wave energy converters. The data-based WEC model is developed by a Gaussian process (encompassing mean predictions and symmetric uncertainties) for a more accurate description of nonlinear and unmodeled system dynamics. A cross-entropy solver for data-driven MPC is employed for rapid, high-performance results, which samples trajectories from Gaussian distributions based on the concept of the symmetry principle. The proposed strategy is verified numerically by simulations which demonstrate its superior performance over a classical complex-conjugate controller. Full article

The forthcoming property of this manuscript is its calculating of the goal of norms and lower bounds of matrix operators taken from the weighted sequence space ${\ell }_p(w)$ onto a novel one defined in the present article as the generalized Fibonacci weighted difference sequence space. In this process, first of all the Fibonacci difference matrix $\tilde{F}(r,s)$ and the space composed of sequences of which $\tilde{F}(r,s)$-transforms lie in ${\ell }_p(\tilde{w})$, where $r,s\in \mathbb{R}$ are defined. Additionaly, since the seminormed space ${\ell }_p(\tilde{w},\tilde{F}(r,s))$ has the absolute homogeneous property, the topological characteristics on it are distributed symmetrically everywhere in the space. Full article

Simulation-based optimization design is becoming increasingly important in engineering. However, carrying out multi-point, multi-variable, and multi-objective optimization work is faced with the “Curse of Dimensionality”, which is highly time-consuming and often limited by computational burdens as in aerodynamic optimization problems. In this paper, an active subspace dimensionality reduction method and the adaptive surrogate model were proposed to reduce such computational costs while keeping a high precision. In this method, the active subspace dimensionality reduction technique, three-layer radial basis neural network approach, and polynomial fitting process were presented. For the model evaluation, a NASA standard test function problem and RAE2822 airfoil drag reduction optimization were investigated in the experimental design problem. The efficacy of the method was proved by both the experimental examples in which the adaptive surrogate model in a dominant one-dimensional active subspace is given and the optimization efficiency was improved by two orders. Furthermore, the results show that the constructed surrogate model reduced dimensionality and alleviated the complexity of conventional multivariate surrogate modeling with high precision. Full article

The high-order harmonic generation (HHG) in ZnO is investigated by numerically solving semiconductor Bloch equations (SBEs), which can be explained well by a four-step model. In this model, preacceleration is the first step, in which the electron is accelerated in the valence band until it reaches the point of the minimum band gap. To prove the existence of the preacceleration process, SBE-based k-resolved harmonic spectra and the transient conduction-band population are presented. The results show that the contribution of crystal-momentum channels away from the minimum band gap via preacceleration is non-negligible. Furthermore, the X-shaped distribution in the k-resolved spectra can be described well by the preacceleration process. Based on the above analysis, we can conclude that the preacceleration process plays an important role in HHG. Full article