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In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) of normalized holomorphic and bi-univalent functions in the open unit disk U, which are associated with the Bazilevič functions and the λ-pseudo-starlike functions as well as the Horadam polynomials. We estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to the holomorphic and bi-univalent function class, which we introduce here. Furthermore, we establish the Fekete-Szegö inequality for functions in the family SWΣ(δ,γ,λ,s,t,q,r). Relevant connections of some of the special cases of the main results with those in several earlier works are also pointed out. Our usage here of the basic or quantum (or q-) extension of the familiar Hurwitz-Lerch zeta function Φ(z,s,a) is justified by the fact that several members of this family of zeta functions possess properties with local or non-local symmetries. Our study of the applications of such quantum (or q-) extensions in this paper is also motivated by the symmetric nature of quantum calculus itself.

Graph connectivity theory is important in network implementations, transportation, network routing and network tolerance, among other things. Separation edges and vertices refer to single points of failure in a network, and so they are often sought-after. Chandramouleeswaran et al. introduced the principle of semiring valued graphs, also known as S-valued symmetry graphs, in 2015. Since then, works on S-valued symmetry graphs such as vertex dominating set, edge dominating set, regularity, etc. have been done. However, the connectivity of S-valued graphs has not been studied. Motivated by this, in this paper, the concept of connectivity in S-valued graphs has been studied. We have introduced the term vertex S-connectivity and edge S-connectivity and arrived some results for connectivity of a complete S-valued symmetry graph, S-path and S-star. Unlike the graph theory, we have observed that the inequality for connectivity κ(G)≤κ′(G)≤δ(G) holds in the case of S-valued graphs only when there is a symmetry of the graph as seen in Examples 3–5.

In order to improve the alignment stability of the air vibration isolation device of a high-powered main engine, we established a mechanical model for the air vibration isolation system and analyzed the alignment deviation of the device and the vibration decoupling conditions of the system. Additionally, an optimized design method for the dual-direction support of the air vibration isolators positioned symmetrically on the main engine was proposed. The resultant design showed that when compared to the conventional inclined support of air springs for the main engines onboard ships, the dual-direction support design proposed in this paper for air vibration isolation could eliminate the adverse effect of the output torque reaction on the alignment of the main engine and decouple the system to reduce the number of peaks in the frequency response of vertical force transmission. The optimized design could effectively improve the alignment performance of the device for tilted or swinging operating conditions and maintain the good alignment stability of the device when a single vertical support air spring fails. A single vertical support air spring failure mainly affects the stability of the main engine under the reaction of the output torque, especially the air springs arranged in the corner, while the air springs arranged in the middle have no effect. The optimized design could also improve the vibration isolation performance. This is important for the design of air spring vibration isolation devices for high power density main engines.

Let G be a graph with no isolated vertex and let N(v) be the open neighbourhood of v∈V(G). Let f:V(G)→{0,1,2} be a function and Vi={v∈V(G):f(v)=i} for every i∈{0,1,2}. We say that f is a strongly total Roman dominating function on G if the subgraph induced by V1∪V2 has no isolated vertex and N(v)∩V2≠∅ for every v∈V(G)\V2. The strongly total Roman domination number of G, denoted by γtRs(G), is defined as the minimum weight ω(f)=∑x∈V(G)f(x) among all strongly total Roman dominating functions f on G. This paper is devoted to the study of the strongly total Roman domination number of a graph and it is a contribution to the Special Issue “Theoretical Computer Science and Discrete Mathematics” of Symmetry. In particular, we show that the theory of strongly total Roman domination is an appropriate framework for investigating the total Roman domination number of lexicographic product graphs. We also obtain tight bounds on this parameter and provide closed formulas for some product graphs. Finally and as a consequence of the study, we prove that the problem of computing γtRs(G) is NP-hard.

Both poor cooling methods and complex heat dissipation lead to prominent asymmetry in transformer temperature distribution. Both the operating life and load capacity of a power transformer are closely related to the winding hotspot temperature. Realizing accurate prediction of the hotspot temperature of transformer windings is the key to effectively preventing thermal faults in transformers, thus ensuring the reliable operation of transformers and accurately predicting transformer operating lifetimes. In this paper, a hot spot temperature prediction method is proposed based on the transformer operating parameters through the particle filter optimization support vector regression model. Based on the monitored transformer temperature, load rate, transformer cooling type, and ambient temperature, the hotspot temperature of a dry-type transformer can be predicted by a support vector regression method. The hyperparameters of the support vector regression are dynamically optimized here according to the particle filter to improve the optimization accuracy. The validity and accuracy of the proposed method are verified by comparing the proposed method with a traditional support vector regression method based on the real operating data of a 35 kV dry-type transformer.

One of the most intriguing issues in the mathematical theory of the stationary Navier–Stokes equations is the regularity of weak solutions. This problem has been deeply investigated for homogeneous fluids. In this paper, the regularity of the solutions in the case of not constant viscosity is analyzed. Precisely, it is proved that for a bounded domain Ω⊂R2, a weak solution u∈W1,q(Ω) is locally Hölder continuous if q=2, and Hölder continuous around x, if q∈(1,2) and |μ(x)−μ0| is suitably small, with μ0 positive constant, an analogous result holds true for a bounded domain Ω⊂Rn(n&gt, 2) and weak solutions in W1,n/2(Ω).

Deep neural networks have been applied for speech enhancements efficiently. However, for large variations of speech patterns and noisy environments, an individual neural network with a fixed number of hidden layers causes strong interference, which can lead to a slow learning process, poor generalisation in an unknown signal-to-noise ratio in new inputs, and some residual noise in the enhanced output. In this paper, we present a new approach for the hearing impaired based on combining two stages: (1) a set of bandpass filters that split up the signal into eight separate bands each performing a frequency analysis of the speech signal, (2) multiple deep denoising autoencoder networks, with each working for a small specific enhancement task and learning to handle a subset of the whole training set. To evaluate the performance of the approach, the hearing-aid speech perception index, the hearing aid sound quality index, and the perceptual evaluation of speech quality were used. Improvements in speech quality and intelligibility were evaluated using seven subjects of sensorineural hearing loss audiogram. We compared the performance of the proposed approach with individual denoising autoencoder networks with three and five hidden layers. The experimental results showed that the proposed approach yielded higher quality and was more intelligible compared with three and five layers.

In a regular (d,k)-CNF formula, each clause has length k and each variable appears d times. A regular structure such as this is symmetric, and the satisfiability problem of this symmetric structure is called the (d,k)-SAT problem for short. The regular exact 2-(d,k)-SAT problem is that for a (d,k)-CNF formula F, if there is a truth assignment T, then exactly two literals of each clause in F are true. If the formula F contains only positive or negative literals, then there is a satisfiable assignment T with a size of 2n/k such that F is 2-exactly satisfiable. This paper introduces the (d,k)-SAT instance generation model, constructs the solution space, and employs the method of the first and second moments to present the phase transition point d* of the 2-(d,k)-SAT instance with only positive literals. When d&lt, d*, the 2-(d,k)-SAT instance can be satisfied with high probability. When d&gt, d*, the 2-(d,k)-SAT instance can not be satisfied with high probability. Finally, the verification results demonstrate that the theoretical results are consistent with the experimental results.

In this paper, the inverse gamma power series (IGPS) class of distributions asymmetric is introduced. This family is obtained by compounding inverse gamma and power series distributions. We present the density, survival and hazard functions, moments and the order statistics of the IGPS. Estimation is first discussed by means of the quantile method. Then, an EM algorithm is implemented to compute the maximum likelihood estimates of the parameters. Moreover, a simulation study is carried out to examine the effectiveness of these estimates. Finally, the performance of the new class is analyzed by means of two asymmetric real data sets.

Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. In robotics, obstacle avoidance is an essential ability for distance sensor-based robots. This type of robot has axisymmetrically distributed distance sensors to acquire obstacle distance, so the state is symmetrical. Training the control policy with a reinforcement learning method is a trend. Considering the complexity of environments, such as narrow paths and right-angle turns, robots will have a better ability if the control policy can control the steering direction and speed simultaneously. This paper proposes the multi-dimensional action control (MDAC) approach based on a reinforcement learning technique, which can be used in multiple continuous action space tasks. It adopts a hierarchical structure, which has high and low-level modules. Low-level policies output concrete actions and the high-level policy determines when to invoke low-level modules according to the environment’s features. We design robot navigation experiments with continuous action spaces to test the method’s performance. It is an end-to-end approach and can solve complex obstacle avoidance tasks in navigation.

The positive definiteness of even-order weakly symmetric tensors plays important roles in asymptotic stability of time-invariant polynomial systems. In this paper, we establish two Brauer-type Z-eigenvalue inclusion sets with parameters by Z-identity tensors, and show that these inclusion sets are sharper than existing results. Based on the new Z-eigenvalue inclusion sets, we propose some sufficient conditions for testing the positive definiteness of even-order weakly symmetric tensors, as well as the asymptotic stability of time-invariant polynomial systems. The given numerical experiments are reported to show the efficiency of our results.

Recently in various theoretical works, path-breaking progress has been made in recovering the well-known Page Curve of an evaporating black hole with Quantum Extremal Islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of Quantum Extremal Islands in the negative (or positive) Cosmological Constant with radiation in the background of Friedmann-Lema$\hat{i}$tre-Robertson-Walker (FLRW) space-time i.e the presence and absence of islands in anti-de Sitter and the de Sitter spacetime having SO(2, 3) and SO(1, 4) isometries respectively. Without using any explicit details of any gravity model, we study the behaviour of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above-mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, Out-of-Time Ordered Correlators, and entanglement entropy of the modes of the squeezed state, in different parameter spaces, we conclude the non-universality of these measures. Their remarkably different features in the different parameter spaces suggest their dependence on the parameters of the model under consideration., Comment: 75 pages, 29 figures, 4 tables, Dr. Sayantan Choudhury would like to dedicate this work to his lovable father and prime inspiration Professor Manoranjan Choudhury who recently have passed away due to COVID 19. Updated and revised version, Accepted for publication in Symmetry (section: Physics and Symmetry/Asymmetry, Special issue: Manifest and Hidden Symmetries in Field and String Theories)

The ordered structures of polynomial idempotent algebras over max-plus algebra are investigated in this paper. Based on the antisymmetry, the partial orders on the sets of formal polynomials and polynomial functions are introduced to generate two partially ordered idempotent algebras (POIAs). Based on the symmetry, the quotient POIA of formal polynomials is then obtained. The order structure relationships among these three POIAs are described: the POIA of polynomial functions and the POIA of formal polynomials are orderly homomorphic, the POIA of polynomial functions and the quotient POIA of formal polynomials are orderly isomorphic. By using the partial order on formal polynomials, an algebraic method is provided to determine the upper and lower bounds of an equivalence class in the quotient POIA of formal polynomials. The criterion for a formal polynomial to be the minimal element of an equivalence class is derived. Furthermore, it is proven that any equivalence class is either an uncountable set with cardinality of the continuum or a finite set with a single element.

The numerical hydroelastic method is used to study the structural response of a hexagon enclosed platform (HEP) of flexible module rigid connector (FMRC) structure that can provide life accommodation, ship berthing and marine supply for ships sailing in the deep ocean. Six trapezoidal floating structures constitute the HEP structure so that it is a symmetrical very large floating structure (VLFS). The HEP has the characteristics of large area and small depth, so its hydroelastic response is significant. Therefore, this paper studies the structural responses of a hexagon enclosed platform of FMRC structure in waves by means of a 3D potential-flow hydroelastic method based on modal superposition. Numerical models, including the hydrodynamic model, wet surface model and finite element method (FEM) model, are established, a rigid connection is simulated by many-point-contraction (MPC) and the number of wave cases is determined. The load and structural response of HEP are obtained and analyzed in all wave cases, and frequency-domain hydroelastic calculation and time-domain hydroelastic calculation are carried out. After obtaining a number of response amplitude operators (RAOs) for stress and time-domain stress histories, the mechanism of the HEP structure is compared and analyzed. This study is used to guide engineering design for enclosed-type ocean platforms.

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

Let G be a simple graph of order n with vertex set V(G) and edge set E(G), and let k be an integer such that 1≤k≤n−1. The k-token graph G{k} of G is the graph whose vertices are the k-subsets of V(G), where two vertices A and B are adjacent in G{k} whenever their symmetric difference A▵B, defined as (A∖B)∪(B∖A), is a pair {a,b} of adjacent vertices in G. In this paper we study the Hamiltonicity of the k-token graphs of some join graphs. We provide an infinite family of graphs, containing Hamiltonian and non-Hamiltonian graphs, for which their k-token graphs are Hamiltonian. Our result provides, to our knowledge, the first family of non-Hamiltonian graphs for which it is proven the Hamiltonicity of their k-token graphs, for any 2&lt, k&lt, n−2.

Normality is the most commonly used mathematical supposition in data modeling. Nonetheless, even based on the law of large numbers (LLN), normality is a strong presumption, given that the presence of asymmetry and multi-modality in real-world problems is expected. Thus, a flexible modification in the normal distribution proposed by Elal-Olivero adds a skewness parameter called Alpha-skew-normal (ASN) distribution, which enables bimodality and fat-tail, if needed, although it is sometimes not trivial to estimate this third parameter (regardless of the location and scale). This work analyzed seven different statistical inferential methods towards the ASN distribution on synthetic data and historical data of water flux from 21 rivers (channels) in the Atacama region. Moreover, the contributions of this paper are related to the estimations of probability surrounding rivers’ flux levels in the surroundings of Copiapó city, which is the most economically important city of the third Chilean region and is known to be located in one of the driest areas on Earth (excluding the North and the South Poles). The results show the competitiveness of the MPS and RADE methods with respect to the MLE method, as well as their excellent performance.

In this paper, using weight functions as well as employing various techniques from real analysis, we establish a few equivalent conditions of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel. To prove our results, we also deduce a few equivalent conditions of two kinds of Hardy-type integral inequalities with a homogeneous kernel in the form of applications. We additionally consider operator expressions. Analytic inequalities of this nature and especially the techniques involved have far reaching applications in various areas in which symmetry plays a prominent role, including aspects of physics and engineering.

In this paper, we first prove that any atom of a permutation obtained by the super-shuffle product of two permutations can only consist of some complete atoms of the original two permutations. Then, we prove that the super-shuffle product and the cut-box coproduct on permutations are compatible, which makes it a bialgebra. As this algebra is graded and connected, it is a Hopf algebra.

In this paper, we provide several bounds for the modulus of the complex Čebyšev functional. Applications to the trapezoid and mid-point inequalities, that are symmetric inequalities, are also provided.

In this paper, the goal is to revolve around discussing the stability of the Method of Fundamental Solutions (MFS) for the use case of wave-current interactions. Further, the reliability of Generating-Absorbing Boundary Conditions (GABCs) applied to the wave-current interactions is investigated using the Method of Fundamental Solutions (MFS), in a Numerical Wave Tank (NWT) within the potential theory where the main regular manifestations are the periodicity, and symmetry of traveling waves. Besides, the investigations cover different aspects of currents (coplanar current, without current, and opposing current), and also different water depths. Furthermore, the accuracy and stability of the numerical method (MFS) used in this work is evaluated for different locations and numbers of source points.

Algebraic structures in which the property of commutativity is substituted by the mediality property are introduced. We consider (associative) graded algebras and instead of almost commutativity (generalized commutativity or $\varepsilon$-commutativity) we introduce almost mediality ("commutativity-to-mediality" ansatz). Higher graded twisted products and "deforming" brackets (being the medial analog of Lie brackets) are defined. Toyoda's theorem which connects (universal) medial algebras with abelian algebras is proven for the almost medial graded algebras introduced here. In a similar way we generalize tensor categories and braided tensor categories. A polyadic (non-strict) tensor category has an $n$-ary tensor product as an additional multiplication with $n-1$ associators of the arity $2n-1$ satisfying a $\left( n^{2}+1\right) $-gon relation, which is a polyadic analog of the pentagon axiom. Polyadic monoidal categories may contain several unit objects, and it is also possible that all objects are units. A new kind of polyadic categories (called "groupal") is defined: they are close to monoidal categories, but may not contain units: instead the querfunctor and (natural) functorial isomorphisms, the quertors, are considered (by analogy with the querelements in $n$-ary groups). The arity-nonreducible $n$-ary braiding is introduced and the equation for it is derived, which for $n=2$ coincides with the Yang-Baxter equation. Then, analogously to the first part of the paper, we introduce "medialing" instead of braiding and construct "medialed" polyadic tensor categories., Comment: 42 pages, 20 diagrams, amslatex

In this paper, we aim to reveal the influence of fault fracture zones on the stability of submarine tunnels and the surrounding rock under different water and drainage measures. Firstly, four typical working conditions of submarine tunnels intersecting with fault fracture zones were selected. On the basis of the typical cross section of the intersections of submarine tunnels and faults, they were divided into four working conditions. Then, the displacement and plastic zones of the surrounding rock of the tunnel were studied, and the stability of the rock surrounding the submarine tunnel was discussed. This research structure indicates that the bending moment and axial force of the lining structure of the submarine tunnel increase with increasing sealing degree, but the safety factor exhibits a downward trend. When the fault fracture zone goes through the section above the tunnel axis, the bending moment and axial force at the lining vault are greater than the other working conditions, and the displacement of the surrounding rock at the vault and spandrel is prominent. When the fault fracture zone completely passes through the tunnel, the safety factor of the lining structure is at its lowest, and the displacement of the surrounding rock at the arch waist develops laterally. When the fault fracture zone passes through the part below the tunnel axis, the arch foot displacement converges significantly, and the surrounding rock displacement exhibits a downward inclination. In addition, the plastic zone is mainly developed in the arch and the shoulder. These research results provide a reliable reference for tunnel design and excavation support.

This paper proposes a phase-field model for the lattice Boltzmann method which has discretized symmetrical directions of velocities in a cartesian grid, to simulate the soluble surfactant in a Multicomponent multiphase system. Despite other existing phase-field models following Langmuir relation, the interfacial tension can be calculated analytically in this proposed model. Parameters playing roles in the models and controlling the surfactant’s strength and interaction with other phases are obtained directly from a given initial interfacial tension and bulk surfactant. Consequently, there is no further need for trial-and-error simulations, and a real system, e.g., oil-water-surfactant, can be simulated with given initial parameters. The model is validated with the analytical result for a planar oil–water-surfactant system. Furthermore, the method for reobtaining numerical interfacial tension for five different cases is tested and compared with the given initial values for an oil droplet surrounded by water and surfactant. The results show that the obtained interfacial tension from the method is in good agreement with the given initial interfacial tension. Furthermore, the spurious velocity of the model is calculated and seen that the magnitude of spurious velocities is proportional to interfacial tension.

Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks is in dimension 13. In the first part of this paper, we shall prove that two arrangements of smooth compact manifolds of any dimension that are connected through smooth functions are homeomorphic. In the second part, we prove this in the affine case in dimension 4.

The existence of cavities in shallow ground strata is one of the important causes of urban road collapse under the disturbance of tunnel excavation. Thus, this paper discusses the convergent deformation mode of ellipsoidal cavities. To this end, the convergent deformation of a cavity and the overall displacement of a tunnel were comprehensively examined. A three-dimensional symmetrical calculation model of the soil deformation under the combined action of the tunnel and the cavity was also established. Moreover, three-dimensional formulas for calculating the soil deformation and the surface settlement of the upper part of the tunnel and the cavity were derived. The influence of the different positions of the cavity on the surface settlement of the upper part of the tunnel was also examined. Further, the change in the soil settlement with the direction of the tunnel excavation and the depth of burial of the cavity was analyzed. The results show that the calculated settlement curves are consistent with the ones reported in the related literature. The cavity can also aggravate the surface settlement and deformation of the soil caused by the tunnel excavation. When the cavity is directly above the tunnel, the surface settlement curve is symmetrically distributed. As the position of the cavity changes, the overall settlement curve shifts to the direction of the cavity, showing asymmetry. Additionally, along the x-axis direction of the shielded tunnel, the surface settlement gradually increases to a limit value with a decrease in x and slowly declines to zero as x rises. Finally, along the depth of burial of the cavity, the settlement of the soil continues to enlarge, also, the growth rate of the soil settlement continues to increase further at positions closer to the cavity and the tunnel until it reaches a critical maximum.

The effect of external and internal elastic strain fields on the anisotropic diffusion of radiation defects (RDs) can be taken into account if one knows the dipole tensor of saddle-point configurations of the diffusing RDs. It is usually calculated by molecular statics, since the insufficient accuracy of the available experimental techniques makes determining it experimentally difficult. However, for an RD with multiple crystallographically non-equivalent metastable and saddle-point configurations (as in the case of di-interstitials), the problem becomes practically unsolvable due to its complexity. In this paper, we used a different approach to solving this problem. The molecular dynamics (MD) method was used to calculate the strain dependences of the RD diffusion tensor for various types of strain states. These dependences were used to determine the dipole tensor of the effective RD saddle-point configuration, which takes into account the contributions of all real saddle-point configurations. The proposed approach was used for studying the diffusion characteristics of RDs, such as di-interstitials in FCC copper (used in plasma-facing components of fusion reactors under development). The effect of the external elastic field on the MD-calculated normalized diffusion tensor (ratio of the diffusion tensor to a third of its trace) of di-interstitials was fully consistent with analytical predictions based on the kinetic theory, the parameters of which were the components of the dipole tensors, including the range of non-linear dependence of the diffusion tensor on strains. The results obtained allowed for one to simulate the anisotropic diffusion of di-interstitials in external and internal elastic fields, and to take into account the contribution of di-interstitials to the radiation deformation of crystals. This contribution can be significant, as MD data on the primary radiation damage in copper shows that ~20% of self-interstitial atoms produced by cascades of atomic collisions are combined into di-interstitials.

This paper deals with an optimization problem for a nonlinear integro-differential system that describes the unsteady plane motion of an incompressible viscoelastic fluid of Jeffreys–Oldroyd type within a fixed bounded region subject to the no-slip boundary condition. Control parameters are included in the initial condition. The objective of control is to match the velocity field at the final time with a prescribed target field. The control model under consideration is interpreted as a continuous evolution system in an infinite-dimensional Hilbert space. The existence of at least one optimal control is proved under inclusion-type constraints for admissible controls.

This paper addresses the projection pursuit problem assuming that the distribution of the input vector belongs to the flexible and wide family of multivariate scale mixtures of skew normal distributions. Under this assumption, skewness-based projection pursuit is set out as an eigenvector problem, described in terms of the third order cumulant matrix, as well as an eigenvector problem that involves the simultaneous diagonalization of the scatter matrices of the model. Both approaches lead to dominant eigenvectors proportional to the shape parametric vector, which accounts for the multivariate asymmetry of the model, they also shed light on the parametric interpretability of the invariant coordinate selection method and point out some alternatives for estimating the projection pursuit direction. The theoretical findings are further investigated through a simulation study whose results provide insights about the usefulness of skewness model-based projection pursuit in the statistical practice.

Symmetry is repetitive self-similarity. We proved the stability problem by replicating the well-known Cauchy equation and the well-known Jensen equation into two variables. In this paper, we proved the Hyers-Ulam stability of the bi-additive functional equation f(x+y,z+w)=f(x,z)+f(y,w) and the bi-Jensen functional equation 4fx+y2,z+w2=f(x,z)+f(x,w)+f(y,z)+f(y,w).

In this paper, we address the estimation of the parameters for a two-parameter Kumaraswamy distribution by using the maximum likelihood and Bayesian methods based on simple random sampling, ranked set sampling, and maximum ranked set sampling with unequal samples. The Bayes loss functions used are symmetric and asymmetric. The Metropolis-Hastings-within-Gibbs algorithm was employed to calculate the Bayes point estimates and credible intervals. We illustrate a simulation experiment to compare the implications of the proposed point estimators in sense of bias, estimated risk, and relative efficiency as well as evaluate the interval estimators in terms of average confidence interval length and coverage percentage. Finally, a real-life example and remarks are presented.

The synthesis and optimization of quantum circuits are essential for the construction of quantum computers. This paper proposes two methods to reduce the quantum cost of 3-bit reversible circuits. The first method utilizes basic building blocks of gate pairs using different Toffoli decompositions. These gate pairs are used to reconstruct the quantum circuits where further optimization rules will be applied to synthesize the optimized circuit. The second method suggests using a new universal library, which provides better quantum cost when compared with previous work in both cost015 and cost115 metrics; this proposed new universal library “Negative NCT” uses gates that operate on the target qubit only when the control qubit’s state is zero. A combination of the proposed basic building blocks of pairs of gates and the proposed Negative NCT library is used in this work for synthesis and optimization, where the Negative NCT library showed better quantum cost after optimization compared with the NCT library despite having the same circuit size. The reversible circuits over three bits form a permutation group of size 40,320 (23!), which is a subset of the symmetric group, where the NCT library is considered as the generators of the permutation group.

In this paper, we consider the inverse scattering problem and, in particular, the problem of reconstructing the spectral density associated with the Yukawian potentials from the sequence of the partial-waves fℓ of the Fourier–Legendre expansion of the scattering amplitude. We prove that if the partial-waves fℓ satisfy a suitable Hausdorff-type condition, then they can be uniquely interpolated by a function f˜(λ)∈C, analytic in a half-plane. Assuming also the Martin condition to hold, we can prove that the Fourier–Legendre expansion of the scattering amplitude converges uniformly to a function f(θ)∈C (θ being the complexified scattering angle), which is analytic in a strip contained in the θ-plane. This result is obtained mainly through geometrical methods by replacing the analysis on the complex cosθ-plane with the analysis on a suitable complex hyperboloid. The double analytic symmetry of the scattering amplitude is therefore made manifest by its analyticity properties in the λ- and θ-planes. The function f(θ) is shown to have a holomorphic extension to a cut-domain, and from the discontinuity across the cuts we can iteratively reconstruct the spectral density σ(μ) associated with the class of Yukawian potentials. A reconstruction algorithm which makes use of Pollaczeck and Laguerre polynomials is finally given.

In this paper, we present the integrable deformations method for a maximally superintegrable system. We alter the constants of motion, and using these new functions, we construct a new system which is an integrable deformation of the initial system. In this manner, new maximally superintegrable systems are obtained. We also consider the particular case of Hamiltonian mechanical systems. In addition, we use this method to construct some deformations of an arbitrary system of first-order autonomous differential equations.

In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation operators. For this new class of approximation operators, we present a Korovkin type theorem and a Grüss-Voronovskaya type theorem, and also study the rate of its convergence. Moreover, we derive several results which are related to the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators in the weighted spaces. Finally, we prove some shape-preserving properties for the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators.

In this paper, we consider a new type of Proinov contraction on the setting of a symmetrical abstract structure, more precisely, the metric space. Our goal is to expand on some results from the literature using admissible mappings and the concept of E-contraction. The considered examples indicate the validity of the obtained results.

The soliton waves’ physical behavior on the pseudo spherical surfaces is studied through the analytical solutions of the nonlinear (1+1)–dimensional Kaup–Kupershmidt (KK) equation. This model is named after Boris Abram Kupershmidt and David J. Kaup. This model has been used in various branches such as fluid dynamics, nonlinear optics, and plasma physics. The model’s computational solutions are obtained by employing two recent analytical methods. Additionally, the solutions’ accuracy is checked by comparing the analytical and approximate solutions. The soliton waves’ characterizations are illustrated by some sketches such as polar, spherical, contour, two, and three-dimensional plots. The paper’s novelty is shown by comparing our obtained solutions with those previously published of the considered model.

The intensity variation of the South Asian high (SAH) plays an important role in the formation and extinction of many kinds of mesoscale systems, including tropical cyclones, southwest vortices in the Asian summer monsoon (ASM) region, and the precipitation in the whole Asia Europe region, and the SAH has a vortex symmetrical structure, its dynamic field also has the symmetry form. Not enough previous studies focus on the variation of SAH daily intensity. The purpose of this study is to establish a day-to-day prediction model of the SAH intensity, which can accurately predict not only the interannual variation but also the day-to-day variation of the SAH. Focusing on the summer period when the SAH is the strongest, this paper selects the geopotential height data between 1948 and 2020 from NCEP to construct the SAH intensity datasets. Compared with the classical deep learning methods of various kinds of efficient time series prediction model, we ultimately combine the Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) method, which has the ability to deal with the nonlinear and unstable single system, with the Permutation Entropy (PE) method, which can extract the SAH intensity feature of IMF decomposed by CEEMDAN, and the Convolution-based Gated Recurrent Neural Network (ConvGRU) model is used to train, test, and predict the intensity of the SAH. The prediction results show that the combination of CEEMDAN and ConvGRU can have a higher accuracy and more stable prediction ability than the traditional deep learning model. After removing the redundant features in the time series, the prediction accuracy of the SAH intensity is higher than that of the classical model, which proves that the method has good applicability for the prediction of nonlinear systems in the atmosphere.

This paper investigates the leader-following regional multiple-bipartite consensus problems of networked Lagrangian systems (NLSs) in coopetition networks. Our framework expands the application scopes of traditional regional consensus in cooperative networks. With the aid of a novel auxiliary variable embedded in the control protocols, the final states of NLSs are guaranteed to realise multi-regional symmetry in the constructed multiple symmetric regions. By utilising the characteristic of acyclic topology in the structurally balanced graph, the stability of the closed system is performed by perturbation analysis theory, nonlinear control theory, functional analysis theory, and so on. Finally, the effectiveness of our approach is verified by numerical simulations.

Establishing a node importance ranking is a problem that has attracted the attention of many researchers in recent decades. For unweighted networks where the edges do not have any attached weight, many proposals have been presented, considering local or global information of the networks. On the contrary, it occurs in undirected edge-weighted networks, where the proposals to address this problem have been more scarce. In this paper, a ranking method of node importance for undirected and edge-weighted is provided, generalizing the measure of line importance (DIL) based on the centrality degree proposed by Opsahl. The experimentation was done on five real networks and the results illustrate the benefits of our proposal.

This paper is concerned with variational methods applied to functionals of the calculus of variations in a multi-dimensional case. We prove the existence of multiple critical points for a symmetric functional whose principal part is not subjected to any upper growth condition. For this purpose, nonsmooth variational methods are applied.

In many situations of survival and reliability test, the withdrawal of units from the test is pre-planned in order to to free up testing facilities for other tests, or to save cost and time. It is known that several risk factors (RiFs) compete for the immediate failure cause of items. In this paper, we derive an inference for a competing risks model (CompRiM) with a generalized type II progressive hybrid censoring scheme (GeTy2PrHCS). We derive the conditional moment generating functions (CondMgfs), distributions and confidence interval (ConfI) of the scale parameters of exponential distribution (ExDist) under GeTy2PrHCS with CompRiM. A real data set is analysed to illustrate the validity of the method developed here. From the data, it can be seen that the conditional PDFs of MLEs is almost symmetrical.

One of the most intriguing phenomenons related to deep learning is the so-called adversarial examples. These samples are visually equivalent to normal inputs, undetectable for humans, yet they cause the networks to output wrong results. The phenomenon can be framed as a symmetry/asymmetry problem, whereby inputs to a neural network with a similar/symmetric appearance to regular images, produce an opposite/asymmetric output. Some researchers are focused on developing methods for generating adversarial examples, while others propose defense methods. In parallel, there is a growing interest in characterizing the phenomenon, which is also the focus of this paper. From some well known datasets of common images, like CIFAR-10 and STL-10, a neural network architecture is first trained in a normal regime, where training and validation performances increase, reaching generalization. Additionally, the same architectures and datasets are trained in an overfitting regime, where there is a growing disparity in training and validation performances. The behaviour of these two regimes against adversarial examples is then compared. From the results, we observe greater robustness to adversarial examples in the overfitting regime. We explain this simultaneous loss of generalization and gain in robustness to adversarial examples as another manifestation of the well-known fitting-generalization trade-off.

Let S and T be two numerical semigroups. We say that T is an I(S)-semigroup if T\{0} is an ideal of S. Given k a positive integer, we denote by ∆(k) the symmetric numerical semigroup generated by {2, 2k + 1}. In this paper we present a formula which calculates the number of I(S)- semigroups with genus g(∆(k)) + h for some nonnegative integer h and which we will denote by i(∆(k), h). As a consequence, we obtain that the sequence {i(∆(k), h)}h∈N is never decreasing. Besides, it becomes stationary from a certain term., FQM-298 and FQM-343 (Junta de Andalucia/Feder), Project MTM2017-84890-P

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana–Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag–Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.

The aim of the present paper is to provide oscillation conditions for fourth-order damped differential equations with advanced term. By using the Riccati technique, some new oscillation criteria, which ensure that every solution oscillates, are established. In fact, the obtained results extend, unify and correlate many of the existing results in the literature. Furthermore, two examples with specific parameter values are provided to confirm our results.

A 2D mechanical metamaterial exhibiting perfectly auxetic behavior, i.e., Poisson’s ratio of −1, is proposed in this paper drawing upon inspiration from an Islamic star formed by circumferential arrangement of eight squares, such as the one found at the exterior of the Ghiyathiyya Madrasa in Khargird, Iran (built 1438–1444 AD). Each unit of the metamaterial consists of eight pairs of pin-jointed Y-shaped rigid elements, whereby every pair of Y-elements is elastically restrained by a spiral spring. Upon intermediate stretching, each metamaterial unit resembles the north dome of Jameh Mosque, Iran (built 1087–1088 AD), until the attainment of the fully opened configuration, which resembles a structure in Agra, India, near the Taj Mahal. Both infinitesimal and finite deformation models of the effective Young’s modulus for the metamaterial structure were established using strain energy approach in terms of the spiral spring stiffness and geometrical parameters, with assumptions to preserve the eight-fold symmetricity of every metamaterial unit. Results indicate that the prescription of strain raises the effective Young’s modulus in an exponential manner until full extension is attained. This metamaterial is useful for applications where the overall shape of the structure must be conserved in spite of uniaxial application of load, and where deformation is permitted under limited range, which is quickly arrested as the deformation progresses.

The paper presents an analytical review of theoretical methods for modeling functional nanostructures. The main evolutionary changes in the approaches of quantum-mechanical modeling are described. The foundations of the first-principal theory are considered, including the stationery and time-dependent Schrödinger equations, wave functions, the form of writing energy operators, and the principles of solving equations. The idea and specifics of describing the motion and interaction of nuclei and electrons in the framework of the theory of the electron density functional are presented. Common approximations and approaches in the methods of quantum mechanics are presented, including the Born–Oppenheimer approximation, the Hartree–Fock approximation, the Thomas–Fermi theory, the Hohenberg–Kohn theorems, and the Kohn–Sham formalism. Various options for describing the exchange–correlation energy in the theory of the electron density functional are considered, such as the local density approximation, generalized and meta-generalized gradient approximations, and hybridization of the generalized gradient method. The development of methods of quantum mechanics to quantum molecular dynamics or the dynamics of Car–Parrinello is shown. The basic idea of combining classical molecular modeling with calculations of the electronic structure, which is reflected in the potentials of the embedded atom, is described.

In this paper, new forms of Maxwell’s equations in vector and scalar variants are presented. The new forms are based on the use of Gauss’s theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms.