In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure f...In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure for the terms of a finite, positively define kernel of operators, is studied. The notion of “stability of the dimension” in truncated, scalar moment problems was introduced in [1]. In this note, the concept of “stability” of the algebraic dimension of the obtained Hilbert space from the space of the polynomials of finite, total degree with respect to the null subspace of a unital square positive functional, in [1], is adapted to the concept of stability of the algebraic dimension of the Hilbert space obtained as the separated space of some space of vectorial functions with respect to the null subspace of a hermitian square positive functional attached to a positive definite kernel of operators. In connection with the stability of the dimension of such obtained Hilbert space, a Hausdorff truncated operator-valued moment problem and the stability of the number of atoms of the representing measure for the terms of the given operator kernel, in this note, is studied.展开更多
Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfull...Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfully. We pointed out that an explanation of quantum jumps can be found to result from Colombeau solutions of the Schrodinger equation alone without additional postulates.展开更多
A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary...A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure , with the property that for every with , the moment of coincides with the term of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied.展开更多
We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty ...We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.展开更多
In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the gen...In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.展开更多
In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor depos...In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.展开更多
The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Th...The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Thus, with a known flow rate Q, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations both constant and linear elements are used. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments.展开更多
We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this te...We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.展开更多
In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and...In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.展开更多
Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting proper...Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting properties. It leads to an alternative definition of the Ultraspherical polynomials by a fixed integral operator in application to powers of the variable u in an analogous way as it is possible for Hermite polynomials. From this follows a generating function which is apparently known only for the Legendre and Chebyshev polynomials as their special case. Furthermore, we show that the Ultraspherical polynomials form a realization of the SU(1,1) Lie algebra with lowering and raising operators which we explicitly determine. By reordering of multiplication and differentiation operators we derive new operator identities for the whole set of Jacobi polynomials which may be applied to arbitrary functions and provide then function identities. In this way we derive a new “convolution identity” for Jacobi polynomials and compare it with a known convolution identity of different structure for Gegenbauer polynomials. In short form we establish the connection of Jacobi polynomials and their related orthonormalized functions to the eigensolution of the Schrödinger equation to Pöschl-Teller potentials.展开更多
In this paper, we propose a unified differential operator method to study mechanical vibrations, solving inhomogeneous linear ordinary differential equations with constant coefficients. The main advantage of this new ...In this paper, we propose a unified differential operator method to study mechanical vibrations, solving inhomogeneous linear ordinary differential equations with constant coefficients. The main advantage of this new method is that the differential operator D in the numerator of the fraction has no effect on input functions (i.e., the derivative operation is removed) because we take the fraction as a whole part in the partial fraction expansion. The method in various variants is widely implemented in related fields in mechanics and engineering. We also point out that the same mistakes in the differential operator method are found in the related references [1-4].展开更多
With the increase of science popularization, evaluation of science popularization has become an urgent demand. Considering science popularization bases as independent agents, a self-determined evaluation approach for ...With the increase of science popularization, evaluation of science popularization has become an urgent demand. Considering science popularization bases as independent agents, a self-determined evaluation approach for science popularization using induced ordered weighted averaging (IOWA) operator and particle swarm optimization (PSO) is proposed in this paper.Firstly, six factors including science popularization personnel, space, fund,media, activity and influence are selected to construct an index system for science popularization evaluation. On this basis, the absolute dominance and relative dominance of evaluation indexes are used as induced components, and the prior order of the evaluation indexes is determined. Besides, the optimization model of index weighted vectors is established by IOWA operator, index weighted vectors are calculated by particle swarm optimization algorithm, and index weighted vectors and evaluation value vectors are obtain. Finally, the optimal evaluation vectors and evaluation results are given according to the Perron-Frobenius decision eigenvalve theorem .展开更多
Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in oper...Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.展开更多
In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theo...In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.展开更多
In this paper, we consider the general quasi-differential expressions each of order n with complex coefficients and their formal adjoints on the interval (a,b). It is shown in direct sum spaces of functions defined on...In this paper, we consider the general quasi-differential expressions each of order n with complex coefficients and their formal adjoints on the interval (a,b). It is shown in direct sum spaces of functions defined on each of the separate intervals with the cases of one and two singular end-points and when all solutions of the equation and its adjoint are in (the limit circle case) that all well-posed extensions of the minimal operator have resolvents which are HilbertSchmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. These results extend those of formally symmetric expression studied in [1-10] and those of general quasi-differential expressions in [11-19].展开更多
The driving necessities of cost reduction and the need to develop fields at ever increasing water depths have led to the use of floating structures. Among these structures are the Floating Production Storage and Offlo...The driving necessities of cost reduction and the need to develop fields at ever increasing water depths have led to the use of floating structures. Among these structures are the Floating Production Storage and Offloading (FPSO) units whose motion analysis is considered in this paper. In actual environmental condition, it is required to accurately determine or predict large amplitude motion of the FPSO before any offshore operation. This paper seeks to present a detailed method of computing the Response Amplitude Operator(s) (RAOs) for the six (6) degrees of freedom using ANSYS AQWA. The results indicate for Heave motion a tendency for the heave peak value to move slightly higher dimensionless encounter-frequency as the wave moves from Head sea to Beam sea direction. A MATLAB source code was developed to validate the result for heave motion at head sea. Although a small difference in predicted heave motion occurred, it is pertinent to note that the comparisons between results generated in the MATLAB program and ANSYS AQWA demonstrate generally good agreement, and the roll response of the FPSO is noted to be critical.展开更多
When D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">...When D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em><em><span style="white-space:nowrap;"></span></em><em></em></span> </span>is a linear differential operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1</sub>: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span> </span></em></span></span>such that <span style="white-space:nowrap;">D<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span></span></em></span>=<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span></span> implies <span style="white-space:nowrap;">D<sub>1</sub><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span>=0</span>. When D is involutive, the procedure provides successive first order involutive operators D1, ..., D<sub>n</sub>, when the ground manifold has dimension <em>n</em>, a result first found by M. Janet as early as in 1920, in a footnote. However, the link between this “Janet sequence” and the “Spencer sequence” first found by the author of this paper in 1978 is still not acknowledged. Conversely, when D<sub>1</sub> is given, a more difficult “inverse problem” is to look for an operator D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><em><span style="white-space:nowrap;">ξ</span></em></em><span style="white-space:nowrap;">→</span><em><em><span style="white-space:nowrap;">η</span></em><em></em><em></em> </em><em></em></span> </span>having the generating CC <span style="white-space:nowrap;">D<sub>1</sub><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span><em></em>=0</span>. If this is possible, that is when the differential module defined by D<sub>1</sub> is torsion-free, one shall say that the operator D<sub>1</sub> is parametrized by D and there is no relation in general between D and D<sub>2</sub>. The parametrization is said to be “minimum” if the differential module defined by D has a vanishing differential rank and is thus a torsion module. The solution of this problem, first found by the author of this paper in 1995, is still not acknowledged. As for the applications of the “differential double duality” theory to standard equations of physics (<em>Cauchy</em> and Maxwell equations can be parametrized while <em>Einstein</em> equations cannot), we do not know other references. When <span style="font-size:10.0pt;font-family:;" "="">erator in arbitrary dimension</span>=1 as in control theory, the fact that controllability is a “built in” property of a control system, amounting to the existence of a parametrization and thus not depending on the choice of inputs and outputs, even with variable coefficients, is still not acknowledged by engineers. The parametrization of the <em>Cauchy</em> stress operator in arbitrary dimension <em>n</em> has nevertheless attracted, “separately” and without any general “guiding line”, many famous scientists (G.B. Airy in 1863 for <em>n </em>= 2, J.C. Maxwell in 1863, G. Morera and E. Beltrami in 1892 for <em style="white-space:normal;">n </em><span style="white-space:normal;">= 3</span> , A. Einstein in 1915 for <em style="white-space:normal;">n </em><span style="white-space:normal;">= 4</span> ). The aim of this paper is to solve the minimum parametrization problem in arbitrary dimension and to apply it through effective methods that could even be achieved by using computer algebra. Meanwhile, we prove that all these works are using the <em>Einstein</em> operator which is self-adjoint and not the <em>Ricci</em> operator, a fact showing that the <em>Einstein</em> operator, which cannot be parametrized, has already been exhibited by Beltrami more than 20 years before <em>Einstein</em>. As a byproduct, they are all based on the same confusion between the so-called <em>div</em> operator induced from the <em>Bianchi </em>operator D<sub>2</sub> and the <em>Cauchy</em> operator which is the formal adjoint of the Killing operator D parametrizing the Riemann operator D<sub>1</sub> for an arbitrary <em>n</em>. We prove that this purely mathematical result deeply questions the origin and existence of gravitational waves. We also present the similar motivating situation met in the study of contact structures when <em>n</em> = 3. Like the Michelson and Morley experiment, it is thus an open historical problem to know whether <em>Einstein</em> was aware of these previous works or not, but the comparison needs no comment.展开更多
Based on a variety of geometric observations for location of solutions, a general and unified region analysis framework for developing constructive solvability of nonlinear operator equations are proposed. Within this...Based on a variety of geometric observations for location of solutions, a general and unified region analysis framework for developing constructive solvability of nonlinear operator equations are proposed. Within this framework, the methods including interval, ball and ellipsoid methods can be studied in a unified way. The ball algorithm, as a typical example, is in particular analysed.展开更多
Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper...Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.展开更多
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted...Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).展开更多
文摘In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure for the terms of a finite, positively define kernel of operators, is studied. The notion of “stability of the dimension” in truncated, scalar moment problems was introduced in [1]. In this note, the concept of “stability” of the algebraic dimension of the obtained Hilbert space from the space of the polynomials of finite, total degree with respect to the null subspace of a unital square positive functional, in [1], is adapted to the concept of stability of the algebraic dimension of the Hilbert space obtained as the separated space of some space of vectorial functions with respect to the null subspace of a hermitian square positive functional attached to a positive definite kernel of operators. In connection with the stability of the dimension of such obtained Hilbert space, a Hausdorff truncated operator-valued moment problem and the stability of the number of atoms of the representing measure for the terms of the given operator kernel, in this note, is studied.
文摘Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfully. We pointed out that an explanation of quantum jumps can be found to result from Colombeau solutions of the Schrodinger equation alone without additional postulates.
文摘A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure , with the property that for every with , the moment of coincides with the term of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied.
文摘We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.
文摘In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.
文摘In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.
文摘The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Thus, with a known flow rate Q, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations both constant and linear elements are used. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments.
基金This research was supported by the National Natural Science Foundation of China （Nos. 41230210 and 41204074）, the Science Foundation of the Education Department of Yunnan Province （No. 2013Z152）, and Statoil Company （Contract No. 4502502663）.
文摘We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.
文摘In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.
文摘Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting properties. It leads to an alternative definition of the Ultraspherical polynomials by a fixed integral operator in application to powers of the variable u in an analogous way as it is possible for Hermite polynomials. From this follows a generating function which is apparently known only for the Legendre and Chebyshev polynomials as their special case. Furthermore, we show that the Ultraspherical polynomials form a realization of the SU(1,1) Lie algebra with lowering and raising operators which we explicitly determine. By reordering of multiplication and differentiation operators we derive new operator identities for the whole set of Jacobi polynomials which may be applied to arbitrary functions and provide then function identities. In this way we derive a new “convolution identity” for Jacobi polynomials and compare it with a known convolution identity of different structure for Gegenbauer polynomials. In short form we establish the connection of Jacobi polynomials and their related orthonormalized functions to the eigensolution of the Schrödinger equation to Pöschl-Teller potentials.
文摘In this paper, we propose a unified differential operator method to study mechanical vibrations, solving inhomogeneous linear ordinary differential equations with constant coefficients. The main advantage of this new method is that the differential operator D in the numerator of the fraction has no effect on input functions (i.e., the derivative operation is removed) because we take the fraction as a whole part in the partial fraction expansion. The method in various variants is widely implemented in related fields in mechanics and engineering. We also point out that the same mistakes in the differential operator method are found in the related references [1-4].
文摘With the increase of science popularization, evaluation of science popularization has become an urgent demand. Considering science popularization bases as independent agents, a self-determined evaluation approach for science popularization using induced ordered weighted averaging (IOWA) operator and particle swarm optimization (PSO) is proposed in this paper.Firstly, six factors including science popularization personnel, space, fund,media, activity and influence are selected to construct an index system for science popularization evaluation. On this basis, the absolute dominance and relative dominance of evaluation indexes are used as induced components, and the prior order of the evaluation indexes is determined. Besides, the optimization model of index weighted vectors is established by IOWA operator, index weighted vectors are calculated by particle swarm optimization algorithm, and index weighted vectors and evaluation value vectors are obtain. Finally, the optimal evaluation vectors and evaluation results are given according to the Perron-Frobenius decision eigenvalve theorem .
基金supported by the National Natural Science Foundation of China(Grant No.52475543)Natural Science Foundation of Henan(Grant No.252300421101)+1 种基金Henan Province University Science and Technology Innovation Talent Support Plan(Grant No.24HASTIT048)Science and Technology Innovation Team Project of Zhengzhou University of Light Industry(Grant No.23XNKJTD0101).
文摘Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.
基金supported by the Key Program of Scientific Research Fund for Young Teachers of AUST(QN2018109)the National Natural Science Foundation of China(11801008)+1 种基金supported by the Fundamental Research Funds for the Central Universities(2017B715X14)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX17_0508)
文摘In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.
文摘In this paper, we consider the general quasi-differential expressions each of order n with complex coefficients and their formal adjoints on the interval (a,b). It is shown in direct sum spaces of functions defined on each of the separate intervals with the cases of one and two singular end-points and when all solutions of the equation and its adjoint are in (the limit circle case) that all well-posed extensions of the minimal operator have resolvents which are HilbertSchmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. These results extend those of formally symmetric expression studied in [1-10] and those of general quasi-differential expressions in [11-19].
文摘The driving necessities of cost reduction and the need to develop fields at ever increasing water depths have led to the use of floating structures. Among these structures are the Floating Production Storage and Offloading (FPSO) units whose motion analysis is considered in this paper. In actual environmental condition, it is required to accurately determine or predict large amplitude motion of the FPSO before any offshore operation. This paper seeks to present a detailed method of computing the Response Amplitude Operator(s) (RAOs) for the six (6) degrees of freedom using ANSYS AQWA. The results indicate for Heave motion a tendency for the heave peak value to move slightly higher dimensionless encounter-frequency as the wave moves from Head sea to Beam sea direction. A MATLAB source code was developed to validate the result for heave motion at head sea. Although a small difference in predicted heave motion occurred, it is pertinent to note that the comparisons between results generated in the MATLAB program and ANSYS AQWA demonstrate generally good agreement, and the roll response of the FPSO is noted to be critical.
文摘When D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em><em><span style="white-space:nowrap;"></span></em><em></em></span> </span>is a linear differential operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1</sub>: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span> </span></em></span></span>such that <span style="white-space:nowrap;">D<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span></span></em></span>=<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span></span> implies <span style="white-space:nowrap;">D<sub>1</sub><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span>=0</span>. When D is involutive, the procedure provides successive first order involutive operators D1, ..., D<sub>n</sub>, when the ground manifold has dimension <em>n</em>, a result first found by M. Janet as early as in 1920, in a footnote. However, the link between this “Janet sequence” and the “Spencer sequence” first found by the author of this paper in 1978 is still not acknowledged. Conversely, when D<sub>1</sub> is given, a more difficult “inverse problem” is to look for an operator D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><em><span style="white-space:nowrap;">ξ</span></em></em><span style="white-space:nowrap;">→</span><em><em><span style="white-space:nowrap;">η</span></em><em></em><em></em> </em><em></em></span> </span>having the generating CC <span style="white-space:nowrap;">D<sub>1</sub><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span><em></em>=0</span>. If this is possible, that is when the differential module defined by D<sub>1</sub> is torsion-free, one shall say that the operator D<sub>1</sub> is parametrized by D and there is no relation in general between D and D<sub>2</sub>. The parametrization is said to be “minimum” if the differential module defined by D has a vanishing differential rank and is thus a torsion module. The solution of this problem, first found by the author of this paper in 1995, is still not acknowledged. As for the applications of the “differential double duality” theory to standard equations of physics (<em>Cauchy</em> and Maxwell equations can be parametrized while <em>Einstein</em> equations cannot), we do not know other references. When <span style="font-size:10.0pt;font-family:;" "="">erator in arbitrary dimension</span>=1 as in control theory, the fact that controllability is a “built in” property of a control system, amounting to the existence of a parametrization and thus not depending on the choice of inputs and outputs, even with variable coefficients, is still not acknowledged by engineers. The parametrization of the <em>Cauchy</em> stress operator in arbitrary dimension <em>n</em> has nevertheless attracted, “separately” and without any general “guiding line”, many famous scientists (G.B. Airy in 1863 for <em>n </em>= 2, J.C. Maxwell in 1863, G. Morera and E. Beltrami in 1892 for <em style="white-space:normal;">n </em><span style="white-space:normal;">= 3</span> , A. Einstein in 1915 for <em style="white-space:normal;">n </em><span style="white-space:normal;">= 4</span> ). The aim of this paper is to solve the minimum parametrization problem in arbitrary dimension and to apply it through effective methods that could even be achieved by using computer algebra. Meanwhile, we prove that all these works are using the <em>Einstein</em> operator which is self-adjoint and not the <em>Ricci</em> operator, a fact showing that the <em>Einstein</em> operator, which cannot be parametrized, has already been exhibited by Beltrami more than 20 years before <em>Einstein</em>. As a byproduct, they are all based on the same confusion between the so-called <em>div</em> operator induced from the <em>Bianchi </em>operator D<sub>2</sub> and the <em>Cauchy</em> operator which is the formal adjoint of the Killing operator D parametrizing the Riemann operator D<sub>1</sub> for an arbitrary <em>n</em>. We prove that this purely mathematical result deeply questions the origin and existence of gravitational waves. We also present the similar motivating situation met in the study of contact structures when <em>n</em> = 3. Like the Michelson and Morley experiment, it is thus an open historical problem to know whether <em>Einstein</em> was aware of these previous works or not, but the comparison needs no comment.
文摘Based on a variety of geometric observations for location of solutions, a general and unified region analysis framework for developing constructive solvability of nonlinear operator equations are proposed. Within this framework, the methods including interval, ball and ellipsoid methods can be studied in a unified way. The ball algorithm, as a typical example, is in particular analysed.
基金supported by the National Natural Science Foundation of China(61402260,61473176)Taishan Scholar Project of Shandong Province(TSQN201812092)
文摘Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.
基金supported by the Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).
