The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this ...The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].展开更多
The existence of several non-symmetric balanced incomplete block designs (BIBDs) is still unknown. This is because the non-existence property for non-symmetric BIBDs is still not known and also the existing constructi...The existence of several non-symmetric balanced incomplete block designs (BIBDs) is still unknown. This is because the non-existence property for non-symmetric BIBDs is still not known and also the existing construction methods have not been able to construct these designs despite their design parameters satisfying the necessary conditions for the existence of BIBD. The study aimed to bridge this gap by introducing a new class of non-symmetric BIBDs. The proposed class of BIBDs is constructed through the combination of disjoint symmetric BIBDs. The study was able to determine that the total number of disjoint symmetric BIBDs (n) with parameters (v = b, r = k, λ) that can be obtained from an un-reduced BIBD with parameters (v, k) is given by n = r - λ. When the n symmetric disjoint BIBDs are combined, then a new class of symmetric BIBDs is formed with parameters v<sup>*</sup><sup> </sup>= v, b<sup>*</sup><sup> </sup>= nb, r<sup>*</sup><sup> </sup>= nr, k<sup>*</sup><sup> </sup>= k, λ<sup>*</sup><sup> </sup>= λ, where 2≤ n ≤ r - λ. The study established that the non-existence property of this class of BIBD was that when is not a perfect square then v should be even and when v<sup>*</sup><sup> </sup>is odd then the equation should not have a solution in integers x, y, z which are not all simultaneously zero. In conclusion, the study showed that this construction technique can be used to construct some non-symmetric BIBDs. However, one must first construct the disjoint symmetric BIBDs before one can construct the non-symmetric BIBD. Thus, the disjoint symmetric BIBDs must exist first before the non-symmetric BIBDs exist.展开更多
The flow through a single fracture is numerically studied by means of the Fluent Software. The results show that the roughness of the fracture significantly affects the hydraulic conductivity in the fracture as compar...The flow through a single fracture is numerically studied by means of the Fluent Software. The results show that the roughness of the fracture significantly affects the hydraulic conductivity in the fracture as compared with the cubic law model widely used to describe the flow between two smooth parallel plates. A new model is proposed in this paper, the non-symmetric sinusoidal fracture model, to simulate the flow in a real fracture. This model involves two sinusoidal-varying walls with different phases to replace the flat planes in the cubic law model. The relationships between the effective hydraulic apertures and the phase retardation for different relative amplitudes and wavelengths are numerically investigated. A simple expression of the effective hydraulic aperture of the fracture is obtained, together with the law of the effective hydraulic aperture against the amplitude, the phase retardation and the wavelength of two sinusoidal-varying walls.展开更多
This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the pe...This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the perturbed form （ε^u ,D（ε^u）） （for some a0 ≥ 0） to be a coercive closed form.展开更多
In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spac...In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces. Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.展开更多
Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the ext...Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the extended stochastic integrals is obtained.展开更多
In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hys...In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.展开更多
Ref. [1] studies problems concerned by using the nature of mixed monotone of two-element nonlinear operators. As for mixed monotone operator, Ref. [2] studies the minimax solution
A three- and an （N＋ 1）-party dense coding scheme in the case of non-symmetric Hilbert spaces of the particles of a quantum channel are investigated by using a multipartite entangled state. In the case of the （N ...A three- and an （N＋ 1）-party dense coding scheme in the case of non-symmetric Hilbert spaces of the particles of a quantum channel are investigated by using a multipartite entangled state. In the case of the （N ＋ 1）-party dense coding scheme, we show that the amount of classical information transmitted from N senders to one receiver is improved.展开更多
We demonstrate that, when computing the LDU decomposition (a typical example of a direct solution method), it is possible to obtain the derivative of a determinant with respect to an eigenvalue of a non-symmetric matr...We demonstrate that, when computing the LDU decomposition (a typical example of a direct solution method), it is possible to obtain the derivative of a determinant with respect to an eigenvalue of a non-symmetric matrix. Our proposed method augments an LDU decomposition program with an additional routine to obtain a program for easily evaluating the derivative of a determinant with respect to an eigenvalue. The proposed method follows simply from the process of solving simultaneous linear equations and is particularly effective for band matrices, for which memory requirements are significantly reduced compared to those for dense matrices. We discuss the theory underlying our proposed method and present detailed algorithms for implementing it.展开更多
This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to ha...This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to handle input deadzone as well as unmeasurable disturbances simultaneously in strictly matched systems. The proposed controller robustly cancels any residual distortion caused by the inaccurate deadzone cancellation scheme. The scheme is shown to successfully cancel the deadzone’s deleterious effect as well as eliminate other unmeasurable disturbances within the span of the input. The new controller ensures the global stability of all states and adaptations, and achieves asymptotic tracking. The asymptotic stability of the closed-loop system is proven by Lyapunov arguments, and simulation results confirm the efficacy of the control methodology.展开更多
An efficient electrochemical access to the non-symmetric biphenols using tri(p-bromophenyl)amine(TBPA)as a redox mediator has been developed.The electrochemical protocol features highly selective cross-coupling produc...An efficient electrochemical access to the non-symmetric biphenols using tri(p-bromophenyl)amine(TBPA)as a redox mediator has been developed.The electrochemical protocol features highly selective cross-coupling products in up to 83% yield,instead of forming homo-coupling ones.展开更多
The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through th...The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations in which the unknown variables are the jumps of displacements across crack surfaces. To Solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials.展开更多
The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In part...The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.展开更多
基金Supported by National Natural Science Foundation of China
文摘The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].
文摘The existence of several non-symmetric balanced incomplete block designs (BIBDs) is still unknown. This is because the non-existence property for non-symmetric BIBDs is still not known and also the existing construction methods have not been able to construct these designs despite their design parameters satisfying the necessary conditions for the existence of BIBD. The study aimed to bridge this gap by introducing a new class of non-symmetric BIBDs. The proposed class of BIBDs is constructed through the combination of disjoint symmetric BIBDs. The study was able to determine that the total number of disjoint symmetric BIBDs (n) with parameters (v = b, r = k, λ) that can be obtained from an un-reduced BIBD with parameters (v, k) is given by n = r - λ. When the n symmetric disjoint BIBDs are combined, then a new class of symmetric BIBDs is formed with parameters v<sup>*</sup><sup> </sup>= v, b<sup>*</sup><sup> </sup>= nb, r<sup>*</sup><sup> </sup>= nr, k<sup>*</sup><sup> </sup>= k, λ<sup>*</sup><sup> </sup>= λ, where 2≤ n ≤ r - λ. The study established that the non-existence property of this class of BIBD was that when is not a perfect square then v should be even and when v<sup>*</sup><sup> </sup>is odd then the equation should not have a solution in integers x, y, z which are not all simultaneously zero. In conclusion, the study showed that this construction technique can be used to construct some non-symmetric BIBDs. However, one must first construct the disjoint symmetric BIBDs before one can construct the non-symmetric BIBD. Thus, the disjoint symmetric BIBDs must exist first before the non-symmetric BIBDs exist.
基金supported by the National Natural Science Foundation of China(Grant No.10932012)the National Natural Science Funds of China for Distinguished Young Scholar(Grant No.10825211)the National Key Basic Research Program of China(973Program,Grant No.2010CB731506)
文摘The flow through a single fracture is numerically studied by means of the Fluent Software. The results show that the roughness of the fracture significantly affects the hydraulic conductivity in the fracture as compared with the cubic law model widely used to describe the flow between two smooth parallel plates. A new model is proposed in this paper, the non-symmetric sinusoidal fracture model, to simulate the flow in a real fracture. This model involves two sinusoidal-varying walls with different phases to replace the flat planes in the cubic law model. The relationships between the effective hydraulic apertures and the phase retardation for different relative amplitudes and wavelengths are numerically investigated. A simple expression of the effective hydraulic aperture of the fracture is obtained, together with the law of the effective hydraulic aperture against the amplitude, the phase retardation and the wavelength of two sinusoidal-varying walls.
基金This research is supported by the NSFC andNSF of Hainan Province (Nos. 80529 and 10001)
文摘This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the perturbed form （ε^u ,D（ε^u）） （for some a0 ≥ 0） to be a coercive closed form.
基金supported by National Natural Science Foundation of China (Grant No.10721101)National Basic Research Program of China (Grant No.2006CB805900)+1 种基金Key Lab of Random Complex Structures and Data Science,Chinese Academy of Sciences (Grant No.2008DP173182)Sino-Germany IGK Project
文摘In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces. Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.
基金supported by National Natural Science Foundation of China (Grant No.10961012)Natural Sciences and Engineering Research Council of Canada (Grant No. 311945-2008)
文摘Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the extended stochastic integrals is obtained.
文摘In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.
文摘Ref. [1] studies problems concerned by using the nature of mixed monotone of two-element nonlinear operators. As for mixed monotone operator, Ref. [2] studies the minimax solution
文摘A three- and an （N＋ 1）-party dense coding scheme in the case of non-symmetric Hilbert spaces of the particles of a quantum channel are investigated by using a multipartite entangled state. In the case of the （N ＋ 1）-party dense coding scheme, we show that the amount of classical information transmitted from N senders to one receiver is improved.
文摘We demonstrate that, when computing the LDU decomposition (a typical example of a direct solution method), it is possible to obtain the derivative of a determinant with respect to an eigenvalue of a non-symmetric matrix. Our proposed method augments an LDU decomposition program with an additional routine to obtain a program for easily evaluating the derivative of a determinant with respect to an eigenvalue. The proposed method follows simply from the process of solving simultaneous linear equations and is particularly effective for band matrices, for which memory requirements are significantly reduced compared to those for dense matrices. We discuss the theory underlying our proposed method and present detailed algorithms for implementing it.
文摘This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to handle input deadzone as well as unmeasurable disturbances simultaneously in strictly matched systems. The proposed controller robustly cancels any residual distortion caused by the inaccurate deadzone cancellation scheme. The scheme is shown to successfully cancel the deadzone’s deleterious effect as well as eliminate other unmeasurable disturbances within the span of the input. The new controller ensures the global stability of all states and adaptations, and achieves asymptotic tracking. The asymptotic stability of the closed-loop system is proven by Lyapunov arguments, and simulation results confirm the efficacy of the control methodology.
基金grants from the National Key Technology R&D Program(No.2016YFD0400801)the National Natural Science Foundation of China(No.21871019).
文摘An efficient electrochemical access to the non-symmetric biphenols using tri(p-bromophenyl)amine(TBPA)as a redox mediator has been developed.The electrochemical protocol features highly selective cross-coupling products in up to 83% yield,instead of forming homo-coupling ones.
基金Project supported by the National Natural Science Foundation of China (Nos.10572043 and 10572155)the Natural Science Foundation for Excellent Young Investigators of Heilongjiang Province(No.JC04-08)
文摘The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations in which the unknown variables are the jumps of displacements across crack surfaces. To Solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials.
基金supported by the State Scholarship Fund of the China Scholarship Council (Grant 2009629129)
文摘The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.
