Simple and effective elements based upon Timoshenko–Mindlin shell theory

The simple and effective mixed models are developed for the analysis of multilayered anisotropic Timoshenko–Mindlin-type shells. The effects of the transverse shear and transverse normal strains, and laminated anisotropic material response are included. The precise representation of rigid body motions in the displacement patterns of curved shell elements is considered. This consideration requires the development of the strain–displacement equations of the Timoshenko–Mindlin-type theory with regard to their consistency with the rigid body motions. The fundamental unknowns consist of six displacements and eleven strains of the face surfaces of the shell, and 11 stress resultants. The element characteristic arrays are obtained by using the Hu–Washizu mixed variational principle. Numerical results are presented to demonstrate the high accuracy and effectiveness of the developed mixed models and to compare their performance with other finite-element models reported in the literature.     

Bang–bang principle for linear and non-linear Goursat–Darboux problems

In this paper, the bang-bang principle for a control system described by a system of non-linear (in control) non-autonomous partial differential equations of hyperbolic type (the so-called Goursat-Darboux problem) is proved. As a particular case the bang-bang principle for a linear system is obtained. The method used for the proof is based on some properties of the Aumann integral.     

Spectral method for constrained linear–quadratic optimal control

A computational method based on Chebyshev spectral method is presented to solve the linear–quadratic optimal control problem subject to terminal state equality constraints and state-control inequality constraints. The method approximates each of the system state variables and each of the control variables by a finite Chebyshev series of unknown parameters. The method converts the optimal control problem into a quadratic programming problem which can be solved more easily than the original problem. This paper gives explicit results that simplify the implementation of the method. To show the numerical behavior of the proposed method, the simulation results of an example are presented.     

Two-photon phase gate with linear optical elements and atom–cavity system

We propose a protocol for implementing \(\pi \) phase gate of two photons with linear optical elements and an atom–cavity system. The evolution of the atom–cavity system is based on the quantum Zeno dynamics. The devices in the present protocol are simple and feasible with current experimental technology. Moreover, the method we proposed here is deterministic with a high fidelity. Numerical simulation shows that the evolution in cavity is efficient and robust. Therefore, the protocol may be helpful for quantum computation field.     

New designing of cryptosystems based on quadratic fields

This paper proposes a method to construct new kind of non-maximal imaginary quadratic order （NIQO＊） by combining the technique of Diophantine equation and the characters of non-maximal imaginary quadratic order. It is proved that in the class group of this new kind of NIQO＊, it is very easy to design provable secure cryptosystems based on quadratic field （QF）. With the purpose to prove that this new kind of QF-based cryptosystems are easy to implement, two concrete schemes are presented, i.e., a Schnorr-like signature and an EIGamel-like encryption, by using the proposed NIQO＊. In the random oracle model, it is proved that： （1） under the assumption that the discrete logarithm problem over class groups （CL-DLP） of this new kind of NIQO＊ is intractable, the proposed signature scheme is secure against adaptive chosen-message attacks, i.e., achieving UF-CMA security; （2） under the assumption that the decisional Diffie-Hellman problem over class groups （CL-DDH） of this new kind of NIQO＊ is intractable, the enhanced encryption in this paper is secure against adaptive chosen-ciphertext attacks, i.e., reaching IND-CCA2 security.     

Mean-field stochastic linear–quadratic optimal control with Markov jump parameters

This paper considers a class of mean-field stochastic linear–quadratic optimal control problems with Markov jump parameters. The new feature of these problems is that means of state and control are incorporated into the systems and the cost functional. Based on the modes of Markov chain, the corresponding decomposition technique of augmented state and control is introduced. It is shown that, under some appropriate conditions, there exists a unique optimal control, which can be explicitly given via solutions of two generalized difference Riccati equations. A numerical example sheds light on the theoretical results established.     

Decentralized linear–quadratic–Gaussian control of networked control systems with asymmetric information

The decentralized linear–quadratic–Gaussian (LQG) control problem for networked control systems (NCSs) with asymmetric information is investigated, where controller 1 shares its historical information with controller 2, and not vice versa. The asymmetry of the information structure leads to the coupling between controller 2 and estimator 1, and hence the classical separation principle fails. Through the assumption of linear control strategy, the coupling between controller 2 and estimator 1 (CCE) is decoupled, but the estimation gain is still coupled with the control gain. It is noted that the control gain conforms to the backward Riccati equation while estimation gain abides by the forward equation, which is computationally challenging. Applying the stochastic maximum principle, the solvability of the decentralized LQG control problem is reduced to that of corresponding forward and backward stochastic difference equations (FBSDEs). Further, necessary and sufficient conditions for the solvability of optimal control problem are presented by two Riccati equations, one of which is nonsymmetric. Moreover, a novel iterative forward method is proposed to calculate the coupled backward control gain and forward estimation gain.     

Gauss–Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis

We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature rules we recently derived (Bartoň and Calo, 2016) act on spaces of the smallest odd degrees and, therefore, are still slightly sub-optimal. In this work, we derive optimal rules directly for even-degree spaces and therefore further improve our recent result. We use optimal quadrature rules for spaces over two elements as elementary building blocks and use recursively the homotopy continuation concept described in Bartoň and Calo (2016) to derive optimal rules for arbitrary admissible numbers of elements. We demonstrate the proposed methodology on relevant examples, where we derive optimal rules for various even-degree spline spaces. We also discuss convergence of our rules to their asymptotic counterparts, these are the analogues of the midpoint rule of Hughes et al. (2010), that are exact and optimal for infinite domains.     

Continuous-time singular linear–quadratic control: Necessary and sufficient conditions for the existence of regular solutions

The purpose of this paper is to provide a full understanding of the role that the constrained generalized continuous algebraic Riccati equation plays in singular linear–quadratic (LQ) optimal control. Indeed, in spite of the vast literature on LQ problems, only recently a sufficient condition for the existence of a non-impulsive optimal control has for the first time connected this equation with the singular LQ optimal control problem. In this paper, we establish four equivalent conditions providing a complete picture that connects the singular LQ problem with the constrained generalized continuous algebraic Riccati equation and with the geometric properties of the underlying system.     

Multiple models,multiplicative noise and linear quadratic control—algorithmic aspects

Numerical solution of certain linear quadratic (LQ) control problems for robust design is addressed. An iterative method is suggested and analysed for solving a minimax multiple model LQ control problem. A convergent iterative method is studied for finding the constant feedback gains of a given linear controller so as to solve a spectral radius functional minimization problem for multiple plants. Furthermore, a convergent iterative method is proposed for solving the maximum entropy parametric LQ control problem with multiplicative noise.     

Sub-optimal solutions of linear control and eigenvalue pattern problems†

The present paper deals with sub-optimal solutions for problems of minimizing integral cost fimetioiuils which consider the state variables alone for stationary linear processes. The control vector and its time derivative are assumed to be bounded. The resulting control policies are linear with respect to the state vector. The performance of the proposed sub-optimal policies is compared with that of classical control systems and a procedure for sub-optimal eigenvalue patterns is presented for systems of any order.     

A linear Uzawa-type FEM–BEM solver for nonlinear transmission problems

We propose a fully discrete Uzawa-type iteration for the Johnson–Nédélec formulation of a Laplace-type transmission problem with possible (strongly monotone) nonlinearity in the interior domain. In each step, we sequentially solve one BEM for the weakly-singular integral equation associated with the Laplace-operator and one FEM for the linear Yukawa equation. In particular, the nonlinearity is only evaluated to build the right-hand side of the Yukawa equation. The algorithm includes the inexact solution of the BEM/FEM part by a preconditioned CG method. We prove that the proposed method leads to linear convergence with respect to the number of Uzawa iterations. Moreover, while the current analysis of a direct FEM–BEM discretization of the Johnson–Nédélec formulation requires some restrictions on the ellipticity (resp. strong monotonicity constant) in the interior domain, our Uzawa-type solver avoids such assumptions.     

A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems

Interactions between an incompressible fluid passing through a flexible tube and the elastic wall is one of the strongly coupled fluid–solid interaction (FSI) problems frequently studied in the literature due to its research importance and wide range of applications. Although incompressible fluid is a prevalent model in many simulation studies, the assumption of incompressibility may not be appropriate in strongly coupled FSI problems. This paper narrowly aims to study the effect of the fluid compressibility on the wave propagation and fluid–solid interactions in a flexible tube. A partitioned FSI solver is used which employs a finite volume-based fluid solver. For the sake of comparison, both traditional incompressible (ico) and weakly compressible (wco) fluid models are used in an Arbitrary Lagrangian–Eulerian (ALE) formulation and a PISO-like algorithm is used to solve the unsteady flow equations on a collocated mesh. The solid part is modeled as a simple hyperelastic material obeying the St-Venant constitutive relation. Computational results show that not only use of the weakly compressible fluid model makes the FSI solver in this case more efficient, but also the incompressible fluid model may produce largely unrealistic computational results. Therefore, the use of the weakly compressible fluid model is suggested for strongly coupled FSI problems involving seemingly incompressible fluids such as water especially in cases where wave propagation in the solid plays an important role.

     

SCUT-COUCH2009—a comprehensive online unconstrained Chinese handwriting database and benchmark evaluation

A comprehensive online unconstrained Chinese handwriting dataset, SCUT-COUCH2009, is introduced in this paper. As a revision of SCUT-COUCH2008 [1], the SCUT-COUCH2009 database consists of more datasets with larger vocabularies and more writers. The database is built to facilitate the research of unconstrained online Chinese handwriting recognition. It is comprehensive in the sense that it consists of 11 datasets of different vocabularies, named GB1, GB2, TradGB1, Big5, Pinyin, Letters, Digit, Symbol, Word8888, Word17366 and Word44208. In particular, the SCUT-COUCH2009 database contains handwritten samples of 6,763 single Chinese characters in the GB2312-80 standard, 5,401 traditional Chinese characters of the Big5 standard, 1,384 traditional Chinese characters corresponding to the level 1 characters of the GB2312-80 standard, 8,888 frequently used Chinese words, 17,366 daily-used Chinese words, 44,208 complete words from the Fourth Edition of “The Contemporary Chinese Dictionary”, 2,010 Pinyin and 184 daily-used symbols. The samples were collected using PDAs (Personal Digit Assistant) and smart phones with touch screens and were contributed by more than 190 persons. The total number of character samples is over 3.6 million. The SCUT-COUCH2009 database is the first publicly available large vocabulary online Chinese handwriting database containing multi-type character/word samples. We report some evaluation results on the database using state-of-the-art recognizers for benchmarking.     

Smoothing projected cyclic Barzilai–Borwein method for stochastic linear complementarity problems

In this paper, we propose a smoothing projected cyclic Barzilai–Borwein (SPCBB) method for solving the expected residual minimization formulation of stochastic linear complementarity problems (SLCPs). The SPCBB method combines the smoothing techniques and the projected Barzilai–Borwein (BB) method, where the cyclic BB scheme which resues the same BB stepsize for several consecutive iterations and a nonmonotone line search that requires an average of the successive function values decreases are employed to accelerate the convergence process. Under mild conditions, we show the convergence of the proposed method to a Clarke stationary point. Preliminary numerical results of randomly generated SLCPs show that the method is promising.     

Generalised Hammerstein–Wiener system estimation and a benchmark application

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The parameter estimation of this model is investigated using a standard prediction error criterion coupled with a robust gradient based search algorithm. This approach is profiled using a Wiener–Hammerstein Benchmark example, which illustrates it to be effective and, via Monte-Carlo simulation, relatively robust against capture in local minima.     

Convolution theorems for the linear canonical transform and their applications

As generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform (FFT), which has much lower computational load than the construction method in the linear canonical domain.     

Mixed L2 and L∞ problems by weight selection in quadratic optimal control

In an attempt to achieve more realistic control objectives, the weighting matrices in the standard LQ1 problem are usually chosen by the designer in an ad hoc manner. This paper shows several optimal control design problems that minimize a quadratic function of the control vector subject to multiple inequality constraints on the output L ₂ norms, L _∞ norms, covariance matrix, and the maximum singular value of the output covariance matrix. The solutions of all four of these problems reduce to standard LQI control problems with different choices of weights. This paper shows how to construct these different weights. The practical significance of these results is that many robustness properties relate directly to these four entities. Hence the given control design algorithm delivers a specified degree of robustness to both parameter errors and disturbances. The results are presented in the deterministic terms of the linear quadratic impulse (LQI)for continuous and discrete systems problem rather than the stochastic LQG problem. The results are easily transferable to the LQG problem.