On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach

This research presents bending responses of FG-GPLRC plates based upon higher order shear deformation theory (HSDT) for various sets of boundary conditions. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the differential quadrature method (DQM). Afterward, a parametric study is done to present the effects of three kinds of FG patterns, weight fraction of the GPLs, radius ratio, and thickness to inner radius ratio on the bending characteristics of the FG-GPLRC disk. Numerical results reveal that in the initial value of the \(Zt/h\), using more GPLs for reinforcing the structure provides an increase in the normal stresses but this matter is inverse for the higher value of the \(Zt/h\). The results show that considering the smaller radius ratio is a reason for boosting the shear stresses of the structure for each \(Zt/h\). Another consequence is that for the negative value of \(Zt/h\), it is true that by increasing \(h/{R}_{i}\) , the normal stresses increases but if there is positive value for \(Zt/h\), the radial and circumferential stresses fall down by having an increase in the \(h/{R}_{i}\).

     

Numerical solution of a phase field model for polycrystallization processes in binary mixtures

We consider the numerical solution of a phase field model for polycrystallization in the solidification of binary mixtures in a domain \( \varOmega \subset \mathbb {R}^2\). The model is based on a free energy in terms of three order parameters: the local orientation \(\varTheta \) of the crystals, the local crystallinity \(\phi \), and the concentration c of one of the components of the binary mixture. The equations of motion are given by an initial-boundary value problem for a coupled system of partial differential equations consisting of a regularized second order total variation flow in \( \varTheta \), an \(L^2\) gradient flow in \(\phi \), and a \(W^{1,2}(\varOmega )^*\) gradient flow in c. Based on an implicit discretization in time by the backward Euler scheme, we suggest a splitting method such that the three semidiscretized equations can be solved separately and prove existence of a solution. As far as the discretization in space is concerned, the fourth order Cahn–Hilliard type equation in c is taken care of by a \(\hbox {C}^0\) Interior Penalty Discontinuous Galerkin approximation which has the advantage that the same finite element space can be used as well for the spatial discretization of the equations in \( \varTheta \) and \( \phi \). The fully discretized equations represent parameter dependent nonlinear algebraic systems with the discrete time as a parameter. They are solved by a predictor corrector continuation strategy featuring an adaptive choice of the time-step. Numerical results illustrate the performance of the suggested numerical method.

     

Numerical simulations based on shifted second-order difference/finite element algorithms for the time fractional Maxwell’s system

In this article, mixed element algorithms with second-order time convergence results for the two-dimensional time fractional Maxwell’s equations in the Cole–Cole dispersive medium are developed. Fully discrete mixed element systems with shifted parameters \(\theta\) at time \(t=t_{n-\theta }\), which are constructed by combining the generalized BDF2-\(\theta\) schemes in temporal direction and a mixed element method in space direction, are formulated. For the two-dimensional case of the fractional Maxwell’s system, the algorithm implementation process based on the rectangular subdivision is shown in detail. Finally, two numerical examples are provided to confirm the validity of our method and to analyze the influence of parameters \(\alpha\), \(\theta\) for numerical solutions.

     

Efficient monitoring of hyperproperties using prefix trees

Hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other and are thus not monitorable by tools that consider computations in isolation. We present the monitoring approach implemented in the latest version of \(\text {RVHyper}\), a runtime verification tool for hyperproperties. The input to the tool are specifications given in the temporal logic \(\text {HyperLTL}\), which extends linear-time temporal logic (LTL) with trace quantifiers and trace variables. \(\text {RVHyper}\) processes execution traces sequentially until a violation of the specification is detected. In this case, a counterexample, in the form of a set of traces, is returned. \(\text {RVHyper}\) employs a range of optimizations: a preprocessing analysis of the specification and a procedure that minimizes the traces that need to be stored during the monitoring process. In this article, we introduce a novel trace storage technique that arranges the traces in a tree-like structure to exploit partially equal traces. We evaluate \(\text {RVHyper}\) on existing benchmarks on secure information flow control, error correcting codes, and symmetry in hardware designs. As an example application outside of security, we show how \(\text {RVHyper}\) can be used to detect spurious dependencies in hardware designs.

     

Adaptive finite-time congestion controller design of TCP/AQM systems based on neural network and funnel control

This work investigates an adaptive finite-time congestion control problem of transmission control protocol/active queue management. By means of the funnel control, neural networks and sliding mode control, a new AQM algorithm is proposed to ensure that the tracking error \(e_{1}\left( t\right) \) converges to the prescribed boundary in finite time and the transient and steady-state performances of \(e_{1}\left( t\right) \) can be satisfied. The stability analysis is given to prove that all the signals of the closed-loop system are finite-time bounded. Finally, a comparison example is considered to demonstrate the feasibility and superiority of the presented scheme.

     

Bounds on Threshold Probabilities for Coloring Properties of Random Hypergraphs

We study the threshold probability for the property of existence of a special-form \(r\)?-?coloring for a random \(k\)?-?uniform hypergraph in the \(H(n,k,p)\) binomial model. A parametric set of \(j\)?-?chromatic numbers of a random hypergraph is considered. A coloring of hypergraph vertices is said to be \(j\)?-?proper if every edge in it contains no more than \(j\) vertices of each color. We analyze the question of finding the sharp threshold probability of existence of a \(j\)?-?proper \(r\)?-?coloring for \(H(n,k,p)\). Using the second moment method, we obtain rather tight bounds for this probability provided that \(k\) and \(j\) are large as compared to \(r\).

     

Large deflection electro-mechanical analysis of composite structures bonded with macro-fiber composite actuators considering thermal loads

In this paper, static analysis of laminated composite plates and shells bonded with macro-fiber composite (MFC) actuators under thermo-electro-mechanical loads is considered. Most earlier studies in the literature focused on the effects of MFC actuation power and fiber orientations on shape deformation of composite plates/shells subjected to electrical voltage only. Also most of the earlier studies on MFC-\(\hbox {d}_{33}\) bonded smart structures in literature are performed by commercial softwares like Ansys or Abaqus using the thermal strain equivalent approach to model the piezomechanical coupling. Here, our earlier developed geometrically nonlinear plate and shell finite elements considering finite rotation theory are extended for MFC actuator-bonded composite structures taking into account additionally the response to temperature gradients. An improved Reissner–Mindlin hypothesis is considered to derive the variational formulation, in which a parabolic assumption of transverse shear strains across the thickness is assumed. MFC actuators dominated by the \(\hbox {d}_{33}\) effect (MFC-\(\hbox {d}_{33}\)) with arbitrary fiber orientations are considered. The numerical model is validated with composite beams and plates by comparing the results of simulations with experimental investigations existing in the literature. An angle-ply composite shell structure is studied in detail concerning geometrically nonlinear analysis of bending and twisting deformations under different MFC-\(\hbox {d}_{33}\) fiber orientations under electric loading. Shape control of thermally induced deformations of composite plates and shells is performed using bonded MFC-\(\hbox {d}_{33}\) actuators and the significance of the present geometrically nonlinear model is highlighted.

     

On topological systems

We establish the reflectivity of the subcategories of \(T_{0}\) and sober topological systems in the category \(\mathbf {TopSys}\) of topological systems. We also introduce a Sierpinski object in the category \(\mathbf {TopSys}\) and point out its connection with \(T_{0}\) and sober topological systems and also with injective \(T_{0}\)-topological systems.     

An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results

In this paper we consider the optimal discrimination of two mixed qubit states for a measurement that allows a fixed rate of inconclusive results. Our strategy is to transform the problem of two qubit states into a minimum error discrimination for three qubit states by adding a specific quantum state \(\rho _{0}\) and a prior probability \(q_{0}\), which behaves as an inconclusive degree. First, we introduce the beginning and the end of practical interval of inconclusive result, \(q_{0}^{(0)}\) and \(q_{0}^{(1)}\), which are key ingredients in investigating our problem. Then we obtain the analytic form of them. Next, we show that our problem can be classified into two cases \(q_{0}=q_{0}^{(0)}\) (or \(q_{0}=q_{0}^{(1)}\)) and \(q_{0}^{(0)}<q_{0}<q_{0}^{(1)}\). In fact, by maximum confidences of two qubit states and non-diagonal element of \(\rho _{0}\), our problem is completely understood. We provide an analytic solution of our problem when \(q_{0}=q_{0}^{(0)}\) (or \(q_{0}=q_{0}^{(1)}\)). However, when \(q_{0}^{(0)}<q_{0}<q_{0}^{(1)}\), we rather supply the numerical method to find the solution, because of the complex relation between inconclusive degree and corresponding failure probability. Finally we confirm our results using previously known examples.     

Combined analytical and numerical approach for auxetic FG-CNTRC plate subjected to a sudden load

In the current work, the dynamic behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate with negative Poisson’s ratio (NPR) is investigated by combining higher-order shear deformation theory and large deflection theory. First, explicit solutions are proposed to predict the effective Poisson’s ratio (EPR) of the laminates. Taking carbon nanotube-reinforced composite (CNTRC) as an example, the maximum NPR is obtained for \(\left( { \pm \theta } \right)_{{3{\text{T}}}}\) laminate as well. Results show that the EPR (\(v_{13}^{\text{e}}\),\(v_{23}^{\text{e}}\)) can range from a positive value of 0.311 to a negative value of 0.63. For the dynamic response problem, the asymptotic solutions with a two-step perturbation approach are derived for FG-CNTRC plates to capture the relationship between the center deflection and time. Several key factors such as functionally graded distribution, variations in the elastic foundation, and thermal stress produced by changing the temperature field are considered in the subsequent analysis. Numerical simulations are carried out to examine the corresponding dynamic behavior of FG-CNTRC plates when these factors are taken into account.

     

Two-Level Penalty Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics Equations

This work is concerned with the study of two-level penalty finite element method for the 2D/3D stationary incompressible magnetohydrodynamics equations. The new method is an interesting combination of the Newton iteration and two-level penalty finite element algorithm with two different finite element pairs \(P_{1}b\)-\(P_{1}\)-\(P_{1}b\) and \(P_{1}\)-\(P_{0}\)-\(P_{1}\). Moreover, the rigorous analysis of stability and error estimate for the proposed method are given. Numerical results verify the theoretical results and show the applicability and effectiveness of the presented scheme.     

New q-ary quantum MDS codes with distances bigger than $$\frac{ q}{2}$$

The construction of quantum MDS codes has been studied by many authors. We refer to the table in page 1482 of (IEEE Trans Inf Theory 61(3):1474–1484, 2015) for known constructions. However, there have been constructed only a few q-ary quantum MDS \([[n,n-2d+2,d]]_q\) codes with minimum distances \(d>\frac{q}{2}\) for sparse lengths \(n>q+1\). In the case \(n=\frac{q^2-1}{m}\) where \(m|q+1\) or \(m|q-1\) there are complete results. In the case \(n=\frac{q^2-1}{m}\) while \(m|q^2-1\) is neither a factor of \(q-1\) nor \(q+1\), no q-ary quantum MDS code with \(d> \frac{q}{2}\) has been constructed. In this paper we propose a direct approach to construct Hermitian self-orthogonal codes over \(\mathbf{F}_{q^2}\). Then we give some new q-ary quantum codes in this case. Moreover many new q-ary quantum MDS codes with lengths of the form \(\frac{w(q^2-1)}{u}\) and minimum distances \(d > \frac{q}{2}\) are presented.     

Data assimilation and sampling in Banach spaces

This paper studies the problem of approximating a function f in a Banach space \(\mathcal{X}\) from measurements \(l_j(f)\), \(j=1,\ldots ,m\), where the \(l_j\) are linear functionals from \(\mathcal{X}^*\). Quantitative results for such recovery problems require additional information about the sought after function f. These additional assumptions take the form of assuming that f is in a certain model class \(K\subset \mathcal{X}\). Since there are generally infinitely many functions in K which share these same measurements, the best approximation is the center of the smallest ball B, called the Chebyshev ball, which contains the set \(\bar{K}\) of all f in K with these measurements. Therefore, the problem is reduced to analytically or numerically approximating this Chebyshev ball. Most results study this problem for classical Banach spaces \(\mathcal{X}\) such as the \(L_p\) spaces, \(1\le p\le \infty \), and for K the unit ball of a smoothness space in \(\mathcal{X}\). Our interest in this paper is in the model classes \(K=\mathcal{K}(\varepsilon ,V)\), with \(\varepsilon >0\) and V a finite dimensional subspace of \(\mathcal{X}\), which consists of all \(f\in \mathcal{X}\) such that \(\mathrm{dist}(f,V)_\mathcal{X}\le \varepsilon \). These model classes, called approximation sets, arise naturally in application domains such as parametric partial differential equations, uncertainty quantification, and signal processing. A general theory for the recovery of approximation sets in a Banach space is given. This theory includes tight a priori bounds on optimal performance and algorithms for finding near optimal approximations. It builds on the initial analysis given in Maday et al. (Int J Numer Method Eng 102:933–965, 2015) for the case when \(\mathcal{X}\) is a Hilbert space, and further studied in Binev et al. (SIAM UQ, 2015). It is shown how the recovery problem for approximation sets is connected with well-studied concepts in Banach space theory such as liftings and the angle between spaces. Examples are given that show how this theory can be used to recover several recent results on sampling and data assimilation.     

USSOR methods for solving the rank deficient linear least squares problem

In order to find the least squares solution of minimal norm to linear system \(Ax=b\) with \(A \in \mathcal{C}^{m \times n}\) being a matrix of rank \(r< n \le m\), \(b \in \mathcal{C}^{m}\), Zheng and Wang (Appl Math Comput 169:1305–1323, 2005) proposed a class of symmetric successive overrelaxation (SSOR) methods, which is based on augmenting system to a block \(4 \times 4\) consistent system. In this paper, we construct the unsymmetric successive overrelaxation (USSOR) method. The semiconvergence of the USSOR method is discussed. Numerical experiments illustrate that the number of iterations and CPU time for the USSOR method with the appropriate parameters is respectively less and faster than the SSOR method with optimal parameters.     

Parameterized complexity of three edge contraction problems with degree constraints

For any graph class \(\mathcal{H}\) , the \(\mathcal{H}\) -Contraction problem takes as input a graph \(G\) and an integer \(k\) , and asks whether there exists a graph \(H\in \mathcal{H}\) such that \(G\) can be modified into \(H\) using at most \(k\) edge contractions. We study the parameterized complexity of \(\mathcal{H}\) -Contraction for three different classes \(\mathcal{H}\) : the class \(\mathcal{H}_{\le d}\) of graphs with maximum degree at most  \(d\) , the class \(\mathcal{H}_{=d}\) of \(d\) -regular graphs, and the class of \(d\) -degenerate graphs. We completely classify the parameterized complexity of all three problems with respect to the parameters \(k\) , \(d\) , and \(d+k\) . Moreover, we show that \(\mathcal{H}\) -Contraction admits an \(O(k)\) vertex kernel on connected graphs when \(\mathcal{H}\in \{\mathcal{H}_{\le 2},\mathcal{H}_{=2}\}\) , while the problem is \(\mathsf{W}[2]\) -hard when \(\mathcal{H}\) is the class of \(2\) -degenerate graphs and hence is expected not to admit a kernel at all. In particular, our results imply that \(\mathcal{H}\) -Contraction admits a linear vertex kernel when \(\mathcal{H}\) is the class of cycles.     

Delay-discretization-based sliding mode $$H_{\infty }$$ load frequency control scheme considering actuator saturation of wind-integrated power system

This paper investigates the combined effect of actuator saturation and time-delay on load frequency control (LFC) of a wind-integrated power system (WIPS). Actuator saturation is represented in two different approaches such as polytopic and sector bounding. Delay-discretization-based sliding mode \(H_{\infty }\) control approach is proposed to design a novel LFC scheme. The proposed control scheme requires present as well as delayed states information as input to the controller. This requirement of control scheme is fulfilled by adopting a finite known delay. This finite known delay used in controller design is discretized into delay intervals. Lyapunov–Krasovskii functional is defined for each delay interval, and \(H_{\infty }\) stabilization criteria for the closed loop WIPS are derived in linear matrix inequality framework using Wirtinger-based inequality. The proposed control scheme is tested by considering a numerical example of two-area WIPS.

     

The representations and computations of generalized inverses $$A^{(1)}_{T,S}$$, $$A^{(1,2)}_{T,S}$$AT,S(1,2) and the group inverse

In this paper, we derive novel representations of generalized inverses \(A^{(1)}_{T,S}\) and \(A^{(1,2)}_{T,S}\), which are much simpler than those introduced in Ben-Israel and Greville (Generalized inverses: theory and applications. Springer, New York, 2003). When \(A^{(1,2)}_{T,S}\) is applied to matrices of index one, a simple representation for the group inverse \(A_{g}\) is derived. Based on these representations, we derive various algorithms for computing \(A^{(1)}_{T,S}\), \(A^{(1,2)}_{T,S}\) and \(A_{g}\), respectively. Moreover, our methods can be achieved through Gauss–Jordan elimination and complexity analysis indicates that our method for computing the group inverse \(A_{g}\) is more efficient than the other existing methods in the literature for a large class of problems in the computational complexity sense. Finally, numerical experiments show that our method for the group inverse \(A_{g}\) has highest accuracy among all the existing methods in the literature and also has the lowest cost of CPU time when applied to symmetric matrices or matrices with high rank or small size matrices with low rank in practice.     

Exploring Dynamic Impact of Foreign Direct Investment on China’s CO$$_{}$$ Emissions Using Markov-Switching Vector Error Correction Model

The impact of foreign direct investment (FDI) on China’s CO\(_{2}\) emissions is an important index to evaluate the effect of foreign investment policy. This paper uses the monthly data of CO\(_{2}\) emissions and FDI from January 1997 to December 2013 to analyze the regime states, switching probability and regime correlation between FDI and CO\(_{2}\) emissions with the help of nonlinear Markov-switching vector error correction model (MS-VECM), The results indicate that the influence of FDI on CO\(_{2}\) emissions shows the two-regime dynamic characteristics, FDI has played a stimulating role in promoting China’s CO\(_{2}\) emissions during the period from January 1997 to October 2003, while played an inhibiting role during the period from November 2003 to December 2013. The duration of the inhibiting effect of FDI on CO\(_{2}\) emissions is longer, and the frequency is higher than that of the stimulating effect. Therefore, the overall influence of FDI on CO\(_{2}\) emissions during the period from January 1997 to December 2013 is inhibitive, which means FDI has contributed to CO\(_{2}\) emissions reduction. The innovation points of this study are mainly reflected in the following two aspects: first, nonlinear MS-VECM is introduced to dynamically study the relationship between FDI and CO\(_{2}\) emissions in contrast to prior studies that simply use static analysis method; second, the effect of China’s foreign investment policies on CO\(_{2}\) emissions is evaluated in each period according to the empirical results of MS-VECM.     

Mutually unbiased maximally entangled bases in $$\mathbb {C}^d\otimes \mathbb {C}^d$$

We study mutually unbiased maximally entangled bases (MUMEB’s) in bipartite system \(\mathbb {C}^d\otimes \mathbb {C}^d (d \ge 3)\). We generalize the method to construct MUMEB’s given in Tao et al. (Quantum Inf Process 14:2291–2300, 2015), by using any commutative ring R with d elements and generic character of \((R,+)\) instead of \(\mathbb {Z}_d=\mathbb {Z}/d\mathbb {Z}\). Particularly, if \(d=p_1^{a_1}p_2^{a_2}\ldots p_s^{a_s}\) where \(p_1, \ldots , p_s\) are distinct primes and \(3\le p_1^{a_1}\le \cdots \le p_s^{a_s}\), we present \(p_1^{a_1}-1\) MUMEB’s in \(\mathbb {C}^d\otimes \mathbb {C}^d\) by taking \(R=\mathbb {F}_{p_1^{a_1}}\oplus \cdots \oplus \mathbb {F}_{p_s^{a_s}}\), direct sum of finite fields (Theorem 3.3).