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There are a number of methods for ranking decision making units (DMUs), among which calculating super efficiency and then ranking the units based on the obtained amount of super efficiency are both valid and efficient. Since most of the proposed models do not provide the projection of Pareto efficiency, a model is developed and presented through this paper based on which in the projection of Pareto-efficient is obtained, in addition to calculating the amount of super efficiency. Moreover, the model is unit invariant, and is always feasible and makes the amount of inefficiency effective in ranking.

Estimating power spectrum density (PSD) is essential in signal processing. This short paper gives a theorem to represent a smoothed PSD estimate with the Cauchy integral. It may be used for the approximation of the smoothed PSD estimate.

A statistical model was developed in this study to describe bioethanol production through a batch fermentation process of sugarcane molasses by locally isolatedSaccharomyces cerevisiaeY-39. Response surface methodology RSM based on central composite face centered design CCFD was employed to statistically evaluate and optimize the conditions for maximum bioethanol production and study the significance and interaction of incubation period, initial pH, incubation temperature, and molasses concentration on bioethanol yield. With the use of the developed quadratic model equation, a maximum ethanol production of 255 g/L was obtained in a batch fermentation process at optimum operating conditions of approximately 71 h, pH 5.6, 38°C, molasses concentration 18% wt.%, and 100 rpm.

The purpose of the paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some results related to Posner's theorem as well as to Mayne's theorem are proved.

A discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. The numerical simulations not only illustrate the consistence with the theoretical analysis, but also exhibit other complex dynamical behaviors, such as bifurcation diagrams, Maximum Lyapunov exponents, and phase portraits. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point by using the feedback control method.

This paper deals with the nonmonotone projection algorithm for constrained nonlinear equations. For some starting points, the previous projection algorithms for the problem may encounter slow convergence which is related to the monotone behavior of the iterative sequence as well as the iterative direction. To circumvent this situation, we adopt the nonmonotone technique introduced by Dang to develop a nonmonotone projection algorithm. After constructing the nonmonotone projection algorithm, we show its convergence under some suitable condition. Preliminary numerical experiment is reported at the end of this paper, from which we can see that the algorithm we propose converges more quickly than that of the usual projection algorithm for some starting points.

In this paper, a propagation path loss model for inland river is proposed by three improvements compared with the Round Earth Loss (REL) model for open-sea environment. Specifically, parameters optimization uses Okumura-Hata model in dB scale to replace the equation transformed from the free space loss in REL model; secondly, diffraction loss caused by the obstacles (e.g., large buildings, bridges, or some other facilities near the river bank) is also taken into account; mixed-path methodology as another improvement is used for Inland River (IR) model because the actual propagation environment between transmitter (TX) antenna and receiver (RX) antenna contains both land part and water part. The paper presents a set of 1.4 GHz measurements conducted along the Yangtze River in Wuhan. According to the comparison between path loss models and experimental results, IR model shows a good matching degree. After that, Root Mean Square Error (RMSE), Grey Relation Grade and Mean Absolute Percentage Error (GRG-MAPE), Pearson Correlation Coefficient, and Mean Absolute Percentage Error (PCC-MAPE) are employed to implement quantitative analysis. The results prove that IR model with consideration of mixed path and deterministic information is more accurate than other classic empirical propagation models for these scenarios.

Recently, LSI (Latent Semantic Indexing) based on SVD (Singular Value Decomposition) is proposed to overcome the problems of polysemy and homonym in traditional lexical matching. However, it is usually criticized as with low discriminative power for representing documents although it has been validated as with good representative quality. In this paper, SVD on clusters is proposed to improve the discriminative power of LSI. The contribution of this paper is three manifolds. Firstly, we make a survey of existing linear algebra methods for LSI, including both SVD based methods and non-SVD based methods. Secondly, we propose SVD on clusters for LSI and theoretically explain that dimension expansion of document vectors and dimension projection using SVD are the two manipulations involved in SVD on clusters. Moreover, we develop updating processes to fold in new documents and terms in a decomposed matrix by SVD on clusters. Thirdly, two corpora, a Chinese corpus and an English corpus, are used to evaluate the performances of the proposed methods. Experiments demonstrate that, to some extent, SVD on clusters can improve the precision of interdocument similarity measure in comparison with other SVD based LSI methods.

Uncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite and the system states are disturbed by uncertain noises. We first transform the uncertain LQ problem into an equivalent deterministic LQ problem. Then, the main result given in this paper is the necessary condition for the constrained indefinite LQ optimal control problem by means of the Lagrangian multiplier method. Moreover, in order to guarantee the well-posedness of the indefinite LQ problem and the existence of an optimal control, a sufficient condition is presented in the paper. Finally, a numerical example is presented at the end of the paper.

The main contribution of this paper is presenting a flexible solution to the box-constrained least squares problems. This solution is applicable to many existing problems, such as nonnegative matrix factorization, support vector machine, signal deconvolution, and computed tomography reconstruction. The key concept of the proposed algorithm is to replace the minimization of the cost function at each iteration by the minimization of a surrogate, leading to a guaranteed decrease in the cost function. In addition to the monotonicity, the proposed algorithm also owns a few good features including the self-constraint in the feasible region and the absence of a predetermined step size. This paper theoretically proves the global convergence for a special case of below-bounded constraints. Using the proposed mechanism, some valuable algorithms can be derived. The simulation results demonstrate that the proposed algorithm provides performance that is comparable to that of other commonly used methods in numerical experiment and computed tomography reconstruction.

Thresholding segmentation based on fuzzy entropy and intelligent optimization is one of the most commonly used and direct methods. This paper takes fuzzy Kapur’s entropy as the best optimal objective function, with modified quick artificial bee colony algorithm (MQABC) as the tool, performs fuzzy membership initialization operations through Pseudo Trapezoid-Shaped (PTS) membership function, and finally, according to the image’s spacial location information, conducts local information aggregation by way of median, average, and iterative average so as to achieve the final segmentation. The experimental results show that the proposed FMQABC (fuzzy based modified quick artificial bee colony algorithm) and FMQABCA (fuzzy based modified quick artificial bee colony and aggregation algorithm) can search out the best optimal threshold very effectively, precisely, and speedily and in particular show exciting efficiency in running time. This paper experimentally compares the proposed method with Kapur’s entropy-based Electromagnetism Optimization (EMO) method, standard ABC, and FDE (fuzzy entropy based differential evolution algorithm), respectively, and concludes that MQABCA is far more superior to the rest in terms of segmentation quality, iterations to convergence, and running time.

This paper presents an analytical solution of the simply supported horizontally composite curved I-beam by trigonometric series considering the effect of partial interaction in the tangential direction. Governing equations and boundary conditions are obtained by using the Vlasov curved beam theory and the principle of minimum potential energy. The deflection functions and the Lagrange multiplier functions are expressed as trigonometric series to satisfy the governing equations and the simply supported constraints at both ends. The numerical results of deflections and forces which are obtained by this method are compared with both FEM results and experimental results, and the inaccuracy between the analytical solutions in this paper and the FEM results is small and reasonable.

A method to evaluate the stability of tunnel face is proposed in the framework of upper bound theorem. The safety factor which is widely applied in slope stability analysis is introduced to estimate the stability of tunnel face using the upper bound theorem of limit analysis in conjunction with a strength reduction technique. Considering almost all geomaterials following a nonlinear failure criterion, a generalized tangential technique is used to calculate the external work and internal energy dissipation in the kinematically admissible velocity field. The upper bound solution of safety factor is obtained by optimization calculation. To evaluate the validity of the method proposed in this paper, the safety factor is compared with those calculated by limit equilibrium method. The comparison shows the solutions derived from these two methods match each other well, which shows the method proposed in this paper can be considered as effective.

This paper is motivated by some papers treating the fractional hybrid differential equations with nonlocal conditions and the system of coupled hybrid fractional differential equations; an existence theorem for fractional hybrid differential equations involving Caputo differential operators of order1<α≤2is proved under mixed Lipschitz and Carathéodory conditions. The existence and uniqueness result is elaborated for the system of coupled hybrid fractional differential equations.

In a recent paper, the authors derived the exact solution for the probability mass function of the geometric distribution of orderk, expressing the roots of the associated auxiliary equation in terms of generating functions for Fuss-Catalan numbers. This paper applies the above formalism for the Fuss-Catalan numbers to treat additional problems pertaining to occurrences of success runs. New exact analytical expressions for the probability mass function and probability generating function and so forth are derived. First, we treat sequences of Bernoulli trials withr≥1occurrences of success runs of lengthkwithl-overlapping. The casel<0, where there must be a gap of at leastltrials between success runs, is also studied. Next we treat the distribution of the waiting time for therthnonoverlapping appearance of a pair of successes separated by at mostk-2failures (k≥2).

Given the importance of protease’s worldwide market, the determination of optimum conditions and the development of a standard protocol are critical during selection of a reliable method to determine its bioactivity. This paper uses quality control theory to validate a modified version of a method proposed by Charney and Tomarelli in 1947. The results obtained showed that using azocasein substrate bromelain had its optimum at 45°C and pH 9 (Glycine-NaOH 100 mM). We also quantified the limit of detection (LoD) and limit of quantification (LoQ) in the above-mentioned optimum (0.072 and 0.494 mg·mL−1of azocasein, resp.) and a calibration curve that correlates optical density with the amount of substrate digested. In all analysed samples, we observed a significant decrease in response after storage (around 17%), which suggests its use must be immediately after preparation. Thus, the protocol presented in this paper offers a significant improvement, given that subjective definitions are commonly used in the literature and this simple mathematical approach makes it clear and concise.

Quantum particle swarm optimization (QPSO) is a population based optimization algorithm inspired by social behavior of bird flocking which combines the ideas of quantum computing. For many optimization problems, traditional QPSO algorithm can produce high-quality solution within a reasonable computation time and relatively stable convergence characteristics. But QPSO algorithm also showed some unsatisfactory issues in practical applications, such as premature convergence and poor ability in global optimization. To solve these problems, an improved quantum particle swarm optimization algorithm is proposed and implemented in this paper. There are three main works in this paper. Firstly, an improved QPSO algorithm is introduced which can enhance decision making ability of the model. Secondly, we introduce synergetic neural network model to mangroves classification for the first time which can better handle fuzzy matching of remote sensing image. Finally, the improved QPSO algorithm is used to realize the optimization of network parameter. The experiments on mangroves classification showed that the improved algorithm has more powerful global exploration ability and faster convergence speed.

This paper deals with the characteristic roots of different types of lattice matrices and proves that a matrix and its transpose have the same characteristic roots. Also this paper introduces the concept of similar lattice matrices and proves that similar lattice matrices have the same characteristic roots.

This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI). Three different types of Lattice Boltzmann (LB) models are computed, namely, single relaxation time (SRT), multiple relaxation time (MRT), and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV-) based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS) are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required.

We investigate a class of memristor-based shunting inhibitory cellular neural networks with leakage delays. By applying a new Lyapunov function method, we prove that the neural network which has a unique almost periodic solution is globally exponentially stable. Moreover, the theoretical findings of this paper on the almost periodic solution are applied to prove the existence and stability of periodic solution for memristor-based shunting inhibitory cellular neural networks with leakage delays and periodic coefficients. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies of Wu (2011) and Chen and Cao (2002).

For the problem of easily losing track target when obstacles appear in intelligent robot target tracking, this paper proposes a target tracking algorithm integrating reduced dimension optimal Kalman filtering algorithm based on phase-path volume integral with Camshift algorithm. After analyzing the defects of Camshift algorithm, compare the performance with the SIFT algorithm and Mean Shift algorithm, and Kalman filtering algorithm is used for fusion optimization aiming at the defects. Then aiming at the increasing amount of calculation in integrated algorithm, reduce dimension with the phase-path volume integral instead of the Gaussian integral in Kalman algorithm and reduce the number of sampling points in the filtering process without influencing the operational precision of the original algorithm. Finally set the target centroid position from the Camshift algorithm iteration as the observation value of the improved Kalman filtering algorithm to fix predictive value; thus to make optimal estimation of target centroid position and keep the target tracking so that the robot can understand the environmental scene and react in time correctly according to the changes. The experiments show that the improved algorithm proposed in this paper shows good performance in target tracking with obstructions and reduces the computational complexity of the algorithm through the dimension reduction.

For the shortcoming of fuzzyc-means algorithm (FCM) needing to know the number of clusters in advance, this paper proposed a new self-adaptive method to determine the optimal number of clusters. Firstly, a density-based algorithm was put forward. The algorithm, according to the characteristics of the dataset, automatically determined the possible maximum number of clusters instead of using the empirical rulenand obtained the optimal initial cluster centroids, improving the limitation of FCM that randomly selected cluster centroids lead the convergence result to the local minimum. Secondly, this paper, by introducing a penalty function, proposed a new fuzzy clustering validity index based on fuzzy compactness and separation, which ensured that when the number of clusters verged on that of objects in the dataset, the value of clustering validity index did not monotonically decrease and was close to zero, so that the optimal number of clusters lost robustness and decision function. Then, based on these studies, a self-adaptive FCM algorithm was put forward to estimate the optimal number of clusters by the iterative trial-and-error process. At last, experiments were done on the UCI, KDD Cup 1999, and synthetic datasets, which showed that the method not only effectively determined the optimal number of clusters, but also reduced the iteration of FCM with the stable clustering result.

This paper proposes an adaptive shape kernel-based mean shift tracker using a single static camera for the robot vision system. The question that we address in this paper is how to construct such a kernel shape that is adaptive to the object shape. We perform nonlinear manifold learning technique to obtain the low-dimensional shape space which is trained by training data with the same view as the tracking video. The proposed kernel searches the shape in the low-dimensional shape space obtained by nonlinear manifold learning technique and constructs the adaptive kernel shape in the high-dimensional shape space. It can improve mean shift tracker performance to track object position and object contour and avoid the background clutter. In the experimental part, we take the walking human as example to validate that our method is accurate and robust to track human position and describe human contour.

The paper deals with the multiple gravity assist trajectories design. In order to improve the performance of the heuristic algorithms, such as differential evolution algorithm, in multiple gravity assist trajectories design optimization, a method combining BFS (breadth-first search) and EP_DE (differential evolution algorithm based on search space exploring and principal component analysis) is proposed. In this method, firstly find the possible multiple gravity assist planet sequences with pruning based BFS and use standard differential evolution algorithm to judge the possibility of all the possible trajectories. Then select the better ones from all the possible solutions. Finally, use EP_DE which will be introduced in this paper to find an optimal decision vector of spacecraft transfer time schedule (launch window and transfer duration) for each selected planet sequence. In this paper, several cases are presented to prove the efficiency of the method proposed.

To study incremental machine learning in tensor space, this paper proposes incremental tensor discriminant analysis. The algorithm employs tensor representation to carry on discriminant analysis and combine incremental learning to alleviate the computational cost. This paper proves that the algorithm can be unified into the graph framework theoretically and analyzes the time and space complexity in detail. The experiments on facial image detection have shown that the algorithm not only achieves sound performance compared with other algorithms, but also reduces the computational issues apparently.

Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in this paper concept of the compensating operator. It enables getting sufficient conditions of weak convergence under the conditions on the local characteristics of output semi-Markov process.