Concepts revolving around "displaced cones" are used to extend the ideas of nondominated solutions in multiobjective programming. Necessary and sufficient conditions are formed around the additive models of DEA to idelltify nondominated solutions. This provdes a basis for effecting contacts with other disciplines and other parts of DEA.

The vibration of thin circular cylindrical shells has been studied extensively. In this paper, the existence and uniqueness of the solution of this system are proved by means of semigroup theory on the Hilbert space, and the eigenvalue problem is discussed. This offers a theoretical basis for solving this kind of engineering problems.

The aim of this paper is to describe and analyse the behaviour of heart rate variability (HRV) during constant-load, high-intensity exercise using a time frequency analysis (Wavelet Transform). Eleven elite cyclists took part in the study (age: 18.6±3.0 years; VO2max: 4.88±0.61 litres·min −1). Initially,
all subjects performed an incremental cycloergometer test to determine load power in a constant load-test (379.55±36.02 W; 89.0%). HRV declined dramatically from the start of testing (p <0.05). The behaviour of power spectral density within the LF band mirrored that of total energy, recording a significant decrease from the outset LF peaks fell rapidly thereafter, remaining stable until the end of the test. HF-VHF fell sharply in the first 20 to 30 seconds. The relative weighting (%) of HF-VHF was inverted with the onset of fatigue, [1.6% at the start, 7.1 (p <0.05) at the end of the first phase,and 43.1% (p <0.05) at the end of the test]. HF-VHFpeak displayed three phases: a moderate initial increase, followed by a slight fall, thereafter increasing to the end of the test. The LF/HF-VHF ratio increased at the start, later falling progressively until the end of the first phase and remaining around minimal values until the end of the test.

In this article, the Bayes linear unbiased estimation (BALUE) of parameters is derived for the partitioned linear model. The
superiorities of the BALUE over ordinary least square estimator (LSE) are studied in terms of the Bayes mean square error matrix
(BMSEM) criterion and Pitman closeness (PC) criterion.

This paper considers an epidemic model of a vector-borne disease which has the vector-mediated transmission only. The incidence term is of the bilinear mass-action form. It is shown that the global dynamics is completely determined by the basic
reproduction number $ R_0 $. If $ R_0\leq 1 $, the disease-free equilibrium is globally stable and the disease dies out. If $ R_0>1 $, a unique endemic equilibrium is globally stable in the interior of the feasible region and the disease persists at the endemic equilibrium. Numerical simulations are presented to illustrate the
results.

The difficulty in crude oil price forecasting, due to inherent complexity, has attracted much attention of academic researchers and business practitioners. Various methods have been tried to solve the problem of forecasting crude oil prices. However, all of the existing models of prediction can not meet practical needs. Very recently, Wang and Yu proposed a new methodology for handling complex systems---TEI@I methodology by means of a systematic integration of text mining, econometrics and intelligent techniques. Within the framework of TEI@I methodology, econometrical models are used to model the linear components of crude oil price time series (i.e., main trends) while nonlinear components of crude oil price time series (i.e., error terms) are modelled by using artificial neural network (ANN) models. In addition, the impact of irregular and infrequent future events on crude oil price is explored using web-based text mining (WTM) and rule-based expert systems (RES) techniques. Thus, a fully novel nonlinear integrated forecasting approach with error correction and judgmental adjustment is formulated to improve prediction performance within the framework of the TEI@I methodology. The proposed methodology and the novel forecasting approach are illustrated via an example.

Complex adaptive systems (cas) -- systems that involve many components that adapt or learn as they interact -- are at the heart of important contemporary problems. The study of cas poses unique challenges: Some of our most powerful mathematical tools, particularly methods involving fixed points, attractors, and the like, are of limited help in understanding the development of cas. This paper suggests ways to modify research methods and tools, with an emphasis on the role of computer-based models, to increase our understanding of cas.

In this paper, an approach to improving consistency of judgement matrix in the Analytic Hierarchy Process (AHP) is presented, which utilizes the eigenvector to revise a pair of entries of judgement matrix each time. By using this method, any judgement matrix with a large $C.R.$ can be modified to a matrix which can both tally with the consistency requirement and reserve the most information that the original matrix contains. An algorithm to derive a judgement matrix with acceptable consistency (i.e., $C.R.<0.1$) and two criteria of evaluating modificatory effectiveness are also given.

In reliability theory and survival analysis, the problem of point estimation based on the censored sample has been discussed in many literatures. However, most of them are focused on MLE, BLUE etc; little work has been done on the moment-method estimation in censoring case. To make the method of moment estimation systematic and unifiable, in this paper, the moment-method estimators(abbr. MEs) and modified moment-method estimators(abbr. MMEs) of the parameters based on type I and type II censored samples are put forward involving mean residual lifetime. The strong consistency and other properties are proved. To be worth mentioning, in the exponential distribution, the proposed moment-method estimators are exactly MLEs. By a simulation study, in the view point of bias and mean square of error, we show that the MEs and MMEs are better than MLEs and the ``pseudo complete sample'' technique introduced in Whitten et al.(1988). And the superiority of the MEs is especially conspicuous, when the sample is heavily censored.

The infinite-horizon linear quadratic regulation (LQR) problem is settled for discrete-time systems with input delay. With the help of an autoregressive moving average (ARMA)innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization.The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems.

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.

Semi-tensor product of matrices is a
generalization of conventional matrix product for the case when the
two factor matrices do not meet the dimension matching condition.
It was firstly proposed about ten years ago. Since then it has
been developed and applied to several different fields. In this
paper we will first give a brief introduction. Then give a survey
on its applications to dynamic systems, to logic, to differential
geometry, to abstract algebra, respectively.

In order to address the study of complex systems, the detection of patterns in their dynamics could play a key role in understanding their evolution. In  articular, global patterns are required to detect emergent concepts and trends, some of them of a qualitative nature. Formal concept analysis (FCA) is a theory whose goal is to discover and extract knowledge from qualitative data (organized in concept lattices). In complex environments, such as sport competitions, the large amount of information currently available turns concept lattices into complex networks. The authors analyze how to apply FCA reasoning in order to increase confidence in sports predictions by means of detecting regularities from data through the management of intuitive and natural attributes extracted from publicly available information. The complexity of concept lattices -considered as networks with complex topological structure- is analyzed. It is applied to building a knowledge based system for confidence-based reasoning, which simulates how humans tend to avoid the complexity of concept networks by means of bounded reasoning skills.

China is experiencing from serious water issues. There are many differences among the Nine Major Rivers basins of China in the construction of dikes, reservoirs, floodgates, flood discharge projects, flood diversion projects, water ecological construction, water conservancy management, etc. The shadow prices of water resources for Nine Major Rivers can provide suggestions to the Chinese government. This article develops a dynamic shadow prices approach based on a multiperiod input--output optimizing model. Unlike previous approaches, the new model is based on the dynamic computable general equilibrium (DCGE) model to solve the problem of marginal long-term prices of water resources. First, definitions and algorithms of DCGE are elaborated. Second, the results of shadow prices of water resources for Nine Major Rivers in 1949--2050 in China using the National Water Conservancy input--holding--output table for Nine Major Rivers in 1999 are listed. A conclusion of this article is that the shadow prices of water resources for Nine Major Rivers are largely based on the extent of scarcity. Selling prices of water resources should be revised via the usage of parameters representing shadow prices.

This paper examines the proxy variables of investor sentiment in Chinese stock market carefully, and tries to construct an investor sentiment index indirectly. We use cross correlation analysis to examine lead-lag relationship between the proxy variables and HS300 index. The results show that net added accounts (NAA), SSE share turnover (TURN), and closed-end fund discount (CEFD) are leading variables to stock market. The average first day return of IPOs (RIPO) and relative degree of active trading in equity market (RDAT) are contemporary variables, while number of IPOs (NIPO) is a lagging variable of stock market. Using the sentiment proxy variables with most possible leading order, and forward selection stepwise regression method, the empirical results on monthly stock returns reveal that three leading proxy variables can be used to form a sentiment index. And the out of sample tests prove that this sentiment index has good predictive power of Chinese stock market, and it is robust.

This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.

In this article, a new method for aggregating fuzzy individual opinions into a group consensus opinion is proposed. To obtain the aggregation weights of each individual opinion, a consistency index of each expert with the other experts is introduced based on similarity and distance. The importance of each expert is also taken into consideration in the process of aggregation. Finally, a numerical example is presented to illustrate the efficiency of the procedure.

This paper describes the methodology of singular spectrum analysis (SSA) and demonstrate that it is a powerful method of time series analysis and forecasting, particulary for economic time series. The authors consider the application of SSA to the
analysis and forecasting of the Iranian national accounts data as provided by the Central Bank of the Islamic Republic of Iran.

Variable feedrate interpolation algorithms for five-axis parametric toolpath are very promising but still rather limited currently. In this paper, an off-line feedrate scheduling method of dual NURBS curve is presented with geometric and kinematical constraints. For a given dual parametric curve, the feedrates of sampling points are first scheduled sequent with confined feedrate of cutter tip and machine pivot, chord error, normal acceleration and angular feedrate. Then, the feedrate profiles of angular feed acceleration sensitive regions of the path are adjusted using a bi-directional scanning algorithm. After that, a linear programming method is used to adjust the feedrate profiles of linear feed acceleration sensitive regions and control the linear feed acceleration of both cutter tip and machine pivot within preset values. Further, a NURBS curve is used to fit the feedrates of sampling points. Finally, illustrative examples are carried out to validate the feasibility of the proposed feedrate scheduling method. The results show that the proposed method has the ability of effectively controlling the
angular feed characters of cutter axis as well as the chord error and linear feed characters of cutter tip and machine pivot, and it has potential to be used in high accuracy and high quality five-axis machining.

This paper investigates a risk-averse inventory model by
balancing the expected profit and conditional value-at-risk (CVaR)
in a newsvendor model setting. We find out that: i) The optimal
order quantity is increasing in the shortage cost for both the CVaR
only criterion and the tradeoff objective. ii) For the case of zero
shortage cost, the optimal order quantity to the CVaR criterion or
tradeoff objective is increasing in the selling price, respectively.
However, it may not be monotonic in the selling price when
incorporating a substantial shortage cost. Moreover, it may be
larger or less than the risk-neutral solution. iii) Under the
tradeoff objective function, although the optimal order quantity for
the model without shortage cost is increasing in the weight put on
the expected profit, this property may not be true in general for
the model with a substantial shortage cost. Some numerical examples
are conducted to verify our results and observations.

This paper is concerned with the resource allocation problem based on data envelopment analysis (DEA) which is generally found in practice such as in public services and in production process. In management context, the resource allocation has to achieve the {effective-efficient-equality} aim and tries to balance the different desires of two management layers: central manager and each sector. In mathematical programming context, to solve the resource allocation asks for introducing many optimization techniques such as multiple-objective programming and goal programming. We construct an algorithm framework by using comprehensive DEA tools including CCR, BCC models, inverse DEA model, the most compromising common weights analysis model, and extra resource allocation algorithm. Returns to scale characteristic is put major place for analyzing DMUs’ scale economies and used to select DMU candidates before resource allocation. By combining extra resource allocation algorithm with scale economies target, we propose a resource allocation solution, which can achieve the {effective-efficient-equality} target and also provide information for future resource allocation. Many numerical examples are discussed in this paper, which also verify our work.

In this paper, we use the plug-in and Whittle methods that are based on spectral regression analysis to test for the long memory property in 12 Asian/dollar daily exchange rates. The results according to the plug-in method show that with the exception of Chinese renminbi all series may have long memory properties. The results based on the Whittle method, on the other hand, show that only Japanese yen and Malaysian ringgit may have long memory properties. It is well known that inference about the differencing parameter, d, in presence of structural break in a series entails considerable difficulties. Therefore, given the financial crisis of 1997–1998 in Asia, further tests for unravelling of the memory property and presence of structural break in the exchange rate series are required.

This paper concerns robust Kalman filtering for systems under norm bounded uncertainties in all the system matrices and error covariance constraints. Sufficient conditions are given for the existence of such filters in terms of Riccati equations. The solutions to the conditions can be used to design the filters. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed design procedure.

When the five-axis CNC system executes the 3D cutter radius compensation function, the angle between two adjacent radius compensation vectors might become very large and the linear axes would move too fast if the tool orientation vector is close to the surface normal. The reason that results in this phenomenon is analyzed based on building the transmission relationship between the cutter contact point and the cutter location point. By taking the square-end tool as an example, an optimization algorithm to control the undesired movements is advanced. For the singular area where sudden change exists, the number of interpolation cycles is determined by the cutter feedrate, the limit speeds of machine axes and the maximum allowable angle between radius compensation vectors of adjacent NC blocks. The radius compensation vector of each interpolation cycle is obtained by a kind of vector rotation method. By maintaining the perpendicularity between the radius compensation vector and the tool orientation vector, the rapid movements of the linear axes are eliminated. A trial-cut experiment is performed to verify the correctness and the effectiveness of the proposed algorithm.

In this note, the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time. For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull, maximum likelihood estimation is investigated.

A brief summary on and comprehensive understanding of fuzzy optimization is presented. This summary is made on aspects of fuzzy modelling and fuzzy optimization, classification and formulation for the fuzzy optimization problems, models and methods. The importance of interpretation of the problem and formulation of the optimal solution in fuzzy sense are emphasized in the summary of the fuzzy optimization.

In applications, the traditional estimation procedure generally begins with model selection. Once a specific model is selected, subsequent estimation is conducted under the selected model without consideration of the uncertainty from the selection process. This often leads to the underreporting of variability and too optimistic
confidence sets. Model averaging estimation is an alternative to this procedure, which incorporates model uncertainty into the estimation process. In recent years, there has been a rising interest in model averaging from the frequentist perspective, and
some important progresses have been made. In this paper, the theory
and methods on frequentist model averaging estimation are surveyed.
Some future research topics are also discussed.

Various mathematical models have been commonly used in time series analysis and forecasting. In these processes, academic researchers and business practitioners often come up against two important problems. One is whether to select an appropriate modeling approach for prediction purposes or to combine these different individual approaches into a single forecast for the different/dissimilar modeling approaches. Another is whether to select the best candidate model for forecasting or to mix the various candidate models with different parameters into a new forecast for the same/similar modeling approaches. In this study, we propose a set of computational procedures to solve the above two issues via two judgmental criteria. Meanwhile, in view of the problems presented in the literature, a novel modeling technique is also proposed to overcome the drawbacks of existing combined forecasting methods. To verify the efficiency and reliability of the proposed procedure and modeling technique, the simulations and real data examples are conducted in this study. The results obtained reveal that the proposed procedure and modeling technique can be used as a feasible solution for time series forecasting with multiple candidate models.

We consider the stability of a random Riccati equation
with a Markovian binary jump coefficient. More specifically, we
are concerned with the boundedness of the solution of a random
Riccati difference equation arising from Kalman filtering with
measurement losses. A sufficient condition for the peak covariance
stability is obtained which has a simpler form and is shown to be
less conservative in some cases than a very recent result in
existing literature. Furthermore, we show that a known sufficient
condition is also necessary when the observability index equals
one.

Let $T$ be a tree with matching number $\mu(T)$. In this paper we obtain the following result: If $T$ has no perfect matchings, then $\mu(T)$ is a lower bound for the number of nonzero Laplacian eigenvalues of $T$ which are smaller than $2$.

Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the threshold parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.

We develop the interpolated finite element method to solve second-order hyperbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation over adjacent elements. We prove that this interpolated finite element solution has superconvergence. This method can easily be applied to generating more accurate gradient either locally or globally, depending on the applications. This method is also completely vectorizable and parallelizable to take the advantages ofmodern computer structures. Several numerical examples are presented to confirm our theoretical analysis.

To eliminate computational problems involved in evaluating multi-attribute bids with different measures, this article first normalizes each individual component of a bid, and then makes use of the weighted product method to present a new scoring function that converts each bid into a score. Two kinds of multi-attribute auction
models are introduced in terms of scoring rules and bidding objective functions. Equilibrium bidding strategies, procurer's revenue comparisons and optimal auction design are characterized in these two models. Finally, this article discusses some improvement of robustness of our models, with respect to the assumptions.

This paper discusses the enumeration of 1-generator quasi-cyclic codes and describes an algorithm which will obtain one, and only one, generator for each 1-generator quasi-cyclic code.

A coupled system of singularly perturbed convection-diffusion equations is considered. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solutions to the system have boundary layers that overlap and interact. The structure of these layers is analyzed, and this leads to the construction of a piecewise-uniform mesh that is a variant of the usual Shishkin mesh. On this mesh an upwind difference scheme is proved to be almost first-order accurate, uniformly in both small parameters. We present the results of numerical experiments to confirm our theoretical results.

A nonlinear version of Krein Rutman Theorem is established. This paper presents a unified proof of the Krein Rutman Theorem for linear operators and for nonlinear operators, and of the Perron-Frobenius theorem for nonnegative matrices and for
nonnegative tensors.

This paper considers the robust stability of state-space models of linear systems subject to real structured perturbations. The "Zero exclusion principle ", which is based on the properties of the Kronecker product and the bialternate product, is employed to derive the new robust stability bounds for time-invariant perturbations. Vaious examples are presented to demonstrate the merit of the method proposed. The examples show that the new bounds are easy to compute numerically and can expect an arbitrary degree of improvement over the previous ones reported by the Lyapunov stability method and the frequency domain approach.

This paper analyzes the network of passes among the players of the Spanish team during the last FIFA World Cup 2010, where they emerged as the  hampion, with the objective of explaining the results obtained from the behavior at the complex network level. The team is considered a network with players as nodes and passes as (directed) edges. A temporal analysis of the resulting passes network is also done, looking at the number of passes, length of the chain of passes, and to network measures such as player centrality and clustering coefficient. Results of the last three matches (the decisive ones) indicate that the clustering coefficient of the pass network remains high, indicating the elaborate style of the Spanish team. The effectiveness of the opposing team in negating the Spanish game is reflected in the change of several network measures over time, most importantly in drops of the clustering coefficient and passing length/speed, as well as in their being able in removing the most talented players from the central positions of the network. Spain’s ability to restore their combinative game and move the focus of the game to offensive positions and talented players is shown to tilt the balance in favor of the Spanish team.

The greedy algorithm is a strong local searching algorithm. The genetic algorithm is generally applied to the global optimization problems. In this paper, we combine the greedy idea and the genetic algorithm to propose the greedy genetic algorithm which incorporates the global exploring ability of the genetic algorithm and the local convergent ability of the greedy algorithm. Experimental results show that greedy genetic algorithm gives much better results than the classical genetic algorithm.

The skewness of the return distribution is one of the important features of the security price. In this paper, the authors try to explore the relationship between the skewness and the coefficient of risk premium. The coefficient of the risk premium is estimated by a GARCH-$M$ model, and the robust measurement of skewness is calculated by Groeneveld-Meeden method. The empirical evidences for the composite indexes from 33 securities markets in the world indicate that the risk compensation requirement in the market where the return distribution is positively skewed is virtually zero, and the risk compensation requirement is positive in a significant level in the market where the return distribution is negative skewed. Moreover, the skewness is negatively correlated with the coefficient of the risk premium.