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This paper considers the delayed age replacement policy, in which the lifetimes of all units are assumed to be uncertain variables, and the lifetime of the first unit has an uncertainty distribution which is different from the others. A delayed age replacement model which is concerned with finding the optimal replacement time to minimize the expected cost is developed. In the policy, the optimal replacement time is irrelevant to the uncertain distribution of lifetime of the first unit over the infinite time span.

This paper studies the take-out route delivery problem (TRDP) with order allocation and unilateral soft time window constraints. The TRDP considers the order allocation and delivery route optimization in the delivery service process. The TRDP is a challenging version of vehicle routing problem. In order to solve this problem, this paper aims to minimize the total cost of delivery, builds an optimization model of this problem by using cumulative time, and adds time dimension in order allocation and path optimization dimensions. It can not only track the real-time location of delivery personnel but also record the delivery personnel to perform a certain task. The main algorithm is the dynamic allocation algorithm designed from the perspective of dispatch efficiency, and the subalgorithm is the improved genetic algorithm. Finally, some experiments are designed to verify the effectiveness of the established model and the designed algorithm, the order allocation and route optimization are calculated with/without the consideration of traffic jam, and the results show that the algorithm can generate better solution in each scene.

Let L = − Δ ℍ n + V be a Schrödinger operator on the Heisenberg group ℍ n , where Δ ℍ n is the sub-Laplacian on ℍ n and the nonnegative potential V belongs to the reverse Hölder class B q with q ∈ Q / 2 , ∞ . Here, Q = 2 n + 2 is the homogeneous dimension of ℍ n . Assume that e − t L t > 0 is the heat semigroup generated by L . The semigroup maximal function related to the Schrödinger operator L is defined by T L ∗ f u ≔ sup t > 0 e − t L f u . The Riesz transform associated with the operator L is defined by R L = ∇ ℍ n L − 1 / 2 , and the dual Riesz transform is defined by R L ∗ = L − 1 / 2 ∇ ℍ n , where ∇ ℍ n is the gradient operator on ℍ n . In this paper, the author first introduces a class of Morrey spaces associated with the Schrödinger operator L on ℍ n . Then, by using some pointwise estimates of the kernels related to the nonnegative potential, the author establishes the boundedness properties of these operators T L ∗ , R L , and R L ∗ acting on the Morrey spaces. In addition, it is shown that the Riesz transform R L = ∇ ℍ n L − 1 / 2 is of weak-type 1 , 1 . It can be shown that the same conclusions are also true for these operators on generalized Morrey spaces.

The force transfer of fully grouted rock bolts is playing a significant effect in determining the rock reinforcement quality. To evaluate the performance of rock bolts, laboratory pulling tests were commonly used. Experimental tests proved that the confining medium diameter had an effect on the rock bolting performance. However, little analytical work has been performed to investigate the impact of the confining medium diameter on rock bolt load-carrying capacity. Therefore, this paper analytically studied the confining medium diameter effect on the load-carrying capacity of rock bolts. It was found that the load-carrying capacity of rock bolts was obviously affected by the confining medium diameter. Moreover, the larger the confining medium diameter, the higher the load-carrying capacity of rock bolts. However, the ascending rate of the load-carrying capacity gradually declined. This load-carrying capacity variation trend consistently agreed with experimental results. Moreover, with the confining medium diameter ascending, the load-carrying capacity variation trend was consistent when the confining medium modulus was under different levels. Last, it was found that, with the confining medium modulus ascending, the critical influence diameter gradually dropped.

In this paper, we consider a quantitative fourth moment theorem for functions (random variables) defined on the Markov triple E , μ , Γ , where μ is a probability measure and Γ is the carré du champ operator. A new technique is developed to derive the fourth moment bound in a normal approximation on the random variable of a general Markov diffusion generator, not necessarily belonging to a fixed eigenspace, while previous works deal with only random variables to belong to a fixed eigenspace. As this technique will be applied to the works studied by Bourguin et al. (2019), we obtain the new result in the case where the chaos grade of an eigenfunction of Markov diffusion generator is greater than two. Also, we introduce the chaos grade of a new notion, called the lower chaos grade, to find a better estimate than the previous one.

We present a counterexample to the main result of the abovementioned paper showing that this result is false and cannot be improved in a simple way.

As a space-filling method, Voronoi Treemaps are used for showcasing hierarchies. Previously presented algorithms are limited to visualize nonspatial data. The approach of spatial Voronoi Treemaps is proposed in this paper to eliminate these problems by enabling the subdivisions for points, lines, and polygons with spatial coordinates and references. The digital distance transformation is recursively used to generate nested raster Voronoi polygons while the raster to vector conversion is used to create a vector-based Treemap visualization in a GIS (geographic information system) environment. The objective is to establish a spatial data model to better visualize and understand the hierarchies in the geographic field.

For a connected graph J, a subset W ⊆ V J is termed as a locating-total dominating set if for a ∈ V J , N a ∩ W ≠ ϕ , and for a , b ∈ V J − W , N a ∩ W ≠ N b ∩ W . The number of elements in a smallest such subset is termed as the locating-total domination number of J. In this paper, the locating-total domination number of unicyclic graphs and bicyclic graphs are studied and their bounds are presented. Then, by using these bounds, an upper bound for cacti graphs in terms of their order and number of cycles is estimated. Moreover, the exact values of this domination variant for some families of cacti graphs including tadpole graphs and rooted products are also determined.

Nevanlinna theory provides us with many tools applicable to the study of value distribution of meromorphic solutions of differential equations. Analogues of some of these tools have been recently developed for difference, q-difference, and ultradiscrete equations. In many cases, the methodologies used in the study of meromorphic solutions of differential, difference, and q-difference equations are largely similar. The purpose of this paper is to collect some of these tools in a common toolbox for the study of general classes of functional equations by introducing notion of a good linear operator, which satisfies certain regularity conditions in terms of value distribution theory. As an example case, we apply our methods to study the growth of meromorphic solutions of the functional equation M(z,f)+P(z,f)=h(z), where M(z,f) is a linear polynomial in f and L(f), where L is good linear operator, P(z,f) is a polynomial in f with degree deg P≥2, both with small meromorphic coefficients, and h(z) is a meromorphic function.

The 3D reconstruction technique using the straight-line segments as features has high precision and low computational cost. The method is especially suitable for large-scale urban datasets. However, the line matching step in the existing method has a mismatching problem. The two main reasons for this problem are the line detection result is not located at the true edge of the image and there is no consistency check of the matching pair. In order to solve this problem, a linear correction and matching method for 3D reconstruction of target line structure is proposed in this paper. Firstly, the edge features of the image are extracted to obtain a binarized edge map. Then, the extended gradient map is calculated using the edge map and the gradient to establish the gradient gravitational map. Secondly, the straight-line detection method is used to extract all the linear features used for the 3D reconstruction image, and the linear position is corrected by the gradient gravitational map. Finally, the point feature matching result is used to calculate the polar line, and the line matching results of the adjacent three images are used to determine the final partial check feature area. Then, random sampling is used to obtain the feature similarity check line matching result in the small neighborhood. The aforementioned steps can eliminate the mismatched lines. The experimental results demonstrate that the 3D model obtained using the proposed method has higher integrity and accuracy than the existing methods.

It is well known that the appearance of the delay in the fractional delay differential equation (FDDE) makes the convergence analysis very difficult. Dealing with the problem with the traditional reproducing kernel method (RKM) is very tricky. The feature of this paper is to gain a more credible approximate solution via fractional Taylor’s series (FTS). We use the FTS to deal with the delay for improving the accuracy of the approximate solutions. Compared with other methods, the five numerical examples demonstrate the accuracy and efficiency of the proposed method in this paper.

This paper is concerned with the perturbed Riemann problem for the Aw-Rascle model with the modified Chaplygin gas pressure. We obtain constructively the solutions when the initial values are three piecewise constant states. The global structure and the large-time asymptotic behaviors of the solutions are discussed case by case. Further, we obtain the stability of the corresponding Riemann solutions as the initial perturbed parameter tends to zero.

As an important part of the social economy, stock market plays an important role in economic development, and accurate prediction of stock price is important as it can lower the risk of investment decision-making. However, the task of predicting future stock price is very difficult. This difficulty arises from stocks with nonstationary behavior and without any explicit form. In this paper, we propose a novel bidirectional Long Short-Term Memory Network (BiLSTM) framework called evolutionary BiLSTM (EBiLSTM) for the prediction of stock price. In the framework, three independent BiLSTMs correspond to different objective functions and act as mutation individuals, then their respective losses for evolution are calculated, and finally, the optimal objective function is identified by the minimum of loss. Since BiLSTM is effective in the prediction of time series and the evolutionary framework can get an optimal solution for multiple objectives, their combination well adapts to the nonstationary behavior of stock prices. Experiments on several stock market indexes demonstrate that EBiLSTM can achieve better prediction performance than others without the evolutionary operator.

This paper mainly studies the influence of dynamic cognitive diagnosis on personalized learning. Considering the influence of knowledge correlation factors and human brain memory factors on learning activities, a knowledge tracing model integrating learning factors is proposed. Firstly, based on the exercise-knowledge association information, the model maps learners and exercises to the knowledge space with clear meaning. Then, the evolution process of learners’ knowledge learning is quantitatively modeled in the knowledge space by integrating the classical learning curve and forgetting curve theory of pedagogy. On the other hand, considering the influence of topic semantics in the learning process, a knowledge tracing model integrating topic semantics is proposed in this paper. Firstly, the model designs a dynamic enhanced memory network to store the common information of knowledge and describes the learners’ dynamic mastery of knowledge. Secondly, the depth representation method of exercise resources is proposed to mine the text personality information and integrate it into the process of learners’ knowledge change modeling. Through a large number of experiments on exercise records, it is verified that the proposed model has accurate prediction performance and knowledge tracing interpretability.

In this paper, the structure of graphs in terms of k-externally stable set (k-ESS) is investigated by a matrix method based on a new matrix product, called semitensor product of matrices. By defining an eigenvector and an eigenvalue of the node subset of a graph, three necessary and sufficient conditions of k-ESS, minimum k-ESS, and k-kernels of graphs are proposed in a matrix form, respectively. Using these conditions, the concepts of k-ESS matrix, minimum k-ESS matrix, and k-kernel matrix are introduced. These matrices provide complete information of the corresponding structures of a graph. Further, three algorithms are designed, respectively, to find all these three structures of a graph by conducting a series of matrix operation. Finally, the correctness and effectiveness of the results are checked by studying an example. The proposed method and results may offer a new way to investigate the problems related to graph structures in the field of network systems.

Teleoperated robotic systems are those in which human operators control remote robots through a communication network. The deployment and integration of teleoperated robot’s systems in the medical operation have been hampered by many issues, such as safety concerns. Elliptic curve cryptography (ECC), an asymmetric cryptographic algorithm, is widely applied to practical applications because its far significantly reduced key length has the same level of security as RSA. The efficiency of ECC on GF (p) is dictated by two critical factors, namely, modular multiplication (MM) and point multiplication (PM) scheduling. In this paper, the high-performance ECC architecture of SM2 is presented. MM is composed of multiplication and modular reduction (MR) in the prime field. A two-stage modular reduction (TSMR) algorithm in the SCA-256 prime field is introduced to achieve low latency, which avoids more iterative subtraction operations than traditional algorithms. To cut down the run time, a schedule is put forward when exploiting the parallelism of multiplication and MR inside PM. Synthesized with a 0.13 um CMOS standard cell library, the proposed processor consumes 341.98k gate areas, and each PM takes 0.092 ms.

Aiming at the mining of traffic events based on large amounts of highway data, this paper proposes an improved fast peak clustering algorithm to process highway toll data. The highway toll data are first analyzed, and a data cleaning method based on the sum of similar coefficients is proposed to process the original data. Next, to avoid the shortcomings of the excessive subjectivity of the original algorithm, an improved fast peak clustering algorithm is proposed. Finally, the improved algorithm is applied to highway traffic condition analysis and abnormal event mining to obtain more accurate and intuitive clustering results. Compared with two classical algorithms, namely, the k-means and density-based spatial clustering of applications with noise (DBSCAN) algorithms, as well as the unimproved original fast peak clustering algorithm, the proposed algorithm is faster and more accurate and can reveal the complex relationships among massive data more efficiently. During the process of reforming the toll system, the algorithm can automatically and more efficiently analyze massive toll data and detect abnormal events, thereby providing a theoretical basis and data support for the operation monitoring and maintenance of highways.

Electronic component recognition plays an important role in industrial production, electronic manufacturing, and testing. In order to address the problem of the low recognition recall and accuracy of traditional image recognition technologies (such as principal component analysis (PCA) and support vector machine (SVM)), this paper selects multiple deep learning networks for testing and optimizes the SqueezeNet network. The paper then presents an electronic component recognition algorithm based on the Faster SqueezeNet network. This structure can reduce the size of network parameters and computational complexity without deteriorating the performance of the network. The results show that the proposed algorithm performs well, where the Receiver Operating Characteristic Curve (ROC) and Area Under the Curve (AUC), capacitor and inductor, reach 1.0. When the FPR is less than or equal 10 − 6 level, the TPR is greater than or equal to 0.99; its reasoning time is about 2.67 ms, achieving the industrial application level in terms of time consumption and performance.

To deal with inconsistencies coming from consideration of criteria, that is, attributes with preference-ordered domains (scales), such as product quality, market share, and debt ratio, the dominance-based rough set approach has been proposed. However, it is not much useful for analyzing incomplete information. In this paper, we attempt to present research focusing on incomplete ordered decision systems where all attributes are considered as criteria and some objects’ criterion values are unknown. Under the assumption that all unknown values are the “do not care” semantics, the concept of tolerance dominance relation is introduced. Then, the rough approximations induced by it are obtained. And their properties are investigated. Especially, the important properties of rough approximations, such as rough inclusion, complementarity, identity, and monotonicity, are preserved well-known in the presented methodology. Moreover, an example is employed to illustrate these results. We expand the potential applications of dominance-based rough set approach.

In this paper, a vector-borne disease model with two delays and reinfection is established and considered. First of all, the existence of the equilibrium of the system, under different cases of two delays, is discussed through analyzing the corresponding characteristic equation of the linear system. Some conditions that the system undergoes Hopf bifurcation at the endemic equilibrium are obtained. Furthermore, by employing the normal form method and the center manifold theorem for delay differential equations, some explicit formulas used to describe the properties of bifurcating periodic solutions are derived. Finally, the numerical examples and simulations are presented to verify our theoretical conclusions. Meanwhile, the influences of the degree of partial protection for recovered people acquired by a primary infection on the endemic equilibrium and the critical values of the two delays are analyzed.

Because the defects in the existing modeling methods for the equivalent mechanical model of a sloshing fluid have led to incorrect or inaccurate results in the existing equivalent models, this paper discusses three different modeling methods for the equivalent models: the traditional method, Housner’s method, and the modified method. The equivalent models obtained by the three methods are, respectively, presented and compared with each other for a liquid in rectangular and upright cylindrical tanks. The results show that the traditional method cannot provide the correct location expressions of the equivalent masses because the two types of different excitations are simultaneously used in one equivalent model. An equivalent model is exclusively applicable to a certain excitation (a translational excitation in a certain direction or a rotational excitation about a certain axis). Housner’s method is based on physical intuition, instead of fluid dynamics theory, therefore the calculation precision of Housner’s solution is not satisfactory. Housner’s method is only suitable for vertical tanks with a flat bottom subjected to a horizontal excitation. Based on a conceptual mistake in the traditional method, the concept of the equivalent model is reclarified, and the modified equivalence method is therefore suggested. A supplementary solution for the equivalent model in a cylindrical tank is presented. The correct models can be acquired using the modified equivalence method, which is applicable to tanks of arbitrary shape.

The preview control problem of a class of linear discrete-time descriptor systems is studied. Firstly, the descriptor system is decomposed into a normal system and an algebraic equation by the method of the constrained equivalent transformation. Secondly, by applying the first-order forward difference operator to the state equation, combined with the error equation, the error system is obtained. The tracking problem is transformed into the optimal preview control problem of the error system. Finally, the optimal controller of the error system is obtained by using the related results and the optimal preview controller of the original system is gained. In this paper, we propose a numerical simulation method for descriptor systems. The method does not depend on the restricted equivalent transformation.

This paper studies the pricing of American carbon emission derivatives and its numerical method under the mixed fractional Brownian motion. To capture the long memory properties such as self-similarity and long-range dependence in the price process, we proposed a model based on a fractional Black–Scholes, which is more in line with the actual characteristics of the option market. We have outlined a power penalty approach using parabolic variation inequality and linear complementarity (LCP) which arises from mixed fractional Brownian motion. In addition, we introduced a nonuniform grid-based modification of the fitted finite volume method for numerical solution. Numerically, we show the impact of Hurst exponent on the pricing and analyze the convergence rates of the proposed penalty method. In conclusion, since mfBm is a well-developed mathematical model of strongly correlated stochastic processes, this model will be an efficient model for pricing carbon financial derivative.

The Kalman filter gain arises in linear estimation and is associated with linear systems. The gain is a matrix through which the estimation and the prediction of the state as well as the corresponding estimation and prediction error covariance matrices are computed. For time invariant and asymptotically stable systems, there exists a steady state value of the Kalman filter gain. The steady state Kalman filter gain is usually derived via the steady state prediction error covariance by first solving the corresponding Riccati equation. In this paper, we present iterative per-step and doubling algorithms as well as an algebraic algorithm for the steady state Kalman filter gain computation. These algorithms hold under conditions concerning the system parameters. The advantage of these algorithms is the autonomous computation of the steady state Kalman filter gain.

Classification learning with association rules has been an active research area during recent years. Thus, it is important to establish some numerical importance measure for association rules. In this paper, we propose a new rule importance measure, called a HD measure, using information theory. A num ber of properties of the new measure are analyzed, and its classification performances are compared with that of other rule measures.

If P(z) is a polynomial of degree n having no zeros in |z|<1, then it is known that, for all α,β∈𝒞 with |α|≤1, |β|≤1, R>r≥1, and p>0, P(Rz)-αP(rz)+β{((R+1)/(r+1))n-|α|}P(rz)p≤([Rn-αrn+β{((R+1)/(r+1))n-|α|}]z+[1-α+β{((R+1)/(r+1))n-α}]p/1+zp)P(z)p. In this paper, we will prove a result which not only generalizes the above inequality but also generalize and refines the various results pertaining to the Lp norm of P(z)∀p>0. We will also prove a result which extends and refines a result of Boas Jr. and Rahman (1962). Also we will see that our results lead to some striking conclusions giving refinements and generalizations of other well-known results.

This paper presents a two-stage soft thresholding algorithm based on discrete cosine transform (DCT) and empirical mode decomposition (EMD). In the first stage, noisy speech is decomposed into eight frequency bands and a specific noise variance is calculated for each one. Based on this variance, each band is denoised using soft thresholding in DCT domain. The remaining noise is eliminated in the second stage through a time domain soft thresholding strategy adapted to the intrinsic mode functions (IMFs) derived by applying EMD on the signal obtained from the first stage processing. Significantly better SNR improvement and perceptual speech quality results for different noise types prove the superiority of the proposed algorithm over recently reported techniques.

The paper presents a numerical investigation of non-Newtonian modeling effects on unsteady periodic flows in a two-dimensional (2D) pipe with two idealized stenoses of 75% and 50% degrees, respectively. The governing Navier-Stokes equations have been modified using the Cartesian curvilinear coordinates to handle complex geometries. The investigation has been carried out to characterize four different non-Newtonian constitutive equations of blood, namely, the (i) Carreau, (ii) Cross, (iii) Modified Casson, and (iv) Quemada models. The Newtonian model has also been analyzed to study the physics of fluid and the results are compared with the non-Newtonian viscosity models. The numerical results are represented in terms of streamwise velocity, pressure distribution, and wall shear stress (WSS) as well as the vorticity, streamlines, and vector plots indicating recirculation zones at the poststenotic region. The results of this study demonstrate a lower risk of thrombogenesis at the downstream of stenoses and inadequate blood supply to different organs of human body in the Newtonian model compared to the non-Newtonian ones.

We establish, in this paper, the closed form analytical solutions of steady fully developed flows of couple stress fluid between two concentric cylinders, generated due to the constant pressure gradient or the translatory motion of the outer cylinder or both, using the slip boundary conditions. The classical solutions for Newtonian fluid in the hydrodynamic case appear as a limiting case of our solutions. The velocity profiles of the flows are presented and the effect of various parameters on velocity is discussed. The results indicate that the presence of couple stresses decreases the velocity of the fluid.

The present paper treats a concept of (h,k)-dichotomy for linear discrete systems. Sufficient conditions for the k-boundedness of the projection sequences that give the dichotomy are presented and an illustrative example shows the connection between the growth of the system and the bound of the sequence of projections. Thus the growth of the system that is assumed in the theorems is essential.

This is a review paper of up-to-date research done on the existence of unique null curves, screen distributions, Levi-Civita connection, symmetric Ricci tensor, and scalar curvature for a large variety of lightlike submanifolds of semi-Riemannian (in particular, Lorentzian) manifolds, supported by examples and an extensive bibliography. We also propose some open problems.

Let R be a commutative ring with identity. The zero-divisor graph of R, denoted Γ(R), is the simple graph whose vertices are the nonzero zero-divisors of R, and two distinct vertices x and y are linked by an edge if and only if xy=0. The genus of a simple graph G is the smallest integer g such that G can be embedded into an orientable surface Sg. In this paper, we determine that the genus of the zero-divisor graph of Zn, the ring of integers modulo n, is two or three.

The water flow-like algorithm (WFA) is a relatively new metaheuristic that performs well on the object grouping problem encountered in combinatorial optimization. This paper presents a WFA for solving the travelling salesman problem (TSP) as a graph-based problem. The performance of the WFA on the TSP is evaluated using 23 TSP benchmark datasets and by comparing it with previous algorithms. The experimental results show that the proposed WFA found better solutions in terms of the average solution and the percentage deviation of the average solution from the best-known solution.

This paper develops an inventory model for items with uncertain deterioration rate, time-dependent demand rate with nonincreasing function, and allowable shortage under fuzzy inflationary situation. The goods are not deteriorating upon reception, but the deteriorating starts after elapsing a specified time. The lead time and inflation rate are both uncertain in the model. The resultant effect of inflation and time value of money is assumed to be fuzzy in nature and also we consider lead time as a fuzzy function of order quantity. Furthermore the following different deterioration rates have been considered: for the first case we consider fuzzy deterioration rate and for the second case we assume that the deterioration rate is time dependent and follows Weibull distribution with three known parameters. Since the inflation rate, deterioration rate, and the lead time are fuzzy numbers, the objective function becomes fuzzy. Therefore the estimate of total costs for each case is derived using signed distance technique for defuzzification. The optimal replenishment policy for the model is to minimize the total present value of inventory system costs, derived for both the above mentioned policies. Numerical examples are then presented to illustrate how the proposed model is applied.

A Cayley graph of a group G is called normal edge-transitive if the normalizer of the right representation of the group in the automorphism of the Cayley graph acts transitively on the set of edges of the graph. In this paper, we determine all connected normal edge-transitive Cayley graphs of the group U6n.

Intuitionistic fuzzy sets IFSs have attracted more and more scholars' attention due to their powerfulness in expressing vagueness and uncertainty. In the course of decision making with IFSs, aggregation operators play a very important role since they can be used to synthesize multidimensional evaluation values represented as intuitionistic fuzzy values into collective values. This paper proposes a family of intuitionistic fuzzy hybrid weighted aggregation operators, such as the intuitionistic fuzzy hybrid weighted averaging operator, the intuitionistic fuzzy hybrid weighted geometric operator, the generalized intuitionistic fuzzy hybrid weighted averaging operator, and the generalized intuitionistic fuzzy hybrid weighted geometric operator. All these newly developed operators not only can weight both the arguments and their ordered positions simultaneously but also have some desirable properties, such as idempotency, boundedness, and monotonicity. To show the applications of our proposed intuitionistic fuzzy hybrid weighted aggregation operators, a simple schema for decision making with intuitionistic fuzzy information is developed. An example concerning the human resource management is given to illustrate the validity and applicability of the proposed method and also the hybrid weighted aggregation operators.

It is proved in this paper that, for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its n-division points is n times that of its y-coordinate.

Most scheduling problems are based on the assumption that machines work continuously during the planning horizon. This assumption is not true in many production environments because the machine may not be available during one or more periods such as during breakdowns or maintenance operations. In this paper, the problem of the single machine scheduling with one unavailability period and nonresumable jobs with the aim of minimizing the number of tardy jobs is studied. A number of theorems are proved and a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes upper and lower bounds and efficient dominance rules. Computational results for 2680 problem instances show that the branch-and-bound approach is capable of solving 98.7% of the instances optimally, bearing witness to the efficiency of the proposed procedure. Our results also indicate that the proposed approaches are more efficient when compared to other methods.

This paper suggests some estimators for population mean of the study variable in simple random sampling and two-phase sampling using information on an auxiliary variable under second order approximation. Bahl and Tuteja (1991) and Singh et al. (2008) proposed some efficient estimators and studied the properties of the estimators to the first order of approximation. In this paper, we have tried to find out the second order biases and mean square errors of these estimators using information on auxiliary variable based on simple random sampling and two-phase sampling. Finally, an empirical study is carried out to judge the merits of the estimators over others under first and second order of approximation.

To date, researchers usually use spectral and pseudospectral methods for only numerical approximation of ordinary and partial differential equations and also based on polynomial basis. But the principal importance of this paper is to develop the expansion approach based on general basis functions (in particular case polynomial basis) for solving general operator equations, wherein the particular cases of our development are integral equations, ordinary differential equations, difference equations, partial differential equations, and fractional differential equations. In other words, this paper presents the expansion approach for solving general operator equations in the form Lu+Nu=g(x),x∈Γ, with respect to boundary condition Bu=λ, where L, N and B are linear, nonlinear, and boundary operators, respectively, related to a suitable Hilbert space, Γ is the domain of approximation, λ is an arbitrary constant, and g(x)∈L2(Γ) is an arbitrary function. Also the other importance of this paper is to introduce the general version of pseudospectral method based on general interpolation problem. Finally some experiments show the accuracy of our development and the error analysis is presented in L2(Γ) norm.

The Stochastic Dynamic Damage Locating Vector approach is a vibration-based damage localization method based on a finite element model of a structure and output-only measurements in both reference and damaged states. A stress field is computed for loads in the null space of a surrogate of the change in the transfer matrix at the sensor positions for some values in the Laplace domain. Then, the damage location is related to positions where the stress is close to zero. Robustness of the localization information can be achieved by aggregating results at different values in the Laplace domain. So far, this approach and in particular the aggregation is deterministic and does not take the uncertainty in the stress estimates into account. In this paper, the damage localization method is extended with a statistical framework. The uncertainty in the output-only measurements is propagated to the stress estimates at different values of the Laplace variable and these estimates are aggregated based on statistical principles. The performance of the new statistical approach is demonstrated both in a numerical application and a lab experiment, showing a significant improvement of the robustness of the method due to the statistical evaluation of the localization information.

This paper investigates the entropy generation in a third-grade fluid flow with variable properties through a channel. Approximate solutions to the nonlinear boundary-value problem are obtained using Adomian decomposition method (ADM). Variation of important parameters on the fluid velocity, temperature distribution, entropy generation and irreversibility ratio are presented graphically and discussed.

This study surveys the ordered weighted averaging OWA operator literature using a citation network analysis. The main goals are the historical reconstruction of scientific development of the OWA field, the identification of the dominant direction of knowledge accumulation that emerged since the publication of the first OWA paper, and to discover the most active lines of research. The results suggest, as expected, that Yager's paperIEEE Trans. Systems Man Cybernet, 181, 183-190, 1988 is the most influential paper and the starting point of all other research using OWA. Starting from his contribution, other lines of research developed and we describe them.

A new load-share reliability model of systems under the changeable load is proposed in the paper. It is assumed that the load is a piecewise smooth function which can be regarded as an extension of the piecewise constant and continuous functions. The condition of the residual lifetime conservation, which means continuity of a cumulative distribution function of time to failure, is accepted in the proposed model. A general algorithm for computing reliability measures is provided. Simple expressions for determining the survivor functions under assumption of the Weibull probability distribution of time to failure are given. Various numerical examples illustrate the proposed model by different forms of the system load and different probability distributions of time to failure.

In a recent communication we reported the self-similarity in radial Walsh filters. The set of radial Walsh filters have been classified into distinct self-similar groups, where members of each group possess self-similar structures or phase sequences. It has been observed that, the axial intensity distributions in the farfield diffraction pattern of these self-similar radial Walsh filters are also self-similar. In this paper we report the self-similarity in the intensity distributions on a transverse plane in the farfield diffraction patterns of the self-similar radial Walsh filters.

The problem of finding the number of irreducible monic polynomials of degree r over Fqn is considered in this paper. By considering the fact that an irreducible polynomial of degree r over Fqn has a root in a subfield Fqs of Fqnr if and only if (nr/s,r)=1, we show that Gauss’s formula for the number of monic irreducible polynomials can be derived by merely considering the lattice of subfields of Fqnr . We also use the lattice of subfields of Fqnr to determine if it is possible to generate a Goppa code using an element lying in a proper subfield of Fqnr.

Let R be a commutative finite principal ideal ring with unity, and let G(R) be the simple graph consisting of nontrivial proper ideals of R as vertices such that two vertices I and J are adjacent if they have nonzero intersection. In this paper we continue the work done by Abu Osba. We calculate the radius, eccentricity, domination number, independence number, geodetic number, and the hull number for this graph. We also determine when G(R) is chordal. Finally, we study some properties of the complement graph of G(R).

This paper proposes an enhancement of the cross-efficiency evaluation through the aggregation of cross-efficiencies by using a particular type of induced ordered weighted averaging IOWA operator. The use of a weighted average of cross-efficiencies for the calculation of the cross-efficiency scores, instead of the usual arithmetic mean, allows us to introduce some flexibility into the analysis. In particular, the main purpose of the approach we present is to provide aggregation weights that reflect the decision maker DM preferences regarding the relative importance that should be attached to the cross-efficiencies provided by the different decision-making units. To do it, an ordering is to be induced in the rows of the matrix of cross-efficiencies, so the IOWA operator weights can be attached accordingly to the elements in each of the columns. The DM can thus incorporate his/her preferences by means of the choice of the variable that induces such ordering, and he/she may also adjust the importance to be attached to the most preferred cross-efficiencies with the level of orness that is used when the aggregation weights are obtained.

When confronted with multiple Nash equilibria, decision makers have to refine their choices. Among all known Nash equilibrium refinements, the perfectness concept is probably the most famous one. It is known that weakly dominated strategies of two-player games cannot be part of a perfect equilibrium. In general, this undominance property however does not extend to n-player games (E. E. C. van Damme, 1983). In this paper we show that polymatrix games, which form a particular class of n-player games, verify the undominance property. Consequently, we prove that every perfect equilibrium of a polymatrix game is undominated and that every undominated equilibrium of a polymatrix game is perfect. This result is used to set a new characterization of perfect Nash equilibria for polymatrix games. We also prove that the set of perfect Nash equilibria of a polymatrix game is a finite union of convex polytopes. In addition, we introduce a linear programming formulation to identify perfect equilibria for polymatrix games. These results are illustrated on two small game applications. Computational experiments on randomly generated polymatrix games with different size and density are provided.

To deal with a system with both randomness and uncertainty, chance theory has been built and an uncertain random variable has been proposed as a generalization of random variable and uncertain variable. Correspondingly, as a generalization of both the stochastic process and the uncertain process, this paper will propose an uncertain random process. In addition, some special types of uncertain random processes such as stationary increment process and renewal process will also be discussed.