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Nowadays, a wide class of problems can be solved by using the classical newsboy model. However, in problems where uncertainty of events and randomness are omnipresent, there is a necessity to adapt the existing solutions and/or find new extensions that will properly answer all requirements. This paper considers a multistage assembly system where interrelated assembly operations with independent stochastic operation times should be planned in an optimal way. Delivery of items in a requested time implies that either delay costs or holding costs appear. The goal is to find optimal safety times. We propose an approximate technique based on successive application of the solution of simpler one-stage problem. The generalized mathematical model suggested is built up on the relaxed hypothesis and can be used in multistage assembly networks. The existence and uniqueness of the solution are proven. The preliminary tests are performed and our approximate technique is compared to exact results. [ABSTRACT FROM AUTHOR]

Robust optimization is a powerful and relatively novel methodology to cope with optimization problems in the presence of uncertainty. The positive aspect of robust optimization approach is its computational tractability that attracts more and more attention. In this paper, we focus on an ambiguous P-model where probability distributions are partially known. We discuss robust counterpart (RC) of uncertain linear constraints under two refined uncertain sets by robust approach and further find the safe tractable approximations of chance constraints in the ambiguous P-model. Because of the probability constraints embedded in the ambiguous P-model, it is computationally intractable. The advantage of our approach lies in choosing an implicit way to treat stochastic uncertainty models instead of solving them directly. The process above can enable the transformation of proposed P-model to a tractable deterministic one under the refined uncertainty sets. A numerical example about portfolio selection demonstrates that the ambiguous P-model can help the decision maker to determine the optimal investment proportions of various stocks. Sensitivity analyses explore the trade-off between optimization and robustness by adjusting parameter values. Comparison study is conducted to validate the benefit of our ambiguous P-model. [ABSTRACT FROM AUTHOR]

When superheated steam flows along the horizontal wellbore, it may change to saturated steam at some point of the wellbore. In this paper, to accurately predict the heat radius of cyclic superheated steam stimulation with horizontal wellbore, the distribution of thermophysical properties of superheated steam along the horizontal wellbore is considered. The heating process is divided into 4 stages for superheated steam and 3 stages for saturated steam when the phase change undergoes in the wellbore. On this basis, the mathematical model for heat radius of cyclic superheated steam stimulation with horizontal wellbore was established according to energy conservation principle and Laplace transformation method. The calculation result of the new mathematical model is in good agreement with that of the numerical simulation (CMG STARS) for the same parameters from a specific heavy oil reservoir, which verified the correctness of the new mathematical model. The effect of degree of superheat and the cycle of stimulation are analyzed in detail after the new mathematical model is validated. The results show that the heat radius of superheated zone, steam zone, and hot fluid zone all decrease with horizontal well length and increase with the cycle of stimulation. The higher the degree of superheat is, the farther from the heel of the horizontal wellbore the phase change undergoes. Besides, the radius of superheated zone, steam zone, and hot fluid zone increases with the degree of superheat, but the value increases little at steam zone and hot fluid zone. [ABSTRACT FROM AUTHOR]

A wireless network system is a pair (Ù;B), where B is a family of some base stations and Ù is a set of their users. To investigate the connectivity of wireless network systems, this paper takes covering approximation spaces as mathematical models of wireless network systems. With the help of covering approximation operators, this paper characterizes the connectivity of covering approximation spaces by their definable subsets. Furthermore, it is obtained that a wireless network system is connected if and only if the relevant covering approximation space has no nonempty definable proper subset. As an application of this result, the connectivity of a teacher-student interactive platform is discussed, which is established in the School of Mathematical Sciences of Soochow University. This application further demonstrates the usefulness of rough set theory in pedagogy andmakes it possible to research education by logical methods and mathematical methods. [ABSTRACT FROM AUTHOR]

The Ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequality. The current paper obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval in terms of the norms of the second derivative of the function. Some new perturbed results are obtained. Application for cumulative distribution function is also discussed. [ABSTRACT FROM AUTHOR]

The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method. [ABSTRACT FROM AUTHOR]

The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much harder problem, a heuristic algorithm is proposed to find approximate solutions. Through computational experiments, the heuristic algorithms’ performance is evaluated with problems up to 500 jobs. [ABSTRACT FROM AUTHOR]

A multi-degree-of-freedom dynamical system with local cubic nonlinearities subjected to super/subharmonic excitation is considered in this paper. The purpose of this paper is to approximate the nonlinear response of system at super/sub harmonic resonance. For many situations, single resonance mode is often observed to be leading as system enters into super/sub harmonic resonance. In this case, the single modal natural resonance theory can be applied to reduce the system model and a simplified model with only a single DOF is always obtained. Thus, an approximate solution and the analytical expression of frequency response relation are then derived using classical perturbation analysis. While the system is controlled by multiple modes, modal analysis for linearized system is used to decide dominant modes. The reduced model governed by these relevant modes is found and results in an approximate numerical solutions. An illustrative example of the discrete mass-spring-damper nonlinear vibration system with ten DOFs is examined. The approximation results are validated by comparing them with the calculations from direct numerical integration of the equation of motion of the original nonlinear system. Comparably good agreements are obtained. [ABSTRACT FROM AUTHOR]

The Cattaneo-Vernotte equation is a generalization of the heat and particle diffusion equations; this mathematical model combines waves and diffusion with a finite velocity of propagation. In disordered systems the diffusion can be anomalous. In these kinds of systems, the mean-square displacement is proportional to a fractional power of time not equal to one. The anomalous diffusion concept is naturally obtained from diffusion equations using the fractional calculus approach. In this paper we present an alternative representation of the Cattaneo-Vernotte equation using the fractional calculus approach; the spatial-time derivatives of fractional order are approximated using the Caputo-type derivative in the range (0,2]. In this alternative representation we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space-time derivatives into the fractional Cattaneo-Vernotte equation. Finally, consider the Dirichlet conditions, the Fourier method was used to find the full solution of the fractional Cattaneo-Vernotte equation in analytic way, and Caputo and Riesz fractional derivatives are considered. The advantage of our representation appears according to the comparison between our model and models presented in the literature, which are not acceptable physically due to the dimensional incompatibility of the solutions. The classical cases are recovered when the fractional derivative exponents are equal to 1. [ABSTRACT FROM AUTHOR]

During the last years, kriging has become one of the most popular methods in computer simulation and machine learning. Kriging models have been successfully used in many engineering applications, to approximate expensive simulation models. When many input variables are used, kriging is inefficient mainly due to an exorbitant computational time required during its construction. To handle high-dimensional problems (100+), one method is recently proposed that combines kriging with the Partial Least Squares technique, the so-called KPLS model. This method has shown interesting results in terms of saving CPU time required to build model while maintaining sufficient accuracy, on both academic and industrial problems. However, KPLS has provided a poor accuracy compared to conventional kriging on multimodal functions. To handle this issue, this paper proposes adding a new step during the construction of KPLS to improve its accuracy for multimodal functions. When the exponential covariance functions are used, this step is based on simple identification between the covariance function of KPLS and kriging. The developed method is validated especially by using a multimodal academic function, known as Griewank function in the literature, and we show the gain in terms of accuracy and computer time by comparing with KPLS and kriging. [ABSTRACT FROM AUTHOR]

This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes. [ABSTRACT FROM AUTHOR]

The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a) by polygonal curve and (b) by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening. [ABSTRACT FROM AUTHOR]

This paper is focused on an assessment of the state of the art of operational modal analysis (OMA) methodologies in estimating modal parameters from output responses of nonlinear structures. By means of the Volterra series, the nonlinear structure excited by random excitation is modeled as best linear approximation plus a term representing nonlinear distortions. As the nonlinear distortions are of stochastic nature and thus indistinguishable from the measurement noise, a protocol based on the use of the random phase multisine is proposed to reveal the accuracy and robustness of the linear OMA technique in the presence of the system nonlinearity. Several frequency- and time-domain based OMA techniques are examined for the modal identification of simulated and real nonlinear mechanical systems. Theoretical analyses are also provided to understand how the system nonlinearity degrades the performance of the OMA algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included. [ABSTRACT FROM AUTHOR]

The efficiency of the compositional verification of invariants depends on the abstraction, which may lead to verification incompleteness. The invariant strengthening and state partitioning techniques are proposed in this paper. The former could refine the overapproximation by removing the unreachable states, and the latter is a variant of counterexample-guided abstraction refinement. Integrated with these two refinement techniques, a unified compositional verification framework is presented to strengthen the abstraction and find counterexamples. Some examples are included to show that the verification of the safety properties in component-based systems has been achieved by our framework. [ABSTRACT FROM AUTHOR]

The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer) in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method. [ABSTRACT FROM AUTHOR]

A class of fractional order three-point boundary value system with resonance is investigated in this paper. Using some techniques of inequalities, a completely new method is incorporated. We transform the problem into an integral equation with a pair of undetermined parameters. The topological degree theory is applied to determine the particular value of the parameters so that the system has a solution. [ABSTRACT FROM AUTHOR]

In recent years several numerical methods have been proposed to identify the five-parameter model of photovoltaic panels from manufacturer datasheets also by introducing simplification or approximation techniques. In this paper we present a fast and accurate procedure for obtaining the parameters of the five-parameter model by starting from its reduced form. The procedure allows characterizing, in few seconds, thousands of photovoltaic panels present on the standard databases. It introduces and takes advantage of further important mathematical considerations without any model simplifications or data approximations. In particular the five parameters are divided in two groups, independent and dependent parameters, in order to reduce the dimensions of the search space. The partitioning of the parameters provides a strong advantage in terms of convergence, computational costs, and execution time of the present approach. Validations on thousands of photovoltaic panels are presented that show how it is possible to make easy and efficient the extraction process of the five parameters, without taking care of choosing a specific solver algorithm but simply by using any deterministic optimization/minimization technique. [ABSTRACT FROM AUTHOR]

A strong designated verifier signature scheme makes it possible for a signer to convince a designated verifier that she has signed a message in such a way that the designated verifier cannot transfer the signature to a third party, and no third party can even verify the validity of a designated verifier signature. In 2005, Lipmaa, Wang, and Bao identified a new essential security property, non delegatability, of designated verifier signature schemes. Briefly, in a non delegatability designated verifier signature scheme, neither a signer nor a designated verifier can delegate the signing rights to any third party without revealing their secret keys. However, this paper shows that four recently proposed strong designated verifier signature schemes are delegatable. These schemes do not satisfy non delegatability secure requirement of strong designated verifier signature schemes. [ABSTRACT FROM AUTHOR]

Many different proposals exist for the definition of lower and upper approximation operators in covering-based rough sets and so many different covering rough set models are built correspondingly. It is meaningful to explore the connection of these covering rough set models for their applications in practice. In this paper, we establish relationships between the most commonly used operators in covering rough set models. We investigate the conditions under which two types of upper approximation operations are identical. [ABSTRACT FROM AUTHOR]

Effective and efficient image comparison plays a vital role in content-based image retrieval (CBIR). The earth mover's distance (EMD) is an enticing measure for image comparison, offering intuitive geometric interpretation and modelling the human perceptions of similarity. Unfortunately, computing EMD, using the simplex method, has cubic complexity. FastEMD, based on min-cost flow, reduces the complexity to (O(N2 logN)). Although both methods can obtain the optimal result, the high complexity prevents the application of EMD on large-scale image datasets. Thresholding the ground distance can make EMD faster and more robust, since it can decrease the impact of noise and reduce the range of transportation. In this paper, we present a new image distance metric, EMD+, which applies a threshold to the ground distance. To compute EMD+, the FastEMD approach can be employed. We also propose a novel linear approximation algorithm. Our algorithm achieves O(N) complexity with the benefit of qualified bins. Experimental results show that (1) our method is 2 to 3 orders of magnitude faster than EMD (computed by FastEMD) and 2 orders of magnitude faster than FastEMD and (2) the precision of our approximation algorithm is no less than the precision of FastEMD. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the minimum length link scheduling (MLLS) in multiuser MIMO (MU-MIMO) networks. Generally, in the networks with MU-MIMO capability, the number of concurrent transmissions can be as large as that of antenna elements at the receiver. As a result, link interference is no longer binary but demonstrates a strong correlation among multiple links, which cannot be captured by the conventional conflict graph interference model. Hence, we propose a novel hypergraph interference model, which can accurately and efficiently characterize the relationship of multiple interferences induced by concurrent transmissions, and provide a tractable formalization of the minimumlength link scheduling in MU-MIMO networks (MU-MIMO MLLS). Afterwards, we prove that the MU-MIMO MLLS problem is NP-hard and introduce two approximation algorithms to find the near-optimal feasible schedule. Finally, extensive simulation experiments are presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with the identification of linear parameter varying (LPV) systems by utilizing a multimodel structure. To improve the approximation capability of the LPV model, asymmetric Gaussian weighting functions are introduced and compared with commonly used symmetric Gaussian functions. By this mean, locations of operating points can be selected freely. It has been demonstrated through simulations with a high purity distillation column that the identified models provide more satisfactory approximation. Moreover, an experiment is performed on real HVAC (heating, ventilation, and air-conditioning) to further validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with financial modeling to describe the behavior of asset returns, through consideration of economic cycles together with the stylized empirical features of asset returns such as fat tails. We propose that asset returns are modeled by a stochastic volatility L'evy process incorporating a regime switching model. Based on the risk-neutral approach, there exists a large set of candidates of martingale measures due to the driving of a stochastic volatility L'evy process in the proposed model which renders the market incomplete in general. We first establish an equivalent martingale measure for the proposed model introduced in risk-neutral version. Regime switching of stochastic volatility L'evy process is employed in an approximation mode for model calibration and the calibration of parameters model done based on EM algorithm. Finally, some empirical results are illustrated via applications to the Bangkok Stock Exchange of Thailand index. [ABSTRACT FROM AUTHOR]

Stochastic delay differential equations with jumps have a wide range of applications, particularly, inmathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a robust Taylor approximation scheme and then examine the convergence of the method in a weak sense. A convergence theorem for the scheme is established and proved. Our analysis and numerical examples show that the proposed scheme of high order is effective and efficient forMonte Carlo simulations for jump-diffusion stochastic delay differential equations. [ABSTRACT FROM AUTHOR]

This paper will consider the implementation of fifth-order directmethod in the formofAdams-Moultonmethod for solving directly second-order delay differential equations (DDEs). The proposed directmethod approximates the solutions using constant step size. The delay differential equations will be treated in their original forms without being reduced to systems of first-order ordinary differential equations (ODEs). Numerical results are presented to show that the proposed direct method is suitable for solving second-order delay differential equations. [ABSTRACT FROM AUTHOR]

This paper discusses the linear parameter varying (LPV) gain scheduling control problem based on the Takagi-Sugeno (T-S) fuzzy linearization approach. Firstly, the affine nonlinear parameter varying (ANPV) description of a class of nonlinear dynamic processes is defined; that is, at any scheduling parameter, the corresponding system is affine nonlinear as usual. For such a class of ANPV systems, a kind of developed T-S fuzzy modeling procedure is proposed to deal with the nonlinearity, instead of the traditional Jacobian linearization approach. More concretely, the evaluation system for the approximation ability of the novelly developed T-S fuzzy modeling procedure is established. Consequently, the LPV T-S fuzzy system is obtained which can approximate the ANPV system with required accuracy. Secondly, the notion of piecewise parameter-dependent Lyapunov function is introduced, and then the stabilization problem and the state-feedback H∞ control problem of the LPV T-S fuzzy system are studied. The sufficient conditions are given in linear matrix inequalities (LMIs) form. Finally, a numerical example is provided to demonstrate the availability of the above approaches. The simulation results show the high approximation accuracy of the LPV T-S fuzzy system to the ANPV system and the effectiveness of the LPV T-S fuzzy gain scheduling control. [ABSTRACT FROM AUTHOR]

This paper suggests two component homotopy method to solve nonlinear fractional integrodifferential equations, namely, Volterra's population model. Padé approximation was effectively used in this method to capture the essential behavior of solutions for the mathematical model of accumulated effect of toxins on a population living in a closed system. The behavior of the solutions and the effects of different values of fractional-order α are indicated graphically. The study outlines significant features of this method as well as sheds some light on advantages of the method over the other. The results show that this method is very efficient, convenient, and can be adapted to fit a larger class of problems. [ABSTRACT FROM AUTHOR]

Most real-life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subgraphs without coding or using assumption. The aim of this paper is to apply near concepts in the Gm-closure approximation spaces. The basic notions of near approximations are introduced and sufficiently illustrated. Near approximations are considered as mathematical tools to modify the approximations of graphs. Moreover, proved results, examples, and counterexamples are provided. [ABSTRACT FROM AUTHOR]

Today's advanced simulators facilitate thorough studies on Vehicular Ad hoc NETworks (VANETs). However the choice of the physical layer model in such simulators is a crucial issue that impacts the results. A solution to this challenge might be found with a hybrid model. In this paper, we propose a semi-deterministic channel propagation model for VANETs called UM-CRT. It is based on CRT (Communication Ray Tracer) and SCME--UM (Spatial Channel Model Extended--Urban Micro) which are, respectively, a deterministic channel simulator and a statistical channel model. It uses a process which adjusts the statistical model using relevant parameters obtained from the deterministic simulator. To evaluate realistic VANET transmissions, we have integrated our hybrid model in fully compliant 802.11 p and 802.11 n physical layers. This framework is then used with the NS-2 network simulator. Our simulation results show that UM-CRT is adapted for VANETs simulations in urban areas as it gives a good approximation of realistic channel propagation mechanisms while improving significantly simulation time. [ABSTRACT FROM AUTHOR]

The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized-sparse- approximate-inverse- (FSAI-) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI-IC preconditioner, which combines the FSAI and the Block Jacobi-IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallel hypre package, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI-Fortran 90 language and exhibits good scalability up to one thousand processors. [ABSTRACT FROM AUTHOR]

The present paper extends the multimodal method, which is well known for liquid sloshing problems, to the free-surface problem modeling the levitating drop dynamics. The generalized Lukovsky-Miles modal equations are derived. Based on these equations an approximate modal theory is constructed to describe weakly-nonlinear axisymmetric drop motions. Whereas the drop performs almost-periodic oscillations with the frequency close to the lowest natural frequency, the theory takes a finite-dimensional form. Periodic solutions of the corresponding finite-dimensional modal system are compared with experimental and numerical results obtained by other authors. A good agreement is shown. [ABSTRACT FROM AUTHOR]

Let F be a Riesz algebra with an extended norm || · ||u such that (F, || · ||u) is complete. Also, let || · ||v be another extended norm in F weaker than || · ||u such that whenever (a) xn→x and xn · y→z in || · ||v, then z = x · y; (b) yn → y and x · yn → z in || · ||v, then z = x · y. Let ε and δ > be two nonnegative real numbers. Assume that a map f : F → F satisfies ||f(x+y) - f(x) - f(y)||u = ε and ||f(x · y) - x · f(y) - f(x) · y||v ≤ δ for all x, y ∈ F. In this paper, we prove that there exists a unique derivation d : F → F such that ||f(x) - d(x)||u ≤ ε, (x ∈ F). Moreover, x · (f(y) - d(y)) = 0 for all x, y ε F. [ABSTRACT FROM AUTHOR]

The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells. [ABSTRACT FROM AUTHOR]