Monotonic solutions of a class of quadratic integral equations of Volterra type

Using the technique associated with measures of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.     

Nondecreasing solutions of a quadratic integral equation of Urysohn type

Applying the technique associated with measures of noncompactness, we prove the existence of nondecreasing solutions of a quadratic integral equation of Urysohn type in the space of real functions defined and continuous on a closed bounded interval.     

Solvability of infinite systems of singular integral equations in Fréchet space of continuous functions

The aim of this paper is to show how some measures of noncompactness in the Fréchet space of continuous functions defined on an unbounded interval can be applied to an infinite system of singular integral equations. The results obtained generalize and improve several ones.     

Solvability of Volterra-Stieltjes operator-integral equations and their applications

We investigate a class of operator-integral equations of Volterra-Stieltjes type and we study the solvability of those equations in the space of continuous functions. Equations in question create a generalization of numerous integral equations considered in nonlinear analysis. The main tool used in our considerations is the technique associated with measures of noncompactness. We show the applicability of our existence result in the study of a few integral equations of Volterra type.     

Well-posedness without semicontinuity for parametric quasiequilibria and quasioptimization

We consider quasiequilibrium and quasioptimization problems. A relaxed level closedness notion is proposed and used together with pseudocontinuity to establish sufficient conditions for parametric well-posedness and well-posedness without semicontinuity assumptions. We prove them in general formulations, though such relaxations allow us to improve some existing results even in simple cases of R¹. Several new well-posedness results are also obtained. For topological settings we use sensitivity analysis while for problems on metric spaces we argue on diameters and Kuratowski’s and Hausdorff’s measures of noncompactness of approximate solution sets.     

Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions

In this paper,we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces.We derive the c...     

Hybrid fixed point theory for strictly monotone increasing multi-valued mappings with applications

In this paper, a general hybrid fixed point theorem for the strict monotone increasing multi-valued mappings in ordered Banach spaces is proved via measure of noncompactness and it is further applied to perturbed functional nonconvex differential inclusions for proving the existence results for the extremal solutions under mixed Lipschitz, compactness and strict monotonic conditions.     

Existence of solutions for a class of nonlinear Volterra singular integral equations

In this paper we prove some results concerning the existence of solutions for a large class of nonlinear Volterra singular integral equations in the space C[0,1] consisting of real functions defined and continuous on the interval [0,1]. The main tool used in the proof is the concept of a measure of noncompactness. We also present some examples of nonlinear singular integral equations of Volterra type to show the efficiency of our results. Moreover, we compare our theory with the approach depending on the use of the theory of Volterra-Stieltjes integral equations. We also show that the results of the paper are applicable in the study of the so-called fractional integral equations which are recently intensively investigated and find numerous applications in describing some real world problems.     

ORDERING FUZZY SETS BY CONSENSUS CONCEPT AND FUZZY RELATION EQUATIONS

A general class of consensus measures of fuzzy sets is introduced in this paper. It is shown that, while the consensus measures are valuations but neither isotone nor antitone with respect to the lattice structure induced by the pointwise maximum and minimum operations to the set of all the fuzzy sets on a nonempty crisp set, they are antitone valuations with respect to the lattice structure induced by the generalized sharpening relation to a quotient set of the set of fuzzy sets. It is also shown that the solutions of a finite fuzzy relation equation that have the maximum consensus measure can be characterized through the join operation of the latter lattice in terms of the maximum solution and some of the minimal solutions of the equation.     

Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses

Control systems in which instantaneous and noninstantaneous impulses occur simultaneously are difficult to handle. In this article, we investigate the solvability and approximate controllability for a new category of stochastic differential equations steered by Poisson jumps with instantaneous and noninstantaneous impulses. Utilizing the theory of fundamental solution, stochastic analysis, the measure of noncompactness, and the fixed-point approach, we establish the presence of a mild solution for the proposed system. We have also constructed a new set of sufficient constraints that assures approximate controllability of the considered system. Next, we discuss the existence of a solution and approximate controllability for an impulsive deterministic control system in which the nonlinear term contains spatial derivatives. Lastly, two examples are presented to encapsulate the abstract results.     

D－稳定鲁棒性分析的一个新判据

本文借助矩阵测度理论，导出了摄动系统保持Ｄ－稳定的一个新的充分条件，并且避免了Ｌｙａｐｕｎｏｖ稳定方程的求解．最后以实例计算来说明这种方法的保守性得到了降低．     

Additive information measures with preference of order β

Mechanical and logical systems admit an “additive” law of measures, while biological and social system may not. We consider generalized additive models which under the sum property get transformed into a generalized functional equation. Solutions of this generalized functional equation characterize the generalized information measures with preference order β. Some particular cases are studied.     

BEM and estimate of actual error for exterior Dirichlet problem for two-dimensional Helmholtz equation

The actual error in the numerical solution of a boundary integral equation cannot be measured unless the true solution is known. Here it is shown that residual error in the H^1/2 norm measures the actual error. Since the solution of the integral equation from the exterior Dirichlet problem for the two-dimensional Helmholtz equation with an arc as its boundary is unbounded near the tips, singular elements are used. The numerical results show that the use of the singular elements significantly reduces the error.     

The impact of policy measures on promoting the modal shift from road to rail

This paper aims to examine the impact of policy measures on promoting a modal shift. Based on the results put forth by previous research, we first formulate hypotheses that describe the effects between policy measures and modal shift. Using these hypotheses, we set up the research framework to complete this study, which is then tested with data (sample size 171) and AMOS 18.0. The paper contributes to the literature in the following ways: First, we verify this impact with statistical analyses through testing hypotheses based on the previous research. Second, we develop the model describing the effects between policy measures and clarify their directivity with structural equation modeling. The directivity of effects accounts for the interaction and relationship between policy measures to promote a modal shift. In this paper, we clear up the effects of policy measures better in order to promote a modal shift, which the previous research discussed conceptually.     

On the quadratic integral equations and their applications

The class of quadratic integral equations contains, as a special case, numerous integral equations encountered in the theory of radiative transfer, the queuing theory, the kinetic theory of gases and the theory of neutron transport. As a pursuit of this, in the following pages, sufficient conditions are given for the existence of positive continuous solutions to some possibly singular quadratic integral equations. Meanwhile, we prove the existence of maximal and minimal solutions of our problems. The method used here depends on both Schauder and Schauder–Tychonoff fixed point principles. Unlike all previous contributions of the same type, no assumptions in terms of the measure of noncompactness were imposed on the nonlinearity of the given functions. As far as we know, the approach presented in this paper, in particular, the discussion of the existence of maximal and minimal solutions to the quadratic integral equations was never applied in the field of the quadratic integral equations and so is new.     

The backlog process in queues with random service speed

This paper examines the backlog (total amount of unfinished work in the system) in a single server queue that works in a ‘random environment’. Specifically, the service speed is described by an exogenous (non-negative) ‘environment’ process. We characterize the time-dependent backlog via a stochastic integral equation and use this equation to compute stationary performance measures. For the M/G/1 queue, our results lead to a generalization of the Pollaczek-Khintchine transform equation for backlog that ‘explains’ why congestion is greater in a queue with random service speed than in an equivalent queue with constant service speed. We provide a numerical example that helps to illustrate our results.     

随机齿侧间隙下行星齿轮系统的修形方法研究

建立一个包含随机齿侧间隙、摩擦、时变啮合刚度等影响齿轮振动因素的行星齿轮系统动力学模型.使用非线性动力学方法对系统进行求解,并分析激励频率对系统的影响.提出修形的主动降噪措施对系统进行改进,重新计算行星齿轮系统的动力学方程.求解并分析激励频率对改进之后系统的影响,并和原始系统得到的结果对比,可以看出修形对于齿轮系统的减振是有效的.     

乙烯深度氧化反应动力学方程的非线性最小二乘回归

介绍了采用非线性最小二乘方法回归乙烯深度氧化反应动力学方程。用高斯-牛顿法求解非线性最小二乘方程组,并推导出简单、适用的迭代公式。针对Gauss-Newton法的局部收敛问题,提出:(1)以任意组合的实验值代入回归方程,求得回归参数作为迭代初值;(2)对不同迭代初值所得的结果择优,作为最终结果。实例计算表明,该方法可以有效地回归Langmuir- Hinshelwood型动力学方程,为乙烯深度氧化反应的研究提供依据。     

Classification of transcranial Doppler signals using their chaotic invariant measures

In this study, chaos analysis was performed on the transcranial Doppler (TCD) signals recorded from the temporal region of the brain of 82 patients as well as of 24 healthy people. Two chaotic invariant measures, i.e. the maximum Lyapunov exponent and the correlation dimension, were calculated for the TCD signals after applying nonlinearity and stationarity tests to them. The sonograms obtained via Burg autoregressive (AR) method demonstrated that the chaotic invariant measures represented the unpredictability and complexity levels of the TCD signals. According to the multiple linear regression analysis, the chaotic invariant measures were found to be highly significant for the regression equation which fitted to the data. This result suggested that the chaotic invariant measures could be used for automatically differentiating various cerebrovascular conditions via an appropriate classifier. For comparison purposes, we investigated several different classification algorithms. The k-nearest neighbour algorithm outperformed all the other classifiers with a classification accuracy of 94.44% on the test data. We used the receiver operating characteristic (ROC) curves in order to assess the performance of the classifiers. The results suggested that the classification systems which use the chaotic invariant measures as input have potential in detecting the blood flow velocity changes due to various brain diseases.