Multiple Integral Problems Research Articles

Correlation analysis of students' success in solving analytic geometry and multiple integral problems

Correlation analysis of students' success in solving analytic geometry and multiple integral problems

Application of improved active disturbance rejection control algorithm in tilt quad rotor

The Tilt Quad Rotor (TQR) has complex dynamics characteristics, especially in conversion mode. It is difficult to build the dynamic model of the TQR and the environmental factors have a great influence on it. To solve the problem of control in conversion mode of TQR, this paper carries out the design of the controller based on improved Active Disturbance Rejection Control (ADRC). According to the characteristics of flight in conversion mode, Tracking Differentiator (TD) with explicit model is used to solve the problem of multiple integrals when the system is high-order system. Extended State Observer (ESO) with Radial Basis Function (RBF) neural network is used to estimate and compensate for internal and external uncertainties, and the adaptive sliding mode control in Nonlinear State Error Feedback (NLSEF) is used to improve the response speed of the controller and reduce the parameters which should be tuned. Through the flight control simulation of the TQR, the validity and rationality of the control system are verified.

Numerical Integration of Arbitrary Function over Multidimensional Cubes using Haar Wavelet Method

In this paper, we investigate numerical integration of arbitrary function over multidimensional cubes by using quadrature method, Haar wavelet method has been used to describe method for multiple integral problems, the high accuracy and wide applicability of the Haar wavelet approach will be illustrated several numerical examples.

Architecting a Geo-Enabled CRM: the Way to Seamless Integration

In the paper the problem of geo-marketing and multiple CRM systems integration is considered in scope of small developers’ team with extremely limited resources. Several alternative CRM systems were assessed for being a candidate as an initial targeting platform for geomarketing integration. These out-of-the-box CRM solutions were chosen to be assessed against developed criteria to determine how good it fits developers’ constraints.

Multi-Bernoulli smoother for multi-target tracking

Multi-target tracking is an important research topic in the field of aerospace. In this paper, a multi-Bernoulli smoother, which consists of forward filtering followed by backward smoothing, is proposed for multi-target tracking. The forward filtering is accomplished by the cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter. For the backward smoothing, the smoothed multi-target probability density is approximated by a multi-Bernoulli density, whose backward recursion is derived by using finite set statistics. To solve the computational problem of multiple integrals in the smoother, a sequential Monte Carlo method is also proposed. Experimental results show that the proposed smoother improves the estimation accuracy of target number and target states over the CBMeMBer filter.

A Survey on the Non Occurence of the Lavrentiev Gap for Convex, Autonomous Multiple Integral Scalar Variational Problems

In a recent paper we proved the non occurrence of the Lavrentiev gap between Lipschitz and Sobolev functions for functionals of the form $$\text {I}(u)={\int }_{\Omega }F(u,\nabla u) u|_{\partial {\Omega }} = \phi $$ when $\phi :\mathbb {R}^{n} \rightarrow \mathbb {R}$ is Lipschitz, Ω belongs to a wide class of open bounded sets in $\mathbb {R}^{n}$ containing Lipschitz domains, and the lagrangian F is assumed to be either convex in both variables or a sum of functions F(s, ξ) = a(s)g(ξ) + b(s) with g convex and s ↦ a(s)g(0) + b(s) satisfying a non oscillatory condition at infinity. In this survey we discuss the state of the art on the subject and give a self-contained proof of our result in the simpler case of a (strongly) star-shaped domain, for a lagrangian depending just on the gradient; in particular we point out what are the main difficulties to overcome in order to get the result without assuming growth conditions. We also formulate, and prove, a characterization of a useful class of star-shaped domains in terms of the radii function.

A Study of Multiple Integrals with Maple

The multiple integral problem is closely related with probability theory and quantum field theory. This paper uses the mathematical software Maple for the auxiliary tool to study two types of multiple integrals. We can obtain the infinite series forms of these two types of multiple integrals by using integration term by term theorem. In addition, we provide some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.

Solving Multiple Integrals Using Maple

The multiple integral problem is closely related to probability theory and quantum field theory. This paper uses the mathematical software Maple for the auxiliary tool to study three types of multiple integrals. We can obtain the infinite series forms of these three types of multiple integrals by using differentiation with respect to a parameter, differentiation term by term, and integration term by term. In addition, we provide some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.

Robust visual tracking based on interactive multiple model particle filter by integrating multiple cues

Visual tracking can be formulated as a state estimation problem of target representation based on observations in image sequences. To investigate the integration of rough models from multiple cue and to explore computationally efficient algorithms, this paper formulates the problem of multiple cue integration and tracking to combine Interactive Multiple Model (IMM) with particle filter (IMM_PF). Interactive Multiple Model can estimate the multiple cue state of a dynamic system with several behavioral models that switch from one to another using model likelihoods and model transition probabilities. For the problem of visual tracking, the model of IMM is adopted to three target observation models: Corrected Background Weighted Histogram (CBWH), Completed Local Ternary Patterns (CLTP) and Histogram of Oriented Gradients (HOG). The probabilities of these models are corresponding to the weights of multiple cues. IMM_PF then dynamically adjusts the weights of different features. Compared with those state-of-the-art methods in the tracking literature, this algorithm can track the object accurately in conditions of rotation, abrupt shifts, as well as clutter and partial occlusions occurring to the tracking object with good robustness, as demonstrated by experimental results.

On the Lavrentiev phenomenon for multiple integral scalar variational problems

We prove the non-occurrence of Lavrentiev gaps between Lipschitz and Sobolev functions for functionals of the formI(u)=∫ΩF(u,∇u),u|∂Ω=ϕ when ϕ:Rn→R is Lipschitz and Ω belongs to a wide class of open bounded sets in Rn containing Lipschitz domains. The Lagrangian F is assumed to be either convex in both variables or a sum of functions F(s,ξ)=a(s)g(ξ)+b(s) with g convex and s↦a(s)g(0)+b(s) satisfying a non-oscillatory condition at infinity. We thus derive the non-occurrence of the Lavrentiev phenomenon for unnecessarily convex functionals of the gradient. No growth conditions are assumed.

A Study on the Multiple Improper Integral Problems with Maple

This paper uses the mathematical software Maple for the auxiliary tool to study the evaluation of two types of multiple improper integrals. We can obtain the infinite series forms of these two types of multiple improper integrals, and we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.

Application of multi-layer fuzzy comprehensive evaluation method for evaluating the performance of military hospitals

Objective To use fuzzy comprehensive evaluation method for rationally evaluating the performance of military hospitals.Methods The performance of a military hospital(2009-2011) was evaluated from the following four domains: patient,finance,internal flow,and learning and growth.Multi-layer fuzzy comprehensive evaluation method was used to obtain the fuzzy membership of all the domains of the subjects,and the evaluation results were subjected to corresponding analysis.Results It was found that the total proportion of "good" and "comparatively good" performance was 76.85% for a military hospital in 2009-2011.The overall performance degree of the hospital was "good" according to the maximal fuzzy membership principle.And corresponding analysis showed that the result was "moderate" for the financial domain,"poor" or "comparatively poor" for the patient domain,"good" for the internal flow domain,and "good" or "comparatively good" for the learning and growth domain.Conclusion Multi-layer fuzzy comprehensive evaluation method can properly handle the problem of multiple parameter integration in a system,and corresponding analysis makes the evaluation results more rational and more objective.

More Efficient Approximation of Multiple Integrals using Steady State Ranked Simulated Sampling

This article extends the concept of using the steady state ranked simulated sampling approach (SRSIS) by Al-Saleh and Samawi (2000) for improving Monte Carlo methods for single integration problem to multiple integration problems. We demonstrate that this approach provides unbiased estimators and substantially improves the performance of some Monte Carlo methods for bivariate integral approximations, which can be extended to multiple integrals’ approximations. This results in a significant reduction in costs and time required to attain a certain level of accuracy. In order to compare the performance of our method with the Samawi and Al-Saleh (2007) method, we use the same two illustrations for the bivariate case.

On the approximation of multiple integrals using multivariate ranked simulated sampling

The idea of using ranked simulated sampling approach (RSIS) to improve the well known Monte Carlo methods of integration, introduced by Samawi [H.M. Samawi, More efficient Monte Carlo methods obtained by using ranked set simulated samples, Commun. Stat. Simulat. 28 (3) (1999) 699–713], is extended to multivariate ranked simulated sampling approach (MVRSIS) for multiple integration problems. It is demonstrated that this approach provides unbiased estimators and improves the performance of some of the Monte Carlo methods of multiple integrals approximation. This, results in large saving in terms of cost and time needed to attain a certain level of accuracy. Two illustrations using simulation are used to compare the relative performance of this approach relative to multivariate uniform simulation.

Grid Requirements for the Integration of Biomedical Information Resources for Health Applications

The goal of this paper is to identify how Grid technology can be applied for the development and deployment of integration systems, bringing together distributed and heterogeneous biomedical information sources for medical applications. The integration of new genetic and medical knowledge in clinical workflows requires the development of new paradigms for information management in which the ability to access and relate disparate data sources is essential. We adopt a requirements perspective based on the user needs we have identified in the development of the INFOGENMED system to assess current Grid technology against those requirements. The gap between Grid features and distributed biomedical information integration needs is characterized. Results from prospective studies are also reported. Grid infrastructures offer advanced features for the deployment of collaborative computational environments across virtual organizations. New Grid developments are in line with the problem of multiple site information integration. From the INFOGENMED point of view, Grid infrastructures need to evolve to implement structured data access services and semantic content description and discovery.

Robust Visual Tracking by Integrating Multiple Cues Based on Co-Inference Learning

Visual tracking can be treated as a parameter estimation problem that infers target states based on image observations from video sequences. A richer target representation may incur better chances of successful tracking in cluttered and dynamic environments, and thus enhance the robustness. Richer representations can be constructed by either specifying a detailed model of a single cue or combining a set of rough models of multiple cues. Both approaches increase the dimensionality of the state space, which results in a dramatic increase of computation. To investigate the integration of rough models from multiple cues and to explore computationally efficient algorithms, this paper formulates the problem of multiple cue integration and tracking in a probabilistic framework based on a factorized graphical model. Structured variational analysis of such a graphical model factorizes different modalities and suggests a co-inference process among these modalities. Based on the importance sampling technique, a sequential Monte Carlo algorithm is proposed to provide an efficient simulation and approximation of the co-inferencing of multiple cues. This algorithm runs in real-time at around 30 Hz. Our extensive experiments show that the proposed algorithm performs robustly in a large variety of tracking scenarios. The approach presented in this paper has the potential to solve other problems including sensor fusion problems.

The Hilbert-Caratheodory form for parametric multiple integral problems in the calculus of variations

We define, and discuss some properties of, a form which bears a relation to the Caratheodory form for multiple integral problems in the calculus of variations similar to the relation that the Hilbert 1-form of Finsler geometry bears to the Poincare–Cartan form for one-dimensional variational problems.

Estimation of Taiwan’s binary monetary policy reaction function

This paper proposes a probit regression with autocorrelated errors (PAR) to estimate the reaction function of monetary policy in Taiwan using newly constructed binary monetary indicators. We develop a practical sampling scheme via the Gibbs sampling algorithm with data augmentation to make posterior inference of the binary monetary policy reaction function. In contrast to the conventional approach, our method avoids the problem of multiple integrals by directly drawing values of latent variables from the relevant full conditional density along with all the other parameters. Empirical results show that the monetary authority responds to macroeconomic conditions asymmetrically. Specifically, in the high‐inflation regime, a contractionary monetary policy is implemented to reduce the inflation rate. Once inflation is under control, that is, in the low‐inflation regime, attention is paid to stimulating the growth of the economy.

CONSTRUCTION OF SINGULAR SURFACES IN MULTIPLE INTEGRAL VARIATIONAL PROBLEM

The classical method of characteristics is a powerful tool for construction of smooth solutions to nonlinear first order PDEs. Certain generalization of this approach (method of singular characteristics (MSC)) is useful for the construction of the surfaces where the solution is non-smooth. In this paper it is shown that the MSC can be used for the construction of singular surfaces (weak waves) in some second order PDEs – Euler-Lagrange equation for multiple integral variational problem. A two dimensional variational wave equation is considered as an example. The phenomenon of bifurcation of the weak waves (singular lines) is found using analytical and numerical methods.

RELIABILITY PREDICTION OF IMPERFECT SWITCHING SYSTEMS SUBJECT TO WEIBULL FAILURES

Reliability prediction plays a very important role in system design and evaluation. In order to accurately predict the system reliability, one should consider the system configuration and the failure distribution of its components. This paper discusses the imperfect switching system with one component in an active state and n spares in a standby state. When the operating component breaks down, the switch detects the failure via the sensor and the defective component is replaced with a functional spare, so the system can resume operation. The Weibull distribution is one of the most flexible failure distributions which is widely used because it can adequately describe the reliability behavior during the lifetime of present day components/systems. This paper assumes the operating components follow Weibull failures, but the spares, sensor and switch failures follow an exponential distribution. In addition, three assumptions are made with regard to its switch failures: (i) under the energized condition, (ii) under the failing-open condition, and (iii) under the failing-closed condition. Due to the intractability of the Weibull distribution in imperfect switching models, it is difficult to solve the multiple integration involved analytically. Therefore, a numerical integration method using Simpson's rule was selected as a tool to address the problem of multiple integration for the Weibull distribution. A recursive algorithm is developed for the reliability prediction of a series system with m imperfect switching sub-systems subject to Weibull failures. Finally, a sensitivity analysis is performed on the two parameters of the Weibull distribution, on the effect of spare addition, as well as different failing conditions (switch and sensor) on system reliability. A numerical example is also given to explain and demonstrate the practical application of the developed reliability prediction models.