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Uniqueness from discrete data in an inverse spectral problem for a pencil of ordinary differential operators

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 2016年第3期94卷 793-813页

作者： Brown, Malcolm Marletta, Marco Symons, Freddy Cardiff Sch Comp Sci & Informat Queens Bldg5 Parade Cardiff CF24 3AA S Glam Wales Cardiff Sch Math 21-23 Senghennydd Rd Cardiff CF24 4AG S Glam Wales

We prove a pair of uniqueness theorems for an inverse problem for an ordinary differential operator pencil of second order. The uniqueness is achieved from a discrete set of data, namely, the values at the points -n2 nN) of (a physically appropriate generalization of) the Weyl-Titchmarsh m-function m() for the problem. As a corollary, we establish a uniqueness result for a physically motivated inverse problem inspired by Berry and Dennis (Boundary-condition-varying circle billiards and gratings: the Dirichlet singularity', J. Phys. A: Math. Theor. 41 (2008) 135203). To achieve these results, we prove a limit-circle analogue to the limit-point m-function interpolation result of Rybkin and Tuan (A new interpolation formula for the Titchmarsh-Weyl m-function', Proc. Amer. Math. Soc. 137 (2009) 4177-4185);however, our proof, using a Mittag-Leffler series representation of m(), involves a rather different method from theirs, circumventing the A-amplitude representation of Simon (A new approach to inverse spectral theory, I. Fundamental formalism', Ann. Math.(2) 150 (1999) 1029-1057). Uniqueness of the potential then follows by appeal to a Borg-Marenko argument.

关键词： THEOREMS (Mathematics) INVERSE problems (Differential equations) interpolation algorithms DIFFERENTIAL equations OPERATOR theory

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Fuzzy Modeling Vapor Pressure Deficit to Monitoring Microclimate in Greenhouses

Fuzzy Modeling Vapor Pressure Deficit to Monitoring Microcli...

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5th IFAC Conference on Sensing, Control and Automation Technologies for Agriculture (AGRICONTROL)

作者： Cesar Ramos-Fernandez, Julio Balmat, Jean-Francois Antonio Marquez-Vera, Marco Lafont, Frederic Pessel, Nathalie Steed Espinoza-Quesada, Eduardo Univ Politecn Pachuca Carr Pachuca Cd Sahagun Km 20 Zempoala 43830 Hgo Mexico Univ Toulon & Var Aix Marseille Univ CNRS ENSAMLSIS UMR 7296CS 60584 F-83041 Toulon 9 France

Instrumentation to measure microclimate in greet-amuses is a task to developing before starting the identification and control moisture and temperature in greenhouses, a variable which best describe the microclimate and helps prevent fungus and disease risks, is the vapor pressure deficit (VPD), it is measured indirectly by means of two inputs: temperature and humidity, by means the psychrometric chart, and another way is using interpolation models. This paper shows methodology to measure VPD, by using fuzzy modeling type Takagi-Sugeno (T-S). Fuzzy modeling is based on expert and human knowledge, additionally this is combined with mathematical techniques to identify parameters of the antecedents and consequents of IF-THEN fuzzy rules, each IF-THEN fuzzy rule defines a submodel or region of interpolation. In this work, expert knowledge is the information described in psychrometric chart. Modeling learning was performed using air temperature and relative humidity, a set of 8 fuzzy rules was proposed to interpolate the VPD. The results of the fuzzy model are illustrated using measurements of an experimental I greenhouse, and was contrasted with a model well known in the literature. The algorithm of fuzzy modelling VPD, was codified in two platform application real time: C to microcontroller and LabVIEW (TM) thus it is possible measuring the instantaneous VPD. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： fuzzy sensors interpolation algorithms microclimate monitoring

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Inference of Foliar Temperature Profile of a Vineyard Using Integrated Sensors Into a Motorized Vehicle

Inference of Foliar Temperature Profile of a Vineyard Using ...

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IEEE International Conference on Automatica (ICA-ACCA)

作者： Ahumada-Garcia, Roberto Poblete-Echeverria, Carlos Besoain, Felipe Reyes-Suarez, Jose Univ Talca Fac Ingn Talca Chile Pontificia Univ Catolica Valparaiso Escuela Agron Quillota Chile Univ Oberta Catalunya Internet Interdisciplinary Inst IN3 Av Carl Friedrich Gauss 5 Barcelona Spain

ISBN: (纸本)9781509011476

Inferring foliar temperatures is motivated by the high cost related to measure each plant's temperatures in a vineyard. Foliar temperature is correlated with the plants water potential, which allows farmers to take irrigation decisions. In order to deal with this situation, we utilized information obtained from several temperature infrared sensors integrated into a motor vehicle that runs a vineyard taking measurements at different heights. This data was interpolated with Kriging and IDW methods. These models were evaluated through RMSE (rootmean-square error) and rRMSE (relative root-mean-square error) as performance measures. Main results indicate that the Krigning approach presents a better performance in comparison with IDW. It is possible to see that the sensors located at lower altitudes show less measured error as RMSE. It was also observed that the spatial distribution of errors is homogeneous, with most of these errors less than or equal to the average RMSE. Finally, no significant changes are observed in the model performance when halving the data employed for interpolation. From these assessments, optimum operation conditions for the monitoring equipment were proposed.

关键词： interpolation algorithms prediction methods inference algorithms

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C¹ Rational Quadratic Trigonometric interpolation Spline for Data Visualization

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-20页

作者： Liu, Shengjun Chen, Zhili Zhu, Yuanpeng Cent South Univ State Key Lab High Performance Complex Mfg Changsha 410083 Peoples R China Cent South Univ Sch Math & Stat Changsha 410083 Peoples R China

A new C-1 piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated as O(h(3)). Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.

关键词： TRIGONOMETRIC functions DATA modeling QUADRATIC fields PARAMETERS (Statistics) APPROXIMATION theory interpolation algorithms

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GM-PHD Filter Combined with Track-Estimate Association and Numerical interpolation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-9页

作者： Chen, Jinguang Xu, Bugao Ma, Lili Sun, Rui Xian Polytech Univ Sch Comp Sci Xian 710048 Peoples R China Univ Texas Austin Sch Human Ecol Austin TX 78712 USA

For the standard Gaussian mixture probability hypothesis density (GM-PHD) filter, the number of targets can be overestimated if the clutter rate is too high or underestimated if the detection rate is too low. These problems seriously affect the accuracy of multitarget tracking for the number and the value of measurements and clutters cannot be distinguished and recognized. Therefore, we proposed an improved GM-PHD filter to tackle these problems. Firstly, a track-estimate association was implemented in the filtering process to detect and remove false-alarm targets. Secondly, a numerical interpolation technique was used to compensate the missing targets caused by low detection rate. At the end of this paper, simulation results were presented to demonstrate the proposed GM-PHD algorithm is more effective in estimating the number and state of targets than the previous ones.

关键词： GAUSSIAN mixture models (Statistics) FILTERING theory (Signal processing) PROBABILITY density function interpolation algorithms FALSE alarms MATHEMATICAL analysis

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4D Model Flow: Precomputed Appearance Alignment for Real-time 4D Video interpolation

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COMPUTER GRAPHICS FORUM 2015年第7期34卷 173-182页

作者： Casas, Dan Richardt, Christian Collomosse, John Theobalt, Christian Hilton, Adrian Univ Surrey Guildford GU2 5XH Surrey England MPI Informat Saarbrucken Germany Intel Visual Comp Inst Saarbrucken Germany

We introduce the concept of 4D model flow for the precomputed alignment of dynamic surface appearance across 4D video sequences of different motions reconstructed from multi-view video. Precomputed 4D model flow allows the efficient parametrization of surface appearance from the captured videos, which enables efficient real-time rendering of interpolated 4D video sequences whilst accurately reproducing visual dynamics, even when using a coarse underlying geometry. We estimate the 4D model flow using an image-based approach that is guided by available geometry proxies. We propose a novel representation in surface texture space for efficient storage and online parametric interpolation of dynamic appearance. Our 4D model flow overcomes previous requirements for computationally expensive online optical flow computation for data-driven alignment of dynamic surface appearance by precomputing the appearance alignment. This leads to an efficient rendering technique that enables the online interpolation between 4D videos in real time, from arbitrary viewpoints and with visual quality comparable to the state of the art.

关键词： Four-dimensional imaging Video recordings interpolation algorithms Geometry Optical flow Visual perception

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Subdivision Schemes Based Collocation algorithms for Solution of Fourth Order Boundary Value Problems

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-18页

作者： Ejaz, Syeda Tehmina Mustafa, Ghulam Khan, Faheem Islamia Univ Bahawalpur Dept Math Punjab 63100 Pakistan Univ Sargodha Dept Math Punjab 40100 Pakistan

We present two collocation algorithms based on interpolating and approximating subdivision schemes for the solution of fourth order boundary value problems arising in the mathematical modeling of viscoelastic, and inelastic flows, deformation of beams, arches, and load bearing members like street lights and robotic arms in multipurpose engineering systems. Numerical examples are given to illustrate the algorithms. We conclude that approximating schemes based collocation algorithms give better solution than interpolating schemes based collocation algorithms. Main purpose of this paper is to explore and seek the applications of interpolating and approximating subdivision schemes in the field of boundary value problems along with intrinsic comparison of the results obtained by algorithms based on these schemes. A comparison with other approaches of this type of boundary value problems in order to see the advantages of the proposed methods is also given.

关键词： COLLOCATION methods BOUNDARY value problems interpolation algorithms APPROXIMATION algorithms VISCOELASTICITY DEFORMATIONS (Mechanics)

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A Reconstruction Algorithm for Blade Surface Based on Less Measured Points

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INTERNATIONAL JOURNAL OF AEROSPACE ENGINEERING 2015年第1期2015卷 1-11页

作者： Liu, Jia Zhao, Ji Yang, Xu Liu, Jiming Qu, Xingtian Wang, Xin Jilin Univ Coll Mech Sci & Engn Changchun 130025 Peoples R China

A reconstruction algorithm for blade surface from less measured points of section curves is given based on B-spline surface interpolation. The less measured points are divided into different segments by the key geometric points and throat points which are defined according to design concepts. The segmentations are performed by different fitting algorithms with consideration of curvature continuity as their boundary condition to avoid flow disturbance. Finally, a high-quality reconstruction surface model is obtained by using the B-spline curve meshes constructed by paired points. The advantage of this algorithm is the simplicity and effectivity reconstruction of blade surface to ensure the aerodynamic performance. Moreover, the obtained paired points can be regarded as measured points to measure and reconstruct the blade surface directly. Experimental results show that the reconstruction blade surface is suitable for precisely representing blade, evaluating machining accuracy, and analyzing machining allowance.

关键词： Rotors (Helicopters) Surface reconstruction Splines interpolation algorithms Curvature singularities Machining

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Engine Excitation Force Identification on the Basis of Discrete Spectrum Correction

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-11页

作者： Xu, Chuanyan Cao, Fengping Shandong Jiaotong Univ Sch Automot Engn Jinan 250023 Peoples R China

The interpolation method of discrete spectrum is applied to the engine excitation force identification. The frequency, amplitude, and phase of the vibration response of each measuring point on cylinder surface are obtained accurately based on the interpolation method. Combination with the inertia parameters and the dynamic properties of the mounts, the excitation force, and moment at the center of gravity of engine can be exactly retrieved. The nonlinear problem caused by the imprecise phase of the measurement points is avoided, and the identified method is simplified. Simulation results confirm the importance of the interpolation method on the accurate identification of the excitation force. Influences on the excitation force identification are analyzed quantitatively. The reasons causing the errors are analyzed and the avoidance methods are given too. Through the multi-rigid-body dynamics model simulation, the excitation force identification method is confirmed. Then, the proposed method is carried out on an engine.

关键词： ENGINES testing EXCITATION spectrum DISCRETE systems interpolation algorithms VIBRATION (Mechanics)

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Special version of the collocation method for integral equations of the second kind with singularities in the kernel

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DIFFERENTIAL EQUATIONS 2015年第9期51卷 1236-1242页

作者： Gabbasov, N. S. Galimova, Z. Kh. Kazan Fed Univ Naberezhnye Chelny Inst Naberezhnye Chelny Russia Kazan Inst Econ Management & Law Naberezhnye Chelny Branch Naberezhnye Chelny Russia

We study a linear integral equation of the second kind with fixed singularities in the kernel. For its approximate solution in the space of "pointwise smooth" functions, we suggest and justify a new version ... 详细信息

关键词： INTEGRAL equations SINGULARITIES (Mathematics) KERNEL (Mathematics) SMOOTHNESS of functions interpolation algorithms

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