scholarly journals A New Approach to Newton-Type Polynomial Interpolation with Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Le Zou ◽  
Liangtu Song ◽  
Xiaofeng Wang ◽  
Thomas Weise ◽  
Yanping Chen ◽  
...  
Keyword(s):  
Polynomial Interpolation ◽  
Information Matrix ◽  
Divided Differences ◽  
Mathematical Representation ◽  
Interpolation Algorithm ◽  
New Approach ◽  
Multiple Parameters ◽  
Parameter Values ◽  
The Given ◽  
Interpolation Functions

Newton’s interpolation is a classical polynomial interpolation approach and plays a significant role in numerical analysis and image processing. The interpolation function of most classical approaches is unique to the given data. In this paper, univariate and bivariate parameterized Newton-type polynomial interpolation methods are introduced. In order to express the divided differences tables neatly, the multiplicity of the points can be adjusted by introducing new parameters. Our new polynomial interpolation can be constructed only based on divided differences with one or multiple parameters which satisfy the interpolation conditions. We discuss the interpolation algorithm, theorem, dual interpolation, and information matrix algorithm. Since the proposed novel interpolation functions are parametric, they are not unique to the interpolation data. Therefore, its value in the interpolant region can be adjusted under unaltered interpolant data through the parameter values. Our parameterized Newton-type polynomial interpolating functions have a simple and explicit mathematical representation, and the proposed algorithms are simple and easy to calculate. Various numerical examples are given to demonstrate the efficiency of our method.

A Unified Approach to H∞ Control of Singular Markovian Jump Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Guoliang Wang ◽  
Hongyi Li
Keyword(s):  
Transition Probability ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
New Approach ◽  
Control Approach ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Bounded Uncertainties ◽  
The Given

This paper considers the H∞ control problem for a class of singular Markovian jump systems (SMJSs), where the jumping signal is not always available. The main contribution of this paper introduces a new approach to a mode-independent (MI) H∞ controller by exploiting the nonfragile method. Based on the given method, a unified control approach establishing a direct connection between mode-dependent (MD) and mode-independent controllers is presented, where both existence conditions are given in terms of linear matrix inequalities. Moreover, another three cases of transition probability rate matrix (TRPM) with elementwise bounded uncertainties, being partially unknown and to be designed are analyzed, respectively. Numerical examples are used to demonstrate the effectiveness of the proposed methods.

A network thermodynamic model of salt and water flow across the kidney proximal tubule

1978 ◽  
Vol 235 (6) ◽  
pp. F638-F648 ◽  
Author(s):  
S. R. Thomas ◽  
D. C. Mikulecky
Keyword(s):  
Proximal Tubule ◽  
Water Flow ◽  
Thermodynamic Model ◽  
Circuit Simulation ◽  
Basolateral Membrane ◽  
Kidney Proximal Tubule ◽  
Network Analyses ◽  
Pump Rate ◽  
Parameter Values ◽  
The Given

This network thermodynamic model of kidney proximal tubule epithelium treats coupled salt and water flow across each component membrane of the epithelium. We investigate the effects of various relative internal parameter values on the concentration of transepithelial flow, the concentrations in the cell and interspace, and the distribution of flows between cellular and paracellular routes. Best fit is obtaine if the apical and basolateral membrane reflection coefficients (or) are equal. The measured transepithelial filtration coefficient, Lp, is a function not only of the component Lps but also of the internal concentrations, or's, and permeabilities. For the given system topology (i.e., connectedness), parameters of component membranes must be within a narrow range to be consistent with experimental results. The dependence of the concentration of transported fluid on the balance between the solute pump rate and the transepithelial volume flow driving force is shown. This has implications for the effects of peritubular or lumen oncotic pressure on salt and water flow. With Appendix B of this paper and a user's guide for a circuit-simulation package (e.g., SPICE or PCAP) the reader can perform similar network analyses of transport models himself.

Development of Advanced CNC Interpolation Algorithm With Consideration of Command and Dynamic Errors

2015 ◽  
Author(s):  
Meng-Shiun Tsai ◽  
Ying-Che Huang
Keyword(s):  
The Other ◽  
Contour Error ◽  
Interpolation Algorithm ◽  
Interpolation Scheme ◽  
Error Equation ◽  
The Past ◽  
Cnc Interpolation ◽  
Dynamic Errors ◽  
Simulation Results ◽  
The Given

In this paper, an integrated acceleration/deceleration with dynamics interpolation scheme is proposed to confine the maximum contour error at the junction of linear junction. The dynamic contour error equation is derived analytically and then it is utilized for the interpolation design. Based on the derived formulations which could predict the command and dynamic errors, the advanced interpolation design could adjust the connecting velocity of the two blocks to confine the overall contour errors under the given tolerance. Simulation results validate the proposed algorithm can achieve higher accurate trajectory as compared to the other interpolation algorithm proposed in the past.

Genetic Algorithms in Fuzzy Engineering Design

1999 ◽  
Author(s):  
Ralf Schleiffer ◽  
Hans-Jürgen Sebastian ◽  
Erik K. Antonsson
Keyword(s):  
Engineering Design ◽  
Clustering Algorithm ◽  
Computer Application ◽  
Test Problems ◽  
Important Class ◽  
New Approach ◽  
Design Task ◽  
Evolutionary Technique ◽  
The Given ◽  
Real World Problems

Abstract Problems in the field of engineering design represent an important class of real world problems that typically require a fuzzy and imprecise representation. This article presents and discusses a new approach to model this type of problem, by incorporating linguistic descriptions together with a variety of user-defined trade-off strategies. An interactive computer application is introduced, using stochastic optimization to solve the design task by producing a specially desired output under the given environmental conditions which are partly caused by the personal preferences of the engineer and by the expectations of the customer. It utilizes a randomized evolutionary technique, made suitable for the class of problems at hand, to generate and to optimize design solutions that are later identified by a clustering algorithm. Moreover test problems that were solved by the application are considered. In all cases the good solutions were obtained by evaluating only an extremely small fraction of all possible designs.

A simultaneous decomposition for three quaternion tensors with applications in color video signal processing

2020 ◽  
pp. 1-35
Author(s):  
Zhuo-Heng He ◽  
Chen Chen ◽  
Xiang-Xiang Wang
Keyword(s):  
Signal Processing ◽  
Video Signal ◽  
New Approach ◽  
Video Signal Processing ◽  
Encryption And Decryption ◽  
Color Video ◽  
The Given ◽  
Einstein Product

In this paper, we establish a simultaneous decomposition for three quaternion tensors via Einstein product. This simultaneous decomposition transforms the given three quaternion tensors into nice forms which have only 1 and 0. We conclude with an application in the color video signal processing. This new approach only need to store four keys to realize the simultaneous encryption and decryption of three videos.

scholarly journals A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Alvaro H. Salas S ◽  
Jairo E. Castillo H ◽  
Darin J. Mosquera P
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytical Solution ◽  
Initial Conditions ◽  
Negative Ions ◽  
Nonlinear Problems ◽  
New Approach ◽  
Weierstrass Elliptic Function ◽  
Electronegative Plasma ◽  
The Given

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z ″ = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.

A New Approach to the Classification and Measurement of Stuttering

1972 ◽  
Vol 37 (2) ◽  
pp. 242-251 ◽  
Author(s):  
Eleanor S. Wertheim
Keyword(s):  
Quantitative Relationship ◽  
Management Plan ◽  
Clinical Validity ◽  
New Approach ◽  
Quantitative Estimates ◽  
The Social ◽  
Method Of Measurement ◽  
Qualitative Pattern ◽  
The Stability ◽  
The Given

A quantitative, multidimensional approach to clinical diagnosis and management of stuttering is proposed. This approach would involve (1) the measurement of stuttering behavior under a number of contrived social conditions relevant to the given population of stutterers; (2) a method of measurement which provides separate quantitative estimates of the qualitative aspects of the stuttering pattern, for example, total frequency of disfluencies as well as incidence of hard blocking; (3) an analysis of the quantitative relationship between the social context and the qualitative pattern of stuttering and its severity; (4) a diagnostic formulation of “stutterogenic” situations for a given individual and of the stability and severity of the stuttering pattern across the total range of situations; and (5) a management plan geared to these diagnostic considerations. The approach is illustrated, using the findings of an experimental study primarily designed to test the author’s recently postulated bioadaptive theory of stuttering. Further research is needed to refine the proposed diagnostic approach and to establish its clinical validity and usefulness.

Highly accurate technique for studying some chaotic models described by ABC-fractional differential equations of variable-order

2020 ◽  
pp. 2150018
Author(s):  
M. M. Khader ◽  
Ibrahim Al-Dayel
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Polynomial Interpolation ◽  
Numerical Technique ◽  
Variable Order ◽  
Lagrange Polynomial ◽  
Efficient Tool ◽  
Fractional Differential ◽  
The Given

The propose of this paper is to introduce and investigate a highly accurate technique for solving the fractional Logistic and Ricatti differential equations of variable-order. We consider these models with the most common nonsingular Atangana–Baleanu–Caputo (ABC) fractional derivative which depends on the Mittag–Leffler kernel. The proposed numerical technique is based upon the fundamental theorem of the fractional calculus as well as the Lagrange polynomial interpolation. We satisfy the efficiency and the accuracy of the given procedure; and study the effect of the variation of the fractional-order [Formula: see text] on the behavior of the solutions due to the presence of ABC-operator by evaluating the solution with different values of [Formula: see text]. The results show that the given procedure is an easy and efficient tool to investigate the solution for such models. We compare the numerical solutions with the exact solution, thereby showing excellent agreement which we have found by applying the ABC-derivatives. We observe the chaotic solutions with some fractional-variable-order functions.

Research and Realization of a New Curve Grinding Method

2009 ◽  
Vol 16-19 ◽  
pp. 1305-1309
Author(s):  
Tian Zhong Sui ◽  
Lei Wang ◽  
Wen Bo Zhang ◽  
Di Sun
Keyword(s):  
Contact Zone ◽  
Contact Point ◽  
Linear Interpolation ◽  
Grinding Wheel ◽  
Central Plane ◽  
Interpolation Algorithm ◽  
Contact Points ◽  
Grinding Method ◽  
The Given ◽  
Nc Grinding

The curve NC grinding methods in presnet are analyzed. On the basis of this, a new curve NC grinding method―region contact grinding (RCG) method is proposed. With this method, the contact point between grinding wheel and workpiece can be controlled in the given contact zone. The problom of grinding wheel's distortion which is produced by contact point excessively deviating from symmetrical central plane of grinding wheel can be overcome. In order to the grinding mode, a new interpolation algorithm―region equiangular linear interpolation (RELI) is proposed. Namely, in terms of the convex-concave property of processing curve, some grinding regions are divided. In each grinding region, the grinding wheel's swing angle within each interpolation cycle is evenly distributed. Thereby, in the process of grinding a convex-concave curve, grinding wheel's contact points totally locate in the range of contact zone angle.

The Technology of Mig-Mag Welding with Low-Frequency Modulation of Arc Current

2014 ◽  
Vol 682 ◽  
pp. 426-430 ◽  
Author(s):  
S.A. Solodsky ◽  
N.Yu. Lugovtsova ◽  
I.S. Borisov
Keyword(s):  
Weld Pool ◽  
Theoretical Study ◽  
Low Frequency ◽  
Metal Structure ◽  
New Approach ◽  
Deposited Metal ◽  
Arc Current ◽  
Favorable Conditions ◽  
Pool Formation ◽  
The Given

The given paper suggests a new approach towards implementation of arc current low frequency modulating method in MAG, MIG-welding. The process facilitates controlling heat and crystallization processes, regulates the time of the weld pool formation and crystallization. Theoretical study allowed formulating the main criteria of receiving strong permanent joints to produce structures with advanced reliability as it creates favorable conditions for producing a more balanced deposited metal structure and reducing the heat-affected zone. Regulating the time of weld pool formation and crystallization improves weld formation and increases labor productivity when welding sheet metals.

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