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interpolation functions and inequalities

LINEAR & MULTILINEAR ALGEBRA 2022年第20期70卷 4897-4906页

作者： Osaka, Hiroyuki Udagawa, Yoichi Ritsumeikan Univ Dept Math Sci Kusatsu Shiga Japan

Using interpolation classes and the generalized Petz's trace inequality we give a new matrix inequality which might play an important role in the quantum information theory: For any pair of positive definite matrices A, B is an element of M-n(C) we have Tr((A - B)(exp(A) - exp(B)) <= Tr(vertical bar A(exp(A) - 1) - B(exp(B) - 1)).

关键词： interpolation functions matrix monotone functions operator monotone functions trace inequalities

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Two families of two-dimensional finite element interpolation functions of general degree with general continuity

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2023年第10期124卷 2171-2195页

作者： de Almeida, J. P. Moitinho Univ Lisbon Dept Civil Engn Architecture & Georesources Inst Super Tecn Lisbon Portugal

This work presents a generalization of the functions used in Fraeijs de Veubeke's quadrilateral (FVQ) element and in Hsieh, Clough and Tocher's (HCT) triangle, allowing for an arbitrary degree of the approximation, d, and for arbitrary order of continuity, r. These functions can be used to define finite elements that lead by direct assembly to C-r approximations. Their determination for each element is procedural, generalizing the reasoning used by Zienkiewicz to explain the FVQ element. The completeness of each basis is confirmed by comparing its dimension with that of a broken basis, defined primitive element wise, upon which the continuity constraints are successively imposed. The order of continuity at the vertices that is required to enable the independent definition of the normal derivatives at the sides is confirmed numerically. The corresponding interpolation functions are symbolically derived using Mathematica, and simple matlab codes using the data thus obtained are made available, to illustrate their application.

关键词： C-1 continuity C-2 continuity C-r continuity finite elements interpolation functions

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An Alternative sEMG based Isolated Word Subvocal Speech Recognition System based on interpolation functions

An Alternative sEMG based Isolated Word Subvocal Speech Reco...

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International Conference on Big Data and Artificial Intelligence and Software Engineering (ICBASE)

作者： Yang, Meng Zhang, Ming China Univ Min & Technol Beijing Dept Comp Sci & Technol Sch Mech Elect & Informat Engn Beijing Peoples R China Zhejiang Univ Inst Cyber Syst & Control State Key Lab Ind Control Technol Hangzhou Zhejiang Peoples R China

ISBN: (纸本)9781728196190

Surface electromyography (sEMG) based speech recognition has been widely studied in the last decade. The recognition is based on the signals captured by some electrodes which collect the ion currents generated by surface muscle activities. Therefore, the recognition could be carried out even the speech is inaudible. To address the temporal variance issue in isolated word recognition system, we developed an alternative way to process the signals, which is using interpolation functions to resize the signal segments. Results show that our method is practical by comparing it with the typical sEMG based isolated word speech recognition system.

关键词： sEMG subvocal speech recognition interpolation functions

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INEQUALITIES FOR interpolation functions

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BANACH JOURNAL OF MATHEMATICAL ANALYSIS 2015年第1期9卷 67-74页

作者： Dinh Trung Hoa Osaka, Hiroyuki Duy Tan Univ Inst Res & Dev Da Nang Vietnam Ton Duc Thang Univ Inst Computat Sci INCOS Ho Chi Minh City Vietnam Ton Duc Thang Univ Fac Civil Engn Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Univ Econ & Law Fac Econ Math Ho Chi Minh City Vietnam Ritsumeikan Univ Dept Math Sci Kusatsu Shiga 5258577 Japan

In this paper, in relation with interpolation functions we study some generalized Powers-Stormer's type inequalities and monotonicity inequality of indefinite type which generalizes a result of Ando.

关键词： interpolation functions operator monotone functions traces spaces with indefinite inner product monotonicity inequality of indefinite type

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interpolation functions of a hybrid-Trefftz perforated super-element featuring nodes on the hole boundary

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2014年第0期91卷 40-47页

作者： Hennuyer, C. Leconte, N. Langrand, B. Markiewicz, E. Off Natl Etud & Rech Aerosp French Aerospace Lab F-59045 Lille France UVHC LAMIH UMR CNRS 8201 F-59313 Valenciennes 9 France

The topic of the paper is related to the macroscopic modelling of riveted assemblies for full-scale aircraft structures subjected to crash/impact loadings. "Super-elements" have been developed to model the rivet and its rupture. However, stress concentrations in riveted assemblies can also initiate cracks from hole boundaries that propagate to the next ones and can lead to the catastrophic loss of the airplane by dismantlement of structural parts. An hybrid-Trefftz perforated super-element has been previously developed by the authors. However, the hole boundary of this super-element is a traction-free analytical boundary, preventing any connection with rivet elements. As a necessary first step to make the connection with the rivet possible, it is proposed to formulate additional nodes on the hole boundary of the perforated super-element. However, increasing the number of nodes implies increasing the super-element interpolation functions series order. Their ability to accurately describe the strain and stress Fields is evaluated, it is found that when the series order is increased, the mechanical fields are still well described, but are a little less accurate than lower order interpolation functions. This evolution is discussed and seems to be linked to the ill-conditioning of the system. The accuracy is however still sufficient for the formulation of a 16-node super-element featuring eight nodes on the hole boundary. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Riveted assemblies Hybrid-Trefftz FE interpolation functions

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3D formulation of mono-symmetrical composite beams with deformable connection

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2024年 237卷

作者： Wardi, Yassir Keo, Pisey Hjiaj, Mohammed Univ Rennes LGCGM Struct Engn Res Grp INSA RennesEA 3913 20 Ave Buttes Coesmes F-35700 Rennes France

This paper deals with a 3D linear formulation for mono-symmetric composite beams with deformable connection, taking into account non -uniform torsion. To simplify the development of the analytical solution, it is assumed that the warping of each layer of the composite section has no contribution on the stress resultants of each layer. Therefore, the warping function obtained with the classical St-Venant beam theory can be used for each subsection. As a result, the variables associated to both connection shearing plans become uncoupled. Using the virtual work principle, the governing equations are derived, and solved in closed-form. Based on the analytical expressions of the displacement fields, the exact stiffness matrix of the composite beam is computed. In addition, a displacement-based formulation is suggested. Appropriate polynomial interpolation functions are selected to circumvent slip-locking phenomenon. It has been shown that the slip-locking can be avoided by using quadratic shape function for axial displacement interpolations, by providing an additional middle node in each layer. Four examples are investigated in this paper. The prediction as well as the performance of the proposed direct stiffness method, are compared against an existing solution from the literature. In addition, slip-locking problem is addressed and the performance of the displacement-based method against the exact formulation is evaluated. The influence of warping effects on the composite beam response is assessed. Finally, a parametric study is conducted to evaluate the influence of connection rigidity and the coupling of the displacement fields on slip distributions.

关键词： Composite beam Direct stiffness method interpolation functions Slip Locking

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Solved structural dynamic mathematical models via novel technique approach

Solved structural dynamic mathematical models via novel tech...

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13th International Conference on Materials, Processing and Characterization (ICMPC)

作者： Ganesh, Engammagari Ramana, P. V. Shrimali, M. K. Malaviya Natl Inst Technol NCDMM Jaipur 302017 India

Dynamic problems are solved using this technique, considering the forcing term is free forced vibration, constantly forced vibration and harmonic function. Two different interpolation functions have been considered for solving such problems, the first one x = a + bt and the second one x = acosxt + bsinxt. The results achieved from this method using these interpolation functions are compared with the precise solutions. Not only this method other methods such as the Newmark-beta method, Runge-Kutta fourth-order and Laplace transforms have been applied to the same structural dynamic problems. The method gave exact solutions for most of the problems. It is observed that the complementary function of the solution obtained using the interpolation function x = acosxt + bsinxt is to be divided by the number of iterations to obtain the precise solution. This technique gave an exact solution for cases where there is no force acting and in cases where a constant force is acting. In cases where a harmonic force is acting, this method is overestimated. The paper aims to obtain approximate dependent variable quantities for distinct displacement interpolation functions for various structural dynamic natural *** (c) 2022 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the International Conference on Materials, Processing & Characterization.

关键词： interpolation functions Harmonic function Free forced vibration Constant forced vibration

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Unsolved structural dynamic mathematical models via Novel technique approach

Unsolved structural dynamic mathematical models via Novel te...

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2nd International Conference on Engineering Materials, Metallurgy and Manufacturing (ICEMMM)

作者： Ganesh, Engammagari Ramana, P. V. Shrimali, M. K. Malaviya Natl Inst Technol NCDMM Jaipur 302017 India

Dynamic problems are solved using the Novel technique, considering the forcing term is free forced vibration, constantly forced vibration and harmonic function with mass and stiffness terms zeros. Two different interpolation functions have been considered for solving such problems, the first one x = a + bt and the second one x = acosxt + bsinxt. The results achieved from the novel technique using these interpolation functions are compared with the precise solutions. Not only this method other methods such as the Newmark-beta method, Runge-Kutta fourth-order and Laplace transforms have been applied to the same structural dynamic problems. The paper employs the novel technique method to various initial value problems such as emotional problems. This method has been adapted in various fields of Engineering. Limited research has been done in the past in the dynamics field using this method. So, an attempt has been made to examine the validity of such a method. The method gave exact solutions for most of the problems. It is observed that the complementary function of the solution obtained using the interpolation function x = acosxt + bsinxt is to be divided by the number of iterations to obtain the precise solution. The Novel technique gave an exact solution for cases where there is no force acting and in cases where a constant force is acting. In the cases in which a harmonic force is acting, when the mass term is zero, the novel technique method is overestimated. In the case of stiffness term zero, it is underestimated. The paper aims to obtain approximate dependent variable quantities for distinct displacement interpolation functions for various structural dynamic natural problems. Copyright (C) 2022 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the Second International Conference on Engineering Materials, Metallurgy and Manufacturing.

关键词： Novel Technique interpolation functions Harmonic Function Free Forced Vibration Constant Forced Vibration Mass Less Model

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An interpolation function of multiple harmonic sum

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RESEARCH IN NUMBER THEORY 2022年第4期8卷 1-11页

作者： Kusunoki, Yusuke Nakamura, Yayoi EX Corp Pias Tower 20FToyosaki 3-19-3 Osaka Japan Kindai Univ 3-4-1 Kowakae Higashiosaka Osaka Japan

An interpolation function of the multiple harmonic sum is defined. Its basic properties, asymptotic behaviors and derivatives, which play fundamental roles in the study of the multiple polylogarithm and multiple zeta ... 详细信息

关键词： Multiple harmonic sum interpolation functions Multiple zeta values Harmonic product

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Fractional Pseudospectral Schemes With Applications to Fractional Optimal Control Problems

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JOURNAL OF MATHEMATICS 2024年第1期2024卷

作者： Sahabi, M. Cherati, A. Yazdani Univ Mazandaran Fac Math Sci Dept Appl Math Babolsar Iran

This research endeavors to introduce novel fractional pseudospectral methodologies tailored for addressing fractional optimal control problems encompassing inequality constraints and boundary conditions. Leveraging fractional Lagrange interpolation functions, we formulate differential and integral pseudospectral matrices pivotal in discretizing fractional optimal control problems. The stability of these matrices is ensured through the utilization of M & uuml;ntz-Legendre polynomials. Discretization of fractional optimal control problems entails employing integral and differential fractional matrices, with collocation strategically positioned at both Gauss and flipped Radau-type points. Our results demonstrate that the proposed method is well suited for practical problems with larger domains. Furthermore, it proves effective for Bang-Bang type problems and offers substantial benefits for problems with nonsmooth solutions. Comprehensive numerical evaluations on benchmark fractional optimal control problems substantiate the effectiveness of the devised pseudospectral methodologies, showcasing their commendable performance and potential for practical applications.

关键词： fractional optimal control problem interpolation functions Jacobi-Gauss points pseudospectral methods

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