• 제목/요약/키워드: fractional function

검색결과 336건 처리시간 0.026초

TWO-WEIGHT NORM ESTIMATES FOR SQUARE FUNCTIONS ASSOCIATED TO FRACTIONAL SCHRÖDINGER OPERATORS WITH HARDY POTENTIAL

  • Tongxin Kang;Yang Zou
    • 대한수학회보
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    • 제60권6호
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    • pp.1567-1605
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    • 2023
  • Let d ∈ ℕ and α ∈ (0, min{2, d}). For any a ∈ [a*, ∞), the fractional Schrödinger operator 𝓛a is defined by 𝓛a := (-Δ)α/2 + a|x|, where $a^*:={\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}(d-{\alpha})/4)^2}}$. In this paper, we study two-weight Sobolev inequalities associated with 𝓛a and two-weight norm estimates for several square functions associated with 𝓛a.

DEVELOPMENT OF A NON-STANDARD FINITE DIFFERENCE METHOD FOR SOLVING A FRACTIONAL DECAY MODEL

  • SAID AL KATHIRI;EIHAB BASHIER;NUR NADIAH ABD HAMID;NORSHAFIRA RAMLI
    • Journal of applied mathematics & informatics
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    • 제42권3호
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    • pp.695-708
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    • 2024
  • In this paper we present a non-standard finite difference method for solving a fractional decay model. The proposed NSFDM is constructed by incorporating a non-standard denominator function, resulting in an explicit numerical scheme as easy as the conventional Euler method, but it provides very accurate solutions and has unconditional stability. Two examples from the literature are presented to demonstrate the performance of the proposed numerical scheme, which is compared to three methods from the literature. It is found that the method's estimated errors are extremely minimal, such as within the machine precision.

Flutter reliability analysis of suspension bridges based on multiplicative dimensional reduction method

  • Guo, Junfeng;Zheng, Shixiong;Zhang, Jin;Zhu, Jinbo;Zhang, Longqi
    • Wind and Structures
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    • 제27권3호
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    • pp.149-161
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    • 2018
  • A reliability analysis method is proposed in this paper based on the maximum entropy (MaxEnt) principle in which constraints are specified in terms of the fractional moments instead of integer moments. Then a multiplicative dimensional reduction method (M-DRM) is introduced to compute the fractional moments. The method is applicable for both explicit and implicit limit state functions of complex structures. After two examples illustrate the accuracy and efficiency of this method in comparison to the Monte Carlo simulation (MCS), the method is used to analyze the flutter reliability of suspension bridge. The results show that the empirical formula method in which the limit state function is explicitly represented as a function of variables is only a too conservative estimate for flutter reliability analysis but is not accurate adequately. So it is not suitable for reliability analysis of bridge flutter. The actual flutter reliability analysis should be conducted based on a finite element method in which limit state function is implicitly represented as a function of variables. The proposed M-DRM provide an alternate and efficient way to analyze a much more complicated flutter reliability of long span suspension bridge.

Quasiconcave Bilevel Programming Problem

  • Arora S.R.;Gaur Anuradha
    • Management Science and Financial Engineering
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    • 제12권1호
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    • pp.113-125
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    • 2006
  • Bilevel programming problem is a two-stage optimization problem where the constraint region of the first level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel quadratic/linear fractional programming problem in which the objective function of the first level is quasiconcave, the objective function of the second level is linear fractional and the feasible region is a convex polyhedron. Considering the relationship between feasible solutions to the problem and bases of the coefficient submatrix associated to variables of the second level, an enumerative algorithm is proposed which finds a global optimum to the problem.

Monte Carlo Simulation of the Molecular Properties of Poly(vinyl chloride) and Poly(vinyl alcohol) Melts

  • Moon, Sung-Doo;Kang, Young-Soo;Lee, Dong-J.
    • Macromolecular Research
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    • 제15권6호
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    • pp.491-497
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    • 2007
  • NPT Monte Carlo simulations were performed to calculate the molecular properties of syndiotactic poly(vinyl chloride) (PVC) and syndiotactic poly(vinyl alcohol) (PVA) melts using the configurational bias Monte Carlo move, concerted rotation, reptation, and volume fluctuation. The density, mean square backbone end-to-end distance, mean square radius of gyration, fractional free-volume distribution, distribution of torsional angles, small molecule solubility constant, and radial distribution function of PVC at 0.1 MPa and above the glass transition temperature were calculated/measured, and those of PVA were calculated. The calculated results were compared with the corresponding experimental data and discussed. The calculated densities of PVC and PVA were smaller than the experimental values, probably due to the very low molecular weight of the model polymer used in the simulation. The fractional free-volume distribution and radial distribution function for PVC and PVA were nearly independent of temperature.

THE PRODUCT OF ANALYTIC FUNCTIONALS IN Z'

  • Li, Chenkuan;Zhang, Yang;Aguirre, Manuel;Tang, Ricky
    • 대한수학회지
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    • 제45권2호
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    • pp.455-466
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    • 2008
  • Current studies on products of analytic functionals have been based on applying convolution products in D' and the Fourier exchange formula. There are very few results directly computed from the ultradistribution space Z'. The goal of this paper is to introduce a definition for the product of analytic functionals and construct a new multiplier space $F(N_m)$ for $\delta^{(m)}(s)$ in a one or multiple dimension space, where Nm may contain functions without compact support. Several examples of the products are presented using the Cauchy integral formula and the multiplier space, including the fractional derivative of the delta function $\delta^{(\alpha)}(s)$ for $\alpha>0$.

Harmonic Winding Factors and MMF Analysis for Five-phase Fractional-slot Concentrated Winding PMSM

  • Kang, Huilin;Zhou, Libing;Wang, Jin
    • Journal of international Conference on Electrical Machines and Systems
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    • 제3권1호
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    • pp.20-26
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    • 2014
  • To enhance torque density by harmonic current injection, optimal slot/pole combinations for five-phase permanent magnet synchronous motors (PMSM) with fractional-slot concentrated windings (FSCW) are chosen. The synchronous and the third harmonic winding factors are calculated for a series of slot/pole combinations. Two five-phase PMSM, with general FSCW (GFSCW) and modular stator FSCW (MFSCW), are analyzed and compared in detail, including the stator structures, star of slots diagrams, and MMF harmonic analysis based on the winding function theory. The analytical results are verified by finite element method, the torque characteristics and phase back-EMF are also taken into considerations. Results show that the MFSCW PMSM can produce higher average torque, while characterized by more MMF harmonic contents and larger ripple torque.

A FINITE DIFFERENCE/FINITE VOLUME METHOD FOR SOLVING THE FRACTIONAL DIFFUSION WAVE EQUATION

  • Sun, Yinan;Zhang, Tie
    • 대한수학회지
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    • 제58권3호
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    • pp.553-569
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    • 2021
  • In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂βtu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂βtu by using an interpolation of derivative type. The truncation error of this formula is of O(△t2+δ-β)-order if function u(t) ∈ C2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t3-β) if u(t) ∈ C3 [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H1-norm and L2-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

SOME PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTION

  • Rao, Snehal B.;Patel, Amit D.;Prajapati, Jyotindra C.;Shukla, Ajay K.
    • 대한수학회논문집
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    • 제28권2호
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    • pp.303-317
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    • 2013
  • In present paper, we obtain functions $R_t(c,{\nu},a,b)$ and $R_t(c,-{\mu},a,b)$ by using generalized hypergeometric function. A recurrence relation, integral representation of the generalized hypergeometric function $_2R_1(a,b;c;{\tau};z)$ and some special cases have also been discussed.

비국부 적분 연산기로 표현되는 페리다이나믹 방정식의 수렴성 (Convergence of Nonlocal Integral Operator in Peridynamics)

  • 조광현;하윤도
    • 한국전산구조공학회논문집
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    • 제34권3호
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    • pp.151-157
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    • 2021
  • 본 연구에서는 비국부 적분 연산기로 표현되는 페리다이나믹 방정식의 수렴성을 검토한다. 정적/준정적 손상 해석 문제를 효율적으로 해석하기 위해 페리다이나믹 방정식의 implicit 정식화가 필요하다. 이 과정에서 페리다이나믹 비국부 적분 방정식으로부터 대수방정식 형태가 나타나게 되어 시스템 행렬 계산을 위해 많은 시간이 소요되기 때문에, 효율적인 계산을 위해 수렴성이 중요한 요소가 된다. 특히 radial influence 함수를 적분 kernel로 사용하는 경우 fractional Laplacian 적분 방정식이 유도된다. 비국부 적분 연산기의 교윳값 성질에 의해 대수방정식의 condition number가 radial influence 함수의 차수 및 비국부 영역의 크기에 영향을 받는 것이 수학적으로 확인되었다. 본 연구에서는 이를 토대로 균열이 있는 페리다이나믹 정적 해석 문제를 Newton-Raphson 방법으로 해석할 때 적분 커널의 차수, 비국부 영역의 크기 등이 대수방정식의 condition number와 preconditioned conjugate gradient (PCG) 방법으로 계산 시 수렴성 및 계산 시간에 미치는 영향을 수치적으로 분석한다.