scholarly journals Sharp results in the integral-form John–Nirenberg inequality

2011 ◽  
Vol 363 (08) ◽  
pp. 4135-4135 ◽  
Author(s):  
L. Slavin ◽  
V. Vasyunin
Keyword(s):  
Integral Form ◽  
Nirenberg Inequality

ДОСВІД У ДИСКУСІЙНОМУ ПОЛІ ПОЗИЦІЮВАННЯ КАТЕГОРІЇ "ТВОРЧИЙ ПОТЕНЦІАЛ"

1970 ◽  
Vol 6 (1) ◽  
pp. 62-71
Author(s):  
Лариса Міщиха
Keyword(s):  
Coming Out ◽  
Motion Vector ◽  
Integral Form ◽  
Phenomenological Approach ◽  
Humanistic Psychology ◽  
Creative Potential ◽  
Form Of Life ◽  
Conceptual Background ◽  
Creative Experience ◽  
The One

У статті зроблено спробу проаналізувати феномен "досвід" у форматі дослідження творчого потенціалу особистості. Теоретико-методологічними засадами заявленої вище проблеми стали концептуальні засади гуманістичної психології, феноменологічного підходу. Досвід, як вагома складова творчого потенціалу особистості, розглядається у співвідношенні таких провідних тенденцій, як стереотипність та оригінальність. Наголошується, що досвід, з одного боку, може сприяти все більшій алгоритмізації та стереотипізації, консерватизму у розв’язанні нових задач, що безумовно перешкоджає творчості. З іншого боку, в осіб з високим творчим потенціалом він стає інтегрованою формою життєтворчості, де в структурі старих знань завжди знайдеться місце новим знанням як привнесених "ззовні", так і знанням, що їх отримує автор через власні ініціації, пошук, накреслюючи власноруч вектор руху. Звідси він отримує "побічний продукт" творчої діяльності – саморозвиток. Відтак творчий досвід трактується як такий, що містить у собі акумуляцію та інтеграцію усіх прижиттєвих творчих напрацювань особистості, готовність її до творчої діяльності та безперервної освіти. Суб’єкт творчої діяльності залишається відкритим новому досвіду, сповнений готовності до нового пізнання, творчих пошуків. In the article there was an attempt to analyze the phenomenon "experience" in the form of investigating a person’s creative potential. The theoretic methodological background of the performed above problem is conceptual background of humanistic psychology and phenomenological approach. Experience as an essential part of a person’s creative potential is regarded in relation to such leading trends as stereotype and originality. On the one hand, the experience is emphasized to be able to promote the model of algorithm and stereotype, conservatism in solving new tasks that is certain to inhibit creativity. On the other hand, personalities with high creative potential have an experience that is becoming an integral form of life work where in the structure of old knowledge you can always find a place for both new ones coming out "from inside" and the ones the author takes due to his own initiation and search. In this way he sketches motion vector and gets the "by-product" of his creativity, it means self-development. Hence, creative experience is interpreted as the one to absorb accumulation and integration of all creative experience in a person’s life; also his/her readiness to creativity and continuing education. The subject of creativity remains opened to a new experience that is fully ready for a new cognition and creativity.

Structure of minimizers of Cafarelli-Kohn-Nirenberg inequality

2020 ◽  
Vol 72 (4) ◽  
pp. 551-567
Author(s):  
Jann-Long Chern ◽  
Chih-Her Chen ◽  
Gyeongha Hwang
Keyword(s):  
Nirenberg Inequality

scholarly journals Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 174
Author(s):  
Janez Urevc ◽  
Miroslav Halilovič
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integral Form ◽  
Collocation Methods ◽  
Nonlinear Odes ◽  
New Class ◽  
New Methods ◽  
Runge Kutta

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

scholarly journals Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

2020 ◽  
Vol 23 (2) ◽  
pp. 378-389
Author(s):  
Ferenc Izsák ◽  
Gábor Maros
Keyword(s):  
Fractional Order ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Elliptic Problems ◽  
Integral Form ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Potential Operators

AbstractFractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

scholarly journals Extending the global-direction stencil with “face-area-weighted centroid” to unstructured finite volume discretization from integral form

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Lingfa Kong ◽  
Yidao Dong ◽  
Wei Liu ◽  
Huaibao Zhang
Keyword(s):  
Convergence Rate ◽  
Finite Volume ◽  
Differential Form ◽  
Integral Form ◽  
Finite Volume Methods ◽  
Reconstruction Method ◽  
Computational Accuracy ◽  
Face Area ◽  
Finite Volume Discretization ◽  
Skewness Reduction

AbstractAccuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work [Kong, et al. Chin Phys B 29(10):100203, 2020], we explored a novel global-direction stencil and combined it with the face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Greatly inspired by the differential form, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization from integral form on both second and third-order finite volume solver. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has superiorities on both computational accuracy and convergence rate.

scholarly journals Electrodynamics of a magnet moving through a conducting pipe

2006 ◽  
Vol 84 (4) ◽  
pp. 253-271 ◽  
Author(s):  
M Hossein Partovi ◽  
Eliza J Morris
Keyword(s):  
Drag Force ◽  
Eddy Currents ◽  
Numerical Study ◽  
Full Range ◽  
Magnetic Behavior ◽  
Integral Form ◽  
Asymptotic Formulas ◽  
Pipe Material ◽  
Point Dipole ◽  
Axially Symmetric

The popular demonstration involving a permanent magnet falling through a conducting pipe is treated as an axially symmetric boundary-value problem. Specifically, Maxwell's equations are solved for an axially symmetric magnet moving coaxially inside an infinitely long, conducting cylindrical shell of arbitrary thickness at nonrelativistic speeds. Analytic solutions for the fields are developed and used to derive the resulting drag force acting on the magnet in integral form. This treatment represents a significant improvement over existing models, which idealize the problem as a point dipole moving slowly inside a pipe of negligible thickness. It also provides a rigorous study of eddy currents under a broad range of conditions, and can be used for magnetic braking applications. The case of a uniformly magnetized cylindrical magnet is considered in detail, and a comprehensive analytical and numerical study of the properties of the drag force is presented for this geometry. Various limiting cases of interest involving the shape and speed of the magnet and the full range of conductivity and magnetic behavior of the pipe material are investigated and corresponding asymptotic formulas are developed.PACS Nos.: 81.70.Ex, 41.20.–q, 41.20.Gz

scholarly journals The dynamic generalization of the Eshelby inclusion problem and its static limit

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160256 ◽  
Author(s):  
Luqun Ni ◽  
Xanthippi Markenscoff
Keyword(s):  
Integral Form ◽  
Transformation Strain ◽  
The Self ◽  
Eshelby Tensor ◽  
Inclusion Problem ◽  
Static Limit ◽  
Governing System ◽  
Eshelby Inclusion ◽  
Interior Domain ◽  
Eshelby Problem

The dynamic generalization of the celebrated Eshelby inclusion with transformation strain is the (subsonically) self-similarly expanding ellipsoidal inclusion starting from the zero dimension. The solution of the governing system of partial differential equations was obtained recently by Ni & Markenscoff (In press. J. Mech. Phys. Solids ( doi:10.1016/j.jmps.2016.02.025 )) on the basis of the Radon transformation, while here an alternative method is presented. In the self-similarly expanding motion, the Eshelby property of constant constrained strain is valid in the interior domain of the expanding ellipsoid where the particle velocity vanishes (lacuna). The dynamic Eshelby tensor is obtained in integral form. From it, the static Eshelby tensor is obtained by a limiting procedure, as the axes' expansion velocities tend to zero and time to infinity, while their product is equal to the length of the static axis. This makes the Eshelby problem the limit of its dynamic generalization.

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