Particular Solution of Poisson Problems Using Cardinal Lagrangian Polyharmonic Splines

2009 ◽  
pp. 1-16 ◽  
Author(s):  
Barbara Bacchelli ◽  
Mira Bozzini
Keyword(s):  
Particular Solution ◽  
Polyharmonic Splines

scholarly journals AN APPROACH TO SOLVE SLAVNOV–TAYLOR IDENTITY IN D4 ${\mathcal N}=1$ SUPERGRAVITY

2004 ◽  
Vol 19 (17) ◽  
pp. 1291-1296 ◽  
Author(s):  
IGOR KONDRASHUK
Keyword(s):  
Effective Action ◽  
Spin Connection ◽  
Classical Action ◽  
Local Invariant ◽  
Particular Solution ◽  
Physical Part

We consider a particular solution to Slavnov–Taylor identity in four-dimensional supergravity. The consideration is performed for pure supergravity, no matter superfields are included. The solution is obtained by inserting dressing functions into ghost part of the classical action for supergravity. As a consequence, physical part of the effective action is local invariant with respect to diffeomorphism and structure groups of transformation for dressed effective superfields of vielbein and spin connection.

Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Małgorzata Klimek ◽  
Marek Błasik
Keyword(s):  
Differential Equations ◽  
Arbitrary Order ◽  
Continuous Solution ◽  
Initial Value ◽  
Uniqueness Results ◽  
Banach Theorem ◽  
Arbitrary Partition ◽  
Particular Solution ◽  
Stationary Function ◽  
Fractional Differential

AbstractTwo-term semi-linear and two-term nonlinear fractional differential equations (FDEs) with sequential Caputo derivatives are considered. A unique continuous solution is derived using the equivalent norms/metrics method and the Banach theorem on a fixed point. Both, the unique general solution connected to the stationary function of the highest order derivative and the unique particular solution generated by the initial value problem, are explicitly constructed and proven to exist in an arbitrary interval, provided the nonlinear terms fulfil the corresponding Lipschitz condition. The existence-uniqueness results are given for an arbitrary order of the FDE and an arbitrary partition of orders between the components of sequential derivatives.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

scholarly journals Binary Large Object-Based Approach for QR Code Detection in Uncontrolled Environments

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Omar Lopez-Rincon ◽  
Oleg Starostenko ◽  
Vicente Alarcon-Aquino ◽  
Juan C. Galan-Hernandez
Keyword(s):  
Recognition Rate ◽  
Qr Code ◽  
Large Object ◽  
Position Detection ◽  
Object Based ◽  
Geometrical Features ◽  
Particular Solution ◽  
Variable Illumination ◽  
Low Performance ◽  
Iterative Filtering

Quick Response QR barcode detection in nonarbitrary environment is still a challenging task despite many existing applications for finding 2D symbols. The main disadvantage of recent applications for QR code detection is a low performance for rotated and distorted single or multiple symbols in images with variable illumination and presence of noise. In this paper, a particular solution for QR code detection in uncontrolled environments is presented. The proposal consists in recognizing geometrical features of QR code using a binary large object- (BLOB-) based algorithm with subsequent iterative filtering QR symbol position detection patterns that do not require complex processing and training of classifiers frequently used for these purposes. The high precision and speed are achieved by adaptive threshold binarization of integral images. In contrast to well-known scanners, which fail to detect QR code with medium to strong blurring, significant nonuniform illumination, considerable symbol deformations, and noising, the proposed technique provides high recognition rate of 80%–100% with a speed compatible to real-time applications. In particular, speed varies from 200 ms to 800 ms per single or multiple QR code detected simultaneously in images with resolution from 640 × 480 to 4080 × 2720, respectively.

scholarly journals Generalized F(R, T) cosmological models with fermionic fields

2021 ◽  
Vol 2090 (1) ◽  
pp. 012063
Author(s):  
Koblandy Yerzhanov ◽  
Gulnur Bauyrzhan ◽  
Ratbay Myrzakulov
Keyword(s):  
Mathematical Model ◽  
Cosmological Model ◽  
Main Idea ◽  
Scale Factor ◽  
Specific Form ◽  
Fermion Field ◽  
Fermionic Fields ◽  
Particular Solution ◽  
The Universe ◽  
Symmetry Method

Abstract We investigated the gravity model F (R, T), which interacts with a fermion field in a uniform and isotropic at spacetime FLRW. The main idea and purpose of the work donewas to create a mathematical model and find a particular solution for the scale factor a, since it describes the dynamics of the evolution of the Universe. The solutions for this universe are obtained using the Noether symmetry method. With its help, a specific form of the Lagrangian is obtained. And the possible types of the scale factor were found. The evolution of the resulting cosmological model has been investigated.

scholarly journals MHD convection ow in a constricted channel

2018 ◽  
Vol 26 (2) ◽  
pp. 267-283
Author(s):  
M. Tezer-Sezgin ◽  
Merve Gürbüz
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Particular Solution ◽  
Laminar Convection ◽  
Long Channel ◽  
Velocity Pressure

Abstract We consider the steady, laminar, convection ow in a long channel of 2D rectangular constricted cross-section under the inuence of an applied magnetic field. The Navier-Stokes equations including Lorentz and buoyancy forces are coupled with the temperature equation and are solved by using linear radial basis function (RBF) approximations in terms of the velocity, pressure and the temperature of the fluid. RBFs are used in the approximation of the particular solution which becomes also the approximate solution of the problem. Results are obtained for several values of Grashof number (Gr), Hartmann number (M) and the constriction ratios (CR) to see the effects on the ow and isotherms for fixed values of Reynolds number and Prandtl number. As M increases, the ow is flattened. An increase in Gr increases the magnitude of the ow in the channel. Isolines undergo an inversion at the center of the channel indicating convection dominance due to the strong buoyancy force, but this inversion is retarded with the increase in the strength of the applied magnetic field. When both Hartmann number and constriction ratio are increased, ow is divided into more loops symmetrically with respect to the axes.

scholarly journals On generalized Lemaitre–Tolman–Bondi metric: Fractal matter at the end of matter–antimatter recombination

2021 ◽  
pp. 2150086
Author(s):  
Sergio L. Cacciatori ◽  
Alessio Marrani ◽  
Federico Re
Keyword(s):  
Dark Matter ◽  
Relativistic Effects ◽  
Partial Explanation ◽  
First Order ◽  
Acceleration Of The Universe ◽  
Particular Solution ◽  
Ancient Times ◽  
The Universe ◽  
Recombination Epoch ◽  
Ltb Metric

Many recent researches have investigated the deviations from the Friedmannian cosmological model, as well as their consequences on unexplained cosmological phenomena, such as dark matter and the acceleration of the Universe. On one hand, a first-order perturbative study of matter inhomogeneity returned a partial explanation of dark matter and dark energy, as relativistic effects due to the retarded potentials of far objects. On the other hand, the fractal cosmology, now approximated by a Lemaitre–Tolman–Bondi (LTB) metric, results in distortions of the luminosity distances of SNe Ia, explaining the acceleration as apparent. In this work, we extend the LTB metric to ancient times. The origin of the fractal distribution of matter is explained as the matter remnant after the matter–antimatter recombination epoch. We show that the evolution of such a inhomogeneity necessarily requires a dynamical generalization of LTB, and we propose a particular solution.

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