Results 11 to 20 of about 7,066 (206)

Neural Controlled Differential Equation and Its Application in Pharmacokinetics and Pharmacodynamics. [PDF]

CPT Pharmacometrics Syst Pharmacol
Neural controlled differential equations (NCDE), driven by control variables, are capable to learn the discontinuous dynamics in the PK and PD datasets. ABSTRACT With the recent advances in machine learning (ML) and artificial intelligence (AI), data‐driven modeling approaches for pharmacokinetics (PK) and pharmacodynamics (PD) have gained popularity ...
Wu Z, Luo P, Chen R, Liu Y, Jian W, Zhou T.   +5 more
europepmc   +2 more sources

The Grad–Shafranov Equation in Cap-Cyclide Coordinates: The Heun Function Solution

Mathematics, 2023
The Grad–Shafranov plasma equilibrium equation was originally solved analytically in toroidal geometry, which fitted the geometric shape of the first Tokamaks.
Flavio Crisanti, Clemente Cesarano, Artur Ishkhanyan   +2 more
doaj   +1 more source

A massless scalar particle coupled to the Wahlquist metric

European Physical Journal C: Particles and Fields, 2021
We study the solutions of the wave equation where a massless scalar field is coupled to the Wahlquist metric, a type-D solution. We first take the full metric, and then write simplifications of the metric by taking some of the constants in the metric ...
T. Birkandan, M. Hortaçsu
doaj   +1 more source

On generalized Heun equation with some mathematical properties

Acta Polytechnica, 2022
We study the analytic solutions of the generalized Heun equation, (α0 + α1 r + α2 r2 + α3 r3) y′′ + (β0 + β1 r + β2 r2) y′ + (ε0 + ε1 r) y = 0, where |α3| + |β2|≠ 0, and {αi}3i=0, {βi}2i=0, {εi}1i=0 are real parameters.
Nasser Saad
doaj   +1 more source

TVB C++: A Fast and Flexible Back-End for The Virtual Brain. [PDF]

Adv Sci (Weinh)
TVB C++ is a streamlined and fast C++ Back‐End for The Virtual Brain (TVB), designed to make it as flexible as TVB, and FAST. Another pillar is to be fully compatible with TVB so easy bindings can be created from Python. Users can easily configure TVB C++ to execute the same code but with enhanced performance and parallelism.
Martín I, Zamora-López G, Fousek J, Schirner M, Ritter P, Jirsa V, Deco G, Patow G.   +7 more
europepmc   +2 more sources

Heun equations and quasi exact solubility [PDF]

Journal of Physics A: Mathematical and General, 1995
Summary: We consider the Heun equations in the context of quasi-exactly-solvable spectral problems and establish the conditions for this class of equations to admit algebraic solutions. The Schrödinger operators that can be associated with Heun equations are constructed explicitly; in some cases, we present their supersymmetric partners.
Brihaye, Y., Giller, Stefan, Kosinski, Piotr   +2 more
openaire   +1 more source

Orthogonal polynomials, asymptotics, and Heun equations [PDF]

Journal of Mathematical Physics, 2019
The Painlevé equations arise from the study of Hankel determinants generated by moment matrices, whose weights are expressed as the product of “classical” weights multiplied by suitable “deformation factors,” usually dependent on a “time variable” t. From ladder operators [see A. Magnus, J. Comput. Appl. Math. 57(1-2), 215–237 (1995)], one finds second
Yang Chen, Galina Filipuk, Longjun Zhan
openaire   +2 more sources

Asymptotic form of quasi-normal modes of large AdS black holes [PDF]

, 2003
We discuss a method of calculating analytically the asymptotic form of quasi-normal frequencies for large AdS black holes in five dimensions. In this case, the wave equation reduces to a Heun equation.
Baez, Birmingham, Birmingham, Cardoso, Cardoso, Cardoso, Cardoso, Cardoso, Chan, George Siopsis, Govindarajan, Horowitz, Horowitz, Kokkotas, Konoplya, Konoplya, Kurita, Motl, Motl, Musiri, Nollert, Slavyanov, Son, Starinets, Suphot Musiri, Wang, Wang, Wang, Zhu   +28 more
core   +1 more source

Dirac Equation on the Kerr–Newman Spacetime and Heun Functions

Advances in High Energy Physics, 2021
By employing a pseudoorthonormal coordinate-free approach, the Dirac equation for particles in the Kerr–Newman spacetime is separated into its radial and angular parts.
Ciprian Dariescu, Marina-Aura Dariescu, Cristian Stelea   +2 more
doaj   +1 more source

Middle Convolution and Heun's Equation [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2009
Heun's equation naturally appears as special cases of Fuchsian system of differential equations of rank two with four singularities by introducing the space of initial conditions of the sixth Painlev equation. Middle convolutions of the Fuchsian system are related with an integral transformation of Heun's equation.
openaire   +4 more sources