17 papers · ranked by Valyu relevance
Valeri P. Frolov, Pavel Krtouš, David Kubizňák
The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to…
José F. Cariñena, Fernando Falceto, Janusz Grabowski, Manuel F. Rañada
'Manuel F. Rañada'] In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way. It turns…
José F. Cariñena, Manuel F. Rañada, Fernando Falceto, Janusz Grabowski
'Janusz Grabowski'] After a short review of the classical Lie theorem, a finite dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way will be discussed, determining also the number of…
Javad Sarvestan, Ingrid Scharlau, Lu Zheng, Hye Sun Yun + 9 more
'Mohsen Khosravi' 'Oluwafemi Oloruntoba' 'Chukwuma Udensi' 'Suraj Kath' 'Yushu Liu' 'Chenxi Liu' 'Jianing Zheng' 'Chang Xu' 'Dan Wang'] Background The integration of artificial intelligence (AI) in health care has significant potential, yet its acceptance by health care professionals (HCPs) is essential for successful…
Finlay Gunneberg, Jonathan Gratus, Harvey Stanfield
Plasma kinematics is typically performed on either the mass shell or a lab bundle, seven-dimensional phase spaces equipped with a Vlasov vector field. This choice of phase space encodes the parametrisation of the differential equations governing particle dynamics. By replacing the Vlasov vector field and related…
Verena Bögelein, Frank Duzaar, Christoph Scheven
In this paper we establish a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The proof is based on a new intrinsic scaling that involves both the solution and its spatial gradient. It allows to compensate for the different scaling of the system in |u|…
L. I. Petrova
Quantum Structures Authors: ['L. I. Petrova'] It is shown with the help of skew-symmetric forms that the mathematical physics equations, on which no additional conditions are imposed, have quantum properties. And this is due to the integrability properties of differential equations, which depends on the consistency of…
R. Azuaje, A. M. Escobar-Ruiz
As a generalization and extension of our previous paper [Escobar-Ruiz and Azuaje, J. Phys. A: Math. Theor. 57, 105202 (2024)], in this work, the notions of particular integral and particular integrability in classical mechanics are extended to the formalisms of cosymplectic, contact and cocontact geometries. This…
Anatolij K. Prykarpatski, Petro Y. Pukach, Myroslava I. Vovk, Alexander Toikka + 1 more
'Alexander Toikka' 'Dmitry Gromov'] A thermodynamically unstable spin glass growth model described by means of the parametrically-dependent Kardar-Parisi-Zhang equation is analyzed within the symplectic geometry-based gradient-holonomic and optimal control motivated algorithms. The finitely-parametric functional…
Frédéric Barbaresco, Mathieu Arnoux, Pascal Boulet, Armin Feldhoff + 4 more
'Gaël Giraud' 'Christophe Goupil' 'Eric Herbert' 'Marie-Christine Record'] The explanation of thermodynamics through geometric models was initiated by seminal figures such as Carnot, Gibbs, Duhem, Reeb, and Carathéodory. Only recently, however, has the symplectic foliation model, introduced within the domain of…
Yili Qian, Domitilla Del Vecchio
Feedback control systems with integral action have the unique ability to perfectly reach constant set-points and to reject constant disturbances. Due to these properties, they are ubiquitous in engineering systems and frequently found in natural biological systems that achieve homeostasis and adaptation. Recently…
Khristo N. Boyadzhiev
There are various methods for evaluating integrals: substitution, integration by parts, partial fractions, using the residue theorem, or Cauchy's integral formula, etc. A beautiful special technique is the differentiation with respect to a parameter inside the integral. We review this technique here by providing…
Pavel Suprun
We collect evidence that the notion of path–ordered non–abelian integration admits an extension to two dimensions. We propose the corresponding notion of non–abelian 2–form along the lines of Lie algebroid theory and argue it is an appropriate one. The processes of parallel transport and integration turn out to be…
Han Geurdes
In this paper we ask if there is an interesting twist in mathematics of the Feynman propagator of the present day [1] formalism for the Dirac equation. The case studied is with only a potential function V . If there is no special integration order per step for e.g. dx(0) = dx1dx2dx3 and dp(0) = dp1dp2dp3, then a delta…
Kelvin J McQueen, Naotsugu Tsuchiya
Under what conditions are material objects, such as particles, parts of a whole object? This is the composition question and is a longstanding open question in philosophy. Existing attempts to specify a non-trivial restriction on composition tend to be vague and face serious counterexamples. Consequently, two extreme…
Carl Winsløw
Analysis, as construed here, is a domain of mathematics which treats problems related to limits, real and complex functions, and linear operators. While some of these problems have been known for thousands of years, the fundamentals of contemporary analysis – which include a rigorous theory of real numbers – have been…
Robert E. Ulanowicz
Dualism has been a viable concept in physics since the 1920s, when Arthur Compton demonstrated the corpuscular nature of photons as distinct from its wave nature. More recently, information theory applied to ecological dynamics has portrayed the behavior of whole ecosystems as being, not only dual, but actually…