相关论文: Generalized Newton transformation and its applicat…
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…
We embed the geometries of the generalized $\lambda$-deformations into the framework of the Double Field Theory.
In this paper we develop a framework allowing a natural extension of the Lorentz transformations. To begin, we show that by expanding conventional four-dimensional spacetime to eight-dimensions that a natural generalization is indeed…
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
A previous calculation of Newton's gravitational coupling constant G is generalized. This generalization makes it possible to have "atoms of two-dimensional space" with an integer dimension d_{atom} of the internal space, where the case…
Galilean transformation properties of different physical quantities are investigated from the point of view of four dimensional Galilean relativistic (non-relativistic) space-time. The objectivity of balance equations of general heat…
In order to apply thermodynamics to systems in which entropy is not extensive, it has become customary to define generalized entropies. While this approach has been effective, it is not the only possible approach. We suggest that some…
We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultradistributions we show that this complex plane-generalization overcomes all…
We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement…
In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized submanifolds of higher dimension. For it we introduce what we have called…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
Applications of the three-dimensional transformation for rotating coordinate systems to quantum mechanics, general theory relativity and optics are considered.
This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this…
The non isotropic noncentral elliptical shape distributions via pseudo-Wishart distribution are founded. This way, the classical shape theory is extended to non isotropic case and the normality assumption is replaced by assuming a…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…