Related papers: Generalizations of Hagge's Theorems
We have derived the relationship between the radial proper distance, h, and the polar angle, phi, for a light ray that is emitted and travels in the neighborhood of the Earth's surface. General relativity predicts that, even locally, the…
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study…
A pair of symmetric expressions for the second law of thermodynamics is put forward. The conservation and transfer of entropy is discussed and applied to problems like biology, culture and life itself. A new explanation is given to the…
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an "apparent horizon", separating the black hole region from the rest of the spacetime, are…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also generalize fixed point theorems of J. Harjani,…
The apparent discrepancy between the bending of light predicted by the equivalence principle and its corresponding value in general relativity is resolved by evaluating the deflection of light with respect to a direction that is parallel…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
By establishing a connection between bi-directional Helmholtz machines and information theory, we propose a generalized Helmholtz machine. Theoretical and experimental results show that given \textit{shallow} architectures, the generalized…
We begin with a deformation of a differential graded algebra by adding time and using a homotopy. It is shown that the standard formulae of It\^o calculus are an example, with four caveats: First, it says nothing about probability. Second,…
This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…
We formulate a generalization of Vojta's conjecture in terms of log pairs and variants of multiplier ideals. In this generalization, a variety is allowed to have singularities. It turns out that the generalized conjecture for a log pair is…
Two common misconceptions about the theory of Special Relativity that are actively taught in textbooks are discussed. It is shown, first, that the Lorentz transformations are actually transformations of the coordinates of a photon, not the…
In special relativity a gyroscope that is suspended in a torque-free manner will precess as it is moved along a curved path relative to an inertial frame S. We explain this effect, which is known as Thomas precession, by considering a real…
A general principle of non-equivalence for bodies and observers in different G potentials (GP) was derived from correspondence of the Einstein's equivalence principle either with optical physics or with gravitational experiments in which…
Understanding how torsion theories are described and constructed is crucial to the study of torsion theory. Mutations of torsion theories have been studied as a method of constructing another torsion theory from a given one. We have already…
We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $\Omega$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$…