In order to describe the quantum mechanics of a particle confined to a curve or a surface in R Schrödinger’s equation must be modified in two ways. The kinetic energy operator must be written in terms of the metric g induced on the surface from the flat space metric Gij = δij . The potential energy term must be modified by the inclusion of a geometric potential, necessary to constrain the parti...

The Energy Problem (EP) in General Relativity (GR) is analyzed in the context of GR’s axiomatic inconsistencies. EP is classified according to its local and global aspects. The local aspects of the EP include noncovariance of the energy-momentum pseudotensor (EMPT) of the gravitational field, non-uniqueness of the EMPT, asymmetry of EMPT and vanishing metric energy-momentum tensor. The global a...

We revisit the problem of defining non-minimal gravity in the first order formalism. Specializing to scalar-tensor theories, which may be disguised as ‘higher-derivative’ models with the gravitational Lagrangians that depend only on the Ricci scalar, we show how to recast these theories as Palatini-like gravities. The correct formulation utilizes the Lagrange multiplier method, which preserves ...

Quantizing any model in which a Lagrange multiplier (LM) field is used to restrict configurations those that satisfy the classical equations of motion, leads at most one-loop radiative corrections. This approach can be with both Yang–Mills (YM) and Einstein–Hilbert (EH) action; resulting theory renormalizable unitary, has positive energy spectrum no negative norm states contributing physical pr...

Abstract Let $g_0$ be a smooth pinched negatively curved Riemannian metric on complete surface N , and let $\Lambda _0$ basic hyperbolic set of the geodesic flow with Hausdorff dimension strictly smaller than two. Given small perturbation g real-valued function f unit tangent bundle to respect $L_{g,\Lambda ,f}$ (respectively $M_{g,\Lambda ) Lagrange Markov) spectrum asymptotic highest highest)...

As the digital version of a continuous-time delay, concept fractional delay (FD) is exploited to approximate desired that not multiple sampling interval. However, in FD filters, there always severe distortion at beginning delayed signals, referred as head distortion. This letter identifies cause and proposes solution this problem for reducing overall filters. For purpose performance evaluation,...

The work proposes a general background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza– Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on highe...

We consider a version of Palais’ Principle of Symmetric Criticality (PSC) that is applicable to the Lie symmetry reduction of Lagrangian field theories. PSC asserts that, given a group action, for any group-invariant Lagrangian the equations obtained by restriction of Euler-Lagrange equations to group-invariant fields are equivalent to the Euler-Lagrange equations of a canonically defined, symm...

Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange mu...