Related papers: Fritz John's equation in mechanism design
We introduce a refinement of the usual Ehrenfeucht-Fra\"{\i}ss\'e game. The new game will help us make finer distinctions than the traditional one. In particular, it can be used to measure the size formulas needed for expressing a given…
In the present note we elucidate how physical considerations based on Planck's oscillator led to the construction of Heisenberg's mechanics.
This paper proves that protomechanics, previously introduced in quant-ph/9909025, deduces both quantum mechanics and classical mechanics. It does not only solve the problem of the arbitrariness on the operator ordering for the quantization…
We present a study of constrained mechanical systems and of their quantisation, emphasising the importance of the role played by Poisson brackets in the study of gauge theories.
We report on recent study [1] of the role of the kinematical constraint in the CCFM equation and its non-linear extension. We compare numerical results obtained by solving the CCFM equation and argue that kinematical constraint represents…
By using Jet Calculus as a consistent framework to describe multiparton dynamics we explain the peculiar evolution equation of fracture functions by means of the recently introduced extended fracture functions.
The Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order…
The Friedrichs operator of a domain (in $\mathbb{C}^n$) is closely related to its Bergman projection and encodes crucial information (geometric, quadrature, potential theoretic etc.) about the domain. We show that the Friedrichs operator of…
The Feynman integral is given a stochastic interpretation in the framework of Nelson's stochastic mechanics employing a time-symmetric variant of Nelson's kinematics recently developed by the author.
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…
In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and…
We study some mechanical problems in which a friction force is acting on the system. Using the fundamental concepts of state, time evolution and energy conservation we explain how to extend Newtonian mechanics to thermodynamics. We arrive…
The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure…
Fractional classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented for the fractional classical mechanics.…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.
The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first-order matrix-valued differential equations on the real…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
We establish an analogue of the first fundamental theorem of calculus for functions defined on the Wasserstein space of probability measures. Precisely, we show that if a function on the Wasserstein space is sufficiently regular in the…