相关论文: The physical meaning of Lagrange multipliers

We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing…

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…

There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…

Means are used in several applications from electronic engeneering to information theory, however there is no general theorem on how to extend a given M(x, y) mean function to multiple variable forms. In this article we would like to…

The relationship between various methods to calculate the physical degrees of freedom for gauge invariant systems of a general form is established. The set of hidden parameters caused for the superfluous degrees of freedom is revealed.

The (classical) Lagrange spectrum is a closed subset of the positive real numbers defined in terms of diophantine approximation. Its structure is quite involved. This article describes a polynomial time algorithm to approximate it in…

In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers…

In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate…

This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some aspects of the theory of such polynomials. We then give a…

In this study, it is introduced paracomplex analogue of Lagrangians and Hamiltonians with constraints in the framework of para-Kaehlerian manifolds. The geometrical and mechanical results on the constrained mechanical system have also been…

A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…

I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…

The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…

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.

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…

This is a short review on the applications of Lieb-Robinson bounds for a general readership of mathematical physicists.

Physical laws are a set of rules in the relationship between observations made by the experimenter. All these observations are made through a mechanism that links the external world to the experimenter's awareness, a mechanism which is not…

Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.

We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation

Mechanical quantum systems, such as resonators and levitated particles, offer unique opportunities for quantum metrology. Particularly, their significant mass and quantum-level control enable applications in measuring gravitational effects.…