Search results for "Mathematica"

Causality and Localization Operators

2005

The evolution of the expectation values of one and two points scalar field operators and of positive localization operators, generated by an istantaneous point source is non local. Non locality is attributed either to zero point vacuum fluctuations, or to non local operations or to the microcausality principle being no satisfied.

(H, ρ)-induced dynamics and the quantum game of life

2017

Abstract We propose an extended version of quantum dynamics for a certain system S , whose evolution is ruled by a Hamiltonian H, its initial conditions, and a suitable set ρ of rules, acting repeatedly on S . The resulting dynamics is not necessarily periodic or quasi-periodic, as one could imagine for conservative systems with a finite number of degrees of freedom. In fact, it may have quite different behaviors depending on the explicit forms of H, ρ as well as on the initial conditions. After a general discussion on this (H, ρ)-induced dynamics, we apply our general ideas to extend the classical game of life, and we analyze several aspects of this extension.

Topological Decompositions of the Pauli Group and their Influence on Dynamical Systems

2021

In the present paper we show that it is possible to obtain the well known Pauli group $P=\langle X,Y,Z \ | \ X^2=Y^2=Z^2=1, (YZ)^4=(ZX)^4=(XY)^4=1 \rangle $ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere $S^3$. The first of these spaces of orbits is realized via an action of the quaternion group $Q_8$ on $S^3$; the second one via an action of the cyclic group of order four $\mathbb{Z}(4)$ on $S^3$. We deduce a result of decomposition of $P$ of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.

The effects of lasers on bond strength to ceramic materials: A systematic review and meta-analysis

2018

Lasers have recently been introduced as an alternative means of conditioning dental ceramic surfaces in order to enhance their adhesive strength to cements and other materials. The present systematic review and meta-analysis aimed to review and quantitatively analyze the available literature in order to determine which bond protocols and laser types are the most effective. A search was conducted in the Pubmed, Embase and Scopus databases for papers published up to April 2017. PRISMA guidelines for systematic review and meta-analysis were followed. Fifty-two papers were eligible for inclusion in the review. Twenty-five studies were synthesized quantitatively. Lasers were found to increase bo…

Further monotonicity and convexity properties of the zeros of cylinder functions

1992

AbstractLet cvk be the kth positive zero of the cylinder function Cv(x,α)=Jv(x) cos α−Yv sin α, 0⩽α<π, where Jv(x) and Yv(x) are the Bessel functions of the first and the second kind, respectively. We prove that the function v(d2cvkddv2+δ)cvk increases with v⩾0 for suitable values of δ and k−απ⩾ 0.7070… . From this result under the same conditions we deduce, among other things, that cvk+12δv2 is convex as a function of v⩾0. Moreover, we show some monotonicity properties of the function c2vkv. Our results improve known results.

Infinite lie groups of point transformations leaving invariant the linear equation which describes in the hodograph plane the isentropic one-dimensio…

1991

Abstract The group analysis of the hodograph equation which is equivalent to the non-linear system of one-dimensional isentropic gas dynamics reveals the existence of infinite groups of symmetry in correspondence with particular pressure laws. These turn out to be polytropes with selected indices, as is expected, as well as a new type of pressure. In all these cases the hodograph equation can be transformed, by a suitable change of variables, into the wave equationψ ζ = 0.

A remark on differentiable functions with partial derivatives in Lp

2004

AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.

SHARING THE BENEFITS OF COOPERATION IN HIGH SEAS FISHERIES: A CHARACTERISTIC FUNCTION GAME APPROACH

1998

Opinion dynamics in coalitional games with transferable utilities

2014

This paper studies opinion dynamics in a large number of homogeneous coalitional games with transferable utilities (TU), where the characteristic function is a continuous-time stochastic process. For each game, which we can see as a “small world”, the players share opinions on how to allocate revenues based on the mean-field interactions with the other small worlds. As a result of such mean-field interactions among small worlds, in each game, a central planner allocates revenues based on the extra reward that a coalition has received up to the current time and the extra reward that the same coalition has received in the other games. The paper also studies the convergence and stability of op…

On the use of fractional calculus for the probabilistic characterization of random variables

2009

In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…