Related papers: On the expected value of energy in groups
Preliminary results on $e^+ e^- \to f \bar{f}$, $f=e, \mu, \tau, q$, including all LEP2 data are discussed. Good agreement is found with the Standard Model up to the highest energies. Limits on possible new physics are extracted.
The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential reported in [Phys. Rev. C 72, 027001 (2005)] is extended to the fractional forms using the generalized fractional derivative…
Recently, it became possible to experimentally generate and characterize a very thin silica system on a substrate which can be basically described as a 2D random network. The key structural properties, in particular related to the ring…
The experimental emission probabilities of complex fragments by low energy compound nuclei and their dependence upon energy and atomic number are compared to the transition state rates. Intermediate-mass-fragment multiplicity distributions…
We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them generalize known relations between energy,…
We compute the pressure of the random energy model (REM) and generalized random energy model(GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's ``broken replica symmetry bounds",and…
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one…
Natural protein sequences contain a record of their history. A common constraint in a given protein family is the ability to fold to specific structures, and it has been shown possible to infer the main native ensemble by analyzing…
In the last several years, the Casimir energy for a variety of 1+1-dimensional integrable models has been determined from the exact S-matrix. It is shown here how to modify the boundary conditions to project out the lowest-energy state,…
Recently, an exact Green's function of the diffusion equation for a pair of spherical interacting particles in two dimensions subject to a backreaction boundary condition was derived. Here, we use the obtained Green's function to calculate…
In this paper we consider estimating the number of solutions to multiplicative equations in finite fields when the variables run through certain sets with high additive structure. In particular, we consider estimating the multiplicative…
We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…
Precise formulas are derived for the expected values $<\xi>$, $<\eta>$ and variances $\delta \xi ^2$, $\delta \eta ^2$ of random variables $\xi$, $\eta$ describing the spin asymmetry of some reaction when a background process contribution…
A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any $\frac{1}{2}\leq \alpha\leq\beta\leq1$, there is a group $\Gamma$ with measure $\mu$ equidistributed on a finite…
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…
We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< \epsilon \le \mu \le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes…
We find estimates on the norms commutators of the form [f(x), y] in terms of the norm of [x, y] assuming that x and y are contractions in a C*-algebra A, with x normal and with spectrum within the domain of f. In particular we discuss [x^2,…
We study the growth of typical groups from the family of $p$-groups of intermediate growth constructed by the second author. We find that, in the sense of category, a generic group exhibits oscillating growth with no universal upper bound.…
A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing…
We obtain upper bounds on the number of finite sets $\mathcal S$ of primes below a given bound for which various $2$ variable $\mathcal S$-unit equations have a solution.