Experimental evidence for the separability of compound-nucleus and fragment properties in fission

The large body of experimental data on nuclear fission is analyzed with a semi-empirical ordering scheme based on the macro-microscopic approach and the separability of compound-nucleus and fragment properties on the fission path. We apply the statistical model to the non-equilibrium descent from saddle to scission, taking the influence of dynamics into account by an early freeze out. The present approach reveals a large portion of common features behind the variety of the complex observations made for the different systems. General implications for out-of-equilibrium processes are mentioned.Comment: 11 pages, 3 figure

On doubly universal functions

submitted to a journal on september 27th, 2015Let $(\lambda_n)$ be a strictly increasing sequence of positive integers. Inspired by the notions of topological multiple recurrence and disjointness in dynamical systems, Costakis and Tsirivas have recently established that there exist power series $\sum_{k\geq 0}a_kz^k$ with radius of convergence 1 such that the pairs of partial sums $\{(\sum_{k=0}^na_kz^k,\sum_{k=0}^{\lambda_n}a_kz^k): n=1,2,\dots\}$ approximate all pairs of polynomials uniformly on compact subsets $K\subset\{z\in\mathbb{C} :\vert z\vert>1\},$ with connected complement, if and only if $\limsup_{n}\frac{\lambda_n}{n}=+\infty.$ In the present paper, we give a new proof of this statement avoiding the use of advanced tools of potential theory. It allows to obtain the algebraic genericity of the set of such power series and to study the case of doubly universal infinitely differentiable functions. Further we show that the Ces\`aro means of partial sums of power series with radius of convergence 1 cannot be frequently universal

Universality and ultra differentiable functions: Fekete's theorem

The purpose of this article is to establish extensions of Fekete's Theorem concerning the existence of universal power series of C8 functions defined by estimates on successive derivatives. © 2010 American Mathematical Society

ABEL UNIVERSAL SERIES

Given a sequence = (r n) n ∈ [0, 1) tending to 1, we consider the set U A (D,) of Abel universal series consisting of holomorphic functions f in the open unit disc D such that for any compact set K included in the unit circle T, different from T, the set {z → f (r n •)| K : n ∈ N} is dense in the space C(K) of continuous functions on K. It is known that the set U A (D,) is residual in H(D). We prove that it does not coincide with any other classical sets of universal holomorphic functions. In particular, it not even comparable in terms of inclusion to the set of holomorphic functions whose Taylor polynomials at 0 are dense in C(K) for any compact set K ⊂ T different from T. Moreover we prove that the class of Abel universal series is not invariant under the action of the differentiation operator. Finally an Abel universal series can be viewed as a universal vector of the sequence of dilation operators T n : f → f (r n •) acting on H(D). Thus we study the dynamical properties of (T n) n such as the multi-universality and the (common) frequent universality. All the proofs are constructive

UNIVERSAL APPROXIMATION THEOREM FOR DIRICHLET SERIES

The paper deals with an extension theorem by Costakis and Vlachou on simultaneous approximation for holomorphic function to the setting of Dirichlet series, which are absolutely convergent in the right half of the complex plane. The derivation operator used in the analytic case is substituted by a weighted backward shift operator in the Dirichlet case. We show the similarities and extensions in comparing both results. Several density results are proved that finally lead to the main theorem on simultaneous approximation

ABEL UNIVERSAL SERIES

Given a sequence = (r n) n ∈ [0, 1) tending to 1, we consider the set U A (D,) of Abel universal series consisting of holomorphic functions f in the open unit disc D such that for any compact set K included in the unit circle T, different from T, the set {z → f (r n •)| K : n ∈ N} is dense in the space C(K) of continuous functions on K. It is known that the set U A (D,) is residual in H(D). We prove that it does not coincide with any other classical sets of universal holomorphic functions. In particular, it not even comparable in terms of inclusion to the set of holomorphic functions whose Taylor polynomials at 0 are dense in C(K) for any compact set K ⊂ T different from T. Moreover we prove that the class of Abel universal series is not invariant under the action of the differentiation operator. Finally an Abel universal series can be viewed as a universal vector of the sequence of dilation operators T n : f → f (r n •) acting on H(D). Thus we study the dynamical properties of (T n) n such as the multi-universality and the (common) frequent universality. All the proofs are constructive