Intermittency in the Fisher's droplet model

Intermittent behaviour of fragment multiplicity distributions in the nuclear liquid-gas phase transition is studied in terms of the droplet model of Fisher. The anomalous fractal dimensions are compared with data on heavy ion reactions and classical molecular dynamics simulations. A signature of the transition in the anomalous fractal dimensions is shown.We thank Profs. S. Ayik, M. Di Toro and V. Kondratyev for discussions. One of us (T.K.) acknowledges the support of INFN-LNS.     

The many faces of a character

We prove an identity between three infinite families of polynomials which are defined in terms of bosonic, fermionic, and one-dimensional configuration sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine su(2) algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-ansatz solution of the Heisenberg spin chain.     

Neutron diffraction study of crystal structure and antiferromagnetic ordering in the heavy fermion compound CePd2Al3

Nuclear and magnetic structures of an annealed polycrystalline sample of the heavy-fermion compound CePd₂Al₃ prepared by arc-melting were investigated by neutron powder diffraction. The chemical structure corresponds well to the ordered hexagonal PrNi₂Al₃-type structure. The antiferromagnetic structure of CePd₂Al₃ with an ordered magnetic moment _Ce=0.47(2) _B at saturation is remarkably similar to that in the heavy fermion superconductor UPd₂Al₃. The additional incommensurate magnetic structures reported previously both for UPd₂Al₃ and CePd₂Al₃ are not observed in the present sample of CePd₂Al₃. At 1.4 K the magnetoresistivity of CePd₂Al₃ measured up to 14 T indicates only one field-induced phase transition at 3.0 T.     

Comparison of the elastic and inelastic scatterings between152Sm+12C and148 Nd+16O

Angular distributions of elastic and inelastic scattering have been measured for¹⁵²Sm+¹²C at 63.2 MeV and¹⁴⁸Nd+¹⁶O at 90.9 MeV. An evident interference pattern in the inelastic scattering has been observed for the first time in a strong Coulomb coupling system.We are indebted to Dr. S. Pieper for supplying the Ptolemy Program. One of us (Chenglie Jiang) would like to acknowledge the Argonne National Laboratory for the opportunity given, to perform theoretical calculations with the code Ptolemy during his visit there. Thanks are also due to Mr. H. Folger (GSI, Germany) for supplying the targets. This work was supported in part by China National Nature Science Fundation.     

Laser chemical processing of magnetic materials for recording-head application

A laser-induced thermochemical reaction has been used to etch single crystalline magnetic ferrite for industrial application to recording-head processing. Scanning focused Ar-ion laser irradiation to ferrite in flowing aqueous solutions of KOH or H₃PO₄ resulted in etch rates of 350–400 m/s with aspect ratios of up to 40. Metal-In-Gap (MIG) head structures with Sendust (FeAlSi) have been successfully fabricated using laser chemical processing. The MIG head fabricated by laser chemical processing showed better performance than that by conventional mechanical machining.Presented at LASERION '93, June 21–23, 1993 München (Germany)     

Inclusion-exclusion: Exact and approximate

It is often required to find the probability of the union of givenn eventsA ₁ ,...,A _n . The answer is provided, of course, by the inclusion-exclusion formula: Pr(A _i )= _i – _i<j Pr(A _i A _j )±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A _i ), from the above data with an additive error of exp . In the present article we develop an expression that can be computed in polynomial time, that, given the sums _|S|=j Pr( _iS A _i ) forj=1,...k, approximates Pr(A _i ) with an additive error of exp . This error is optimal, up to the logarithmic factor implicit in the notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v _l ^m C _i is an instance of the general problem that had been extensively studied [7]. HereA _i is the set of assignments that satisfyC _i , and Pr( _iS A _i )=a _S /2ⁿ where _iS C _i is satisfied bya _S assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa _S for, say, all cardinalities . Quite surprisingly, already the numbersa _S over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation.     

Finding the αn-th largest element

We describe an algorithm for selecting the n-th largest element (where 0<<1), from a totally ordered set ofn elements, using at most (1+(1+o(1))H())·n comparisons whereH() is the binary entropy function and theo(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1+H())·n comparisons. The algorithm obtained beats the global 3n upper bound of Schönhage, Paterson and Pippenger for <1/3.     

On depth first search strees inm-out digraphs

We consider depth first search (DFS for short) trees in a class of random digraphs: am-out model. Let _i be thei ^th vertex encountered by DFS andL(i, m, n) be the height of _i in the corresponding DFS tree. We show that ifi/n asn, then there exists a constanta(,m), to be defined later, such thatL(i, m, n)/n converges in probability toa(,m) asn. We also obtain results concerning the number of vertices and the number of leaves in a DFS tree.     

On the complexity of the disjoint paths problem

In this paper we consider the disjoint paths problem. Given a graphG and a subsetS of the edge-set ofG the problem is to decide whether there exists a family of disjoint circuits inG each containing exactly one edge ofS such that every edge inS belongs to a circuit inC. By a well-known theorem of P. Seymour the edge-disjoint paths problem is polynomially solvable for Eulerian planar graphsG. We show that (assumingPNP) one can drop neither planarity nor the Eulerian condition onG without losing polynomial time solvability. We prove theNP-completeness of the planar edge-disjoint paths problem by showing theNP-completeness of the vertex disjoint paths problem for planar graphs with maximum vertex-degree three. This disproves (assumingPNP) a conjecture of A. Schrijver concerning the existence of a polynomial time algorithm for the planar vertex-disjoint paths problem. Furthermore we present a counterexample to a conjecture of A. Frank. This conjecture would have implied a polynomial algorithm for the planar edge-disjoint paths problem. Moreover we derive a complete characterization of all minorclosed classes of graphs for which the disjoint paths problem is polynomially solvable. Finally we show theNP-completeness of the half-integral relaxation of the edge-disjoint paths problem. This implies an answer to the long-standing question whether the edge-disjoint paths problem is polynomially solvable for Eulerian graphs.Supported by Sonderforschungsbereich 303 (DFG)     

Computational complexity of inner and outerj-radii of polytopes in finite-dimensional normed spaces

This paper studies the complexity of computing (or approximating, or bounding) the various inner and outer radii of ann-dimensional convex polytope in the space ⁿ equipped with an _p norm or a polytopal norm. The polytopeP is assumed to be presented as the convex hull of finitely many points with rational coordinates (V-presented) or as the intersection of finitely many closed halfspaces defined by linear inequalities with rational coefficients (-presented). The innerj-radius ofP is the radius of a largestj-ball contained inP; it isP's inradius whenj = n and half ofP's diameter whenj = 1. The outerj-radius measures how wellP can be approximated, in a minimax sense, by an (n — j)-flat; it isP's circumradius whenj = n and half ofP's width whenj = 1. The binary (Turing machine) model of computation is employed. The primary concern is not with finding optimal algorithms, but with establishing polynomial-time computability or NP-hardness. Special attention is paid to the case in whichP is centrally symmetric. When the dimensionn is permitted to vary, the situation is roughly as follows: (a) for general -presented polytopes in _p spaces with 1相似文献