On the Initial Boundary Value Problems for the Enskog Equation in Irregular Domains

The paper is concerned with the Enskog equation with a constant high density factor for large initial data in L ¹(R ⁿ). The initial boundary value problem is investigated for bounded domains with irregular boundaries. The proof of an H-theorem for the case of general domains and boundary conditions is given. The main result guarantees the existence of global solutions of boundary value problems for large initial data with all v-moments initially finite and domains having boundary with finite Hausdorff measure and satisfying a cone condition. Existence and uniqueness are first proved for the case of bounded velocities. The solution has finite norm where q = (t ₀, x) is taken on all possible n-dimensional planes Q(v) in R ^n+l intersecting a fixed point and orthogonal to vectors (1, v), v R ⁿ.     

Hydrodynamic correlation functions of hard-sphere fluids at short times

The short-time behavior of the coherent intermediate scattering function for a fluid of hard-sphere particles is calculated exactly through ordert ⁴, and the other hydrodynamic correlation functions are calculated exactly through ordert ². It is shown that for all of the correlation functions considered the Enskog theory gives a fair approximation. Also, the initial time behavior of various Green-Kubo integrands is studied. For the shear-viscosity integrand it is found that at densityn³=0.837 the prediction of the Enskog theory is 32% too low. The initial value of the bulk viscosity integrand is nonzero, in contrast to the Enskog result. The initial value of the thermal conductivity integrand at high densities is predicted well by Enskog theory.     

Microscopic calculation of pion production in nucleus-nucleus collisions around 1 GeV·A

New phonon operators are introduced for describing deformed nuclei which consist of the electric and magnetic parts. The Hamiltonian of the quasiparticle-phonon nuclear model is constructed and the basic equations for the finite rank separable isoscalar and isovector multipole and spin-multipole particle-hole and particle-particle interactions between quasiparticles are derived. It is shown that calculations of one-phonon states in the RPA encounter some difficulties due to the finite rankn _max>1 separable interaction of the electric and magnetic type. The use of complex separablen _max>1 interactions does not lead to complication of the QPNM equations for describing fragmentation of vibrational states. The matrix elements are obtained for describingE- andM- transitions between excited states of deformed nuclei. It is stated that the QPNM can serve as a basis for calculating many characteristics of excited states of deformed nuclei.     

Casimir force between two Aharonov-Bohm solenoids

The vacuum structure for the massive charged scalar field in the region of two parallel, infinitely long and thin solenoids confining the fluxesn ₁ andn ₂ is studied. By using the Green function method, it is found that the vacuum expectation value of the system's energy has a finite mutual interaction term depending on the distance a between the solenoids, which implies an attractive force per unit length given by F _n1n2 =–(c/²)(n ₁ n ₂)²/a ³.     

2-[2-[4-[2-[2-[1,3-Dihydro-1,1-bis(4-hydroxyphenyl)-3-oxo-5-isobenzofuranthioureidyl]ethylaminocarbonyl]ethyl]phenyl] ethylamino]-5′-N-ethylcarboxamidoadenosine (FITC-APEC): A fluorescent ligand for A2a-adenosine receptors

The fluorescein conjugate, FITC-APEC (2-[2-[4-[2-[2-[1,3-dihydro-1,1-bis(4-hydroxyphenyl)-3-oxo-5-isobenzofuranthioureidyl]ethylaminocarbonyl]ethyl] phenyl]ethylamino]-5-N-ethylcarboxamidoadenosine), is a novel ligand derived from a series of functionalized congeners that act as selective A_2a-adenosine receptor agonists. The binding of FITC-APEC to bovine striatal A_2a-adenosine receptors measured by fluorescence techniques was saturable and of a high affinity, with aB _max of 2.3±0.3 pmol/mg protein andK _D of 57±2 nM. TheK _D value estimated by fluorescence was consistent with theK _i (11±0.3 nM) obtained by competition studies with [³H]CGS 21680. Additionally, theB _max value found by FITC-APEC measurement was in agreement withB _max values obtained using radioligand binding. FITC-APEC exhibited rapid and reversible binding to bovine striatum. The potencies of chemically diverse A_2a-adenosine receptor ligands estimated by inhibition of FITC-APEC binding were in good agreement with their potencies determined using radioligand binding techniques (r=0.97,P=0.0003). FITC-APEC binding was not altered by purine derivatives that do not recognize A_2a-adenosine receptors. These findings demonstrate that the novel fluorescent ligand FITC-APEC can be used in the quantitative characterization of ligand binding to A_2a-adenosine receptors.     

A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

Reaktionskinetik der Ozonbildung in der Sauerstoffglimmentladung

Hg-light absorption at λ = 2537 ǎ by O₃ has been used to measure the concentration of O₃ in the positive column of an oxygen glow discharge under the nonstationary conditions of the Q-form (tube diameter 3:4 cm). For all gas pressures investigated (p = 7 — 12 torr) the O₃ density (n₃) as a function of the current reaches a remarkable maximum at i ≈ 15 mA. n₃ ^max was found to increase almost linearly with the gas pressure. At i = 80 mA, on the other hand, n₃ increases according to a quadratic relation. In order to understand the dependence of n₃ on the pressure and on the current density (or equivalently on the electron density n_e) a kinetic model previously developed has been used involving the following particles . For example, it can be shown that in the region of the maximum of n₃ one main production process of ozone is the associative detachment reaction . The calculated maximum of the ozone density is higher than the measured one and appears at higher electron density.     

Nontrivial extensions of a massless representation with definite helicity of the Poincaré group in 3+1 dimensions by the tensor product of two other massless representations with definite helicity

Let U _n (a, ) be a massless, helicity n/2, representation of the Poincaré group in 3+1 dimensions. U _n (a, ) is realized in an adapted nuclear space D _n. We explicitly determine the various classes of cohomology for the extension of U _n (a, ) by U _n1 (a, ) U _n2 (a, ).     

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀( n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^–2/3 , followed byr _s ^/–4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being –0.481915 Rydbergs.     

Quantum fluctuations in a single electron box

Recent experiments have demonstrated that the numbern of additional electrons on a small metallic island is a staircase function of a continuous external chargen _x for temperaturesT small compared to the single electron charging energyU. We show that the finite conductanceg of the tunnel barrier connecting the island to the external gate gives rise to quantum fluctuations inn which lead to a smearing of the staircase even at zero temperature. In the experimentally relevant case of wide junctions and in the limit of small conductanceg1 the slope <n>/n _x at the turning point between two plateaus saturates at a finite value of order 1/g asT0 instead of diverging likeU/T as predicted with thermal fluctuations only. The experimentally observed broadening however is still much larger which is probably due to extrinsic effects.     

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a ₀ ? l _P (where l _P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n _F ) to energy density ε(n _F ) dependent on the number density of fermions n _F . As the early Universe expands, the dimensionless quantity ν(n _F ) = P(n _F )/ε(n _F ) decreases with decreasing n _F from its maximum value ν_max = 1 for n _F → ∞ to zero for n _F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n _F )–ε(n _F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R _c =–μ²/ξ and radius a _c ? a ₀. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G _N .     

Self-gravitating radiation in anti-de sitter space

Equilibrium configurations of self-gravitating massless thermal radiation inside spherical boxes of radiusR in asymptotically anti-de Sitter space (A = -3/b ₂) are constructed numerically for a range of central densities. For each box radius considered (R/b = 0, 1/2, 1, 2, 4, ), there is a unique configuration with maximal total mass and entropy, and another (at a lower central density) with maximum asymptotic red-shifted temperature. With the box removed toR=, the maximum total mass and entropy of self-gravitating thermal radiation areM _max 0.4598b0.7964(–A)^–1/2 andS _max1.3560a ^1/4 b ^3/2 3.0910a ^1/4(–A)^–3/4, and the maximum red-shifted temperature is     

High resolution FTIR spectroscopy of pentafluoroethane: perturbations in the Coriolis doublet of ν4 and ν13

The FTIR spectrum of pentafluoroethane (R125) was measured in the mid infrared region from 900 to 4000 cm⁻¹. Vibrational assignments for R125 are revised by comparison of previous and current experimental data with ab initio calculations at both the MP2/6-311+(d,p) and B3LYP/TZV+(3df,3p) levels of theory. High resolution FTIR spectra were recorded at room temperature and in an enclosive flow cell at a rotational temperature of 140 K. The cold spectrum was sufficiently resolved to enable rovibrational analyses of the overlapping ν₄ (1200.7341 cm⁻¹) and ν₁₃ (1223.3 cm⁻¹) bands, which have a/c hybrid and b-type character, respectively. Ground state combination differences were used to confirm assignment of 2375 lines to ν₄ (J_max = 86, K_{a max} = 50) and 2921 lines to ν₁₃ (J_max = 60, K_{a max} = 54). Effective rotational and centrifugal distortion constants were determined for ν₄, and the polarization ratio was found to be . Severe Coriolis perturbations prevent any satisfactory fit to the ν₁₃ band.     

Hypergeometric series in a series expansion of the directed-bond percolation probability on the square lattice

The asymmetric directed-bond percolation (ADBP) problem with an asymmetry parameterk is introduced and some rigorous results are given concerning a series expansion of the percolation probability on the square lattice. It is shown that the first correction term,d _n,1 (k) is expressed by Gauss' hypergeometric series with a variablek. Since the ADBP includes the ordinary directed bond percolation as a special case withk=1, our results give another proof for the Baxter-Guttmann's conjecture thatd _n,1(1) is given by the Catalan number, which was recently proved by Bousquet-Mélou. Direct calculations on finite lattices are performed and combining them with the present results determines the first 14 terms of the series expansion for percolation probability of the ADBP on the square lattice. The analysis byDlog Padé approximations suggests that the critical value depends onk, while asymmetry does not change the critical exponent of percolation probability.     

Small representations of quantum affine algebras

We characterize the finite-dimensional representations of the quantum affine algebra U _q ( _n+1) (whereq ^× is not a root of unity) which are irreducible as representations of U _q (sl _n+1). We call such representations small. In 1986, Jimbo defined a family of homomorphismsev _a from U _q (sl _n+1) to (an enlargement of) U _q (sl_,n+1), depending on a parametera ^·. A second family,ev ^a can be obtained by a small modification of Jimbo's formulas. We show that every small representation of U _q ( _n+1) is obtained by pulling back an irreducible representation of U _q (sl _n+1) byev _a orev ^a for somea ^·.     

Classification of the indecomposable bounded admissible modules over the Virasoro Lie algebra with weightspaces of dimension not exceeding two

In view of [1,2] any bounded admissible moduleA over the Virasoro Lie algebra is a finite length extension of irreducible modules with one-dimensional weightspaces. To each extension of finite lengthn are associatedn+1 invariants (a₁, ₁, ..., _n ). We prove that we have _i – _j {0, 1, ... 6(n – 1b)} for all (i, j) with 1ijn. In the casen=2 this result allows us to construct all the indecomposable bounded admissible modules, where the dimensions of the weightspaces are less than or equal to two. In particular we obtain all the extensions of two irreducible bounded-modules.     

Reaction-diffusion processes of hard-core particles

We study a 12-parameter stochastic process involving particles with two-site interaction and hard-core repulsion on ad-dimensional lattice. In this model, which includes the asymmetric exclusion process, contact processes, and other processes, the stochastic variables are particle occupation numbers taking valuesn _x=0,1. We show that on a ten-parameter submanifold thek-point equal-time correlation functions n _x1...n _xk satisfy linear differential-difference equations involving no higher correlators. In particular, the average density n _x satisfies an integrable diffusion-type equation. These properties are explained in terms of dual processes and various duality relations are derived. By defining the time evolution of the stochastic process in terms of a quantum HamiltonianH, the model becomes equivalent to a lattice model in thermal equilibrium ind+1 dimensions. We show that the spectrum ofH is identical to the spectrum of the quantum Hamiltonian of ad-dimensional anisotropic, spin-1/2 Heisenberg model. In one dimension our results hint at some new algebraic structure behind the integrability of the system.     

RenormalizedG-convolution ofN-point functions in quantum field theory: Convergence in the Euclidean case I

The notion of Feynman amplitude associated with a graphG in perturbative quantum field theory admits a generalized version in which each vertexv ofG is associated with ageneral (non-perturbative)n _v-point functionH ⁿ _v,n _v denoting the number of lines which are incident tov inG. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle'sG-convolution procedure.In the present work we propose a generalization ofG-convolution which includes the case when the functionsH ⁿ _v arenot integrable at infinity but belong to a suitable class of slowly increasing functions. A finite part of theG-convolution integral is then defined through an algorithm which closely follows Zimmermann's renormalization scheme. In this work, we only treat the case of Euclideanr-momentum configurations.The first part which is presented here contains together with a general introduction, the necessary mathematical material of this work, i.e., Sect. 1 and appendices A and B.The second part, which will be published in a further issue, will contain the Sects. 2, 3 and 4 which are devoted to the statement and to the proof of the main result, i.e., the convergence of the renormalizedG-convolution product.The table of references will be given in both parts.     

Analogs in general relativity of Ferraro's law of isorotation

Two relativistic analogs of Ferraro's law of isorotation for a fluid with infinite electrical conductivity are given. In the first case it is assumed that the flow is shear-free withH ^a =0 and it is shown that £(H) ^a =0. In the second case it is assumed that there exists a space-like Killing vector field parallel toH _a , and it is proved that, _a H ^a =0.