Dimension and Dynamical Entropy for Metrized <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">*</Emphasis></Superscript>-Algebras

 We introduce notions of dimension and dynamical entropy for unital C ^* -algebras ``metrized' by means of , which are complex-scalar versions of the Lip-norms constitutive of Rieffel's compact quantum metric spaces. Our examples involve the UHF algebras and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the canonical coincides with the topological entropy of its commutative analogue. Received: 13 February 2002 / Accepted: 20 August 2002 Published online: 22 November 2002     

A Duality Theorem for Ergodic Actions of Compact Quantum Groups on <Emphasis Type="Italic">C</Emphasis><Superscript>*</Superscript>-Algebras

The spectral functor of an ergodic action of a compact quantum group G on a unital C ^*-algebra is quasitensor, in the sense that the tensor product of two spectral subspaces is isometrically contained in the spectral subspace of the tensor product representation, and the inclusion maps satisfy natural properties. We show that any quasitensor ^*-functor from Rep(G) to the category of Hilbert spaces is the spectral functor of an ergodic action of G on a unital C ^*-algebra. As an application, we associate an ergodic G-action on a unital C ^*-algebra to an inclusion of Rep(G) into an abstract tensor C ^*-category . If the inclusion arises from a quantum subgroup K of G, the associated G-system is just the quotient space K\G. If G is a group and has permutation symmetry, the associated G-system is commutative, and therefore isomorphic to the classical quotient space by a subgroup of G. If a tensor C ^*-category has a Hecke symmetry making an object ρ of dimension d and μ-determinant 1, then there is an ergodic action of S _μ U(d) on a unital C ^*-algebra having the as its spectral subspaces. The special case of is discussed.     

Torus Equivariant Spectral Triples for Odd-Dimensional Quantum Spheres Coming from <Emphasis Type="Italic">C</Emphasis><Superscript>*</Superscript>-Extensions

The torus group (S ¹)^ℓ+1 has a canonical action on the odd-dimensional sphere S _q ^2ℓ+1. We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on that space and equivariant with respect to that action. This characterization gives a construction of an optimum family of equivariant spectral triples having nontrivial K-homology class thus generalizing our earlier results for SU _q (2). We also relate the triple we construct with the C ^*-extension      

Self-organization of N<Superscript>*</Superscript> inclusions in SmC<Superscript>*</Superscript> free-standing films

The behaviour of freely suspended smectic-C* ( SmC^*) films at the bulk SmC^*-cholesteric ( N^*) phase transition has been investigated using polarized-reflected-light microscopy. Our experimental observations show that above the bulk SmC^*- N^* phase transition the N^* order appears in different ways according to the film thickness. In thin films, the conventional layer-by-layer thinning occurs. In films of intermediate thickness N^* inclusions nucleate inside the SmC^* film. The distortions of the in-plane orientational order of the SmC^* host phase induce elastic interactions between the inclusions and lead to their self-organization in chain-like structures. Both the dynamic of the chaining and the parameters driving the equilibrium distance between the inclusions in the chain are investigated. In thick films, N^* fingers grow inside the film. The influence of the experimental conditions on the various processes is analysed. Received 1 July 2002 / Published online: 15 April 2003 RID="a" ID="a"e-mail: Philippe.cluzeau@univ-lille1.fr     

Dynamical decay process of <Superscript>219, 220</Superscript>Ra<Superscript>*</Superscript> formed in <Superscript>10, 11</Superscript>B + <Superscript>209</Superscript>Bi reactions

The excitation functions for both the evaporation residue and fission have been calculated for ¹⁰B + ²⁰⁹Bi and ¹¹B + ²⁰⁹Bi reactions forming compound systems ^{219, 220}Ra^* , using the dynamical cluster-decay model (DCM) with effects of deformations and orientations of the nuclei included in it. In addition to this, the excitation functions for complete fusion (CF) are obtained by summing the fission cross-sections, neutron evaporation and charged particle evaporation residue cross-sections produced through the axn\ensuremath \alpha xn and pxn\ensuremath pxn (x = 2, 3, 4) emission channels for the ²¹⁹Ra system at various incident centre-of-mass energies. Experimentally the CF cross-sections are suppressed and the observed suppression is attributed to the low binding energy of ^{10, 11}B which breaks up into charged fragments. The reported complete fusion (CF) and incomplete fusion (ICF) excitation functions for the ²¹⁹Ra system are found to be nicely fitted by the calculations performed in the framework of DCM, without invoking a significant contribution from quasi-fission. Although DCM has been applied for a number of compound nucleus decay studies in the recent past, the same is being used here in reference to ICF and subsequent decay processes along with the CF process. Interestingly the main contribution to complete fusion cross-section comes from the fission cross-section at higher incident energies, which in DCM is found to consist of an asymmetric fission window, shown to arise due to the deformation and orientation effects of formation and decay fragments.     

Diffractive production of two ρ<Superscript>0</Superscript><Subscript>L</Subscript> mesons in e<Superscript>+</Superscript>e<Superscript>-</Superscript> collisions

We present an estimate of the cross-section for the exclusive production of a ρ_L ⁰-meson pair in e⁺e^- scattering, which will be studied in the future high-energy International Linear Collider. For this aim, we complete calculations of the Born order approximation of the amplitudes γ^* _L,T(Q₁ ²)γ^* _L,T(Q₂ ²)→ρ_L ⁰ρ_L ⁰, for arbitrary polarization of virtual photons and longitudinally polarized mesons, in the kinematical region s≫-t,Q₁ ²,Q₂ ². These processes are completely calculable in the hard region Q₁ ²,Q₂ ²≫Λ² _QCD, and we perform most of the calculations in an analytical way. The resulting cross-section turns out to be large enough for this process to be measurable with foreseen luminosity and energy, for Q₁ ² and Q₂ ² in the range of a few GeV².     

Metastable helium cluster He<Stack><Subscript>4</Subscript><Superscript>*</Superscript></Stack>

The existence of a metastable cluster He ₄ ^* with total spin S = 2 is predicted. The cluster consists of two covalently bound excited spin-polarized triplet He ₂ ^* molecules and is rectangular in shape. The electron wavefunctions, the dependence of the energy He ₄ ^* system on the distance between the He ₂ ^* triplet molecules, the atomic spacing, the frequency spectrum of natural oscillations of the cluster, and other characteristics are calculated from first principles. It is shown that the metastable state is formed if one of the excited He ₂ ^* molecules is in the ³Σ _u ⁺ state, while the other is in the ³Π_g state. The radiation lifetime τ of the metastable cluster He ₄ ^* is calculated; it is found to range from 100 to 200 s, which is much longer than the lifetime τ ≈ 20 s of the triplet molecule He ₂ ^* (³Σ _u ⁺ ). The height U ≈ 0.5 eV of the potential barrier preventing the departure from the local energy minimum is determined. The energy E_acc ≈ 9 eV/atom accumulated in the He ₄ ^* cluster is calculated; this energy considerably exceeds the energy of known chemical energy carriers. It is shown that the accumulated energy is released virtually completely during decomposition of the He ₄ ^* cluster into individual helium atoms. This means that helium clusters are a promising material with a high accumulated energy density (HEDM).     

Electron-impact ionization and dissociation of C<Subscript>2</Subscript>D<Superscript>+</Superscript>

Absolute cross sections for electron-impact single ionization, dissociative excitation and dissociative ionization of the ethynyl radical ion (C₂D⁺)^+) have been measured for electron energies ranging from the corresponding reaction thresholds to 2.5 keV. The animated crossed electron-ion beam experiment is used and results have been obtained for the production of C₂D²⁺, C²⁺, C₂⁺_2^+ , CD⁺, C⁺ and D⁺. The maximum of the cross section for single ionization is found to be (2.01 ± 0.02) × 10^-17 cm², at the incident electron energy of 105 eV. Absolute total cross sections for the various singly charged fragments production are observed to decrease by a factor of almost three, from the largest cross-section measured for C⁺, over C₂⁺_2^+ and CD⁺ down to that of D⁺. The maxima of the cross sections are obtained to be (14.5 ± 0.5) × 10^-17 cm² for C₂⁺_2^+, (12.1 ± 0.1) × 10^-17 cm² for CD⁺, (27.7 ± 0.2) × 10^-17 cm² for C⁺ and (11.1 ± 0.8) × 10^-17 cm² for D⁺. The smallest cross section is measured to be (1.50 ± 0.04) × 10^-18 cm² for the production of the doubly charged ion C²⁺. Individual contributions for dissociative excitation and dissociative ionization are determined for each singly-charged product. The cross sections are presented in closed analytic forms convenient for implementation in plasma simulation codes. Kinetic energy release distributions of dissociation fragments are seen to extend from 0 to 6 eV for the heaviest fragment C₂⁺_2^+, up to 11.0 eV for CD⁺, 14.2 eV for C⁺ and 11.2 eV for D⁺ products.     

Theoretical study of charge-exchange and excitation processes in collisions of He<Superscript>+</Superscript> ions with C<Superscript>5+</Superscript>, N<Superscript>6+</Superscript>, and O<Superscript>7+</Superscript> hydrogen-like ions

Data on the cross sections for single-electron charge exchange and excitation in collisions of He⁺ ions with C⁵⁺, N⁶⁺, and O⁷⁺ ions in the He⁺ ion energy range of 0.2–3.0 MeV are obtained for the first time. The cross sections for the single-electron charge transfer into the singlet and triplet 1snl states of C⁴⁺, N⁵⁺, and O⁶⁺ (2≤n≤5) ions and for the 1s → 2p _{0, ±1} electronic excitation of He⁺(1s) ions are calculated. The calculations were performed by solving close-coupling equations on the basis of ten two-electron quasi-molecular states.     

A miniature tunable TEA CO<Subscript>2</Subscript> laser using isotope <Superscript>13</Superscript>C<Superscript>16</Superscript>O<Subscript>2</Subscript> and <Superscript>12</Superscript>C<Superscript>16</Superscript>O<Subscript>2</Subscript>

A miniature tunable TEA CO₂ laser using isotope ¹³C¹⁶O₂ as the active medium is developed to extend the spectral range of CO₂ lasers for further application. The optimization of the energy parameters of the tunable TEA ¹³C¹⁶O₂ laser and the same laser using ¹²C¹⁶O₂ are studied. When a gas mixture (¹³C¹⁶O₂: N₂: He = 1: 1: 3) at a total pressure of 6.4 × 10⁴ Pa is used, the TEA ¹³C¹⁶O₂ laser of a 45-cm³ active volume obtains 51 emission lines in the [00⁰1–10⁰0] and [00⁰1–02⁰0] bands. The maximum pulse energy of the TEA ¹³C¹⁶O₂ laser is about 357 mJ. The same laser using the conventional gas mixture (¹²C¹⁶O₂: N₂: He = 1: 1: 3) at a pressure of 6.66 × 10⁴ Pa is measured to obtain 69 laser emission lines and the maximum pulse energy of laser radiation is about 409 mJ.     

Partial-wave analysis and baryon spectroscopy<Superscript>⋆</Superscript>

We continue to update our PWA of fundamental reactions as new data become available. Of primary interest to the N^* program are πN elastic scattering and the photo- and electroproduction of pions. Other photo-reactions are more model dependent, but may reveal resonances coupling weakly to πN final states. We also mention recent results from nucleon-nucleon elastic scattering, which have a less well-known connection to experimental programs proposing to extract N ^* properties from complete experiments.     

Non-Semi-Regular Quantum Groups Coming from Number Theory

 In this paper, we study C^*-algebraic quantum groups obtained through the bicrossed product construction. Examples using groups of adeles are given and they provide the first examples of locally compact quantum groups which are not semi-regular: the crossed product of the quantum group acting on itself by translations does not contain any compact operator. We describe all corepresentations of these quantum groups and the associated universal C^*-algebras. On the way, we provide several remarks on C^*-algebraic properties of quantum groups and their actions. Received: 10 October 2002 / Accepted: 10 October 2002 Published online: 24 January 2003 Communicated by A. Connes     

Remarks on the Goldstone theorem in theC *-algebraic approach

A Goldstone theorem in theC ^*-algebraic approach is obtained under a weak derivability assumption on the one-parameter group of internal symmetry automorphisms.     

Interaction of <Superscript>3</Superscript>He<Superscript>2+</Superscript> and Ar<Superscript>6+</Superscript> ions with acetylene,ethylene, and ethane molecules

Time-of-flight mass spectroscopy methods are employed for studying processes occurring during capture of electrons by ³He²⁺ and Ar⁶⁺ multiply charged ions with energy 6z keV (z is the ion charge) from C₂H _n molecules (n = 2, 4, 6) with different multiplicities of C-C bonds. Fragmentation schemes of the molecular ions formed in such processes are established from analysis of correlations of recording times for all fragment ions. The absolute values of the cross sections of capture of an electron and capture with ionization are measured, as well as the cross sections of formation of fragment ions in these processes. The absolute values of total capture cross sections for several electrons are determined.     

The Representation of Isometric Operators on <Emphasis Type="Italic">C</Emphasis><Superscript>(1)</Superscript>(<Emphasis Type="Italic">X</Emphasis>)

In this paper,we introduce a new norm on C ⁽¹⁾(X), which is induced by a hexagon on R ², and prove that every isometric operator on C ⁽¹⁾(X) can be induced by a homeomorphism of X, where X is a connected subset of R.     

Pre-irradiation with low-dose <Superscript>12</Superscript>C<Superscript>6+</Superscript> beam significantly enhances the efficacy of <Emphasis Type="Italic">AdCMV-p53</Emphasis> gene therapy in human non-small lung cancer

The combination of ionizing radiation and gene therapy has been investigated. However, there are very few reports about the combination of heavy-ion irradiation and gene therapy. To determine if the pre-exposure to low-dose heavy ion beam enhances the suppression of AdCMV-p53 on non-small lung cancer (NSLC), the cells pre-irradiated or non-irradiated were infected with 20, 40 MOl of AdCMV-p53. Survival fraction and the relative biology effect (RBE) were determined by clonogenic assay. The results showed that the proportions of p53 positive cells in 12C6 beam induced AdCMV-p53 infected cells were more than 90%, which were significantly more than those in γ-ray induced AdCMV-p53 infected cells. The pre-exposure to low-dose 12C6 beam significantly prevented the G0/G1 arrest and activated G2/M checkpoints. The pre-exposure to 12C6 beam significantly improved cell to apoptosis. RBEs for the 12C6 AdCMV-p53 infection groups were 30%-60%, 20% -130% and 30%-70% more than those for the 12C6 -irradiated only, AdCMV-p53 infected only, and γ-irradiation induced AdCMVp53 infected groups, respectively. The data suggested that the pre-exposure to low-dose 12C6 beam significantly promotes exogenous p53 expression in NSLC, and the suppression of AdCMV-p53 gene therapy on NSLC.     

Polarization in hyperon photo- and electro-production<Superscript>⋆</Superscript>

Multiple polarization observables must be measured to access the amplitude structure of pseudoscalar meson photoproduction off the proton. The hyperon-producing reactions are especially attractive to study, since the weak decays allow straightforward measurement of the induced and recoil polarization observables. In this paper we emphasize γ + p → K ⁺ + Λ , discussing recent measurements of C_x, C_z, and P for this reaction. An empirical constraint on the helicity amplitudes is obtained. A simplified model involving spin-flip and spin-non-flip amplitudes is presented. Finally, a semi-classical model of how the polarization may arise is presented.     

Study of K<Superscript>*</Superscript><Subscript>0</Subscript>(1430) and a<Subscript>0</Subscript>(980) from B→K<Superscript>*</Superscript><Subscript>0</Subscript>(1430)π and B→a<Subscript>0</Subscript>(980)K decays

We use the decay modes B→K^* ₀(1430)π and B→a₀(980)K to study the scalar mesons K^* ₀(1430) and a₀(980) within the framework of perturbative QCD. For B→K^* ₀(1430)π, we perform our calculation in two scenarios for the scalar meson spectrum. The results indicate that scenario II is more favored by the experimental data than scenario I. The important contribution from annihilation diagrams can enhance the branching ratios by about 50% in scenario I and about 30% in scenario II. The direct CP-asymmetries in B→K^* ₀(1430)π are small, which is consistent with the present experiments. The predicted branching ratio of B→a₀(980)K in scenario I differs from the experiments by a factor of 2, which indicates that a₀(980) cannot be interpreted as q̄q.     

Optical characteristics of radiation from N<Stack><Subscript>2</Subscript><Superscript>*</Superscript></Stack> dimers in a barrier discharge

The spectral and power characteristics of radiation of the second positive system of nitrogen (C ³Π _u → B ³Π _g ) in Ar-N₂ and Ar-N₂-Cl₂ mixtures excited by barrier discharge have been studied experimentally. Addition of argon to N₂ increased the radiation power by sixfold. In the triple mixture Ar-N₂-Cl₂ = 210/0.5/0.005, minor chlorine additions increased the intensity of the C ³Π _u → _B ³Π _g transition by 26% compared to Ar-N₂ mixtures. Radiation power density of 2.7 mW/cm² has been achieved. In both binary and triple mixtures, the second positive system of nitrogen was the major contributor to radiation, while the contributions of the fourth positive system of N ₂ ^* (D ³Σ _u ⁺ → B ³Π _g ), the Vegard-Kaplan transition of N ₂ ^* (A ³Σ _u ⁺ → X ¹Σ _g ⁺ ), and the D′ → A′ band of Cl ₂ ^* were negligibly small.     

Extraction of the neutron charge form factor G<Superscript>n</Superscript><Subscript>E</Subscript>(Q<Superscript>2</Superscript>) from the charge form factor of deuteron G<Superscript>d</Superscript><Subscript>C</Subscript>(Q<Superscript>2</Superscript>)

We extract the neutron charge form factor G ⁿ _E(Q ²) from the charge form factor of deuteron G ^d _C(Q ²) obtained from T ₂₀(Q ²) data at 0≤Q ²≤ 1.717 (GeV/c)². The extraction is based on the relativistic impulse approximation in the instant form of the relativistic Hamiltonian dynamics. Our results (12 new points) are compatible with existing values of the neutron charge form factor of other authors. We propose a fit for the whole set (36 points) taking into account the data for the slope of the form factor at Q ² = 0. Received: 26 July 2002 / Accepted: 18 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: krutov@ssu.samara.ru RID="b" ID="b"e-mail: troitsky@theory.sinp.msu.ru Communicated by V.V. Anisovich