On the Uniqueness of Gravitational Centre

The dual volume of order α of a convex body A in R ⁿ is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R³ coincides with the maximizer of dual volume of order 2, thus it is unique.      

Stability of the positively charged manganese centre in GaAs heterostructures examined theoretically by the effective mass approximation calculation near the Γ critical point

This paper describes an n-i-p-i-n model heterostructure with a manganese (Mn)-doped p-type base region to check the stability of a positively charged manganese A_Mn⁺ centre with two holes weakly bound by a negatively charged 3d⁵(Mn) core of a local spin S=5/2 in the framework of the effective mass approximation near the Γ critical point (k～0). By including the carrier screening effect, the ground state energy and the binding energy of the second hole in the positively charged centre A_Mn⁺ are calculated within a hole concentration range from 1 × 10¹⁶ cm^-3 to 1 × 10¹⁷ cm^-3, which is achievable by biasing the structure under photo-excitation. For comparison, the ground-state energy of a single hole in the neutral A_Mn⁰ centre is calculated in the same concentration range. It turns out that the binding energy of the second hole in the A_Mn⁺ centre varies from 9.27 meV to 4.57 meV. We propose that the presence of the A_Mn⁺ centre can be examined by measuring the photoluminescence from recombination of electrons in the conduction band with the bound holes in the A_Mn⁺ centre since a high frequency dielectric constant of varepsilon _∞ =10.66 can be safely adopted in this case. The novel feature of the ability to tune the impurity level of the A_Mn⁺ centre makes it attractive for optically and electrically manipulating local magnetic spins in semiconductors.     

The AΠu state of : Electric properties, fine and hyperfine coupling constants, and magnetic moments (g-factors). A theoretical study

Several properties are calculated for A²Π_u of —the majority for the first time—including electric and magnetic moments, and fine/hyperfine structure (fs/hfs) parameters. The new results are compared with our previous ones for X² and B² of [P.J. Bruna, F. Grein, J. Mol. Spectrosc. 227 (2004) 67–80]. The electric quadrupole Θ and hexadecapole Φ moments, polarizability α, and hfs constants a, b, c, d, eQq₀, eQq₂ are evaluated at the density functional theory (DFT) level [B3LYP/aug-cc-pVQZ]. The fs constants (spin–orbit coupling A_Π, Λ-doubling p, q, spin-rotation γ_Π), and magnetic moments (g-factors) are obtained via 2nd-order sum-over-states expansions, using wavefunctions and matrix elements obtained with a multireference configuration interaction (MRDCI) method, and the Breit–Pauli Hamiltonian. At equilibrium, 2nd-order properties of A²Π_u are dominated by its coupling with B². For the A state, two independent components are reported for traceless tensor properties (multipoles Θ and Φ; hfs parameters c/d and q₀/q₂) and three for traced properties (polarizability α and g-factors), i.e., one more component than for axially symmetric Σ states. The currently available experimental data on — limited to A_Π, p, and q—are well reproduced by our theoretical results.     

Analysis of the 2ν3 band of CD3F at 5.06 μm recorded under high resolution

The 2ν₃(A₁) band of ¹²CD₃F near 5.06 μm has been recorded with a resolution of 20–24 × 10⁻³ cm⁻¹. The value of the parameter (α^B − α^A) for this band was found to be very small and, therefore, the K structure of the R(J) and P(J) manifolds was unresolved for J < 15 and only partially resolved for larger J values. The band was analyzed using standard techniques and values for the following constants determined: ν₀ = 1977.178(3) cm⁻¹, B″ = 0.68216(9) cm⁻¹, D″_J = 1.10(30) × 10⁻⁶ cm⁻¹, α^B = (B″ − B′) = 3.086(7) × 10⁻³ cm⁻¹, and β^J = (D″_J − D′_J) = −3.24(11) × 10⁻⁷ cm⁻¹. A value of α^A = (A″ − A′) = 2.90(5) × 10⁻³ cm⁻¹ has been obtained through band contour simulations of the R(J) and P(J) multiplets.     

The ν2, ν5 Raman band system of CH3F

The anisotropic and isotropic components of the ν₂, ν₅ rotation-vibrational Raman bands of ¹³CH₃F were obtained separately. The two upper states are coupled by a strong second-order Coriolis resonance. The anisotropic spectrum was analyzed by means of a program system due to R. Escribano. A contour simulation and a least-squares fit of 233 assigned transitions yielded values for ν₅, ΔA₅, ΔA₂, and Aζ_{5a, 5b^(z)}. The ¹³C shifts of ν₂ and ν₅ were obtained from the isotropic spectrum.     

Analysis of the Coriolis-coupled band system of ν5, ν2, and 2ν3 of methyl-d3 iodide

The Coriolis-coupled band system of ν₅, ν₂, and 2ν₃ of CD₃I was analyzed by making use of all of the experimental data now available. These data included the high-resolution infrared spectra, microwave spectra, and laser Stark spectra. The analysis gave values, more precise than before, of the spectroscopic constants for ν₅, ν₂, and 2ν₃ and the interaction constants. The determination of the rotational constant A for 2ν₃ gave a value for , with which all of the α^A constants for CD₃I have been completed. These α^A values were incorporated with the known value of A₆ to give a value for A₀.     

Absolutely Singular Dynamical Foliations

Let A ³ be the product of the automorphism of T ² and of the identity on T ¹. A small perturbation g of A ³ among volume preserving diffeomorphisms will have an invariant family of smooth circles Γ forming a continuous foliation of T ³. Corresponding to the vector bundle tangent to the circles Γ there is a “central” Lyapunov exponent of (g, volume), which is nonzero for an open set of ergodic g's. This surprising result of Shub and Wilkinson is complemented here by showing that the volume on T ³ has atomic conditional measures on the Γ's: there is a finite k such that almost every Γ carries $k$ atoms of mass 1/k. Received: 26 September 2000 / Accepted: 8 December 2000     

Conductometric and thermodynamic studies on the ionic association of HCOONH4, phCOONH4, HCOONa and phCOONa in aqueous–organic solvents

The specific conductance of ammonium formate, ammonium benzoate, sodium formate and sodium benzoate in (10%, 20% and 30% (W/W)) methanol–water, ethanol–water and glycerol–water mixtures at different temperatures (293, 298, 303 and 308 K) was measured.The molar conductance (Λ), limiting molar conductance (Λ₀), limiting ionic conductance (λ₀), association constants (K_A), the activation energy of the transport process (E_a), Walden product (Λ₀η₀), hydrodynamic radii (1/r_s⁺ + 1/r_s⁻)^− 1, transfer numbers of the studied ions (t), standard thermodynamic parameters of association (ΔG_A, ΔH_A and ΔS_A) were calculated and discussed.The results show that, the molar conductance and the limiting molar conductance values were decreased as the relative permittivity of the solvent decreased while, the association constant increased. Also the results show that the molar conductance, the limiting molar conductance and the association constant values were increased as the temperature increased indicating that the association process is an endothermic one.     

On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper''s operator

Harper's operator is the self-adjoint operator on defined by

Full-size image

. We first show that the determination of the spectrum of the transition operator on the Cayley graph of the discrete Heisenberg group in its standard presentation, is equivalent to the following upper bond on the norm of H_θ,: H_{θ,≤ 2(1 + √2 + cos(2πθ))}. We then prove this bound by reducing it to a problem on periodic Jacobi matrices, viewing H_θ, as the image of H_θ = U_θ + _θ^* + V_θ + V_θ^* in a suitable representation of the rotation algebra A_θ. We also use powers of H_θ to obtain various upper and lower bounds on H_θ = maxH_θ,. We show that “Fourier coefficients” of H_θ^k in A_θ have a combinatorial interpretation in terms of paths in the square lattice ². This allows us to give some applications to asymptotics of lattice paths combinatorics.     

On a Measure on the Inductive Limit of Projection Logics

The aim of the paper is to measure the logic of J-projections from inductive limit of W J-algebras studied. The main result isTheorem. Let А be a W^∗ J-factor of countable type (type of А is different from I₂) and let А be the inductive limit of W^∗ J-factors А_α different from I₂. If (1) А be a W^∗ P-factor or (2) А and all А_α are W^∗ K-factors, then any indefinite measure ν : ∪_αА^h_α→ R can be unique by the strong operator topology extended to an indefinite measure on A^h.     

Differentiating the Absolutely Continuous Invariant Measure of an Interval Map <Emphasis Type="Italic">f</Emphasis> with Respect to <Emphasis Type="Italic">f</Emphasis>

Let the map f:[−1,1]→[−1,1] have a.c.i.m. ρ (absolutely continuous f-invariant measure with respect to Lebesgue). Let δρ be the change of ρ corresponding to a perturbation X=δf○f⁻¹ of f. Formally we have, for differentiable A,but this expression does not converge in general. For f real-analytic and Markovian in the sense of covering (−1,1) m times, and assuming an analytic expanding condition, we show thatis meromorphic in C, and has no pole at λ=1. We can thus formally write δρ(A)=Ψ(1).     

Lepton flavour violating heavy Higgs decays within the and their detection at the LHC

Within the νMSSM, a Minimal Supersymmetric neutrino See-saw Model, Lepton Flavour Violating Higgs couplings are strongly enhanced at large tanβ (30), which can lead to BR(H⁰/A⁰→τμ)O(10⁻⁴), for M_H⁰/A⁰160 GeV. Enhancements on the production of Higgs bosons, through the gluon fusion mechanism, gg→H⁰/A⁰, and the associated production channel , whose rates grow with tanβ, as well as the mass degeneracy that occurs between the H⁰ and A⁰ states in this regime, also contribute to further the possibilities to detect a heavy Higgs signal into τμ pairs. We show that the separation of τμ Higgs events from the background at the upcoming CERN Large Hadron Collider could be done for Higgs masses up to about 600 GeV for 300 fb⁻¹ of luminosity, for large tanβ values. However, even with as little as 10 fb⁻¹ one can probe H⁰/A⁰ masses up to 400 GeV or so, if tanβ=60. Altogether, these processes then provide a new Higgs discovery mode as well as an independent test of flavour physics.     

Extensions of Lieb’s Concavity Theorem

The operator function (A,B)→ Trf(A,B)(K ^*)K, defined in pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. We obtain, as a special case, a new proof of Lieb’s concavity theorem for the function (A,B)→ TrA ^p K ^* B ^q K, where p and q are non-negative numbers with sum p+q ≤ 1. In addition, we prove concavity of the operator function

The spectra and structure of indium iodide: The rotational and vibrational constants of the A0 state

The rotational constants of the A0⁺ state of InI are reported for the first time as B_e = 0.038077 cm⁻¹ and α_e = 0.0002373 cm⁻¹, while T_e = 24402.91 cm⁻¹ for the A0⁺-X0⁺ transition. Accurate vibrational constants for both the A0⁺ and X0⁺ states are computed from the derived band origins.     

Cube–Root Boundary Fluctuations¶for Droplets in Random Cluster Models

For a family of bond percolation models on ℤ² that includes the Fortuin–Kasteleyn random cluster model, we consider properties of the “droplet” that results, in the percolating regime, from conditioning on the existence of an open dual circuit surrounding the origin and enclosing at least (or exactly) a given large area A. This droplet is a close surrogate for the one obtained by Dobrushin, Kotecky and Shlosman by conditioning the Ising model; it approximates an area-A Wulff shape. The local part of the deviation from the Wulff shape (the “local roughness”) is the inward deviation of the droplet boundary from the boundary of its own convex hull; the remaining part of the deviation, that of the convex hull of the droplet from the Wulff shape, is inherently long-range. We show that the local roughness is described by at most the exponent 1/3 predicted by nonrigorous theory; this same prediction has been made for a wide class of interfaces in two dimensions. Specifically, the average of the local roughness over the droplet surface is shown to be O(l ^1/3(log l)^2/3) in probability, where is the linear scale of the droplet. We also bound the maximum of the local roughness over the droplet surface and bound the long-range part of the deviation from a Wulff shape, and we establish the absense of “bottlenecks”, which are a form of self-approach by the droplet boundary, down to scale log l. Finally, if we condition instead on the event that the total area of all large droplets inside a finite box exceeds A, we show that with probability near 1 for large A, only a single large droplet is present. Received: 20 January 2000 / Accepted: 7 August 2001     

Pseudo scalar contributions to light-by-light correction of muon in AdS/QCD

We have performed a holographic calculation of the hadronic contributions to the anomalous magnetic moment of the muon, using the gauge/gravity duality. As a gravity dual model of QCD with three light flavors, we study a U(3)_L×U(3)_R flavor gauge theory in the five-dimensional AdS background with a hard-wall cutoff. The anomalous (electromagnetic) form factors for the pseudo scalars, π⁰, η and η^′, are obtained from the 5D Chern–Simons term of the gravity dual, which correctly reproduce the asymptotic behavior of the form factor, dictated by QCD. We find the total light-by-light contributions of pseudo scalars to the muon anomalous magnetic moment, , which is consistent with previous estimates, based on other approaches.     

A new electronic transition of antimony chloride in the visible region

The emission spectrum of SbCl has been photographed at high resolution in the region 400 to 640 nm. In addition to bands of two previously reported transitions in this region, A₁-X and A₂-X, 36 bands of a new system have been identified. A vibrational analysis has been made with ν₀₀ ≈ 20 679 cm⁻¹, and 7 of the bands have been rotationally analyzed. The electronic transition has ΔΩ = 0 with lower state constants which match published data for the ground state X³Σ⁻(0⁺). The upper state is characterized by the following ¹²¹Sb³⁵Cl molecular parameters: B′₀ = 0.0922 cm⁻¹, D′₀ = 3.1 × 10⁻⁸ cm⁻¹.     

Formality Theorem for Hochschild Cochains via Transfer

We construct a 2-colored operad Ger _∞ which, on the one hand, extends the operad Ger _∞ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy algebras. We show that Tamarkin’s Ger _∞-structure on the Hochschild cochain complex C ^•(A, A) of an A _∞-algebra A extends naturally to a Ger⁺_￥{{\bf Ger}^+_{\infty}}-structure on the pair (C ^•(A, A), A). We show that a formality quasi-isomorphism for the Hochschild cochains of the polynomial algebra can be obtained via transfer of this Ger⁺_￥{{\bf Ger}^+_{\infty}}-structure to the cohomology of the pair (C ^•(A, A), A). We show that Ger⁺_￥{{\bf Ger}^+_{\infty}} is a sub DG operad of the first sheet E ¹(SC) of the homology spectral sequence for the Fulton–MacPherson version SC of Voronov’s Swiss Cheese operad. Finally, we prove that the DG operads Ger⁺_￥{{\bf Ger}^+_{\infty}} and E ¹(SC) are non-formal.     

High-Resolution Laser Spectroscopy of YbCl: The AΠ–XΣ Transition

The A²Π–X²Σ⁺ transition of ¹⁷⁴Yb³⁵Cl and ¹⁷²Yb³⁵Cl has been rotationally analyzed for the first time. Doppler-limited laser excitation spectroscopy with selective detection of fluorescence was used to obtain spectra of the 0–0 and 1–0 bands with a measurement accuracy of approximately 0.0035 cm⁻¹. Resolved fluorescence was used to record the 0–1, 0–2, and 0–3 bands and to unequivocally assign the rotational numbering, N, to the laser excitation spectra. In total, over 1300 line positions have been measured and assigned for each of the two isotopomers and employed in least-squares fits of molecular parameters. The principal results for the A²Π state are A_e = 1491.494(2) cm⁻¹ and R_e = 2.4433(1) Å, and for the X²Σ⁺ state, R_e = 2.4883(2) Å and γ_e = 4.59(2) × 10⁻³ cm⁻¹. The interaction between the X²Σ⁺ and A²Π states has been investigated and is shown to be the main contributor to the spin–rotation splitting in the ground state.     

High-Resolution Study of the BaI AΠ Electronic State

Near-infrared and visible spectra of the A²Π–X²Σ⁺, C²Π_1/2–A²Π_1/2, C²Π_1/2–B²Σ⁺, and C²Π_1/2–X²Σ⁺ band systems of the BaI molecule were recorded by using Fourier transform spectroscopy (FTS). The spectra were produced from the chemiluminescent reaction Ba + I₂ and also by using laser-induced fluorescence (LIF) technique in which the laser sources were a Ti:sapphire single-mode laser, a dye single-mode laser, and a Kr⁺ multimode ion laser. Resolved rotational data, originating from 19 vibrational levels (0 ≤ v ≤ 5 and 7 ≤ v ≤ 19) of the A²Π state, 24 vibrational levels (0 ≤ v ≤ 18 and 20 ≤ v ≤ 24) of the X²Σ⁺ state, and 8 vibrational levels (1 ≤ v ≤ 2 and 9 ≤ v ≤ 14) of the C²Π state, were used in the final analysis. Previously recorded data for the B²Σ⁺–X²Σ⁺ and C²Π–X²Σ⁺ systems, taken from R. F. Gutterres, J. Vergès, and C. Amiot, J. Mol. Spectrosc. 196, 29–44 (1999) and from C. A. Leach, A. A. Tsekouras, and R. N. Zare, J. Mol. Spectrosc. 153, 59–72 (1992), were added to the present work data field. Accurate and improved molecular constants, for the X²Σ⁺, B²Σ⁺, A²Π, and C²Π states, were derived from a simultaneous treatment of the whole data set.