Solid Substrate-Room Temperature Phosphorescence Method for the Determination of Trace Mn(II) Based on Oxidizing Reaction of Hydrogen Peroxide Using α,α′-Bipyridine as Sensitizer

A new solid substrate-room temperature phosphorescence (SS-RTP) method for the determination of trace manganese (II) has been established. It bases on the fact that fullerol (R) emits strong and stable room temperature phosphorescence (RTP) on filter paper substrate. H₂O₂ can oxidize R to cause the SS-RTP quenching. But manganese (II) can obstruct H₂O₂ to oxidize R, and enhance the RTP of R. α,α′-Bipyridine (Bipy) can sensitize the RTP. After adding Bipy, the ΔI _p enhances 7 times than that without Bipy. Under the optimum conditions, the linear dynamic range of this method is 0.016–1.12 pg spot⁻¹ with a detection limit (L.D.) of 4.6 fg spot⁻¹ ( is the absolute mass of Mn²⁺), and the regression equation of working curve is ΔI _p=25.20 + 63.55 (pg spot⁻¹), n=6, r=0.9983. For 0.016 and 1.12 pg spot⁻¹ Mn²⁺, RSDS are 4.3 and 4.8%, respectively (n=7). This method has been applied to the determination of trace manganese (II) in actual sample with high sensitivity and good selection. And the reaction mechanism of SS-RTP is discussed.     

Bethe Algebra of Homogeneous <Emphasis Type="Italic">XXX</Emphasis> Heisenberg Model has Simple Spectrum

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional -modules. As a byproduct we show that there exist exactly two-dimensional vector subspaces with a basis such that deg f = l, deg g = n − l + 1 and f (u)g(u − 1) − f (u − 1)g(u) = (u + 1) ⁿ . Supported in part by NSF grant DMS-0601005. Supported in part by RFFI grant 08-01-00638. Supported in part by NSF grant DMS-0555327.     

A Variational Principle in the Dual Pair of Reproducing Kernel Hilbert Spaces and an Application

Given a positive definite, bounded linear operator A on the Hilbert space ₀≔l ²(E), we consider a reproducing kernel Hilbert space ₊ with a reproducing kernel A(x,y). Here E is any countable set and A(x,y), x,y∊ E, is the representation of A w.r.t. the usual basis of ₀. Imposing further conditions on the operator A, we also consider another reproducing kernel Hilbert space ₋ with a kernel function B(x,y), which is the representation of the inverse of A in a sense, so that ₋⊃ ₀⊃ ₊ becomes a rigged Hilbert space. We investigate the ratios of determinants of some partial matrices of A and B. We also get a variational principle on the limit ratios of these values. We apply this relation to show the Gibbsianness of the determinantal point process (or fermion point process) defined by the operator A(I+A)⁻¹ on the set E. 2000 Mathematics Subject Classification: Primary: 46E22 Secondary: 60K35     

Finite-Time Singularities of an Aggregation Equation in $${\mathbb {R}^n}$$ with Fractional Dissipation

We consider an aggregation equation in , n ≥ 2 with fractional dissipation, namely, , where 0 ≤ γ < 1 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e ^−|x|. We prove that for a class of smooth initial data, the solutions develop blow-up in finite time.     

A study of the nuclear-medium influence on neutral-strange-particle production in deep-inelastic neutrino scattering

The influence of nuclear effects on the production of neutral strange particles (V ⁰) is investigated using the data obtained with SKAT propane-freon bubble chamber irradiated in the neutrino beam (with E _v =3−30 GeV) at the Serpukhov accelerator. The mean multiplicity of V ⁰ particles in nuclear interactions, , is found to exceed significantly that in “quasideuteron” interactions, . The ratio of is larger than that for π⁻ mesons, . It is shown that the multiplicity gain of V ⁰ particles can be explained by intranuclear interactions of produced pions. The text was submitted by the authors in English.     

Highly Selective and Anions Controlled Fluorescent Sensor for Hg<Superscript>2+</Superscript> in Aqueous Environment

A highly selective PET fluorescent sensor B1 for Hg²⁺ containing a BODIPY fluorophore and a NS₂O₂ penta-chelating receptor has been synthesized and characterized. Its absorption maximum wavelength (498 nm) and emission maximum wavelength (512 nm) are both in the visible range. The fluorescence quantum yields of the B1 and Hg²⁺-bound states of BHg1 are 0.008 and 0.58 in 70% aqueous ethanol solution, respectively. The pKa of 1.97 is the lowest in metal ions PET chemo sensors reported up till now as we know. Thus, B1 can detect the Hg²⁺ in a wide pH span, which indicates that it has more potential and further practical applications for biology and toxicology. Furthermore, BHg1 also displays response to some anions such as Cl⁻(Br⁻), , SCN⁻ and CH₃COO⁻, which is attributed to the significant coordinating ability of these anions to Hg²⁺.     

Kernel and trace formula for the exponential of the Laplace-Beltrami operator on a decorated graph

For the kernel of the Laplace operator Δ^Λ with potential Σ _j=1 ^k c _j δ _{q j} (x) on a manifold, (the operator is given by a Lagrangian plane Λ ⊂ ℂ ^k ⊕ ℂ ^k ), an isomorphism Γ: ker Δ^Λ → Λ ∩ L is described, where L is a special Lagrangian plane (whose explicit form is evaluated). A similar assertion holds for the Laplace operator on a decorated graph; for such a graph (obtained by decorating a connected finite graph with n edges and v vertices) with “continuity” conditions, the inequality 1 ≤ dimker ≤ n − v + 2 is obtained. It is also proved that the quantity n − v + 1-dim ker cannot reduce when adding new edges and manifolds. The first terms of the expansion of Tr(exp(-tH ^Λ)) are found. Dedicated to the memory of V. A. Geyler     

CP -violation effects in the decays B ? → D * K *? and method for determining the weak phase γ

A method for determining the angle γ and the ratio of the amplitudes A _λ(B ⁻ → K ^*−) and A _λ)B ⁻ → D ^*0 K ^*−), r _Bλ, for all three vector-meson polarization states by using the decays B ^∓ → D ^* K ^*∓ is proposed. This method relies on the interference between the decays B ⁻ → D ^*0 K ^*− and B ⁻ → K ^*−, which arises if D ^*0 and decay to D ⁰/ π ⁰ and D ⁰/ γ, whereupon D ⁰ and mesons decay to common final hadron states. The doubly Cabibbo-suppressed modes of D ⁰-meson decay are chosen here to specify such final states. Original Russian Text ? V.A. Kovalchuk, 2007, published in Yadernaya Fizika, 2007, Vol. 70, No. 4, pp. 754–763.     

Millimeter-wave Detectors Based on Antenna-coupled Low-barrier Schottky Diodes

The principles of construction of millimeter wave detectors based on low-barrier Schottky diodes and planar antennas are discussed. The modified planar slot antenna with low beam spillover at the resonant frequency of 94 GHz has been developed. Experiments have been carried out to investigate detecting characteristics of the diodes with differential contact resistances at zero bias. Experimental data are well correspond to calculations in a simple model of detector. At the maximum of rf-to-dc voltage sensitivity - more than 10000 V/W - is obtained. At lower values of a better noise equivalent power (NEP), around 10⁻¹² W Hz^−1/2, is predicted.     

One-and-a-Half Quantum de Finetti Theorems

When n − k systems of an n-partite permutation-invariant state are traced out, the resulting state can be approximated by a convex combination of tensor product states. This is the quantum de Finetti theorem. In this paper, we show that an upper bound on the trace distance of this approximation is given by , where d is the dimension of the individual system, thereby improving previously known bounds. Our result follows from a more general approximation theorem for representations of the unitary group. Consider a pure state that lies in the irreducible representation of the unitary group U(d), for highest weights μ, ν and μ + ν. Let ξ_μ be the state obtained by tracing out U _ν. Then ξ_μ is close to a convex combination of the coherent states , where and is the highest weight vector in U _μ. For the class of symmetric Werner states, which are invariant under both the permutation and unitary groups, we give a second de Finetti-style theorem (our “half” theorem). It arises from a combinatorial formula for the distance of certain special symmetric Werner states to states of fixed spectrum, making a connection to the recently defined shifted Schur functions [1]. This formula also provides us with useful examples that allow us to conclude that finite quantum de Finetti theorems (unlike their classical counterparts) must depend on the dimension d. The last part of this paper analyses the structure of the set of symmetric Werner states and shows that the product states in this set do not form a polytope in general.     

L p -Boundedness of the Wave Operator for the One Dimensional Schrödinger Operator

Given a one dimensional perturbed Schrödinger operator H =  ? d ²/dx ² + V(x), we consider the associated wave operators W  _± , defined as the strong L ² limits $\lim_{s\to\pm\infty}e^{isH}e^{-isH_{0}}Given a one dimensional perturbed Schr?dinger operator H = − d ²/dx ² + V(x), we consider the associated wave operators W _± , defined as the strong L ² limits . We prove that W _± are bounded operators on L ^p for all 1 < p < ∞, provided , or else and 0 is not a resonance. For p = ∞ we obtain an estimate in terms of the Hilbert transform. Some applications to dispersive estimates for equations with variable rough coefficients are given.     

Maximum Solutions of Normalized Ricci Flow on 4-Manifolds

We consider the maximum solution g(t), t ∈ [0,  + ∞), to the normalized Ricci flow. Among other things, we prove that, if (M, ω) is a smooth compact symplectic 4-manifold such that and let g(t), t ∈ [0, ∞), be a solution to (1.3) on M whose Ricci curvature satisfies that |Ric(g(t))| ≤ 3 and additionally χ(M) = 3τ (M) > 0, then there exists an , and a sequence of points {x _j,k ∈ M}, j = 1, . . . , m, satisfying that, by passing to a subsequence,

A Negative Mass Theorem for the 2-Torus

Let M be a closed surface. For a metric g on M, denote the area element by dA and the Laplace-Beltrami operator by Δ = Δ _g . We define the Robin mass m(p) at the point to be the value of the Green function G(p, q) at q = p after the logarithmic singularity has been subtracted off, and we define trace . This regularized trace can also be obtained by regularization of the spectral zeta function and is hence a spectral invariant which heuristically measures the total wavelength of the surface.We define the Δ-mass of (M, g) to equal , where is the Laplacian on the round sphere of area A. This scale invariant quantity is a non-trivial analog for closed surfaces of the ADM mass for higher dimensional asymptotically flat manifolds.In this paper we show that in each conformal class for the 2-torus, there exists a metric with negative Δ-mass. From this it follows that the minimum of the Δ-mass on is negative and attained by some metric . For this minimizing metric g, one gets a sharp logarithmic Hardy-Littlewood-Sobolev inequality and an Onofri-type inequality.We remark that if the flat metric in is sufficiently long and thin then the minimizing metric g is non-flat. The proof of our result depends on analyzing the ordinary differential equation which is equivalent to h′′ = 1 − 1/h. The solutions are periodic and we need to establish quite delicate, asymptotically sharp inequalities relating the period to the maximum value. The author was supported by the National Science Foundation #DMS-0302647.     

Diffusion Coefficients of Several Rhodamine Derivatives as Determined by Pulsed Field Gradient–Nuclear Magnetic Resonance and Fluorescence Correlation Spectroscopy

Rhodamine derivatives are popular, photostable fluorophores that are used in a number of fluorescent based techniques, including fluorescence correlation spectroscopy (FCS). Indeed, in FCS, both rhodamine 6G (R6G) and rhodamine 110 (R110) are used as calibration standards to determine the dimensions of the instrument confocal volume. In spite of a requirement for precise values of the diffusion coefficients, literature values are scarce and vary over an order of magnitude. In this paper, the diffusion coefficients of four rhodamine fluorophores (rhodamine 6G (R6G), rhodamine B (RB), rhodamine 123 (R123), rhodamine 110 (R110)) were determined by pulsed field gradient nuclear magnetic resonance (PFG-NMR) spectrometry and then validated by comparison with fluorescence correlation spectroscopy. With the objective of validating the FCS calibration, diffusion coefficients of several dextrans and a polystyrene nanoparticle were also determined and compared with literature values or theoretical values that were based upon the Stoke–Einstein equation. The work presented here lead us to conclude that the diffusion coefficients for R6G and R110 have generally been underestimated in the literature. We propose revised values of 4.4 × 10⁻¹⁰ m² s⁻¹ for R110 and 4.0 × 10⁻¹⁰ m² s⁻¹ for R6G. Using the revised D value for R110 to calibrate the FCS instrument, diffusion coefficients have then been systematically determined for different conditions of pH, ionic strength and concentration. To correct for differences due to solvent effects (D₂O vs. H₂O), an isotopic correction factor, of 1.23, was determined from both FCS and from the solvent auto-diffusion coefficients obtained by NMR.     

Bounds on neutrino mixing with exotic singlet neutrinos

We examine the effects of mixing induced non-diagonal light-heavy neutrino weak neutral currents on the amplitude for the process (with a=e, μ or τ). By imposing constraint that the amplitude should not exceed the perturbative unitarity limit at high energy , we obtain bounds on light-heavy neutrino mixing parameter sin² where is the mixing angle. In the case of one heavy neutrino (mass mξ) or mass degenerate heavy neutrinos, for Λ=1 TeV, no bound is obtained for mξ<0.50 TeV. However, sin² ≤3.8 × 10⁻⁶ for mξ=5 TeV and sin ≤6.0 × 10⁻⁸ for mξ=10 TeV. For Λ=∞, no constraint is obtained for mξ<0.99 TeV and sin² ≤3.8 × 10⁻² (for mξ=5 TeV) and sin² ≤9.6 × 10⁻³ (for mξ=10 TeV).     

A Negative Mass Theorem for Surfaces of Positive Genus

Let M be a closed surface. For a metric g on M, denote the Laplace-Beltrami operator by Δ = Δ _g . We define trace , where dA is the area element for g and m(p) is the Robin constant at the point , that is the value of the Green function G(p, q) at q = p after the logarithmic singularity has been subtracted off. Since trace Δ⁻¹ can also be obtained by regularization of the spectral zeta function, it is a spectral invariant. Heuristically it represents the sum of squares of the wavelengths of the surface. We define the Δ-mass of (M, g) to equal , where is the Laplacian on the round sphere of area A. This is an analog for closed surfaces of the ADM mass from general relativity. We show that if M has positive genus, the minimum of the Δ-mass on each conformal class is negative and attained by a smooth metric. For this minimizing metric, there is a sharp logarithmic Hardy-Littlewood-Sobolev inequality and a Moser-Trudinger-Onofri type inequality. The author would like to acknowledge the support of the Institute for Advanced Study.     

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_ϕ)⁻¹ with the dwell time τ_D through the cavity and the dephasing rate τ _ϕ ⁻¹ , we find an exponential suppression of weak localization by a factor of ∝ exp[− /τ_ϕ], where is the system-dependent parameter. In the dephasing probe model, coincides with the Ehrenfest time, ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F. The text was submitted by the authors in English.     

High-temperature creep of nickel under conditions of grain-boundary diffusion of impurities from the surface

Comparative investigations of the effect of diffusion streams of copper atoms (a weakly segregating impurity) and silver atoms (a strongly segregating impurity) from the surface in the high-temperature plastic deformation of nickel have been carried out. It has been established that in the high-temperature plastic deformation of nickel, when there are diffusion streams of copper and silver from the surface, there is a reduction in the creep resistance of nickel due to an increase in the contribution of grain-boundary slip to the overall deformation. Two stages, characterized by different values of the rate sensitivity factor m, are observed on the curve of the stress against the rate of deformation over a certain temperature range for each impurity. In the region of deformation rates of sec⁻¹, m≊0.2, and for sec⁻¹, m becomes less than 0.05. Institute of Physics of the Strength and Study of Materials. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 119–125, July, 1997.