Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z ^d , 〈,〉 denotes nearest neighbors inZ ^d ;J>0 andh={h(x)>0,x∈Z ^d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h ^?δ dμ(h)<∞ for some δ>0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z ^d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _x,h,J <∞.     

New spiro[benzotetraphene-fluorene] Derivatives: Synthesis and Application in Sky-Blue Fluorescent Host Materials

Blue light-emitting spiro[benzotetraphene-fluorene] (SBTF)-based host materials, 3-(1-naphthyl)-10-naphthylspiro[benzo[ij]tetraphene-7,9′-fluorene] (1), 3-(2-naphthyl)-10-naphthylspiro[benzo[ij]tetraphene-7,9′-fluorene] (2), and 3-[2-(6-phenyl)naphthyl]-10-naphthylspiro[benzo[ij]tetraphene-7,9′-fluorene] (3) were designed and prepared via multi-step Suzuki coupling reactions. Introducing various aromatic groups into SBTF core lead to a reduction in band gap and a determination of the color purity and luminescence efficiency. Typical sky-blue fluorescent organic light emitting diodes with the configuration of ITO/N,N′-di(1-naphthyl)-N,N′-bis[(4-diphenylamino)phenyl]-biphenyl-4,4′-diamie (60 nm)/N,N,N′,N′-tetra(1-biphenyl)-biphenyl-4,4′-diamine (30 nm)/host: dopant (30 nm, 5 %)/LG201 (electron transporting layer, 20 nm)/LiF/Al were developed using SBTF derivatives as a host material and p-bis(p-N,N-diphenyl-aminostyryl)benzene (DSA-Ph) as a sky-blue dopant material. A device obtained from three materials doped with DSA-Ph showed color purity of 0.148 and 0.239, a luminance efficiency of 7.91 cd/A, and an external quantum efficiency >4.75 % at 5 V.     

Decay of helicity in homogeneous turbulence

The self-similar relaxation of helicity in homogeneous turbulence has been considered taking into account integral invariants ∫ ₀ ^∞ r ^m 〈u(x)ω(x + r)〉 dr = I _m ^h (where ω = curlu and r = |r|). It has been shown that integral invariants with m = 3 for both helicity and energy are possible in addition to helical analogs of Loitsyanskii (m = 4) and Birkhoff-Saffman (m = 2) invariants associated with the conservation laws of momentum and angular momentum, respectively. Helicity always relaxes more rapidly than the energy. Its decay exponent is in the interval from ?3/2 to ?5/2 versus the interval from ?6/5 to ?10/7 for the energy.     

Design,synthesis, and anti-tobacco mosaic virus (TMV) activity of glycoconjugates of phenanthroindolizidines alkaloids

Glycoconjugates of phenanthroindolizidine alkaloids targeting tobacco mosaic virus (TMV) RNA were designed, synthesized, and evaluated for their antiviral activity against TMV for the first time. The glycoconjugation of $(S)$ -6-O-desmethylantofine (2) and 14-hydroxyltylophorines (3–6) was accomplished in three ways (O-glycosylation manner, using carbamoyloxy as linker arm, and using 1,2,3-triazole as linker arm) with three different sugar units (glucose, galactose, and mannose). The glycoconjugates showed improved water solubility and molecule polarity compared with phenanthroindolizidine alkaloids. The bioassay results showed that C6 was a suitable position for glycoconjugation and O-glycosylation can increase the antiviral activity of phenanthroindolizidine alkaloids indicating that the introduction of sugar units can improve the antiviral activity profile of glycoconjugates. Two O-glycosides of $(S)$ -6-O-desmethylantofine, (13aS)-6-O- $\upbeta $ -d-galactopyranosyl-2,3-dimethoxyphenanthro [9,10-b]-11-indolizidinone (10) and (13aS)-6-O- $\upbeta $ -d-mannopyranosyl-2,3-dimethoxyphenanthro [9,10-b]-11-indolizidinone (11) displayed significant higher activity than commercial ningnanmycin, and thus could be considered for novel therapy against plant virus infection.     

Bis-Benzimidazolyl Diamide Based Fluorescent Probe for Copper(II): Synthesis, Structural and Fluorescence Studies

A new fluorescent probe based on a bis-benzimidazole diamide N ²,N ^2′-bis[(1-ethyl-benzimidazol-2-yl)methyl]biphenyl-2,2′-dicarboxamide ligand L ₁ with a biphenyl spacer group and a Copper(II) trinuclear metallacycle has been synthesized and characterized by X-ray single crystallography, elemental and spectral (FT-IR, ¹H & ¹³C NMR, UV-Visible) analysis. The fluorescence spectra of L ₁ in MeOH show an emission band centered at 300 nm. This band arises due to benzimidazolyl moiety in the ligating system. The diamide L ₁ in the presence of Cu²⁺ show the simultaneous ‘quenching’ of (300 nm) and ‘enhancement’ of (375 nm) emission band. Similar fluorescence behavior was found in water–methanol mixture (9:1). The new emission band at 375 nm is attributed to intra ligand π–π* transition of the biphenyl moiety. L ₁ exhibited high selectivity and sensitivity towards Cu²⁺ in both the medium over other common metal ions like Ni²⁺, Co²⁺, Mn²⁺, Mg²⁺, Zn²⁺, Pb²⁺ and Hg²⁺. The binding constant with Cu²⁺ was calculated by the Benesi-Hildebrand equation. Selective “off-on-off” behavior of L ₁ in methanol has also been studied. The fluorescent intensity of 375 nm bands in L ₁ enhances (turns-on) upon addition of Cu²⁺ and quenches (turn-off) upon addition of Na₂-EDTA.     

One-range Addition Theorems for Noninteger n Slater Functions using Complete Orthonormal Sets of Exponential Type Orbitals in Standard Convention

By the use of complete orthonormal sets of ${\psi ^{(\alpha^{\ast})}}$ -exponential type orbitals ( ${\psi ^{(\alpha^{\ast})}}$ -ETOs) with integer (for α ^* = α) and noninteger self-frictional quantum number α ^*(for α ^* ≠ α) in standard convention introduced by the author, the one-range addition theorems for ${\chi }$ -noninteger n Slater type orbitals ${(\chi}$ -NISTOs) are established. These orbitals are defined as follows $$\begin{array}{ll}\psi _{nlm}^{(\alpha^*)} (\zeta ,\vec {r}) = \frac{(2\zeta )^{3/2}}{\Gamma (p_l ^* + 1)} \left[{\frac{\Gamma (q_l ^* + )}{(2n)^{\alpha ^*}(n - l - 1)!}} \right]^{1/2}e^{-\frac{x}{2}}x^{l}_1 F_1 ({-[ {n - l - 1}]; p_l ^* + 1; x})S_{lm} (\theta ,\varphi )\\ \chi _{n^*lm} (\zeta ,\vec {r}) = (2\zeta )^{3/2}\left[ {\Gamma(2n^* + 1)}\right]^{{-1}/2}x^{n^*-1}e^{-\frac{x}{2}}S_{lm}(\theta ,\varphi ),\end{array}$$ where ${x=2\zeta r, 0<\zeta <\infty , p_l ^{\ast}=2l+2-\alpha ^{\ast}, q_l ^{\ast}=n+l+1-\alpha ^{\ast}, -\infty <\alpha ^{\ast} <3 , -\infty <\alpha \leq 2,_1 F_1 }$ is the confluent hypergeometric function and ${S_{lm} (\theta ,\varphi )}$ are the complex or real spherical harmonics. The origin of the ${\psi ^{(\alpha ^{\ast})} }$ -ETOs, therefore, of the one-range addition theorems obtained in this work for ${\chi}$ -NISTOs is the self-frictional potential of the field produced by the particle itself. The obtained formulas can be useful especially in the electronic structure calculations of atoms, molecules and solids when Hartree–Fock–Roothan approximation is employed.     

On the number of negative eigenvalues for a Schrödinger operator with magnetic field

We consider the Schrödinger operator with magnetic field $$H = \sum\limits_{j = 1}^n {\left( {\frac{1}{i}\frac{\partial }{{\partial x_j }} - a_j } \right)^2 + Vin\mathbb{R}^n .} $$ Under certain conditions on the magnetic fieldB=curla, we generalize the Fefferman—Phong estimates (Bull. A. M. S.9, 129–206 (1983)) on the number of negative eigenvalues for ?Δ+V to the operatorH. Upper and lower bounds are established. Our estimates incorporate the contribution from the magnetic field. The conditions onB in particular are satisfied if the magnetic potentialsa _j (x) are polynomials.     

Secular-free solution up to third order of a model nonlinear equation for dispersive waves

The perturbation method of Lindstedt is applied to study the non linear effect of a nonlinear equation $$\nabla ^2 {\rm E} - \frac{1}{{c^2 }}\frac{{\partial ^2 {\rm E}}}{{\partial t^2 }} - \frac{{\omega _0^2 }}{{c^2 }}{\rm E} + \frac{{2v}}{{c^2 }}\frac{{\partial {\rm E}}}{{\partial t}} + E^2 \left[ {\frac{{\partial {\rm E}}}{{\partial t}} \times A} \right] = 0,$$ where (A. E)=0 andA,c, ω ₀ andν are constants in space and time. Amplitude dependent frequency shifts and the solution up to third order are derived.     

Neutral and anionic duality of 1,2,4-triazole α-amino acid scaffold in 1D coordination polymers

A tiny supramolecular synthon, 4H-1,2,4-triazol-4-yl acetic acid (HGlytrz) which is bifunctional by design having an electronic asymmetry and conformational flexibility has been introduced to synthesize iron(II) complexes. Having 1,2,4-triazole or carboxylic extremities on the same framework HGlytrz could display dual functionality by acting as a neutral as well as anionic ligand based on the possibility of deprotonation of carboxylic group. Four new iron(II) HGlytrz complexes with ClO $_{4}^{-}$ (1), NO $_{3}^{-}$ (2), BF $_{4}^{-}$ (3) and CF₃SO $_{3}^{-}$ (4) anions were prepared. Formulation of their composition which is complicated due to ligand deprotonation is discussed. Unlike its ester protected counterpart ethyl-4H-1,2,4-triazol-4-yl-acetate (αGlytrz) which show hysteretic room temperature spin crossover, 1–4 remain in the high-spin state as revealed by ⁵⁷M?ssbauer spectroscopy. Prospects of such 1D coordination polymers with dangling unbounded carboxylic entities in the realm of self-assembled monolayer (SAM) are discussed.     

9, 10-Bis(8-Quinolinoxymethyl)Anthracene—A Fluorescent Sensor for Nanomolar Detection of Cu2+ with Unusual Acid Stability of Cu2+-Complex

In this work, the dipod 9,10-bis(8-quinolinoxymethyl)anthracene (1) and for comparison, monopod 9-(8-quinolinoxymethyl)anthracene (2) have been synthesized. The fluoroionophore 1 in pH 7.1 HEPES buffered CH₃CN:H₂O (4:1 v/v) solution shows quenching only with Cu²⁺ with lowest limit of detection 150 nM, amongst various metal ions. Fluoroionophore 1 could also be applied to sense Co²⁺ with lowest limit of detection 600 nM. By modulating the pH of the solution and concentration of Cu²⁺, 1 shows respective “On-Off-On” and “On-Off” fluorescent switching. The self-assembly of two Cu²⁺ ions and two molecules of fluoroionophore 1 to form closed structure [Cu₂(L)₂]⁴⁺ seems to be responsible for nanomolar sensitivity towards Cu²⁺. The combination of delayed second protonation of 1 (pK_a2?=?2.6) and stepwise protonation of [Cu₂ L ₂]⁴⁺ causes unusual stability of [Cu(LH)₂]⁴⁺ even at pH?<?2.

The discovery of 3-(1-aminoethylidene)quinoline-2, 4(1H,3H)-dione derivatives as novel PSII electron transport inhibitors

Based on the structures of the 4-hydroxyphenylpyruvate dioxygenase inhibitor mesotrione and natural product fischerellin A, a series of imine derivatives of ( $E$ )-3-acyl-quinoline-2,4(1H,3H)-dione (6, 12 and 16) were designed, synthesized and systematically evaluated for their herbicidal activity. The bioassay results indicated that most of the synthesized compounds displayed good to excellent herbicidal activity, of which 6e, 6g, 6h, 6q and 6t exhibited more than 50 % inhibition against Brassica napus L., Amaranthus retroflexu or Digitaria adscendens at a dosage of $94\,\hbox {g}\,\hbox {ha}^{-1}$ or lower. The symptom of injured leaves in vivo, the high Hill reaction inhibitory activity of 6h in vitro ( $\hbox {IC}_{50}\,0.1\, \upmu \hbox {g}\,\hbox {mL}^{-1})$ and the computer-based binding model of compound 6h with D1 protein in photosystem II (PSII) reaction centre suggest this novel structure to likely be a new type of PSII electron transport inhibitor. Thus, we have found a novel type of diketone enamine structure targeted at the PSII reaction centre.     

Analyticity of the scattering operator for the nonlinear Klein-Gordon equation with cubic nonlinearity

The wave and scattering operators for the equation $$\left( {\square + m^2 } \right)\varphi + \lambda \varphi ^2 = 0$$ withm>0 and λ>0 on four-dimensional Minkowski space are analytic on the space of finite-energy Cauchy data, i.e.L ₂ ¹ (R ³)⊕L ₂(R ³).     

Laser-Rf double-resonance studies of the hyperfine structure of metastable atomic states of55Mn

The hyperfine structure (hfs) of the metastable atomic states 3d⁶4s⁶ D _{1/2, 3/2, 5/2, 7/2, 9/2} of⁵⁵Mn was measured using theABMR- LIRF method (atomicbeammagneticresonance, detected bylaserinducedresonancefluorescence). The hfs constantsA andB, corrected for second order hfs perturbations, could be derived from these measurements. The theoretical interpretation of these correctedA- andB-factors was performed in the intermediate coupling scheme taking into account the configurations 3d ⁵4s ², 3d ⁶4s and 3d ⁷. Examining the influence of the composition of the eigenvectors on the hfs parameters \(\left\langle {r^{ - 3} } \right\rangle ^{k_s k_l } \) it was found, that for the configuration 3d ⁶4s the two-body magnetic interaction should be considered in the calculation of the eigenvectors. Investigating second order electrostatic configuration interactions and relativistic effects and using calculated relativistic correction factors we obtained for the nuclear quadrupole moment of the nucleus⁵⁵Mn a value ofQ=0.33(1) barn, which is not perturbed by a shielding or antishielding Sternheimer factor. The following hfs constants have been obtained: $$\begin{gathered} A\left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 882.056\left( {12} \right)MHz \hfill \\ A\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 469.391\left( 7 \right)MHzB\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 65.091\left( {50} \right)MHz \hfill \\ A\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 436.715\left( 3 \right)MHzB\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 46.769\left( {30} \right)MHz \hfill \\ A\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 458.930\left( 3 \right)MHzB\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 21.701\left( {40} \right)MHz \hfill \\ A\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 510.308\left( 8 \right)MHzB\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 132.200\left( {120} \right)MHz \hfill \\ \end{gathered} $$      

Localization for a Random Walk in Slowly Decreasing Random Potential

We consider a continuous time random walk X in a random environment on ?⁺ such that its potential can be approximated by the function V:?⁺→? given by $V(x)=\sigma W(x) -\frac {b}{1-\alpha}x^{1-\alpha}$ where σW a Brownian motion with diffusion coefficient σ>0 and parameters b, α are such that b>0 and 0<α<1/2. We show that P-a.s. (where P is the averaged law) $\lim_{t\to\infty} \frac{X_{t}}{(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}}=1$ with $C^{*}=\frac{2\alpha b}{\sigma^{2}(1-2\alpha)}$ . In fact, we prove that by showing that there is a trap located around $(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}$ (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the “pure” Sinai’s regime, where the location of this trap is random on the scale ln² t.     

Integrable structure of conformal field theory,quantum KdV theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight Virasoro modules. TheT-operators depend on the spectral parameter λ and their expansion around λ=∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. TheT-operators can be viewed as the continuous field theory versions of the commuting transfermatrices of integrable lattice theory. In particular, we show that for the values $c = 1 - 3\frac{{3(2n + 1)^2 }}{{2n + 3}}$ ,n=1,2,3 .... of the Virasoro central charge the eigenvalues of theT-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of the massless Thermodynamic Bethe Ansatz for the minimal conformal field theoryM _2,2n+3; in general they provide a way to generalize the technique of the Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator Φ_1,3. The relation of theseT-operators to the boundary states is also briefly described.     

Hyperfine structure investigations of some odd levels of Co I by level crossing and optical methods

Using the level crossing technique the ratios and absolute values of the hyperfine structure (hfs) constants of the levelsz ⁴F_9/2 andz ⁴F_7/2 of the configuration 3d ⁷4s4p of Co I were measured:z ⁴ F _9/2: ¦A¦=(811±12)MHz; ¦B¦=(48±93) MHz;B/A=?0.06±0.11 A>0; B<0z ⁴ F _7/2: ¦A¦ = (659 ±11)MHz; ¦B¦=(33±84)MHz;B/A=?0.05±0.13 A>0; B<0. In addition the hfs constants of three other excited levels of Co I could be determined by optical methods:z ⁴ F _9/2:A=525±26 MHz;B=200 MHzy ⁴ F _9/2:A=300±30 MHz;B=?500 MHzy ⁴ G _11/2:A=315±20 MHz;B=400 MHz. The experimental results are compared with known experimental and also with theoretical values which where calculated using the parametric potential method.     

On the field dependence of random walks in the presence of random fields

Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or ?E. The probability density¯P(x, t) is found to scale asymptotically as $$\left\{ {[A(E)]^{\beta /2} /\ln ^2 t} \right\}\exp \left( { - \left\{ {x[A(E)]^{\beta /2} /\ln ^2 t} \right\}^\alpha } \right)$$ withA(E)=ln[(1+E)/(1-E)],β=4.25, and α=1.25. The mean square displacement scales as \(\langle x^2 \rangle \sim [A(E)]^{ - \beta } F[tA^\beta (E)]\) , where F(u)～ln⁴ u asymptotically.     

Nuclear physics with a medium-energy Electron-Ion Collider

Level structures of ¹¹³In have been studied through the fusion-evaporation reaction ¹¹⁰Pd (⁷Li ,4n ¹¹³In at a beam energy of 50MeV. More than 40 new $ \gamma$ transitions have been observed in ¹¹³In . Two new dipole bands are established and one of them is proposed as a magnetic rotation band with the configuration of $\ensuremath \pi g_{9/2}^{-1}\otimes\nu h_{11/2}^{2} g_{7/2}^{2}$ . Self-consistent tilted axis cranking relativistic mean field calculations have been performed to interpret the rotational structure. Several decay paths of the $\ensuremath \pi h_{11/2}$ intruder band have been established, by which the level energies and spins of the $\ensuremath \pi h_{11/2}$ intruder band are determined.     

Aging effect in CaLaBa{Cu1???xFex}3O7???�� with 0 �� x �� 0.07 studied by M?ssbauer spectroscopy

In this work, we study the long-term aging effect caused by Fe atoms in the superconductor CaLaBa{Cu_1???xFe_x}₃O_7????? with 0 ?? x ?? 0.07. XRD confirms that this system has a YBCO-like structure. The critical temperature (T_c) is strongly affected by aging and depends on the amount of Fe in the structure. Room temperature Mössbauer spectroscopy reveals the presence of the typical species A, B?CB ??, C and new species E ?? and F. Interestingly; A, which corresponds to the Fe^3?+? atom located in the Cu(1) of the chains with spin S _z = 3/2, shows a drastic reduction which means migration to the species B, B ?? and C. Species B and B ?? correspond to the Fe^3?+? in the Cu(2) site forming planar quasi-octahedral and planar square pyramidal, while the C specie is a square pyramidal with O(5) respectively (spin S_z = 3/2 in all these cases). Aging causes loss of superconductivity in the samples with 5 and 7% of iron content.