Synthesis,Aggregation Induced Emission and Mechanochromic Luminescence of New <Emphasis Type="Italic">β</Emphasis>-Diketone Derivatives Bearing Tetraphenylene Moieties

A series of β-diketone derivatives bearing tetraphenylene (TPE) moieties were synthesized and characterized. Their photophysical properties were investigated systematically via spectroscopic and theoretical methods. All compounds exhibit broad absorption bands between 300 and 450 nm, which are assigned to the ¹π-π* transition of the conjugated system mixed intramolecular charge-transfer (ICT) transitions. Meanwhile, the emission of these compounds in solution at room temperature (λ _em = 458 ~ 509 nm) can be attributed to the ¹π,π*/¹ICT state. Introduction of freely rotatable TPE to conventional β-diketone luminophors quenches their light emissions in the solutions, but endows these molecules with aggregation-induced emission (AIE) characteristics in the condensed phase due to the restriction of intramolecular rotation. The spectroscopic studies and theoretical calculations indicate that the photophysical properties of these β-diketone derivatives can be tuned by the appended substituents, which would be useful for rational design of AIE compounds with high solid state luminescence performance. Furthermore, these AIE-active compounds exhibited distinct piezofluorochromic properties and switched reversibly upon grinding-fuming. Their photophysical properties have been investigated with the aim to provide a basis for elucidating the structure-property correlations and developing new multi-stimuli responsive luminescent materials.     

Inverse Scattering at Fixed Energy on Surfaces with Euclidean Ends

On a fixed Riemann surface (M ₀, g ₀) with N Euclidean ends and genus g, we show that, under a topological condition, the scattering matrix S _V (λ) at frequency λ > 0 for the operator Δ+V determines the potential V if \({V\in C^{1,\alpha}(M_0)\cap e^{-\gamma d(\cdot,z_0)^j}L^\infty(M_0)}\) for all γ > 0 and for some \({j\in\{1,2\}}\) , where d(z, z ₀) denotes the distance from z to a fixed point \({z_0\in M_0}\) . The topological condition is given by \({N\geq \max(2g+1,2)}\) for j = 1 and by N ≥ g + 1 if j = 2. In \({\mathbb {R}^2}\) this implies that the operator S _V (λ) determines any C ^{1, α} potential V such that \({V(z)=O(e^{-\gamma|z|^2})}\) for all γ > 0.     

A Variable Temperature X- and W-Band EPR Study of Fe-Doped SiCN Ceramics Annealed at 1000, 1100, and 1285 °C: Dangling Bonds,Ferromagnetism and Superparamagnetism

Polymer-derived SiCN ceramics, annealed (also referred to as pyrolyzed) at 1000, 1100, and 1285 °C, and doped with Fe(III) acetylacetonate, are investigated by electron paramagnetic resonance (EPR) from 4 to 120 K at X-band (9.425 GHz). In addition, the SiCN ceramic, annealed at 1100 °C, was studied by EPR at 300 K at W-band (93.96 GHz). There was observed a significant increase in EPR linewidth due to dangling bonds (g = 2.001) below 20 K at X-band. The low-field X-band FMR line (g ≈ 12) indicated the presence of ferromagnetic Fe₅Si₃ crystallites. There were found two EPR lines due to carbon-related dangling bonds: (1) those present as defects on the surface of the free-carbon phase (as sp² carbon-related dangling bonds with g = 2.0011) and (2) those present within the bulk of carbon phase (as sp³ carbon-related dangling bonds with g = 2.0033). On the other hand, the intense low-field EPR signal observed at X-band was not observed at W-band. As well, there was observed splitting of the single broad EPR signal observed at g = 2.05 at X-band into two signals at W-band at g = 1.99 and g = 2.06, due to two different Fe-containing superparamagnetic nanocrystallites. Two new EPR signals, not observed at X-band, were observed at W-band, namely at g = 2.28 and g = 3.00, which are also due to g_∥ of these superparamagnetic nanocrystallites.     

Ferrimagnetic nanoparticles for self-controlled magnetic hyperthermia

Based on the Heisenberg model including single-site uniaxial anisotropy and using aGreen’s function technique we studied the influence of size and composition effects on theCurie temperature T _C , saturationmagnetization M _S and coercivityH _C of spherical nanoparticles with astructural formulaM e _1?x Zn _x Fe₂O₄,Me = Ni, Cu, Co, Mn. It is shown that for x = 0.4–0.5and d = 10–20 nm these nanoparticles have aT _C  = 315 K and are suitable for aself-controlled magnetic hyperthermia.     

On the Negative Spectrum of the Two-Dimensional Schrödinger Operator with Radial Potential

For a two-dimensional Schrödinger operator H _{α V}  = ?Δ ?αV with the radial potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N _?(H _{α V} ) of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth N _?(H _{α V} ) = O(α) and for the validity of the Weyl asymptotic law.     

Variable Temperature Single Crystal EPR Studies of Cu(II) in Dipotassium Diaquabis(Malonato-<Emphasis Type="Italic">κ</Emphasis><Superscript>2</Superscript><Emphasis Type="Italic">O,O</Emphasis>′) Nickelate Dihydrate: An Example of Contaminated Ground State

Single crystal X-band electron paramagnetic resonance (EPR) studies on divalent copper ions embedded in dipotassium diaquabis(malonato-κ ² O,O′) nickelate dihydrate have been performed at 300, 123 and 77 K to understand the nature of Jahn–Teller distortion in the paramagnetic host lattice. The angular variation of the EPR spectra reveals the presence of two sites, with one site not showing hyperfine resolution even at 77 K. The spin-Hamiltonian parameters of this six-coordinated Cu(II) ion, evaluated from EPR spectra at various temperatures, are:

• 300 K: g ₁₁ = 2.125, g ₂₂ = 2.118, g ₃₃ = 2.290, no copper hyperfine resolution
• 123 K: g ₁₁ = 2.229, g ₂₂ = 2.113, g ₃₃ = 2.319 and A ₁₁ = 5.02, A ₂₂ = 3.82, A ₃₃ = 6.87 mT
• 77 K: g ₁₁ = 2.224, g ₂₂ = 2.114, g ₃₃ = 2.324 and A ₁₁ = 5.32, A ₂₂ = 3.90, A ₃₃ = 7.06 mT

respectively. The low value observed for A ₃₃ at 123 and 77 K has been explained by assuming a ground state \({\text{d}}_{{x^{2} - y^{2} }}\) wave function for Cu(II) ions, contaminated with the excited state \({\text{d}}_{{z^{2} }}\). From the temperature dependence of the EPR spectra, the Cu(II) ions can be considered as a static Jahn–Teller system, with contaminated ground state. The admixture coefficients and bonding parameters have also been calculated by combining EPR and optical data. The EPR spectrum of powder sample confirms single crystal data.

     

Das Kernquadrupolmoment des Mn55

With a recording photoelectric Fabry-Perot spectrometer and an atomic-beam light source the hyperfine structure of the Mn I-resonance linesλ=4031 Å,λ=4033 Å,λ=4034 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁶ P _7/2,5/2,3/2 ⁰)and of the inter-combination linesλ=5395 Å andλ=5433 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁸ P _7/2,5/2 ⁰) was measured. Furthermore the resonance lines have been measured with a pulsed atomic-beam in absorption. In this case the quotient (I ₀(ν)?I(ν))/I ₀(ν) was recorded, whereI(ν)=I ₀(ν) exp(?α(ν)d) is the observed intensity with absorption andI ₀(ν) the intensity of the light source. From the hyperfine structure splitting the value of the electric quadrupole moment of Mn⁵⁵ was derived to be:Q(Mn⁵⁵)=+(0.35±0.05)·10^?24 cm².     

Der Zerfall des 1,5 min-Isomers Co54m

Co^54m (T _1/2=1.43 min) was produced in iron-foils by irradiation with_dE=19 MeV deuterons. The gamma ray spectrum was investigated using a NaJ(Tl) scintillation spectrometer, a coincidence circuit and a Ge(Li)-counter. There were observed three gamma rays having the following energies and intensities per Co_54m decay: 411 keV (0.97±0.07), 1130keV (0.98±0.05), 1407 keV (1.00±0.05). The directional correlation between the pairs of gamma rays were determined. These results correspond to spin and parityJ _π=2⁺ for the 1407 keV,J _π=4⁺ for the 2537 keV, andJ _π=6⁺ for the 2948 keV energy level of Fe⁵⁴. The last-mentioned level was not excited in previous scattering experiments. Our results are compatible withE=210keV andJ _π=6⁺ or 7⁺ of the isomeric state of Co^54m .     

The formation of the superheavy hydrogen isotope <Superscript>6</Superscript>H in the absorption of stopped π<Superscript>−</Superscript>-mesons by nuclei

An experimental search for the superheavy hydrogen isotope ⁶H was conducted through studying the absorption of stopped π^?-mesons by ⁹Be and ¹¹B nuclei. A structure in the missing mass spectrum caused by the resonance states of ⁶H was observed in three reaction channels, namely, ⁹Be(π^?, pd)X, ¹¹B(π^?, d³He)X, and ¹¹B(π^?, p⁴He)X. The parameters of the lowest state E_r=6.6±0.7 MeV and Γ=5.5±2.0 MeV (E_r is the resonance energy with respect to the disintegration into the triton and three neutrons) are evidence that ⁶H is a more weakly bound system than ⁴H and ⁵H. Three excited states of ⁶H were observed. Their resonance levels (E_1r=10.7±0.7 MeV, Γ_1r=4±2 MeV, E_2r=15.3±0.7 MeV, Γ _2r=3±2 MeV, and E_3r=21.3±0.4 MeV, Γ_3r=3.5±1.0 MeV) are energetically capable of disintegrating into six free nucleons.     

Absorbing phase transition in energy exchange models

We study energy exchange models with dissipation (λ) and noise (of amplitude σ) and show that in presence of a threshold these models undergo an absorbing phase transition when either dissipation or noise strength or both are varied. Using Monte Carlo simulations we find that the behaviour along the critical line, which separates the active phase from the absorbing one, belongs to directed percolation (DP) universality class. We claim that the conserved version with λ = 1 and σ = 0 also shows a DP transition; the apparent non-DP behaviour observed earlier is an artifact of undershooting in the decay of activity density starting from a random initial condition.     

Photoionization of the Xe atom and Xe@C<Subscript>60</Subscript> molecule

Photoionization of the Xe atom and Xe@C₆₀ molecule have been studied usingthe random phase approximation with exchange (RPAE) method. The Xe atom was described byrelaxed orbitals including overlap integrals. The C₆₀ fullerene has beenrepresented by an attractive short range spherical well with potentialV(r), given byV(r) =  ?V ₀ forr _i  < r < r _o ,otherwise V(r) = 0 wherer _i andr _o are respectively, the inner and outerradii of the spherical shell. The time independent Schrödinger equation was solved usingboth regular and irregular solutions and the continuous boundary conditions atr _i andr _o . The results demonstrate improvementto previous calculations for both the Xe atom and Xe@C₆₀ molecule and comparevery well with the recent experimental data.     

Correlation between structural and giant magnetoresistance properties of Fe–Ag nanogranular films

Fe _x Ag_1?x granular thin-films, with the atomic Fe concentration, x, ranging from 0 up to 0.5, were deposited by dc magnetron co-sputtering. The giant magnetoresistance (GMR) intensity is maximum at x _I  = 0.32, while the maximum of GMR efficiency, γ, i.e., the change of GMR intensity for a unit change of reduced squared magnetization, is observed at x _γ = 0.26. Owing to the spin-dependent scattering features, the GMR intensity and γ depend on both the concentration and the arrangement of the magnetic material. Therefore, to explain the difference between x _I and x _γ and to understand how the structural properties affect the magnetoresistive behaviour, we performed magnetization, Mössbauer and X-ray diffraction measurements as a function of x. X-ray data indicate that the granular films exhibit three different regimes: for x < 0.2, they can be described as a Fe–Ag solid solution; for 0.2 < x < 0.32 the Fe–Ag solid solution is still observed and very small Fe precipitates are found; finally, for x > 0.32, a Fe–Ag saturated solid solution is detected, containing bcc Fe clusters whose size is about 10 nm. Differently, for all the concentrations, magnetization data show the presence of Fe precipitates, whose size increases with x, and the Mössbauer investigation confirms this picture. We find that the samples grown at x = x _γ display the finest Fe dispersion within the Ag matrix, as the Fe–Ag solid solution is nearly at saturation and the Fe cluster size is of the order of a few nanometers; this arrangement possibly maximizes the magnetic/non-magnetic interface extension thus enhancing the GMR efficiency. If x is slightly increased, the increase in total Fe content compensates the GMR efficiency reduction, so the GMR intensity maximum is observed.     

The Boundary Control Approach to the Titchmarsh-Weyl <Emphasis Type="Italic">m</Emphasis>–Function. I. The Response Operator and the <Emphasis Type="Italic">A</Emphasis>–Amplitude

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A?amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m?function associated with the Schrödinger operator H = ?? _x ²  + q(x) on L ₂(0, ∞) with Dirichlet boundary condition at x = 0.     

A Liouville-type Theorem for Schrödinger Operators

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P ₁, such that a nonzero subsolution of a symmetric nonnegative operator P ₀ is a ground state. Particularly, if P _j : = ?Δ + V _j , for j = 0,1, are two nonnegative Schrödinger operators defined on \(\Omega\subseteq \mathbb{R}^d\) such that P ₁ is critical in Ω with a ground state φ, the function \(\psi\nleq 0\) is a subsolution of the equation P ₀ u = 0 in Ω and satisfies \(\psi_+\leq C\varphi\) in Ω, then P ₀ is critical in Ω and \(\psi\) is its ground state. In particular, \(\psi\) is (up to a multiplicative constant) the unique positive supersolution of the equation P ₀ u = 0 in Ω. Similar results hold for general symmetric operators, and also on Riemannian manifolds.     

Solutions of a Particle with Fractional <Emphasis Type="Italic">δ</Emphasis>-Potential in a Fractional Dimensional Space

A Fourier transformation in a fractional dimensional space of order λ (0<λ≤1) is defined to solve the Schrödinger equation with Riesz fractional derivatives of order α. This new method is applied for a particle in a fractional δ-potential well defined by V(x)=?γ δ ^λ (x), where γ>0  and δ ^λ (x) is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if 0<λ<α. The results for λ=1 and α=2 are in exact agreement with those presented in the standard quantum mechanics.     

Using a chiral anomaly to determine the number of colors

The N_c dependence of PPPγ vertices, where P is a pseudoscalar meson and N_c is the number of colors, is analyzed with allowance for the N_c dependence of the quark charges. It is shown that the reactions Kγ → Kπ and π^±γ → π^±η and the decay η → π⁺π^?γ are the best processes for determining N_c. The cross section σ(π^?γ → π^?η) as measured by using the VES facility at IHEP agrees with the value of N_c=3.     

Komar energy and Smarr formula for noncommutative inspired Schwarzschild black hole

We calculate the Komar energy E for a noncommutative inspired Schwarzschild black hole. A deformation from the conventional identity E = 2ST _H is found in the next to leading order computation in the noncommutative parameter θ (i.e. \({\mathcal{O}(\sqrt{\theta}e^{-M^2/\theta})}\)) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point T _H  = 0 of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result M = 2ST _H , where the mass (M) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter–Schwarzschild geometry.     

Derg R -Faktor des 2+-Rotationsniveaus von Er168

The rotation of the angular correlation between theγ-group at about 820 keV and the 80 keV radiation in the decay of Tm¹⁶⁸ has been observed in an external magnetic field of 20300 gauss. The result:ω _R·τ=0,485±0,051 yields for theg _R -factor of the 80 keV state of Er¹⁶⁸:g _R =+0,25±0,03. The evaluation includes a paramagnetic correction factor of:β=7,26, (B _eff=β·B _ext). The angular correlation is slightly attenuated by internal fields. For a liquid source of Tm (NO₃)₃ solved in 3 n HNO₃, a measurement of the differential angular correlation as a function of the delay time gave:λ ₂=(5,8±2,9)·10⁷sec^?1, assumingA ₂(t)=A ₂(0)·e ^?λ ₂·t. The half life of the 80 keV state was found to be:T _1/2=(1,92±0,04)·10^?9sec in agreement with earlier measurements.     

Paramagnetische Relaxation von CeCl3

The paramagnetic relaxation in CeCl₃ was investigated in the temperature interval between 1.07°K and 4.21°K using a mutual inductance bridge at frequencies between 3 Hz and 3200 Hz. The dependence of the complex susceptibility on temperature below theλ point is given by a Debye function. Above this temperature, however, deviations occur. The temperature dependence of the relaxation time forT<T _λ can be described byτ～T ^?n where 1.82≦n≦2.35 for 470 Oe≦H≦3360 Oe. At the highest temperatures Orbach Processes occur over the first excited crystal field component which according to these measurements lies atE _II=k(56±10)°K. In the entire temperature range the relaxation processes are determined by further relaxation mechanisms in addition to the spin lattice relaxation. The nature of these could not, however, be determined.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.