On extension and refinement of the Poincaré inequality

The aim of this paper is to analyze the heat semigroup ${(\mathcal{N}_{t})_{t >0 } = \{e^{t \Delta}\}_{t >0 }}$ generated by the usual Laplacian operator Δ on ${\mathbb{R}^{d}}$ equipped with the d-dimensional Lebesgue measure. We obtain and study, via a method involving some semigroup techniques, a large family of functional inequalities that does not exist in the literature and with the local Poincaré and reverse local Poincaré inequalities as particular cases. As a consequence, we establish in parallel a new functional and integral inequality related to the Ornstein–Uhlenbeck semigroup.     

再散射输运模型与K+/π+比的系统学

用含再散射效应的简单的强子输运模型,研究了AGS能量(14.6AGeV/c)下p+p、p+Au和Si+Au反应的K⁺/π⁺比值,再现了该比值由P十P到Si十Au不断增长的实验事实.CERN能量(200AGeV/c)和AGS能量下,K⁺/π⁺比值相近的实验事实也得到了解释.     

An effective method for the reduction of the device utilization amount in experimental realization of a fractional-order system

This study focuses on the experimental realization of the fractional-order FitzHugh–Nagumo (FHN) neuron model. Firstly, a second-order approximation function is included to the FHN neuron model to satisfy the fractional-order definition. Since these approximation functions can meet the response of the ideal system only in a limited frequency band, the identification of their center frequency is very critical. Thus, the center frequency ‘ω_c’ of this second-order approximation functions is swept until getting the spiking responses of this neuron model for the first time in this study. After the center frequency is determined, this approximation function is transferred into the ‘z’ domain by employing the Tustin discretization operator. This achieved discrete defined and fractional-order FHN neuron model becomes suitable for implementation on the digital platforms. To verify the proficiency of the proposed sweeping process experimentally, the fractional-order FHN model in ‘z’ domain is implemented on the FPGA platform. After these applications, the order of the approximation function is reduced to one. Once this followed frequency sweeping process is repeated for the first-order approximation, the fractional-order FHN neuron model, which is built by this least-order approximation function, is also implemented with the FPGA. Therefore, the reductions of the device utilization amounts by using this least-order approximation function and the importance of the specific frequency identification process are seen clearly.

     

Synthesis, structure and magnetic properties of two new azido-Co(II) coordination architectures: from ferromagnetic coupling to single-chain-magnets

Two new azido-Co(II) complexes with pyrazine carboxylato ligands, [Co(N(3))(L)·H(2)O](n) (L = pyrazine-2-carboxylato) (1) and [CoNa(N(3))(2)(L)](n) (2), have been obtained by carefully tuning the Co(II):N(3)(-) ratio. Here we present the structural and magnetic characterization of these new species. Modulation of the coordination environment of Co(II) leads to a variation of the magnetic properties of the obtained compounds. Complex 1 exhibits ferromagnetically coupled [Co(2)] units that form the rungs of the ladder with a nearly negligible coupling between these units, while complex 2 is a 2D arrangement of 1D Co(II) single-chain magnets.     

A Density Functional Theory Study on Electronic Structure and Second—order Nonlinear Optical Properties of Some Push—Pull Molecules

Time-dependent density-functional theory(TDDFT)has been applied to calculate the electronic structure and second-order nonlinear optical(NLO) properties of some organic molecules.The two-dimensional(2-D)charge transfer charateristics of calculated molecules were studied and compared with corresponding experimental results.All the theoretical results agree well with the measurement.For 2-D molecule with two-fold symmetry,the dominant charge transfer is off-diagonal,while for three-fold symmetry 2-D molecule,the dominant charge transfer is not only between branches and central group but also among branches.     

Three lanthanide complexes with mixed salicylate and 1,10-phenanthroline: syntheses,crystal structures,and luminescent/magnetic properties

Three new lanthanide complexes incorporating salicylate (HSA or SA) and 1,10-phenanthroline (phen), Ln₃(HSA)₅(SA)₂(phen)₃ [Ln = Ho (1) and Er (2)], and Sm₂(HSA)₂(SA)₂(phen)₃ (3), have been synthesized. X-ray structural analysis reveals that 1 and 2 are isostructural with a trinuclear pattern, and 3 exhibits a binuclear structure. Comparison of the structural differences between 1/2 and 3 suggests that the identity of metal plays an important role in construction of such complexes. The magnetic properties of 1 are discussed. Moreover, 2 and 3 are both photoluminescent materials, and their emission properties are closely related to their corresponding Ln^III centers.     

Two manganese(II) complexes based on anthracene-9-carboxylate: Syntheses,crystal structures,and magnetic properties

Abstract  To explore the influence of the anthracene ring skeleton, with a large conjugated π-system, on the structures and properties of its complexes, two Mn^II complexes with anthracene-9-carboxylate ligand were synthesized and structurally characterized: {[Mn(L)₂(H₂O)₂](H₂O)}_∞ (1) and [Mn₂(L)₄(phen)₂(μ-H₂O)](CH₃OH) (2) (L = anthracene-9-carboxylate and phen = 1,10-phenanthroline). Complex (1) has a one-dimensional (1D) chain structure that is further assembled to form a two-dimensional (2D) sheet, and then an overall three-dimensional (3D) network by π···π stacking and/or C–H···π interactions. Complex (2) makes a dinuclear structure by incorporating the chelating phen ligand, which is further interlinked via inter-molecular π···π stacking and C–H···π interactions to generate a higher-dimensional supramolecular network along the different crystallographic directions. The results reveal that the bulky anthracene ring skeleton in L, by virtue of intra- and/or inter-molecular π···π stacking and C–H···π interactions, plays an important role in the formation of complexes (1) and (2). The magnetic properties of (1) and (2) were further investigated. As expected, the very long inter-metallic separations result in weak magnetic coupling, with the corresponding coupling constant values of J = −10 cm⁻¹ for (1) and J = −2.46 cm⁻¹ for (2). Graphical abstract  The constructions of two new Mn^II complexes comprising 1D chain (1) and dinuclear subunit (2) structures have been successfully achieved by using a bulky anthracene-9-carboxylic acid (HL), together with incorporating the chelating 1,10-phenanthroline as a co-ligand for (2). The result reveals that the bulky anthracene ring skeleton of HL, by virtue of intra- and/or inter-molecular π···π stacking and C–H···π interactions, plays an important role in the formation of the supramolecular architectures of (1) and (2). Moreover, magnetic properties of the complexes have been investigated.      

一个各向异性磁稀释杂化钙钛矿系列[CH3NH3][CoxZn1-x(HCOO)3]

Inorganic-organic or hybrid perovskite materials, which are the complementary counterparts of pure inorganic perovskites, can provide many new opportunities in the researches of phase transitions, critical phenomena, and relevant properties, as they combine the characteristics of inorganic and organic components. Therefore, the hybrid perovskites of ammonium metal formate framework are very promising, and their properties have been found to be strongly dependent on the characteristics of the constituent metal ions and/or ammonium ions. Herein, we used solid solution strategies, borrowed from solid state chemistry, to investigate the anisotropic diluted magnetic hybrid perovskite system of [CH₃NH₃][Co_xZn_1-x(HCOO)₃], wherein the B-sites are occupied by the mixed metal ions of Co²⁺ and Zn²⁺. The solid solution compounds of this series in the range x = 0–1 (or the molar percent Co% = 0–100%) were successfully prepared using conventional solution chemistry methods. The resulting compounds were demonstrated to be iso-structural by using both single-crystal and powder X-ray diffraction analyses. The solid solution crystals belong to the orthorhombic space group Pnma, with the cell parameters being a = 8.3015(2)–8.3207(3) Å, b = 11.6574(4)–11.6811(5) Å, c = 8.1315(3)–8.1427(4) Å, and V = 787.89(5)–790.98(7) ų. The perovskite structure consists of a simple cubic anionic metal-formate framework and CH₃NH₃⁺ cations which are located in the framework cavities, with N―H···O hydrogen bonds formed between the framework and the cation. The members of this series showed negligible changes (< 0.4%) in their respective lattice and structural parameters. Thus, the prepared solid solution compounds constitute good molecule-based examples for the study of magnetic dilution under almost the same structural parameters and molecular geometries. Upon dilution, the magnetization per mole of Co at low temperatures and low fields was suppressed by the magnetic anisotropy of Co²⁺ and gradual destruction of the large spin canting between coupled Co²⁺ ions, in contrast to the magnetization enhancement observed in the isotropic diluted system of [CH₃NH₃][Mn_xZn_1-x(HCOO)₃] with the same perovskite structure. The percolation limit was estimated as (Co%)_P = 27(1)% (or x_P = 0.27(1)) from the magnetic data, which was slightly lower than that predicted by the percolation theory for a simple cubic lattice (31%); this trend was due to the strong magnetic anisotropy of the present system. In addition, rare incommensurate phase transitions were primarily detected below ~120 K for the pure Co and Zn members, which may also affect the magnetic properties of the materials.     

Investigation of neutron emission from relativistic heavy ion interactions by nuclear tracks

Fast neutrons produced in 44 and 22 GeV ¹²C+Cu interactions have been recorded and analysed with a CR-39 detector stack. The irradiation of the CR-39 stack to fast neutrons was carried out at the accelerator Synchrophasotron, Joint Institute for Nuclear Research, Dubna, Russia. Areal and volume densities of tracks induced by fast neutrons in the CR-39 at different positions and for different etching time have been measured. The neutron production ratio of 44 GeV to 22 GeV ¹²C+Cu interactions has been obtained, which is 2.17 ± 0.30 by areal track density, or 2. 12±0.33 by step etch technique, or 2.03±0.34 by volume track density measurement. These results confirm that the production rate at 44 GeV ¹²C+Cu interactions is more than theoretical estimation.