Abstract:
Inthispaper,by introducing a generalized homogeneous kernel and estimating the weight function,a new reverse Hilbert-type integral inequality with some parameters and a best constant factor is established.Furthermore, the corresponding equivalent form is considered.

Abstract:
The asymmetric unit of the title compound, C19H15FN2O2, contains two molecules, A and B, in which the dihedral angles between the ring systems are 46.4 (2) and 17.24 (14)°, respectively. In the crystal, molecules are linked into [010] chains of alternating A and B species by N—H...O hydrogen bonds.

Abstract:
The molecule of the title compound, C19H15BrN2O2, displays a pseudo-trans conformation about the N—N bond [C—N—N=C torsion angle = 164.7 (2)°]. The dihedral angle between the planes of the benzene ring and the naphthyl system is 70.1 (2)°. In the crystal, molecules are linked into C(4) chains along the c axis by N—H...O hydrogen bonds.

Abstract:
In the centrosymmetric binuclear title complex, [Cu2(C13H19N2O)2(N3)2], the CuII atom adopts an elongated CuON4 square-based pyramidal coordination geometry, arising from the N,N′,O-tridentate ligand and two bridging end-on azide anions. The O atom is in the basal plane, one of the azide N atoms is in the apical site and the Cu...Cu separation is 3.2365 (3) . A pair of intramolecular N—H...O hydrogen bonds helps to establish the molecular conformation.

Abstract:
The title molecule, C14H11BrN2O2, displays a trans configuration about the C=N and C—N bonds. The dihedral angle between the two benzene rings is 18.5 (3)°. An intramolecular O—H...N hydrogen bond is observed. In the crystal structure, the molecules are linked into a chain along the c axis by N—H...O and C—H...O hydrogen bonds.

Abstract:
Regarding the self-collision detection efficiency during cloth simulation, this paper presents a quad tree based self-collision detection method. In this paper, we construct a quad bounding box tree for cloth according to the spatial location of its geometric primitives from top to down. And it divides the self-collision detection process into two stages. During the first rough detection stage, with normal cone method and detection of distance between triangle pairs’ centroids, we reduce triangles pairs for accurate elements intersection

Abstract:
Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single photon qutrit in spatial modes. It will make arbitrary unitary operation on such bi-photonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.

Abstract:
We present a scheme to generate two-dimensional cluster state efficiently. The number of the basic gate-entangler-for the operation is in the order of the entanglement bonds of a cluster state, and could be reduced greatly if one uses them repeatedly. The scheme is deterministic and uses few ancilla resources and no quantum memory. It is suitable for large-scale quantum computation and feasible with the current experimental technology.

Abstract:
We present a simple architecture for deterministic quantum circuits operating on single photon qubits. Few resources are necessary to implement two elementary gates and can be recycled for computing with large numbers of qubits. The deterministic realization of some key multi-qubit gates, such as the Fredkin and Toffoli gate, is greatly simplified in this approach.

Abstract:
In view of the recent Fermi observations of GRB prompt emission spectra, we develop a theory of photosphere emission of a hybrid relativistic outflow with a hot fireball component (defined by dimensionless entropy $\eta$) and a cold Poynting-flux component (defined by magnetization $\sigma_0$ at the central engine). We consider the scenarios both without and with sub-photospheric magnetic dissipations. Based on a simplified toy model of jet dynamics, we develop two approaches: a "bottom-up" approach to predict the temperature (for a non-dissipative photosphere) and luminosity of the photosphere emission and its relative brightness for a given pair of $(\eta,\sigma_0)$; and a "top-down" approach to diagnose central engine parameters ($\eta$ and $\sigma_0$) based on the observed quasi-thermal photosphere emission properties. We show that a variety of observed GRB prompt emission spectra with different degrees of photosphere thermal emission can be reproduced by varying $\eta$ and $\sigma_0$ within the non-dissipative photosphere scenario. In order to reproduce the observed spectra, the outflows of most GRBs need to have a significant $\sigma$, both at the central engine, and at the photosphere. The $\sigma$ value at $10^{15}$ cm from the central engine (a possible non-thermal emission site) is usually also greater than unity, so that internal-collision-induced magnetic reconnection and turbulence (ICMART) may be the mechanism to power the non-thermal emission. We apply our top-down approach to GRB 110721A, and find that the temporal evolution behavior of its blackbody component can be well interpreted with a time-varying $(\eta,\sigma_0)$ at the central engine, instead of invoking a varying engine base size $r_0$ as proposed by previous authors.