Extending slow manifold near generic transcritical canard point

We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method.     

一类混合型Szàsz-Beta算子的强逆不等式(英文)

In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤ λ ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.     

Joint remote preparation of an arbitrary three-qubit state via EPR-type pairs

In this work, we propose a scheme to realize a joint remote preparation of an arbitrary three-qubit state using six EPR-type pairs as the shared quantum resource. By determining the right measurement bases for the preparers and right ancilla-assisted unitary transformation/recovery operations for the receiver, our scheme applies to the most general case when all the coefficients of the state to be prepared and the EPR-type pairs are complex. The total success probability is found to be dependent only on the “smaller” coefficients of the EPR-type pairs shared between the receiver and one of the preparers.     

Study of structural stabilities and optical properties of HgTe under high pressure

A theoretical investigation on the structural stabilities and electronic properties of HgTe under high pressure was conducted using first principles based on density functional theory. Our results demonstrate that the sequence of the pressure-induced phase transitions of HgTe is from the zinc blende, to cinnabar, rocksalt, orthorhombic, and CsCl-type structures. The pressure effects on the optical properties were discussed and compared with previous calculations and experimental data whenever available.     

Deep‐Ultraviolet Nonlinear Optics in a Borate Framework with 21‐Ring Channels

A new borate LiBa₃(OH)[B₉O₁₆][B(OH)₄], which combines the uniform porosity of open‐frameworks with the extraordinary NLO properties of borates, has been obtained under hydrothermal conditions by using mixed lithium and barium ions as templates. The framework displays an acs‐type net with large 21‐ring channels. The second harmonic generation (SHG) measurement shows that it is a type I phase‐matchable material with a strong SHG signal intensity about 3.1 times that of KDP (KH₂PO₄). UV/Vis–NIR diffuse reflectance analysis indicates that the compound has a wide transparency range with the short‐wavelength absorption edge below 200 nm. These characteristics reveal that the compound is a promising deep‐UV nonlinear optical material.     

Biological homochirality as result from a single event

The parity-violating effect of the weak force is much too small to be statistically significant for the origin of biological homochirality. Other physical interactions such as with circularly polarized light (CPL) are larger and are discussed in the literature as an effect on small molecules such as amino acids or sugars. To enable their polymerization, they must have existed in large quantities, so that statistical fluctuations may have been smaller than the CPL effect. However, the subsequent formation of the first polymer with good self-reproducing ability was very improbable and may indeed have happened only once. (Such a polymer is isotactic, containing only homochiral constituents.) In this case, the enantiomer excess was 100%, the sign emerging by pure chance without any deterministic influence. The single-event hypothesis can also easily explain why many natural sugars and related compounds (e.g. ascorbic acid) belong exclusively to the l-series, while with others both enantiomers are represented, although Nature uses only d-glucose and d-ribose. It is also pointed out that in the sugar series the sign of physical effects not only varies from species to species but even in the easily equilibrating anomers. It is, however, not excluded that a chemical deterministic effect may have supported the formation of a self-reproducing polymer: enantiomer enrichment by adsorption on a mineral surface.     

Spin-dependent quantum transport through an Aharonov--Bohm structure spin splitter

Using the tight-binding model approximation, this paper investigates theoretically spin-dependent quantum transport through an Aharonov-Bohm （AB） interferometer. An external magnetic field is applied to produce the spinpolarization and spin current. The AB interferometer, acting as a spin splitter, separates the opposite spin polarization current. By adjusting the energy and the direction of the magnetic field, large spin-polarized current can be obtained.     

Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters

This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.     

On pointwise estimate for Gamma operators

For linear combinations of Gamma operators, if 0＜a＜2r, 1/2-1/2r≤λ≤l, or 0≤λ＜1/2-1/2r(r≥2),0＜a＜r+10＜a<(r+1)/1-λ, we obtain an equivalent theorem with ωuλρ(f ,t) instead of ωrλφ(f,t), where ωuφ(f,t) is theDitzian-Totik moduli of smoothness.     

上协边类纤维丛表示的若干性质

本文研究了底空间为实射影空间时上协边类纤维丛表示的若干性质．