Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

Dirac方程的特征函数的迹公式

本文研究具有周期有限带位势的Dirac算子, 利用Dirac算子与单值算子的交换性,定义Bloch函数和乘子曲线, 进而获得揭示Bloch函数与位势间内在关系的Dubrovin-Novikov型公式; 通过复球面上的留数计算, 最终分别得到相应于谱带左端点、右端点以及双侧端点的特征函数的迹公式.     

Dirac reduction for nonholonomic mechanical systems and semidirect products

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange–Dirac and Hamilton–Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler–Poincaré–Suslov equations with advected parameters and the implicit Lie–Poisson–Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin–Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper.     

Synthesis and Neurotropic Activity of New Heterocyclic Systems: Pyridofuro[3,2-d]pyrrolo[1,2-a]pyrimidines,Pyridofuro[3,2-d]pyrido[1,2-a]pyrimidines and Pyridofuro[3′,2′:4,5]pyrimido[1,2-a]azepines

Background: Neurotic disturbances, anxiety, neurosis-like disorders, and stress situations are widespread. Benzodiazepine tranquillizers have been found to be among the most effective antianxiety drugs. The pharmacological action of benzodiazepines is due to their interaction with the supra-molecular membrane GABA-a-benzodiazepine receptor complex, linked to the Cl-ionophore. Benzodiazepines enhance GABA-ergic transmission and this has led to a study of the role of GABA in anxiety. The search for anxiolytics and anticonvulsive agents has involved glutamate-ergic, 5HT-ergic substances and neuropeptides. However, each of these well-known anxiolytics, anticonvulsants and cognition enhancers (nootropics) has repeatedly been reported to have many adverse side effects, therefore there is an urgent need to search for new drugs able to restore damaged cognitive functions without causing significant adverse reactions. Objective: Considering the relevance of epilepsy diffusion in the world, we have addressed our attention to the discovery of new drugs in this field Thus our aim is the synthesis and study of new compounds with antiepileptic (anticonvulsant) and not only, activity. Methods: For the synthesis of compounds classical organic methods were used and developed. For the evaluation of biological activity some anticonvulsant and psychotropic methods were used. Results: As a result of multistep reactions 26 new, five-membered heterocyclic systems were obtained. PASS prediction of anticonvulsant activity was performed for the whole set of the designed molecules and probability to be active Pa values were ranging from 0.275 to 0.43. The studied compounds exhibit protection against pentylenetetrazole (PTZ) seizures, anti-thiosemicarbazides effect as well as some psychotropic effect. The biological assays evidenced that some of the studied compounds showed a high anticonvulsant activity by antagonism with pentylenetetrazole. The toxicity of compounds is low and they do not induce muscle relaxation in the studied doses. According to the study of psychotropic activity it was found that the selected compounds have an activating behavior and anxiolytic effects on the models of “open field” and “elevated plus maze” (EPM). The data obtained indicate the anxiolytic (anti-anxiety) activity of the derivatives of pyrimidines, especially pronounced in compounds 6n, 6b, and 7c. The studied compounds increase the latent time of first immobilization on the model of “forced swimming” (FST) and exhibit some antidepressant effect similarly to diazepam. Docking studies revealed that compound 6k bound tightly in the active site of GABA_A receptor with a value of the scoring function that estimates free energy of binding (ΔG) at −7.95 kcal/mol, while compound 6n showed the best docking score and seems to be dual inhibitor of SERT transporter as well as 5-HT_1A receptor. Conclusions: Тhe selected compounds have an anticonvulsant, activating behavior and anxiolytic effects, at the same time exhibit some antidepressant effect.     

Flavone-Rich Fractions and Extracts from Oroxylum indicum and Their Antibacterial Activities against Clinically Isolated Zoonotic Bacteria and Free Radical Scavenging Effects

Oroxylum indicum extracts from the seeds collected from Lampang and Pattani provinces in Thailand, and young fruits and flowers exhibited in vitro display antioxidant and antibacterial activities against clinically isolated zoonotic bacteria including Staphylococcus intermedius, Streptococcus suis, Pseudomonas aeruginosa, β-hemolytic Escherichia coli and Staphylococcus aureus. The orange crystals and yellow precipitates were obtained from the preparation processes of the seed extracts. The orange-red crystals from the seeds collected from Lampang province exhibited strong in vitro 2,2-diphenyl-1-picrylhydrazyl (DPPH) scavenging effects (EC₅₀ value = 25.99 ± 3.30 μg/mL) and antibacterial effects on S. intermedius and β-hemolytic E. coli while the yellow precipitate from the same source exhibited only antioxidant activity. Quantitative analysis of phytochemicals in O. indicum samples by spectrophotometric and HPLC techniques showed that they contained different amounts of total phenolic, total flavonoid and three major flavones; baicalin, baicalein and chrysin contents. Young fruit extract, which contained low amounts of flavone contents, still promoted antibacterial effects against the tested bacteria with IC₅₀ values lower than 1 mg/mL and MIC values between 4 to 10 mg/mL in S. intermedius, S. aureus and S suis while higher IC₅₀ and MIC values against P. aeruginosa and β-hemolytic E. coli were found. From scanning electron microscopy, the extract of the young fruit of O. indicum promoted morphological changes in the bacterial cells by disrupting the bacterial cell walls, inducing leakage of the cellular content, and generating the abnormal accumulation of cells. The mechanism of action of the extract for this antibacterial effect may be the disruption of the cell membrane and abnormal cell aggregations. Regression analysis of the results suggests the correlation between total phenolic and total flavonoid contents and antioxidant and antibacterial effects. Baicalin was found to have a high correlation with an inhibitory effect against β-hemolytic E. coli while three unidentified peaks, which could be flavones, showed high correlations with an inhibitory effect against S. intermedius, S. suis, P. aeruginosa and S. aureus.     

球形Dirac方程的空间格点求解及假态问题

本文在空间格点上利用虚时间步长方法求解了球形Dirac方程, 着重研究了出现的假态问题. 利用三点数值导数公式离散方程中一阶导数项, 可以证明对于量子数为 κ 和 -κ的单粒子能级能量是完全相同的, 其中一个为物理解, 另一个为假态. 通过在径向Dirac方程中引入Wilson 项, 可以解决假态问题, 得到全部物理解. 文章以 Woods-Saxon 势为例, 考虑 Wilson 项后, 得到与打靶法一致的结果.     

Small Data Scattering for the One-Dimensional Nonlinear Dirac Equation with Power Nonlinearity

We study scattering problems for the one-dimensional nonlinear Dirac equation (?_t + α?_x + iβ)Φ = λ|Φ|^p?1Φ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operators D(t)xD(?t) and t?_x + x?_t ? α/2, where {D(t)}_t∈? is the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties of D(t)xD(?t) and t?_x + x?_t ? α/2.