Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Functional sample path properties of subsequence's C-R increments for a Wiener process in Hlder norm

In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by H¨older norm, we discuss the functional sample path properties of subsequence's C-R increments for a Wiener process in H¨older normThe obtained results,generalize the corresponding results of Chen and the classic Strassen's law of iterated logarithm for a Wiener process.     

Tuning of Photonic band gap via combined effect of electric and optical fields in a blue phase liquid crystal composite

ABSTRACT

Blue phase liquid crystals are soft 3D photonic crystals in which the liquid crystal molecules self-assemble to form a cubic structure with lattice spacing of a few hundred nanometers resulting in selective reflection of colours in the visible spectrum. The corresponding wavelength or the ‘photonic band gap’ can be tuned using various external stimuli such as thermal, electric, magnetic and optical fields. Here, we report efficient tuning of photonic band gap by utilising the combination of electric and optical fields in a blue phase liquid crystalline system. The studies indicate that the chirality of the medium has a direct bearing on the direction of the wavelength shift and the extent of the photonic band gap tunability. More importantly, the synergistic effect of the two fields helps in reversible tuning of the band gap.     

Central Sets Theorem along filters and some combinatorial consequences

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions and extensions of this theorem. All of these theorems deal with central sets, and its origin from the algebra of Stone–?ech compactification of arbitrary semigroup, say $\beta S$. It can be proved that every closed subsemigroup of $\beta S$ is generated by a filter. We will show that, under some restrictions, one can derive the Central Sets Theorem for any closed subsemigroup of $\beta S$. We will derive this theorem using the corresponding filter and its algebra. Later we will also deal with how the notions of largeness along filters are preserved under some well behaved homomorphisms and give some consequences.     

Functional analysis of repositioned anilide derivatives as anticancer compounds

Off the different types cancers 40% of the population have been observed to be affected by leukemia. Contemporary therapeutics is focusing on generation of new synthetic analogues that can exert maximum positive physiological effect with minimum dosage and negligible deleterious side effects. New generation pharmacists are focusing on such promising effects of Imatinib (a potential anti-cancer drug molecule), Dasatinib, Pelitinib and Nilotinib. The present research study focuses on novel synthesized anilides derivative against BCR-ABL kinase as potential anti-leukemic agent. Validation of the compounds by molecular docking with specific BCR-ABL kinase confirmed their activity. Toxicity prediction of these compounds helped to identify sustainability as therapeutic molecules. The IC₅₀ values were calculated (211 ug, 175 ug, 272ug for compounds A, B, C resp.) and the mode of cell death was gauged by DNA laddering assay. The cells were observed to be induced for programmed cell death. By validating and in-vivo testing of three synthesized compounds, the compound B was observed to be more stable thermodynamically with a potentially vital active site and appears to be a promising anti-leukemic factor. The present research thus lays a preliminary platform in world of pharmaceutics, where these new analogues appear to be efficient, target specific and less toxic molecules.     

Analysis of the interaction between the ? meson and nucleus

In this study, we systematically investigate the ? meson and nucleus interaction by analyzing and fitting the cross sections of \begin{document}$ \gamma N $\end{document}\begin{document}$ \rightarrow \phi $\end{document}N reactions near the threshold, where N represents the nucleus. Using the vector meson dominant model, the distribution of the ?-N scattering length is presented as a function of energy, and the results show that there is a slight increase in scattering length with increasing energy. Based on this, the average scattering length of a ?-proton is obtained as\begin{document}$ 0.10\pm0.01 $\end{document} fm by combining experimental data and theoretical models. Moreover, the average scattering length of the ?-deuteron interaction is derived to be \begin{document}$ 0.014\pm0.002 $\end{document} fm for the first time. Furthermore, the effect of the momentum transfer \begin{document}$|t_{{\rm min}}|$\end{document} on the ?-N scattering length at the threshold is discussed. The obtained results not only provide important theoretical information for a more comprehensive and accurate study of the ?-N scattering length, but also a basis for future experimental measurements of ? meson production.     

三维钴基MOF[KCo7(OH)3(ip)6(H2O)4]·12H2O作为超级电容器的高容量电极材料

为了开发较高能量密度的超级电容器,我们通过简单的溶剂热反应合成了一种三维的钴基金属有机框架(MOF)化合物([KCo7(OH)3(ip)6(H2O)4]·12H2O,Co?ip;ip=间苯二甲酸根),并考察了其作为超级电容器电极材料的性能。Co?ip电极显示出高比电容、良好的循环稳定性和优良的倍率性能。在1 mol·L^-1 KOH溶液中,电流密度为1 A·g^-1时,其最大比电容为1660 F·g^-1。在电流密度为2 A·g^-1条件下,循环3000次后,其比电容的保持率为82.7%。优异的超级电容性能可归因于Co?ip具有纳米尺寸颗粒和三维的多孔结构。     

吡啶-2-甲醛酰腙镉配合物的合成、晶体结构与荧光性质

合成了3个不同结构的吡啶?2?甲醛缩对氯苯氧乙酰腙(HL)与镉的配合物。通过X射线单晶衍射、红外光谱、紫外光谱、荧光光谱以及热重等分析,对其进行晶体结构和性质的研究。单晶衍射结构解析表明:配合物1属单斜晶系,C2/c空间群,是一个通过氯离子桥联的二聚体,分子式为[Cd(HL)Cl2]2;配合物2属单斜晶系,P21/c空间群,是一个含2个有机配体、蝴蝶状的单核分子,其分子式为[Cd(HL)2Br2];配合物3属三斜晶系,P1空间群,配合物中只含有一个有机配体,其分子式为[Cd(HL)I2]。固体荧光分析表明:配体和配合物均有很强的荧光性,且发绿光。