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.     

Synthesis,X‐ray characterization and density functional theory studies of N6‐benzyl‐N6‐methyladenine–M(II) complexes (M = Zn,Cd): The prominent role of π–π, C–H···π and anion–π interactions

We report the synthesis and X‐ray characterization of the N⁶‐benzyl‐N⁶‐methyladenine ligand (L) and three metal complexes, namely [Zn(HL)Cl₃]·H₂O ( 1 ), [Cd(HL)₂Cl₄] ( 2 ) and [H₂L]₂[Cd₃(μ‐L)₂(μ‐Cl)₄Cl₆]·3H₂O ( 3 ). Complex 1 consists of the 7H‐adenine tautomer protonated at N3 and coordinated to a tetrahedral Zn(II) metal centre through N9. The octahedral Cd(II) in complex 2 is N⁹‐coordinated to two N⁶‐benzyl‐N⁶‐methyladeninium ligands (7H‐tautomer protonated at N3) that occupy apical positions and four chlorido ligands form the basal plane. Compound 3 corresponds to a trinuclear Cd(II) complex, where the central Cd atom is six‐coordinated to two bridging μ‐L and four bridging μ‐Cl ligands. The other two Cd atoms are six‐coordinated to three terminal chlorido ligands, to two bridging μ‐Cl ligands and to the bridging μ‐L through N3. Essentially, the coordination patterns, degree of protonation and tautomeric forms of the nucleobase dominate the solid‐state architectures of 1 – 3 . Additionally, the hydrogen‐bonding interactions produced by the endocyclic N atoms and NH groups stabilize high‐dimensional‐order supramolecular assemblies. Moreover, energetically strong anion–π and lone pair (lp)–π interactions are important in constructing the final solid‐state architectures in 1 – 3 . We have studied the non‐covalent interactions energetically using density functional theory calculations and rationalized the interactions using molecular electrostatic potential surfaces and Bader's theory of atoms in molecules. We have particularly analysed cooperative lp–π and anion–π interactions in 1 and π⁺–π⁺ interactions in 3 .     

Dayaolingzhiols A−E,AchE inhibitory meroterpenoids from Ganoderma lucidum

Ganoderma mushrooms are widely used as effective medicines for treating and preventing chronic diseases. In this study, five new meroterpenoids, dayaolingzhiols A (1) and B (2) featuring a 6/6/6 ring system, dayaolingzhiols C?E (3–5) harboring a γ-lactone motif, along with eight known ones (6–13), were purified from G. lucidum. To clarify their chemical structures, spectroscopic and ECD and OR computational methods were used. In addition, the inhibition of all the new meroterpenoids against AChE was evaluated, disclosing that (+)-4 and (±)-5 possess potent AChE inhibitory activities with respective IC₅₀ values of 8.52?±?1.90?μM and 7.37?±?0.52?μM.     

Green synthesis and characterization of Tb-Fe-O-Cu ceramic nanocomposite and its application in simultaneous electrochemical sensing of zinc,cadmium and lead

In this work, a green technique for preparing TbFeO₃/CuO was reported by employing Crataegus and Lantana Camara leaves as fuel and alkalizing agents, respectively. The new sensor based on the perovskite-type nanocomposite was employed as a sensitive and selective platform to detect Pb(II), Zn(II) and Cd(II) simultaneously. TbFeO₃/CuO/Carbon paste electrode (CPE) exhibited a large specific surface area and great electrical conductivity, which enhanced electron transport in the electrochemical process considerably. Moreover, square wave anodic stripping voltammetry (SWASV) was used for the investigation of some factors influencing the sensor sensitivity like pH, modifier concentration, as well as accumulation time and potential. Therefore, the low detection limit (LOD) and a wide linear range were obtained at optimum conditions. In this study, a linear range between 0.9 and 110 µg/L for three ions and LOD of 0.48, 0.29 and 0.12 for zinc, cadmium and lead were achieved, respectively. Moreover, TbFeO₃/CuO/CPE was employed to detect zinc, cadmium and lead ions simultaneously in the real samples so that the results have shown consistency with a standard inductively coupled plasma (ICP).     

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.