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.     

Acid/Base‐Triggered Switching of Circularly Polarized Luminescence and Electronic Circular Dichroism in Organic and Organometallic Helicenes

Electronic circular dichroism and circularly polarized luminescence acid/base switching activity has been demonstrated in helicene‐bipyridine proligand 1 a and in its “rollover” cycloplatinated derivative 2 a . Whereas proligand 1 a displays a strong bathochromic shift (>160 nm) of the nonpolarized and circularly polarized luminescence upon protonation, complex 2 a displays slightly stronger emission. This strikingly different behavior between singlet emission in the organic helicene and triplet emission in the organometallic derivative has been rationalized by using quantum‐chemical calculations. The very large bathochromic shift of the emission observed upon protonation of azahelicene‐bipyridine 1 a has been attributed to the decrease in aromaticity (promoting a charge‐transfer‐type transition rather than a π–π* transition) as well as an increase in the HOMO–LUMO character of the transition and stabilization of the LUMO level upon protonation.     

Polarization control of an X‐ray free‐electron laser with a diamond phase retarder

A diamond phase retarder was applied to control the polarization states of a hard X‐ray free‐electron laser (XFEL) in the photon energy range 5–20 keV. The horizontal polarization of the XFEL beam generated from the planar undulators of the SPring‐8 Angstrom Compact Free‐Electron Laser (SACLA) was converted into vertical or circular polarization of either helicity by adjusting the angular offset of the diamond crystal from the exact Bragg condition. Using a 1.5 mm‐thick crystal, a high degree of circular polarization, 97%, was obtained for 11.56 keV monochromatic X‐rays, whereas the degree of vertical polarization was 67%, both of which agreed with the estimations including the energy bandwidth of the Si 111 beamline monochromator.     

On a Lyapunov-type inequality and the zeros of a certain Mittag–Leffler function

In this work, a Lyapunov-type inequality is obtained for the case when one is dealing with a fractional differential boundary value problem. We then use that result to obtain an interval where a certain Mittag–Leffler function has no real zeros.     

Circular Dichroism of Amino Acids: Following the Structural Formation of Phenylalanine

Circular dichroism (CD) is frequently used to assess the secondary structure of peptides and proteins, whereas less attention has been given to their building blocks, that is, single amino acids, as they do not possess a secondary structure. Here, we follow the CD signal of amino acids and reveal that several acids exhibit a unique CD pattern as a function of their concentration. Accordingly, we propose an eight‐level classification of the CD signal of the various amino acids. Special focus is given to the CD pattern of phenylalanine (Phe), for which we observe the formation of an ultra‐narrow CD peak (full width at high maximum of only 5 nm). This CD peak can be attributed to the formation of Phe‐based chiral structural features. Further support for the formation of an ordered structure is given by using NMR, and the additional self‐assembly process of Phe to tubular structures.     

Optical Activity in the Near‐IR Region: The λ=980 nm Multiplet of Chiral Yb3+ Complexes

We used a very simplified electrostatic model based on charge and polarizability of atoms and groups on an organic ligand around a lanthanide ion to predict the near‐infrared electronic circular dichroism (NIR ECD) spectra of Yb³⁺ (a monoelectronic ion). We tuned our method by using two widely different complexes. The first was the heterobimetallic species CsYb(hfbc)₄ [hfbc=(?)‐3‐heptafluorobutyrylcamphorate], in which the ligand is a diketonate and, as such, is endowed with a chromophore with strong UV absorption (π–π^*). Its oxygen atoms define a square antiprism, which provides a symmetric coordination polyhedron. The second system was Yb DOTMA [DOTMA=(1R,4R,7R,10R)‐α,α′,α′′,α′′′‐tetramethyl‐1,4,7,10‐tetraazacyclododecane‐1,4,7,10‐tetraacetic acid], a chiral Yb analogue of Gd DOTA (DOTA=1,4,7,10‐tetraazacyclododecane‐1,4,7,10‐tetraacetic acid), in which the ligand lacks relevant electronic transitions and provides a dissymmetric cage. The relative weights of dynamic (ligand polarization) and static contributions to Yb NIR ECD were evaluated, and the spectra appear to have been well predicted by theory through the introduction of a heuristic weight factor. To validate the approach and to confirm the value of the weight factor, we applied it to two other compounds, namely, Na₃Yb(BINOLate)₃ and Yb(BINOLAM)₃ [BINOLate=2,2′‐dihydroxy‐1,1′‐binaphthyl; BINOLAM=3,3′‐bis(diethylaminomethyl)‐1‐1′‐bi‐2‐naphthol].     

DFT‐Aided Vibrational Circular Dichroism Spectroscopy Study of (−)‐S‐cotinine

The implementation of a strategy comprising the use of vibrational circular dichroism spectroscopy and DFT calculations allows determination of the solution‐state conformational distribution in (?)‐S‐cotinine, giving further proof of the extra conformer‐discriminating potential of this experimental technique, which may offer unique molecular fingerprints of subtly dissimilar molecular conformers of chiral samples. Natural bond orbital electronic structure calculations of the rotational barrier height between the two main conformers of the species indicate that hyperconjugative effects are the key force governing the conformational equilibrium. The negligible effect of the solvent’s polarity over both structure and conformational energy profile supports this result.     

Elucidating the Structure of Chiral Molecules by using Amplified Vibrational Circular Dichroism: From Theory to Experimental Realization

Recent experimental observations of enhanced vibrational circular dichroism (VCD) in molecular systems with low‐lying electronically excited states suggest interesting new applications of VCD spectroscopy. The theory describing VCD enhancement through vibronic coupling schemes was derived by Nafie in 1983, but only recently experimental evidence of VCD amplification has demonstrated the extent to which this effect can be exploited as a structure elucidation tool to probe local structure. In this Concept paper, we give an overview of the physics behind vibrational circular dichroism, in particular the equations governing the VCD amplification effect, and review the latest experimental developments with a prospective view on the application of amplified VCD to locally probe biomolecular structure.     

A canonical module characterization of Serre’s (R1)

In this short note, we give a characterization of domains satisfying Serre’s condition (R₁) in terms of their canonical modules. In the special case of toric rings, this generalizes a result of the second author [9 Yanagawa, K. (2015). Dualizing complexes of seminormal a?ne semigroup rings and toric face rings. J. Algebra 425:367–391.[Crossref], [Web of Science ®] , [Google Scholar]] where the normality is described in terms of the “shape” of the canonical module.