Identification of the Domain of the Sturm–Liouville Operator on a Star Graph

This article is devoted to the unique recovering of the domain of the Sturm–Liouville operator on a star graph. The domain of the Sturm–Liouville operator is uniquely identified from the set of spectra of a finite number of specially selected canonical problems. In the general case, the domain of the definition of the original operator can be specified by integro-differential linear forms. In the case when the domain of the Sturm–Liouville operator on a star graph corresponds to the boundary value problem, it is sufficient to choose only finite parts of the spectra of canonical problems for a unique identification of the boundary form. Moreover, the above statement is valid only for a symmetric star graph.

Fourth Hankel Determinant for the Set of Star-Like Functions

In this paper, we derive a bound of the fourth Hankel determinant for the class of star-like functions. We also consider this problem for 2-fold and 3 -fold symmetric star-like functions. In this case, we obtain sharp results.

An Electron-Deficient Tris(triazole)-based Discotic Liquid Crystal that exhibit Fast Electron Transport

A C3-symmetric star-shaped discotic mesogen is reported based on an electron-deficient tris(triazole) central rigid core functionalized with three peripheral trialkoxyphenyl units. The mesogen exhibits an enantiotropic Colh phase that can...

Dynamics of asymmetric star polymers under coarse grain simulations

The asymmetric star polymers are studied by coarse grain simulations. Each polymer chain is represented by number of consecutive soft blobs and additional uncrossability constraints are added to prevent chain crossings. In this work two types of asymmetric star polymers with different backbone lengths are structured. Their dynamical properties are discussed by comparisons with corresponding linear chains, the one covers chain length along with the asymmetric arm through the branch point to one of the symmetric arm, or the backbone chain between two symmetric arm ends, or the largest linear possesses the same molecular weight of the entire star. To reveal the influence of the asymmetric arm length on their relaxation decay times, the autocorrelation function of the vectors from each branching point to corresponding asymmetric arm end are calculated, results are compared with the symmetric star having the same backbone chain.

Synthesis of C 3-symmetric star-shaped molecules containing α-amino acids and dipeptides via Negishi coupling as a key step

We demonstrate a new synthetic strategy toward star-shaped C 3-symmetric molecules containing α-amino acid (AAA) derivatives and dipeptides. In this regard, trimerization and Negishi cross-coupling reactions are used as the key steps starting from readily available 4’-iodoacetophenone and L-serine. These C 3-symmetric molecules containing AAA moieties are useful to design new ligands suitable for asymmetric synthesis and peptide dendrimers.

Black hole formation due to collapsing dark matter in a presence of dark energy in the brane-world scenario

In the last three to four decades, various programs have been studied in order to investigate the final fate of gravitational collapse of massive astronomical objects. In the theoretical context, Black Holes (BHs) are the consequence of final stage of the gravitational collapse. In this work, we investigated the gravitational collapse process of a spherically symmetric star constituted of dark matter (DM), [Formula: see text], and Dark Energy (DE), [Formula: see text] in the context of the brane-world scenario. In our model, we discussed the anisotropy of the pressure in a fluid with Equation of State (EoS) [Formula: see text] and [Formula: see text], [Formula: see text]. We briefly discussed various cases of gravitational collapse and it is found that BH can be formed by the gravitational collapse in brane-world regime while in some cases there is only a naked singularity at their end state.