An anisotropic area-preserving flow for convex plane curves

This paper will deal with an anisotropic area-preserving flow which keeps the convexity of the evolving curve and the limiting curve converges to a homothety of a symmetric smooth strictly convex plane curve.     

Universal deformation rings and self-injective Nakayama algebras

Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring $R(\mathrm{\Lambda },V)$ and we describe $R(\mathrm{\Lambda },V)$ explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups.     

How algebra spoiled recreational problems: A case study in the cross-cultural dissemination of mathematics

This paper deals with a sub-class of recreational problems which are solved by a simple memorized rule resulting from an elementary arithmetical or algebraic solution, called proto-algebraic rules. Their recreational aspect is derived from a surprise or trick solution which is not immediately obvious to the subjects involved. Around 1560 many such problems wane from arithmetic and algebra textbooks to reappear in the eighteenth century. Several hypotheses are investigated why popular Renaissance recreational problems lost their appeal. We arrive at the conclusion that the emergence of algebra as a general problem solving method changed the scope of what is considered recreational in mathematics.     

Coleman automorphisms of finite groups and their minimal normal subgroups

In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the holomorph and wreath product of finite simple groups, among others, have no non-inner Coleman automorphisms. As a further application of our theorems, we provide partial answers to questions raised by M. Hertweck and W. Kimmerle. Furthermore, we characterize the Coleman automorphisms of extensions of a finite nilpotent group by a cyclic p-group. Finally, we note that class-preserving Coleman automorphisms of p-power order of some nilpotent-by-nilpotent groups are inner, extending a result by J. Hai and J. Ge, where p is a prime number.     

Development and validation of a simple solid‐phase extraction method coupled with liquid chromatography–triple quadrupole tandem mass spectrometry for simultaneous determination of lincomycin,tylosin A and tylosin B in royal jelly

We have developed an analytical method for the determination of lincomycin, tylosin A and tylosin B residues in royal jelly using liquid chromatography–triple quadrupole tandem mass spectrometry analysis. For extraction and purification, we employed 1% trifluoroacetic acid and 0.1 m Na₂EDTA solutions along with an Oasis HLB cartridge. The target antibiotics were well separated in a Kinetex EVO C₁₈ reversed‐phase analytical column using a combination of 0.1% formate acid in ultrapure water (A) and acetonitrile (B) as the mobile phase. Good linearity was achieved over the tested concentration range (5–50 μg/kg) in matrix‐matched standard calibration. The coefficients of determination (R²) were 0.9933, 0.9933 and 0.996, for tylosin A, tylosin B and lincomycin, respectively. Fortified royal jelly spiked with three different concentrations of the tested antibiotics (5, 10 and 20 μg/kg) yielded recoveries in the range 80.94–109.26% with relative standard deviations ≤4%. The proposed method was applied to monitor 11 brand of royal jelly collected from domestic markets and an imported brand from New Zealand; all the samples tested negative for lincomycin, tylosin A and tylosin B residues. In conclusion, 1% trifluoroacetic acid and 0.1 m Na₂EDTA aqueous solvents combined with solid‐phase extraction could effectively complete the sample preparation process for royal jelly before analysis. The developed approach can be applied for a routine analysis of lincomycin, tylosin A and tylosin B residues in royal jelly.     

Atomistic insights into the selective therapeutic activity of 6-(2,4-difluorophenoxy)-5-((ethylmethyl)pyridine-3-yl)-8-methylpyrrolo[1,2-a]pyrazin-1(2H)-one towards bromodomain-containing proteins

Cross-target effect has been one of the major mechanisms of drug toxicity, this has necessitated the design of inhibitors that are specifically tailored to target particular biomolecules. 6-(2,4-difluorophenoxy)-5-((ethylmethyl)pyridine-3-yl)-8-methylpyrrolo[1,2-a] pyrazin-1(2H)-one (Cpd38) is an inhibitor possessing high inhibition rate and tailored specificity towards bromodomain-containing protein 4 (BRD4). In this research, we used an array of computational techniques to provide insight at the atomistic level the specific targeting of BRD4 by Cpd38 relative to the binding of Cpd38 with E1A binding protein P300 (EP300); another bromodomain-containing protein (BCP). Comparatively, binding of Cpd38 improved the conformational stability and compactness of BRD4 protein when compared to the Cpd38 bound EP300. Also, Cpd38 induced a conformational change in the active site of BRD4 that facilitated a complementary pose between Cpd38 and BRD4 suitable for effective atomistic interactions. Expectedly, thermodynamic calculations revealed that the Cpd38-BRD4 system had higher binding energy (−36.11 Kcal/mol) than the Cpd38-EP300 system with a free binding energy of −15.86 Kcal/mol. Noteworthy is the opposing role Trp81 (acting as hydrogen bond acceptor) and Pro1074 (acting as hydrogen bond donor) found on the WPF and LPF loops respectively play in maintaining Cpd38 stability. Furthermore, the hydrogen bond acceptor/donator ratio was approximately 4:1 in Cpd38-BRD4 system compared with 2:1 in Cpd38-EP300 system. Taken together, atomistic insights and structural perspectives detailed in this report supplements the experimental report supporting the improved selectivity of Cpd38 for BRD4 ahead of other BCPs while providing leeway for the future design of BET selective agents with better pharmacological profile.