A generalization of a theorem of A. Grothendieck

In this article we characterize the quasi‐barrelledness of the projective tensor product of a coechelon space of type one k ¹(A) with a Fréchet space, including homological conditions as exactness properties of the corresponding tensor product functor k ¹(A) ·: ? → ??, acting from the category of Fréchet spaces to the category of linear spaces, resp. the vanishing of its first right derivative Tor¹_π (k ¹(A),.). This generalizes and extends a classical theorem of A. Grothendieck ([13, Chap. II, §4, No. 3, Theorem 15]). Further we present an analogous theorem for complete coechelon spaces of type zero and the injective tensor product and results concerning the stronger property of barrelledness. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Brieskorn manifolds as contact branched covers of spheres

We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.      

Investigation of heat capacities of proteins by statistical mechanical methods

In this study additional heat capacity of the proteins in water dissociation have been investigated by statistical mechanical methods. For this purpose, taking electric field E$E$ and total dipole moment M$M$ as thermodynamical variables and starting with the first law of thermodynamics, an expression which reveals the thermodynamical relation between additional heat capacity in effective electric field Δ_CE$\mathrm{\Delta }{C}_E$ and additional heat capacity at the constant total dipole moment Δ_CM$\mathrm{\Delta }{C}_M$, has been obtained. It is found that, difference between the heat capacities depends linearly on temperature. To establish the hydration effect during the folding and unfolding of the proteins, physical properties of the apolar dissociation have been used [G. Oylumluoglu, et al., Physica A 361 (2006) 255–262]. In the thermodynamical investigation of the protein system, in order to introduce the chemical potential μ$\mu$ (here it takes place of pH), one has to consider the system as a macro-canonical ensemble. In this study, the macro-canonical ensemble is obtained from the canonical ensemble. In this approach the proteins are taken in a heat bath, and also it is supposed that the system is in a particle reservoir. When this reservoir reaches to an equilibrium the number of particles take an average value. In this study, with the purpose of revealing the additional effect to the heat capacity, the partition functions of the proteins obtained in single protein molecule approach are taken. In this way, additional free energy has been related to heat capacities. Calculating the heat capacity Δ_CE$\mathrm{\Delta }{C}_E$ and taking the heat capacity at constant total dipole moment Δ_CM$\mathrm{\Delta }{C}_M$ from the experimental data, the outcomes of the performed calculations have been investigated for Myoglobin and other proteins.     

Scintillation index of elliptical Gaussian beam in turbulent atmosphere

A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.     

Some properties of q-biorthogonal polynomials

Almost four decades ago, Konhauser introduced and studied a pair of biorthogonal polynomials

     

The normal subgroup structure of the extended Hecke groups

We consider the extended Hecke groups generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups . Then, we determine the abstract group structure of the commutator subgroups , the even subgroup , and the power subgroups of the extended Hecke groups . Also, finally, we give some relations between them.     

The sensitive capillary electrophoretic‐LIF method for simultaneous determination of curcuminoids in turmeric by enhancing fluorescence intensities of molecules upon inclusion into (2‐hydroxypropyl)‐β‐cyclodextrin

Curcuminoids have received great attention in the past decades due to their health benefit properties. The aim of this study is to develop a very simple, rapid, and sensitive capillary zone electrophoresis technique coupled with a laser induced fluorescence detector (LIF) for the simultaneous determination of three major curcuminoids of turmeric, namely, curcumin, demethoxy curcumin (DMC), and bisdemethoxy curcumin (BDMC). Background electrolyte was selected as borate at pH 9.6 and (2‐hydroxypropyl)‐β‐cyclodextrin (2‐HP‐β‐CD) was added to prevent rapid alkali degradation of curcuminoids in buffer and to increase fluorescence intensities of molecules. With the addition of 2‐HP‐β‐CD to the separation electrolyte, the fluorescence signal intensities of curcuminoids were enhanced considerably by 30, 40, and 54 fold for curcumin, DMC, and BDMC, respectively. The three curcuminoids of turmeric were fully separated and quantified in less than 4.5 min. The repeatability of the peak areas of curcuminoids for intra‐day and inter‐day experiments was in the satisfactory range of 2.26 and 2.55%, respectively. The LOD and LOQ values for the developed method were equal to or less than 0.081 and 0.270 μg/mL, respectively, for all curcuminoids. The developed method was successfully applied to find curcuminoids amount in turmeric samples and herbal supplements.     

Enantiospecific Synthesis of (R)‐3‐Amino‐4‐(2,4,5‐trifluorophenyl)butanoic Acid Using (S)‐Serine as a Chiral Pool

Starting from (S)‐serine, a new method was developed for the synthesis of the β‐amino acid part of sitagliptin in ten steps and with an overall yield of 30%. The crucial step of the synthesis was the ring opening of N‐ and O‐protected (R)‐aziridin‐2‐methanol with (2,4,5‐trifluorophenyl)magnesium bromide to give N‐ and O‐protected (R)‐2‐amino‐3‐(2,4,5‐trifluorophenyl)propan‐1‐ol.     

Spectroscopic characterization,X-ray structure and DFT studies on 4-[3-(2,5-dimethylphenyl)-3-methylcyclobutyl]-N-methylthiazol-2-amine

The titled molecule 4-[3-(2,5-dimethylphenyl)-3-methylcyclobutyl]-N-methylthiazol-2-amine (C₁₇H₂₂N₂S) is synthesized and characterized by ¹H NMR, ¹³C NMR, IR, and X-ray single crystal determination. The compound crystallizes in the monoclinic space group P2_1/c with a = 6.3972(4) Å, b = 9.4988(6) Å, c = 26.016(2) Å and β = 93.496(7)°. In addition to the molecular geometry from the X-ray determination, vibrational frequencies and gauge, including the atomic orbital (GIAO), ¹H and ¹³C NMR chemical shift values of the titled compound in the ground state are calculated using the density functional (B3LYP) method with 6-31G(d), 6-31++G(d,p) and 6-311+G(2d,p) basis sets. The calculated results show that the optimized geometries can well reproduce the crystal structure. Moreover, the theoretical vibrational frequencies and chemical shift values show good agreement with the experimental values. The predicted nonlinear optical properties of the titled compound are greater than those of urea. DFT calculations of the molecular electrostatic potentials and frontier molecular orbitals of the titled compound are carried out at the B3LYP/6-31G(d) level of theory.     

Fabrication of photo‐cross‐linked polyethyleneimine‐based barriers for CO2 capture

In this study, first, polyethyleneimine was acrylated and mixed with polyvinyl alcohol solution to prepare photo‐crosslinked polyethyleneimine (PEI)‐based nanofibers by utilizing ultraviolet and electrospinning technique at the same time. For CO₂ permeability testing, same formulations were prepared by using solvent casting technique and exposed to ultraviolet light to have polyethyleneimine‐based membrane films. The chemical structures of the nanofibers were characterized by Fourier transform infrared spectroscopy. The thermal properties of nanofibers were examined by thermal gravimetric analysis and differential scanning calorimeter. The morphology of nanofibers was investigated by scanning electron microscopy. CO₂ permeabilities of samples were also measured. Copyright © 2015 John Wiley & Sons, Ltd.