Variational Operators,Symplectic Operators,and the Cohomology of Scalar Evolution Equations

For a scalar evolution equation u_t = K(t, x, u, u_x, . . . , u_2m+1) with m ≥ 1, the cohomology space H^1,2() is shown to be isomorphic to the space of variational operators and an explicit isomorphism is given. The space of symplectic operators for u_t = K for which the equation is Hamiltonian is also shown to be isomorphic to the space H^1,2() and subsequently can be naturally identified with the space of variational operators. Third order scalar evolution equations admitting a first order symplectic (or variational) operator are characterized. The variational operator (or symplectic) nature of the potential form of a bi-Hamiltonian evolution equation is also presented in order to generate examples of interest.     

On the difference spaces of almost convergent and strongly almost convergent double sequences

In this paper, we study the difference spaces \({\mathcal {F}}(\varDelta )\), \({\mathcal {F}}_0(\varDelta )\), \({\mathcal {[F]}}(\varDelta )\) and \({\mathcal {[F]}}_0(\varDelta )\) of double sequences obtained as the domain of four-dimensional backward difference matrix \(\varDelta \) in the spaces \({\mathcal {F}}\), \({\mathcal {F}}_{0}\), \({\mathcal {[F]}}\) and \({\mathcal {[F]}}_{0}\) of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We examine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces.

     

Concentration Dependence of NMR T1 in Agar Solutions

In this study, in order to explain solvent proton relaxation mechanism, the spin-lattice relaxation time (T1) of agar solutions was measured as a function of agar concentration. Relaxation measurements were carried out by a FT-NMR spectrometer operating at 60 MHz and inversion recovery pulse squence was used. Relaxation rate(1/T1a) was linearly proportional to concentration of agar solution (C), and the T1 mechanism of solvent water protons in agar solutions should be caused by the chemical exchange of water protons between free and bound water.     

A novel method for serum lipoprotein profiling using high performance capillary isotachophoresis

A new capillary isotachophoresis (cITP) method for lipoprotein profiling with superior lipoprotein coverage compared to previous methods has been developed, resolving twice as many lipoprotein species (18 peaks/fractions) in serum or plasma in less than 9.5 min. For this, a novel mixture of 24 spacers, including amino acids, dipeptides and sulfonic acids, was developed and fine-tuned, using predictive software (PeakMaster) and testing of spiked serum samples. Lipoprotein peaks were identified by serum-spiking with reference lipoproteins. Compatibility with common lipophilic stains for selective lipoprotein detection with either UV/Vis or laser-induced fluorescence was demonstrated. A special new capillary with a neutral coating (combining water-compatible OV1701-OH deactivation and methylation) was used for the first time for electrodriven separations, allowing very stable separations in a pH 8.8–9.4 gradient system, being functional for more than 100 injections. Excellent reproducibility was achieved, with coefficients of variation lower than 2.6% for absolute migration times. Comparison was performed with human plasma samples analyzed by NMR, leading to similar results with cITP after multivariate statistics, regarding group-clustering and lipoprotein species correlation. The new cITP method was applied to the analysis of serum samples from a LDL receptor knock-out mice model fed either a normal diet or a western-type diet. Differences in the lipoprotein levels and in the sublipoprotein types were detected, showing a shift to more atherogenic particles due to the high cholesterol diet. In summary, this novel method will allow more detailed and informative profiling of lipoprotein particle subtypes for cardiovascular disease research.     

Associating divisors with quadratic differentials on Klein surfaces

We extend the notion and basic properties of quadratic differential divisors to a Klein surface, using the corresponding form’s divisors from the double cover of the Klein surface.     

Investigation of spectroscopic studies and DFT calculations on glucofuranose derivatives of dithiophosphonates

Abstract

2,4-Bis(4-methoxyphenyl)-1,3,2,4-dithiadiphosphetane-2,4-disulfide (Lawesson’s reagent: LR) was reacted with 1,2:5,6-di-O-cyclohexylidene-α-D-glucofuranose and 1,2:5,6-di-O-isopropylidene-α-D-glucofuranose in toluene and gave rise to crude dithiophosphonic acids. The crude dithiophosphonic acids were treated with excess triethylamine and the triethylammonium salts of dithiophosphonic acids (1) and (2) were isolated by crystallization method. Compounds 1 and 2 were characterized by elemental analysis, IR, and NMR (¹H-, ¹³C- and ³¹P-) spectroscopies and mass spectrometry. In addition, NMR spectra, the electronic properties (the electronic chemical potential, electronegativity, chemical hardness and the global electrophilicity index) and NBO analysis of compound 2 have been calculated by using the Gaussian 16?W program. The electronic properties were calculated using Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO) energies by density functional method (DFT/B3LYP) at 6-31G(d,p) level. The HOMO and LUMO energies are ?5.9 and ?0.72?eV, respectively. The HOMO–LUMO energy difference is 5.18?eV and this value shows that compound 2 has a high stability and low reactivity.