Set Of Multiplets Research Articles

Hodge duality transformations in tensor-hierarchy formulations

We show in arbitrary space-time dimensions that duality-transformations are possible in general tensor-hierarchy with field-strengths of arbitrary ranks. We first consider the non-Abelian tensor field-strength of the potential , and its compensator field-strength of the potential , where is the adjoint index. We next perform duality transformations into their respective Hodge-dual field-strength of the potential and the field-strength of the potential . As a typical application, we show this to take place in dimensions with an N = 1 supersymmetric set consisting of a Yang–Mills vector-multiplet , an extra vector-multiplet , and a compensating chiral multiplet . The λ I and χ I are Majorana spinors, and is an extra vector with the Proca–Stückelberg scalar CI , while EI is a pseudo-scalar. We perform duality-transformations on and to their Hodge-dual fields and , respectively, ending up with the new set of multiplets and . Another example is the set of multiplets and in . Even though has the maximal 4th rank field-strength, its supersymmetric dual system exists with and after a duality-transformation. Our duality-transformations provide previously-unknown-links among supersymmetric tensor-hierarchy formulations.

SYNTHESIS OF NEW HYBRID MOLECULES WITH 1,3,5-TRIAZINE AND HYDROQUINOLINE MOIETIES

The article describes a method for the synthesis of hybrid molecules based on the 1,3,5-triazine platform and containing additional pharmacophore fragments of 2,2,4-trimethyl-1,2-dihydroquinoline, 4-aryl-2,2,4-trimethyl-1,2,3,4-tetrahydroquinoline, indoline or piperidine. The obtained compounds are promising for studying their biological action. The described synthesis method includes the interaction of indolin-1-ylimidoguanidine and piperidine-1-ylimidoguanidine with carbon disulfide to form 4-amino-6-(indolin-1-yl)-1,3,5-triazine-2-thiol and 4-amino-6-(piperidin-1-yl)-1,3,5-triazine-2-thiol, respectively. 4-Amino-6-R-1,3,5-triazine-2-thiols have two nucleophilic centers: an amino and a mercapto group, so they can be introduced in subsequent reactions with electrophilic reagents such as alkyl halides. Alkylation of the latter with N-chloroacetyl derivatives of hydroquinolines gives hybrid heterocyclic matrices: 2-((4-amino-6-(indolin-1-yl)-1,3,5-triazin-2-yl)thio)-1-(2,2,4-trimethylquinolin-1(2H)-yl)ethan-1-ones, 2-((4-amino-6-(piperidin-1-yl)-1,3,5-triazin-2-yl)thio)-1-(2,2,4-trimethylquinolin-1(2H)-yl)ethan-1-ones, 2-((4-amino-6-(indolin-1-yl)-1,3,5-triazin-2-yl)thio)-1-(4-(4-aryl-2,2,4-trimethyl-3,4-dihydroquinolin-1(2H)-yl)ethan-1-ones and 2-((4-amino-6-(piperidin-1-yl)-1,3,5-triazin-2-yl)thio)-1-(4-(4-aryl-2,2,4-trimethyl-3,4-dihydroquinolin-1(2H)-yl)ethan-1-ones. The structure of the obtained compounds was characterized by high performance liquid chromatography with mass spectrometry, as well as by 1H and 13C NMR spectroscopy. For the compounds with the dihydroquinoline fragment in their structure, the singlet of the CH proton of the pyridine cycle of the hydroquinoline fragment, which is visible in the 5.56-5.61 ppm region, is characteristic. In turn, in the spectra of compounds with the tetrahydroquinoline fragment, there is a characteristic signal of the CH2 group of the hydropyridine cycle of the quinoline fragment in the form of two sets of multiplets at 0.99-1.09 and 1.61-1.71 ppm. The presence of several pharmacophore fragments in the molecules determines the high probability of their biological activity. The anticoagulant activity of 2-((4-amino-6-(piperidin-1-yl)-1,3,5-triazin-2-yl)thio)-1-(2,2,4-trimethylquinolin-1(2H)-yl)ethan-1-ones due to their inhibitory effect on blood coagulation factors Xa is described. A series of new hybrid molecules on the platform of 1,3,5-triazine containing additionally linearly linked hydroquinoline and indoline (piperidine) cycles was obtained in the course of this research. Initial screening of anticoagulant activity was performed and moderate activity of 2-((4-amino-6-(piperidin-1-yl)-1,3,5-triazine-2-yl)thio)-1-(2,2,4-trimethylquinoline-1(2H)-yl)ethane-1-ones against coagulation factor Xa was shown.

Comparative analysis of base nutrient composition by NMR spectroscopy

The traditional approach to assessing the quality of nutrient bases involves a determination of amino nitrogen and acidity. The disadvantage of this approach consists in a lack of information, i.e. an inability to detect antibiotics, growth inhibitors and other undesirable compounds. In this regard, more modern and informative methods are required to control the technological process of preparing the nutritional basis and therefore the quality of the products obtained. The aim of this work was to study the physicochemical properties of nutrient bases made from sea and river fish and squid using new approaches (NMR spectroscopy). The following raw materials were used: herring (1), roach (2), pollock (3), squid (4). The raw materials were subjected to enzymatic hydrolysis by the pancreas (according to Hottinger). The qualitative composition of the organic component of hydrolysates (1–4) was determined by 1 H, 13 С and 15 N NMR spectroscopy. All of the 1H NMR spectra had the same appearance, typical of mixtures of amino acids or amino acid sequences. In the high-field part (0.9–2.5 ppm), a set of multiplets was observed, characteristic of aliphatic fragments of molecules. Since most of the signals in the 1H NMR spectra partially overlap, a quantitative assessment of the composition of the organic component appears impossible. All four samples can be confirmed as being qualitatively similar without isolating the dominant compound. Analysis of 2D NMR spectra revealed the presence of the following free amino acids in mixtures of samples (1–4): alanine, valine, threonine, arginine, lysine, leucine, methionine, phenylalanine and glycine. The use of NMR spectroscopy demonstrated that any discrepancies in the component composition of hydrolysates (1–4) were insignificant, allowing manufacturers of nutrient media to choose the most affordable raw materials. The obtained data appear to be applicable for controlling the technological process of preparing the nutrient bases and determining the quality of the resulting products during storage.

Synthetic, electrochemical, spectroscopic, and structural studies of mixed sandwich Co(III) complexes involving Cp or Cp* with tridentate N-donor and S-donor macrocycles

The syntheses, structures, spectroscopy, and electrochemistry for four Co(III) mixed sandwich mononuclear complexes involving tridentate macrocycles and either cyclopentadienyl (Cp) or pentamethylcyclopentadienyl (Cp*) are reported. All complexes have the general formula [Co(CpR)([9]aneX3)](PF6)2, where X = S, 1,4,7-trithiacyclononane, and R = Cp (1) or Cp* (2), or X = N, 1,4,7-triazacyclononane, and R = Cp (3) or Cp* (4), and exhibit a pseudo-octahedral structure involving the carbocyclic η5-CpR ligand and facial κ3-donation from the macrocycle. The structures for all six complexes are supported by 1H and 13C{1H} NMR spectroscopy, and the compounds 1, 2, and 4 are also characterized by single-crystal X-ray crystallography. The 1H NMR shows an AA′BB′ splitting pattern for the coordinated macrocycle, and the dispersion between the two sets of multiplets is dependent upon the identity of the macrocycle. The [9]aneN3 complexes show only a single reversible (4) or irreversible (3) +3/+2 reduction in the −1.0 to −1.4 V range vs. Fc/Fc+. The [9]aneS3 complexes show the same reversible (1) or quasi-reversible (2) reduction in the −0.6 to −0.9 V range vs. Fc/Fc+ as well as a quasi-reversible (1) or irreversible (2) +2/+1 reduction in the −1.5 to −1.8 V range vs. Fc/Fc+.

EXPLORING THE HELIUM CORE OF THE δ SCUTI STAR COROT 102749568 WITH ASTEROSEISMOLOGY

ABSTRACT Based on regularities in rotational splitting, we seek possible multiplets for the observed frequencies of CoRoT 102749568. There are 21 sets of multiplets identified, including four sets of multiplets with l = 1, nine sets of multiplets with l = 2, and eight sets of multiplets with l = 3. In particular, there are three complete triplets (f 10, f 12, f 14), (f 31, f 34, f 35), and (f 41, f 43, f 44). The rotational period of CoRoT 102749568 is estimated to be days. When doing model fittings, three l = 1 modes (f 12, f 34, and f 43) and the radial first overtone f 13 are used. Our results shows that the three nonradial modes (f 12, f 34, and f 43) are mixed modes, which mainly provide constraints on the helium core. The radial first overtone f 13 mainly provides constraint on the stellar envelope. Hence the size of the helium core of CoRoT 102749568 is determined to be = 0.148 ± 0.003 M ⊙ and = 0.0581 ± 0.0007 R ⊙. The fundamental parameters of CoRoT 102749568 are determined to be M = 1.54 ± 0.03 M ⊙, , , , K, R = 2.916 ± 0.039 R ⊙, and L = 17.12 ± 1.13 L ⊙.

Comparison of X-ray photoelectron spectroscopy multiplet splitting of Cr 2p peaks from chromium tris(β-diketonates) with chemical effects

X-ray photoelectron spectra (XPS) measurements of a series of chromium(III) β-diketonato complexes of the Cr 2p spectra was fitted with calculated multiplet peaks. The XPS of these Cr(III) complexes did not exhibit fine structure, however, well-defined line shapes could be fitted to the Cr 2p3/2 envelope. The splitting patterns obtained for the Cr(III) β-diketonato complexes compared well with the multiplet splitting predicted by Gupta and Sen for the free Cr(III) ion. The Cr(III) β-diketonato complexes containing unsymmetrically substituted β-diketonato ligands, which display both the fac and mer isomers, could be fitted with two sets of multiplets and were useful in determining the ratio between the fac and mer isomers, which was compared with the Boltzman calculated ratio obtained from density functional theory energies. The obtained binding energy of the first multiplet splitting peak of the Cr 2p3/2 envelope was found to be dependent on the combined Gordy group electronegativity of the R-groups substituted on the β-diketonato ligand (RCOCHCOR′)−.

Mass Spectrum of Spinor Fields in Extra Dimensions

The mass spectrum for spinor fields in extra dimensions is considered within the framework of the mass creation mechanism proposed in our previous works (Duc and Giao 2013; Duc and Giao J. Mod. Phys. 4(N7), 991, 2013; Duc et al. J. Phys Sci. Appl. (USA) 4(N1), 60, 2014; Duc and Giao J. Mod. Phys. 5(N6), 2014). It is shown that a single spinor field in the whole space-time with extradimensions corresponds to a set of multiplets of effective spinor fields in ordinary 4-dimensional space-time with masses obeying the sum rule expressed in terms of metric for extradimensions and parameter functions dictated from the periodicity conditions.

IMPROVED log( gf ) VALUES OF SELECTED LINES IN Mn I AND Mn II FOR ABUNDANCE DETERMINATIONS IN FGK DWARFS AND GIANTS

The goal of the present work is to produce transition probabilities with very low uncertainties for a selected set of multiplets of Mn I and Mn II. Multiplets are chosen based upon their suitability for stellar abundance analysis. We report on new radiative lifetime measurements for 22 levels of Mn I from the e {sup 8} D, z {sup 6} P, z {sup 6} D, z {sup 4} F, e {sup 8} S, and e {sup 6} S terms and six levels of Mn II from the z {sup 5} P and z {sup 7} P terms using time-resolved laser-induced fluorescence on a slow atom/ion beam. New branching fractions for transitions from these levels, measured using a Fourier-transform spectrometer, are reported. When combined, these measurements yield transition probabilities for 47 transitions of Mn I and 15 transitions of Mn II. Comparisons are made to data from the literature and to Russell-Saunders (LS) theory. In keeping with the goal of producing a set of transition probabilities with the highest possible accuracy and precision, we recommend a weighted mean result incorporating our measurements on Mn I and II as well as independent measurements or calculations that we view as reliable and ofmore » a quality similar to ours. In a forthcoming paper, these Mn I/II transition probability data will be utilized to derive the Mn abundance in stars with spectra from both space-based and ground-based facilities over a 4000 A wavelength range. With the employment of a local thermodynamic equilibrium line transfer code, the Mn I/II ionization balance will be determined for stars of different evolutionary states.« less

StePSIM – a method for stepwise peak selection and identification of metabolites in 1 H NMR spectra

A method for stepwise selection of peaks in NMR spectra from multiple groups is described. This method is based on initial peak-finding among the spectra and uses jacknife classification performance as the basis for selection of peaks. The selection process is followed by the construction of correlation maps to identify sets of multiplets that are related to each of the selected peaks, aiding in the identification of metabolites that are responsible for differences among the groups. For illustrative purposes, this methodology is applied to a data set that contains 52 spectra from renal cell carcinoma and normal renal tissue samples. The new method is denoted as StePSIM, Stepwise Peak Selection and Identification of Metabolites.

Pseudopotentials, correlations, and hierarchy states in quantum hall systems: When the composite Fermion picture works and why

A system of Fermions in a shell of angular momentum l can form a set of multiplets of total angular momentum L . The composite Fermion (CF) picture picks out the lowest lying energy multiplets by selecting from this set a subset that is “Laughlin correlated”, i.e. which maximally avoids pair orbits with the largest pair angular momentum L ′ (or smallest relative angular momentum R = 2 l − L ′ ). We demonstrate that Laughlin correlations occur only when the pseudopotential V ( L ′ ) (the interaction energy of a pair as a function of L ′ ) increases with L ′ more rapidly, than the eigenvalue of L ′ 2 at the value of L ′ (or R ) avoided in the Laughlin correlated state. This requirement is not satisfied for QEs and QHs of the Laughlin ν = 1 / 3 and ν = 1 / 5 states at R = 1 and R = 3 respectively. At ν QE = 1 / 3 and ν QH = 1 / 5 , clustering of QPs gives lower energy than Laughlin correlations. Novel spin polarized incompressible states at ν = 4 / 11 and ν = 4 / 13 cannot be explained as a second generation in the CF hierarchy.

Compatibility of quark and resonant picture excited baryon multiplets in the1/Ncexpansion of QCD

We demonstrate that the two major complementary pictures of large N_c baryon resonances--as single-quark orbital excitations about a closed-shell core [giving SU(2N_F) x O(3) multiplets], and as resonances in meson-baryon scattering amplitudes--are completely compatible in a specific sense: Both pictures give rise to a set of multiplets of degenerate states, for which any complete spin-flavor multiplet within one picture fills the quantum numbers of complete multiplets in the other picture. This result is demonstrated by: (i) straightforward computation of the lowest multiplets in both pictures; (ii) a study of the nature of quark excitations in a hedgehog picture; (iii) direct group-theoretical comparison of the constraints in the two pictures.

Essential fatty acid status in plasma phospholipids of mother and neonate after multiple pregnancy

During singleton pregnancy, maternal essential fatty acid (EFA) status decreases progressively. After multiple pregnancy it can be expected that the neonatal and maternal EFA status is even lower. To study whether the maternal EFA supply to the fetus is a limiting factor to the neonatal EFA status, we compared the plasma phospholipid EFA status of newborn multiplets (30 pairs of twins and 7 sets of triplets) with that of singletons ( n = 89) at birth and that of their mothers at delivery. After correction for gestational age, a slightly lower EFA status was found in maternal and umbilical plasma from multiplets compared to singletons. No relation was found between the difference in birthweight of the smallest and the largest neonate of a set of multiplets and the difference in cord plasma EFA levels. Correlations between maternal and umbilical plasma EFA levels were comparable for multiple and singleton pregnancies. Therefore, adequate dietary intake is required to guarantee an optimal neonatal EFA status, especially during multiple pregnancy.

Cellular multiplets in directional solidification

We report the existence of new branches of steady state cellular structures in directional solidification. These structures consist of repeating cellular subunits, or multiplets, each containing a set of distinct cells separated by unequal grooves. A detailed numerical study of the symmetric model of directional solidification reveals that all multiplets bifurcate off the main singlet solution branch in two sets. Two points on the main branch, one corresponding to the onset of the Eckhaus instability at small cell spacing and the other to a fold of this branch at large spacing, are argued to be separate accumulation points for each set of multiplets. The set of structures bifurcating near the fold are morphologically similar to experimentally observed multiplets. In contrast, those bifurcating near the Eckhaus instability do not resemble experimental shapes. Furthermore, they are argued to be generically unstable.

Supergauge multiplets and superfields

Superfields are defined as functions of the space-time variable x and of anticommuting two-component spinors θ and θ . They have definite transformation properties under supergauge transformations. Their expansion in θ and θ generates a finite number of ordinary fields forming a multiplet. A number of operations are defined which allow the construction of new superfields from given ones. The corresponding set of multiplets is complete, in the sense that the product of any two can be decomposed as a sum of multiplets belonging to the same set.