Five New Steroidal Glycosides from Caralluma dalzielii

Five new pregnane glycosides, caradalzielosides A–E ( 1 – 5 ), were isolated from the aerial parts of Caralluma dalzielii. Their structures were elucidated by extensive 1D‐ and 2D‐NMR spectroscopic analysis as well as by HR‐FAB‐MS experiments.     

2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with automorphisms of odd prime order,and their related Hadamard matrices and codes

We present the full classification of Hadamard 2-(31,15,7), Hadamard 2-(35, 17,8) and Menon 2-(36,15,6) designs with automorphisms of odd prime order. We also give partial classifications of such designs with automorphisms of order 2. These classifications lead to related Hadamard matrices and self-dual codes. We found 76166 Hadamard matrices of order 32 and 38332 Hadamard matrices of order 36, arising from the classified designs. Remarkably, all constructed Hadamard matrices of order 36 are Hadamard equivalent to a regular Hadamard matrix. From our constructed designs, we obtained 37352 doubly-even [72,36,12] codes, which are the best known self-dual codes of this length until now.      

Remarks on multivariate Gaussian Gabor frames

Spanning properties of multivariate Gaussian Gabor systems are far from being fully understood. Our results illustrate that, unlike in dimension one where Gaussian Gabor frames are characterized in terms of lattice density, the behavior of Gaussian Gabor systems in higher-dimensions is intricate and further exploration is a valuable and challenging task.     

Infrared Spectra of the Anion-Radicals of Benzophenone and Some of Its Isotopic Isomers

Abstract

Band assignment of the infrared spectra of the anion-radicals of benzophenone-d_O, -d₁₀ and ¹⁸O has been given on the basis of isotopic shifts. The frequency of the ν_C=O band decreases by ca. 270 cm^?1 with the transformation of neutral keton into anion-radical, due to the strong electron-withdrawing character of the carbonyl group; frequencies of the other modes decrease slightly, down to 30 cm^?1.     

Combined infrared multiphoton dissociation and electron-capture dissociation using co-linear and overlapping beams in Fourier transform ion cyclotron resonance mass spectrometry

A novel set-up for Fourier transform ion cyclotron resonance mass spectrometry (FTICR) is reported for simultaneous infrared multiphoton dissociation (IRMPD) and electron-capture dissociation (ECD). An unmodified electron gun ensures complete, on-axis overlap between the electron and the photon beams. The instrumentation, design and implementation of this novel approach are described. In this configuration the IR beam is directed into the ICR cell using a pneumatically actuated mirror inserted into the ion-optical path. Concept validation was made using different combinations of IRMPD and ECD irradiation events on two standard peptides. The ability to perform efficient IRMPD, ECD and especially simultaneous IRMPD and ECD using lower irradiation times is demonstrated. The increase in primary sequence coverage, with the combined IRMPD and ECD set-up, also increases the confidence in peptide and protein assignments.     

Gyroscopic effect in low-energy classical capture of a rotating quadrupolar diatom by an ion

The low-energy capture of homonuclear diatoms by ions is due mainly to the long-range part of the interpartner potential with leading terms that correspond to charge-quadrupole interaction and charge-induced dipole interaction. The capture dynamics is described by the perturbed-rotor adiabatic potentials and the Coriolis interaction between manifold of states that belong to a given value of the intrinsic angular momentum. When the latter is large enough, it can noticeably affect the capture cross section calculated in the adiabatic channel approximation due to the gyroscopic property of a rotating diatom. This paper presents the low-energy (low-temperature) state-selected partial and mean capture cross sections (rate coefficients) for the charge-quadrupole interaction that include the gyroscopic effect (decoupling of intrinsic angular momentum from the collision axis), quantum correction for the diatom rotation, and the correction for the charge-induced dipole interaction. These results complement recent studies on the gyroscopic effect in the quantum regime of diatom-ion capture (Dashevskaya, E. I.; Litvin, I.; Nikitin, E. E.; Troe, J. J. Chem. Phys. 2004, 120, 9989-9997).     

Entropy and Galilean invariance of lattice Boltzmann theories

A theory of lattice Boltzmann (LB) models for hydrodynamic simulation is developed upon a novel relation between entropy construction and roots of Hermite polynomials. A systematic procedure is described for constructing numerically stable and complete Galilean invariant LB models. The stability of the new LB models is illustrated with a shock tube simulation.     

Novel,Complex Flavonoids from Mallotus philippensis (Kamala Tree)

One new flavanone, 4′‐hydroxyisorottlerin ( 2 ), and two new chalcone derivatives, kamalachalcones C ( 3 ) and D ( 4 ), were isolated from Mallotus philippensis (kamala tree). The largest compound ( 4 ; M_r 1098 g/mol) was shown to possess a unique, fused‐ring system made of two hydroxy‐chalcone units, giving rise to eight fused benzene/pyran units. From the same plant, the following six known compounds were also isolated: kamalachalcone A ( 5 ) and B ( 6 ), isoallorottlerin ( 7 ), isorottlerin ( 8 ), 5,7‐dihydroxy‐8‐methyl‐6‐prenylflavanone ( 9 ); 6,6‐dimethylpyrano(2″,3″: 7,6)‐5‐hydroxy‐8‐methylflavanone ( 10 ), and rottlerin ( 1 ). The structures of the new compounds were confirmed by in‐depth spectral analyses, including 2D‐NMR techniques, and the full ¹³C‐NMR assignments of the known flavanones 1 and 7 – 10 are published for the first time.     

Near-flat space limit of strings on AdS 4×ℂℙ3

The non-linear nature of string theory on non-trivial backgrounds, related to the AdS/CFT correspondence, force one to look for simplifications. Two such simplifications proved to be useful in studying string theory. These are the pp-wave limit, which describes point-like strings, and the so-called “near-flat space” limit which connects two different sectors of string theory—pp-wave and “giant magnons”. Recently another example of AdS/CFT duality emerged—AdS ₄/CFT ₃, which suggests duality between CS theory and superstring theory on . In this paper we study the “near-flat space” limit of strings on an background and discuss possible applications of the limiting theory. R.C. Rashkov is on leave from Department of Physics, Sofia University, Bulgaria.     

Balanced Incomplete Block Designs with Block Size 9 and λ=2,4,8

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: $$\begin{gathered} {\text{ }}\lambda (v - 1) \equiv 0{\text{ mod (}}k - 1{\text{)}} \hfill \\ \lambda v(v - 1) \equiv 0{\text{ mod (}}k - 1{\text{)}} \hfill \\ \end{gathered} $$ In this paper we study k=9 with λ=2,4 or 8. For λ=8, we show these conditions on v are sufficient, and for λ=2, 4 respectively there are 8 and 3 possible exceptions the largest of which are v=1845 and 783. We also give some examples of group divisible designs derived from balanced ternary designs.