Autocorrelation Functions as Translation Invariants in L1 and L2

The Adler-Konheim theorem [Proc. Amer. Math. Soc. 13 (1962), 425-428] states that the collection of nth-order autocorrelation functions is a complete set of translation invariants for real-valued L¹ functions on a locally compact abelian group. It is shown here that there are proper subsets of that also form a complete set of translation invariants, and these subsets are characterized. Specifically, a subset is complete if and only if it contains infinitely many even-order autocorrelation functions. In addition, any infinite subset of is complete up to a sign. While stated here for functions on the proofs presented hold for functions on any locally compact abelian group that is not compact, in particular, on and the integer lattice      

Stereodynamics of 9,11-Diphenyl-10-azatetracyclo[6.3.0.0.(4,11)0.(5,9)]undecanes. Highly Restricted Nitrogen Inversion and Isolated Phenyl Rotation. X-ray Crystallographic, Dynamic NMR, and Molecular Mechanics Studies

The (1)H NMR spectra of 10-benzyl-9,11-diphenyl-10-azatetracyclo[6.3.0.0.(4,11)0.(5,9)]undecane (BnPh(2)()) and 10-methyl-9,11-diphenyl-10-azatetracyclo[6.3.0.0.(4,11)0.(5,9)]undecane (MePh(2)()) decoalesce due to slowing inversion at nitrogen and to slowing isolated bridgehead phenyl rotation. The high nitrogen inversion barriers in MePh(2)() (DeltaG() = 12.2 +/- 0.1 kcal/mol at 250 K) and BnPh(2)() (DeltaG() = 10.6 +/- 0.1 kcal/mol at 215 K) are typical of tertiary amines in which at least one C-N-C bond angle is constrained to a small value. Compared to the minuscule rotation barriers about sp(2)-sp(3) carbon-carbon bonds in simple molecular systems, the bridgehead phenyl rotation barriers in MePh(2)() (DeltaG() = 9.8 +/- 0.1 kcal/mol at 210 K) and BnPh(2)() (DeltaG() = 9.8 +/- 0.1 kcal/mol at 210 K) are unusually high. Molecular mechanics calculations (MMX force field) suggest that the origin of the high phenyl rotation barriers lies in the close passage of an o-phenyl proton and a methyl (or benzylmethylene) proton in the transition state. BnPh(2)() crystallized from hexane as white needles in the monoclinic system Pn. Unit cell dimensions are as follows: a = 12.198(1) ?, b = 6.1399(6) ?, c = 14.938(2) ?, beta = 107.470(4) degrees, V = 1067.1(2) ?(3), Z = 2. In the crystal molecular structure, the imine bridge CNC bond angle in BnPh(2)() is constrained to a small value (96 degrees ). The benzylic phenyl group is oriented gauche to the nitrogen lone pair.     

Epicardial development in the rat: a new perspective.

Development of the epicardium is critical to proper heart formation. It provides all of the precursor cells that form the coronary system and supplies signals that stimulate cardiac myocyte proliferation. The epicardium forms from mesothelial cells associated with the septum transversum and is referred to as the proepicardium (PE). Two different methods by which these PE cells colonize the developing heart have been described. In avians, PE cells form a bridge to the heart over which PE cells migrate onto the heart. In fish and mammals, PE cells form vesicles of cells that detach from the mesothelium, float through the pericardial cavity, and attach to the heart. A previous study of rat PE development investigated this process at the histological level. Protein markers have been developed since this study. Thus, we investigated this important developmental process coupled with these new markers using other visualization techniques such as scanning electron microscopy (SEM) and confocal microscopy. Finally, a novel, three-dimensional (3-D) culture system was used to confirm the identity of the PE cells. In this study, we found convincing evidence that the rat PE cells directly attach to the heart in a manner similar to that observed in avians.     

Superoxide radical anion adduct of 5,5-dimethyl-1-pyrroline N-oxide (DMPO). 2. The thermodynamics of decay and EPR spectral properties

The formation of the superoxide radical anion (O2*-) adduct of the nitrone 5,5-dimethyl-1-pyrroline N-oxide (DMPO) as detected by electron paramagnetic resonance (EPR) spectroscopy is one of the most common techniques for O2*- detection in chemical and biological systems. However, the nature of DMPO-O2H has confounded spin-trapping investigators over the years, since there has been no independently synthesized DMPO-O2H to date. A density functional theory (DFT) approach was used to predict the isotropic hyperfine coupling constants arising from the N, beta-H, and gamma-H nuclei of DMPO-O2H using explicit interactions with water molecules as well as via a bulk dielectric effect employing the polarizable continuum model (PCM). Theoretical calculation on the thermodynamics of DMPO-O2H decay shows favorable intramolecular rearrangement to form a nitrosoaldehyde and a hydroxyl radical as products, consistent with experimental observations. Some pathways for the bimolecular decomposition of DMPO-O2H and DMPO-OH have also been computed.     

Tris(arylmethyl) derivatives of 1,3,5-trimethoxy- and 1,3,5-triethylbenzene

The hexasubstituted benzenes 7 and 9b were synthesized starting from 3 and 8b, respectively. In the crystal, 9b adopts the fully alternated conformation with all arylmethyl groups oriented syn.     

Three new flavonol malonylrhamnosides from Ribes alpinum.

Three new flavonol malonylrhamnosides, 3-O-(4"-O-malonyl)-alpha-L-rhamnopyranosides of mearnsetin, myricetin and quercetin respectively, together with the corresponding mearnsitrin, myricitrin, quercitrin and the 4-O-methyl phloracetophenone 2-O-beta-D-glucopyranoside, were isolated from the leaves of Ribes alpinum and fully characterized by spectrocopic methods including 2D NMR.     

Are α-alkoxyalkyl complexes special? 13CH coupling constant evidence.

Comlexes of type L_nMCH₂O₂CCMe₃ exhibit relatively large values of ¹J_CH for the α-carbon; however, unexpectedly large values are also found for the methyl analogs, L_nMCH₃. Thus technique does not provide evidence for any unusual interactions in the former. Cleavage of the ester linkage by MeLi proceeded cleanly only for L_nM = CpMo(Co)₃, leading to CpMo(CO)₃^?; with L_nM = Mn(CO)₅ or CpFe(CO)₂ electron transfer processes predominate. Such reactions are also observed for simple metal alkyls such as CpFe(CO)₂CH₃.     

The synthesis of the drugstore beetle pheromone (Stegobinone)

2,3-Dihydro-2,3,5-trimethyl-6-(1-methyl-2-oxobutyl)-4H-pyran-4-one ($\text{1}$ (Stegobinone), the sex pheromone of the drugstore beetle, was successfully prepared from 4,6-dimethyl-3,5,7-nonatrione ($\text{2}$) by a biogenetically plausible scheme.     

Progression of Organic Reactions on Resin Supports Monitored by Single Bead FTIR Microspectroscopy

We report the time courses of five solid-phase reactions obtained using single bead FTIR microspectroscopy. This time-resolved information aided in the determination of the required reaction time, the nature of the solid-phase reaction, and resin property, effectively assisting in the initial phase of our combinatorial chemistry efforts. Our results showed that solid-phase organic reactions proceed faster than generally speculated. In addition, we have shown that reactions on the surface and in the interior of the bead occur at the same rate for reactions studied. The reaction on the TentaGel resin was shown to be not faster than reactions on Wang resin, suggesting that the diffusion of the substrate into polystyrene bead copolymerized with 1% divinylbenzene is not rate-limiting. Finally, the capability of obtaining IR spectra from the partial surface of a single bead demonstrated the femtomolar detection limit of single bead FTIR microspectroscopy.     

Thermochemical excess properties of multicomponent systems: Representation and estimation from binary mixing data

A general equation for the estimation of thermodynamic excess properties of multicomponent systems from observed excess properties of the various binary combinations of the components has been developed, based on a simple model of the multicomponent system. This estimation takes the form $$\Delta \bar Z_{12...N}^{ex} = \sum\limits_{i = 1}^N {\sum\limits_{j > i}^N {(X_i + X_j )(f_i + f_j )(\Delta \bar Z_{ij}^{ex} )^* } } $$ in which \((\Delta \bar Z_{ij}^{ex} )^* \) is the molar excess property (enthalpy, entropy, volume, free energy, etc.), of the binary system with components at the same molar ratio as in the multicomponent system, and f_i, f_j are weighted mole fractions using weighting factors based on the excess properties of the binary systems. The important features of this equation are: it is applicable to a broad range of thermodynamic properties, its application to both integral and differential mixing properties is independent of the manner in which the binary mixing data is represented (Redlich-Kister equation, Wilson equation, etc.), and it provides reasonably accurate predictions ranging from quite good for simple systems of nonspecific interactions to only fair for associated solutions. This equation is recommended as a point-of-departure for mathematical representation of experimental data for multicomponent systems.