Nonstatic gas spheres in general relativity

A model for a time-dependent relativistic gas sphere is given. Both pressurep and density are positive inside the outer boundary of the sphere, and they both drop to zero at the boundary itself. Their respective gradients are negative. For expanding models the pressure and the density are decreasing, and for contracting models the pressure and the density are increasing. The adiabatic sound speed is thus real, and for the layers close to the surface of the sphere it is found that the adiabatic sound speed is less than the speed of light. For these layers the condition>3p is also fulfilled. However, the area 4R ² for a sphere of constantr is not an increasing function of comoving radial coordinater.     

Amide interactions in chlorinated solvents

Enthalpies of solution and of transfer of amides for the solvents chloroform (CHCl₃), methylenechloride (CH₂Cl₂), carbontetrachloride (CCl₄), cyclohexane (C₆H₁₂), N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMA), and ethylacetate (EtOAc) have been used to isolate and quantify the solvation interactions of amides in chlorinated solvents. Specific interactions at the aminde carbonyl and N–H groups have been identified. An analysis of the transfer enthalpies of pyrrole and methylpyrrole from cyclohexane to the chlorinated solvents shows that specific interactions between the pyrroles and these solvents are similar in nature. A means of calculating differences in the transfers of different solutes between the same solvent pair is given.Work done at Lebanon Valley College.     

Magnetostriction measurement by means of strain modulated ferromagnetic resonance (SMFMR)

A novel method for measuring magnetostriction constants is presented. A strain, periodic in time, applied to the sample, causes a modulation of the ferromagnetic resonance line position. The height of the signal obtained after phase-sensitive detection is proportional to the strain modulation depth. The appropriate magnetostriction constant λ is obtained by comparing the height of the SMFMR signal with that of the FMR line, as recorded by means of magnetic field modulation. Features of the new technique are:

1. high sensitivity: λ_min? 10_?9 forM=100 Oe and linewidth ΔH _d=1 Oe;
2. λ's belonging to distinct precession modes are separately determined;
3. applicable to thin layers for which strain gauge techniques cannot be used;
4. wide temperature range: 1.2 K<T<300 K;
5. uniform stress.

An illustrative example (YIG layer on GGG substrate) is given.     

The 7‐bromo derivative of 2‐amino‐2′‐deoxytubercidin fluorinated at the sugar moiety

The title compound, 2,4‐diamino‐5‐bromo‐7‐(2‐deoxy‐2‐fluoro‐β‐d ‐arabinofuranosyl)‐7H‐pyrrolo[2,3‐d]pyrimidine, C₁₁H₁₃BrFN₅O₃, shows two conformations of the exocyclic C4′—C5′ bond, with the torsion angle γ (O5′—C5′—C4′—C3′) being 170.1 (3)° for conformer 1 (occupancy 0.69) and 60.7 (7)° for conformer 2 (occupancy 0.31). The N‐glycosylic bond exhibits an anti conformation, with χ = −114.8 (4)°. The sugar pucker is N‐type (C3′‐endo; ³T₄), with P = 23.3 (4)° and τ_m = 36.5 (2)°. The compound forms a three‐dimensional network that is stabilized by several intermolecular hydrogen bonds (N—H...O, O—H...N and N—H...Br).     

Stabilitätsungleichungen für Diskretisierungen von Randwertaufgaben gewöhnlicher Differentialgleichungen

Summary We consider two-point boundary value problems for linear differential equations (of ordern). The main part consists in proving stronger apriori estimates for (mn–1) using discreteL ₁-norms of the involved right-hand sides; thus extending known results for discreteL _p -norms with 2p. These estimates are the main tool in proving sharp estimates for the error \y–y _h \ _h, as well asfor \P _y –P _h y _h \ _h, , whereP _h denotes a consistent approximation of the differential operatorP of ordermn–1, in terms of the discretL ₁-norm of the truncation error. By means of an interpolation technique these estimates yield a correct estimate of the order of convergence, also in case that the solution satisfies locally some Lipschitz-conditions.     

The first enantiomerically pure [n]triangulanes and analogues: sigma-[n]helicenes with remarkable features

(M)-(-)- and (P)-(+)-Trispiro[2.0.0.2.1.1]nonanes [(M)- and (P)-3] as well as (M)-(-)- and (P)-(+)-tetraspiro[2.0.0.0.2.1.1.1]undecanes [(M)- and (P)-4]-enantiomerically pure unbranched [4]- and [5]triangulanes-have been prepared starting from racemic bicyclopropylidenecarboxylic [(1RS)-12] and exo-dispiro[2.0.2.1]heptane-1-carboxylic [(1RS,3SR)-13] acids. The optical resolutions of rac-12 and rac-13 furnished enantiomerically pure acids (S)-(+)-12, (R)-(-)-12, (1R,3S)-(-)-13, and (1S,3R)-(+)-13. The ethyl ester (R)-25 of the acid (R)-(-)-12 was cyclopropanated to give carboxylates (1R,3R)-26 and (1R,3S)-26. The ester (1R,3S)-26 and acids (1R,3S)-13 and (1S,3R)-13 were converted into enantiomerically pure methylene[3]triangulanes (S)-(-)- and (R)-(+)-28. An alternative approach consisted of an enzymatic deracemization of endo-[(1SR,3SR)-dispiro[2.0.2.1]heptyl]methanol (rac-20) or anti-[(1SR,3RS)-4-methylenespiropentyl]methanol (rac-18). This afforded (S)-(-)- and (R)-(+)-28 (starting from rac-20), as well as enantiomerically pure (M)-(-)- and (P)-(+)-1,4-dimethylenespiropentanes [(M)- and (P)-23] starting from rac-18. The methylenetriangulanes (S)-(-)- and (R)-(+)-28 were cyclopropanated furnishing (M)- and (P)-3. The rhodium-catalyzed cycloaddition of ethyl diazoacetate onto (S)-(-)- and (R)-(+)-28 yielded four diastereomeric ethyl trispiro[2.0.0.2.1.1]nonane-1-carboxylates in approximately equal proportions. The enantiomerically pure esters (1R,3S,4S)- and (1S,3R,4R)-30 were isolated by careful distillation and then transformed into [5]triangulanes (M)- and (P)-4 using the same sequence of reactions as applied for (M)- and (P)-3. The structures of the key intermediates (R)-12 and rac-31 were confirmed by X-ray analyses. Although [4]- and [5]triangulanes have no chromophore which would lead to any significant absorption above 200 nm, they have remarkably high specific rotations even at 589 nm with [alpha](20)D=-192.7 [(M)-3, c=1.18, CHCl(3))] or +373.0 [(P)-4, c=1.18, CHCl(3))]. This remarkable optical rotatation is in line with their helical arrangement of sigma bonds, as confirmed by a full valence space single excitation configuration interaction treatment (SCI) in conjunction with DFT computations at the B3LYP/TZVP//B3LYP/6-31+G(d,p) level of theory which reproduce the ORD very well. Thus, it is appropriate to call the helically shaped unbranched [n]triangulanes the "sigma-[n]helicenes", representing the sigma-bond analogues of the aromatic [n]helicenes.     

Reaction of 5,6,7,8-Tetrahydropterin with Iron(III) Acetylacetonate. Detection of Radical Cations by Electrospray Ionization Mass Spectrometry

The experimental conditions developed for the detection of rather stable radical cations in solution by electrospray-ionization mass spectrometry (ESI-MS) of a Fe^II complex of 2-amino-5,6,7,8-tetrahydro-5-methylpteridin-4 (3H)-one ( 1c ) are used to observe the formation of the more unstable radical cations formed from 2-amino-5,6,7,8-tetrahydropteridin-4(3H)-one ( 1a ) and tris(pentane-2,4-dionato)iron(III) ([Fe^III(acac)₃]; 4 ) and to monitor their oxidation to the corresponding p-quinonoid dihydropterin complexes. These results contribute to the understanding of the important role played by 6β-5,6,7,8-tetrahydro-L -biopterin ( 1b ; a homologue of 1a ) together with iron as constituent of some cofactors. The complexes obtained from 1a and iron may be considered, e.g. as a model of the cofactor of the phenylalanine hydroxylase. Moreover, we describe an improved synthesis of 1c .     

AES investigations on starting powders for high performance ceramics

AES depth profiles on ceramic powders (untreated/hydrolyzed/oxidized/ (Al, Y)₂O₃ coated Si₃N₄, [BaO, SiO₂] coated Al₂O₃) are feasible on thin, homogeneous layers or m sized agglomerations prepared on an Au foil. By means of the depth profiles one can qualitatively characterize the coating around the particles. Factor analysis of the depth profiles on the differently treated Si₃N₄ powders suggests the existence of an Si₂N₂O phase on the oxidized sample.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday     

C[triple‐bond]C—H systems as hydrogen‐bond donors and acceptors: trans‐1,2‐diethynylcyclo­hexane‐1,2‐diol and trans‐1,4‐diprop‐2‐ynylcyclo­hexane‐1,4‐diol monohydrate

The title 1,2‐diol derivative, C₁₀H₁₂O₂, crystallizes with two independent but closely similar mol­ecules in the asymmetric unit. Only two of the four OH groups are involved in classical hydrogen bonding; the mol­ecules thereby associate to form chains parallel to the short c axis. The other two OH groups are involved in O—H⋯(C[triple‐bond]C) systems. Additionally, three of the four C[triple‐bond]C—H groups act as donors in C—H⋯O inter­actions. The 1,4‐diol derivative crystallizes with two independent half‐mol­ecules of the diol (each associated with an inversion centre) and one water mol­ecule in the asymmetric unit, C₁₂H₁₆O₂·H₂O. Both OH groups and one water H atom act as classical hydrogen‐bond donors, leading to layers parallel to the ac plane. The second water H atom is involved in a three‐centre contact to two C[triple‐bond]C bonds. One acetyl­enic H atom makes a very short `weak' hydrogen bond to a hydr­oxy O atom, and the other is part of a three‐centre system in which the acceptors are a hydroxy O atom and a C[triple‐bond]C bond.     

Charge-transfer complexes of indenophanes with π-acceptors

The charge-transfer (CT) spectra of the -complexes formed by a number of -acceptors with several indenophanes as well as indene as a model compound have been measured in methylene chloride at 20 °C. Association constants and transition energies of these complexes as well as ionization potentials of the -donors have been determined. The data obtained indicate the existence of transannular electronic interactions in the indenophane nucleus. Furthermore, the pseudo-para- andmeta[2.2]indenophane isomers (3 and4) show a large difference in their -base strength. A good linear relationship has been observed between the association constants and _max of the long wavelength CT bands for the -complexes of these -donors with both tetracyanoethylene (TCNE) and 2,3-dichloro-5,6-dicyanobenzoquinone (DDQ). All CT complexes studied have a 1:1 stoichiometry.

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Charge-transfer-Komplexe aus Indenophanen und -Akzeptoren

Zusammenfassung Die Charge-transfer-Spektren (CT-Spektren) von -Komplexen aus Indenophanen bzw. der Modellverbindung Inden und verschiedenen -Akzeptoren wurden in Methylenchlorid bei 20 °C bestimmt. Die Assoziationskonstanten und Übergangsenergien dieser Komplexe sowie die Ionisationspotentiale der -Donatoren wurden ermittelt. Die Daten sprechen für das Vorliegen transannularer elektronischer Wechselwirkungen im Indenophan-System. Die isomeren pseudo-para- und -meta[2.2]indenophane3 und4 unterscheiden sich in ihrer -Basizität deutlich. Es besteht eine gute lineare Korrelation zwischen den Assoziationskonstanten und _max der langwelligen CT-Banden der verschiedenen -Donatoren mit Tetracyanoethylen (TCNE) und 2,3-Dichlor-5,6-dicyano-p-benzochinon (DDQ). Alle untersuchten CT-Komplexe besitzen 1:1-Stöchiometrie.