A characterization of certain discrete exponential families

For independent random variables X and Y, define % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabofaruWrL9MCNLwyaGqbciaa-bcacqGHHjIUcaWFGaGaa8hw% aiaa-TcacaWFzbaaaa!4551!\[{\rm{S}} \equiv X + Y\]. When the conditional expectations % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGBbqefCuzVj3zPfgaiuGajaaqcaWFNbGccaGGOaGa% amiwaiaacMcacaGG8bGaam4uaiaac2facqGHHjIUcaWGHbGaaiikai% aadofacaGGPaaaaa!4BC4!\[E[g(X)|S] \equiv a(S)\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGBbGaamiAaiaacIcacaWGybGaaiykaiaacYhacaWG% tbGaaiyxaiabggMi6kaadkgacaGGOaGaam4uaiaacMcaaaa!4894!\[E[h(X)|S] \equiv b(S)\]are given, then under certain assumptions, the density function of X has the form of u(x)k()e^ax, where u(x) is uniquely determined by the functions a(·) and b(·).     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

Austauscher mit cyclischen Polyethern als Ankergruppen—II: Anwendungen

Exchangers with cyclic polyethers as anchor groups have a large range of applications such as separations of cations with a common anion, of anions with a common cation, and of neutral organic compounds, and the determination of water by elution chromatography. Some crown ether monomers, especially 4- and 4,4′-alkyl-substituted benzo-derivatives are suitable for extractions and their adducts with heteropoly acids are used as liquid ion-exchangers. The exchangers are also applied in thin-layer chromatography and thin-layer electrophoresis. Furthermore the exchangers are successfully used in preparative chemistry, e.g., in salt conversions in order to isolate salts which are difficult to prepare by other means, in isolation and purification of organic compounds, and for anion activation in organic reactions.     

Measurement of the Compton profiles of CH4 and C2H4 by high energy electron impact spectroscopy

We present a new experimental determination of the Compton profiles of CH₄ and C₂H₄ molecules using high energy electron impact. The observable q range has been extended up to 10 au (6 au for C₂H₄). Good agreement is found with an earlier X-ray scattering experiment and with new theoretical calculations.     

Access to 2-fluoroacrylates and their 3-chloro derivatives by chemical hydrogenolysis of 3,3-dichloro-2-fluoroacrylates

The formation of 3-chloro-2-fluoroacrylates 2 and 2-fluoroacrylates 3 by hydrogenolysis of 3,3-dichloro-2-fluoroacrylates 1 was studied by using Bu₃SnH, zinc, the sodium sulphite/sodium formate mixture or iron pentacarbonyl in the presence of a hydrogen donor (Et₃SiH or CH₃OH). The two last couples can be used to prepare the 3-chloro derivatives 2, whereas for the preparation of the 3,3-dihydro derivatives 3, zinc is the most appropriate reducing agent. Keywords: 2-Fluoroacrylate; 3-Chloro-2-fluoroacrylate; 3,3-Dichloro-2-fluoroacrylate; Tributyltin hydride; Zinc; Sodium sulphite; Sodium formate; Iron pentacarbonyl; NMR spectroscopy; IR spectroscopy     

Natural Abundance 17O-NMR. Study of Some Macrocyclic Complexes with Alkali Metal Cations

Complexation between crown ethers 12C4, 15C5, 18C6 and cryptand 222, and alkali cations Li⁺, Na⁺, K⁺ in various solvents were studied by ¹⁷O-NMR. spectroscopy. Small diamagnetic shifts arising from the cation electric field are observed. They increase according to the sequence K⁺ < Na⁺ < Li⁺. ¹⁷O-linewidth are discussed and compared to the ¹³C relaxation times. Linewidth modification results mainly from modifications of the effective correlation time. In general, for crown ethers, considerable line broadening occurs when the cation fits well into the cavity but line narrowing occurs when the cation is much smaller than the cavity.     

Intramolecular fluorine migration via four-member cyclic transition states

Gaseous CF(3)(+) interchanges F(+) for O with simple carbonyl compounds. CF(3)(+) reacts with propionaldehyde in the gas phase to produce (CH(3))(2)CF(+) via two competing pathways. Starting with 1-(13)C-propionaldehyde, the major pathway (80%) produces (CH(3))(2)CF(+) with the carbon label in one of the methyl groups. The minor pathway (20%) produces (CH(3))(2)CF(+) with the carbon label in the central position. The relative proportions of these two pathways are measured by (19)F NMR analysis of the neutral CH(3)CF=CH(2) produced by deprotonation of (CH(3))(2)CF(+) at <10(-)(3) Torr in an electron bombardment flow (EBFlow) reactor. Formation of alkene in which carbon is directly bonded to fluorine means that (in the minor product, at least) an F(+) for O transposition occurs via adduct formation followed by 1,3-atom transfer and then isomerization of CH(3)CH(2)CHF(+) to the more stable (CH(3))(2)CF(+). Use of CF(4) as a chemical ionization (CI) reagent gas leads to CF(3)(+) adduct ions for a variety of ketones, in addition to isoelectronic transposition of F(+) for O. Metastable ion decompositions of the adduct ions yield the metathesis products. Decompositions of fluorocycloalkyl cations formed in this manner give evidence for the same kinds of rearrangements as take place in CH(3)CH(2)CHF(+). Density functional calculations confirm that F(+) for O metathesis takes place via addition of CF(3)(+) to the carbonyl oxygen followed by transposition via a four-member cyclic transition state. A computational survey of the effects of different substituents in a series of aldehydes and acyclic ketones reveals no systematic variation of the energy of the transition state as a function of thermochemistry, but the Hammond postulate does appear to be obeyed in terms of progress along the reaction coordinate. Bond lengths corresponding to the central barrier correlate with overall thermochemistry of the F(+) for O interchange, but in a sense opposite to what might have been expected: the transition state becomes more product-like as the metathesis becomes increasingly exothermic. This reversal of the naive interpretation of the Hammond postulate is accounted for by the relative positions of the potential energy wells that precede and follow the central barrier.     

Superacid cyclization of 13E,17E- and 13E,17Z-bicyclogeranylfarnesols and their acetates — An effective structurally selective stereospecific route to scalarane sesterterpenoids

Institute of Chemistry, Moldavian SSR Academy of Sciences, Kishinev. Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 759–760, September–October, 1988.