Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

The Role of a Specific Response of Media in the Vavilov-Cherenkov Effect

It is shown that the condition υ > υ_p (ω), which is necessary in order to trigger the Vavilov-Cherenkov effect, determines the interval of radiated frequencies and it alone cannot establish a strong restriction to the velocity of the particle. It is exhibited that it is possible to define a general lower bound for the velocity of the particle, which does not depend on the frequency when both, a specific response of the medium is taken into account and the mentioned condition is considered. The minimum value of the phase velocity of light in the medium determines the existence of such general lower bound.     

Excess molar enthalpy of binary mixtures of hexane+ethyl benzene, <Emphasis Type="Italic">o</Emphasis>-xylene, <Emphasis Type="Italic">m</Emphasis>-xylene and <Emphasis Type="Italic">p</Emphasis>-xylene at 298.15 K

Summary This paper reports excess molar enthalpies of the binary systems hexane+ethyl benzene, hexane+o-xylene, hexane+m-xylene and hexane+p-xylene at 298.15 K and atmospheric pressure, over the whole composition range. The data was measured directly using a Calvet microcalorimeter. The excess magnitude was correlated to a Redlich-Kister type equation for each mixture. Also, we will discuss the results for the four mixtures studied here and by comparison with the same binary systems but containing propyl propanoate as first component. Finally, we will correlate our results with the Nitta-Chao and the three UNIFAC theoretical approximations.     

CH2CHOH2+ + PN: a proton-transfer triple play

Quantum chemical calculations are used to explore the proton-transfer reactivity of O-protonated vinyl alcohol, CH2CHOH2+, with phosphorus nitride, PN. This reaction is relevant to the chemical evolution of interstellar clouds, since O-protonated vinyl alcohol has been postulated (and tentatively identified) as a product of the association reaction between interstellar H3O+ and C2H2, while PN is the most widespread and abundant phosphorus-containing molecule seen in astrophysical environments. Furthermore, the reaction exhibits an unusual mechanistic feature, namely, an extended "proton-transport catalysis" mechanism, which we characterize here as a "proton-transfer triple play". The reaction proceeds initially by proton transfer from CH2CHOH2+ to PN, then from PNH+ to CH2CHOH, and finally from CH3CHOH+ to PN, where the emphasized atom indicates the resultant site of protonation/deprotonation. Thus, the ultimate overall bimolecular proton-transfer reaction is expected to occur as CH2CHOH2+ + PN --> CH3CHO + PNH+; that is, the apparent favored product channel exhibits not only proton transfer but also keto/enol tautomerization. The triple-play mechanism can be rationalized in terms of the proton affinities of vinyl alcohol, acetaldehyde, and phosphorus nitride, which here are satisfactorily reproduced by high-level ab initio calculations. Other neutrals with a proton affinity appropriate for the possible triple-play mechanism converting CH2CHOH2+ to CH3CHO are also identified, with a view to encouraging experimental investigation of this mechanism.     

Normsets and determination of unique factorization in rings of algebraic integers

The image of the norm map from to (two rings of algebraic integers) is a multiplicative monoid . We present conditions under which is a UFD if and only if has unique factorization into irreducible elements. From this we derive a bound for checking if is a UFD.

     

The classification of ϕ-symmetric Sasakian manifolds

A -symmetric spaceM is a complete connected regular Sasakian manifold, that fibers over an Hermitian symmetric spaceN, so that the geodesic involutions ofN lift to define global (involutive) automorphisms of the Sasakian structure onM. In the present paper the complete classification of -symmetric spaces is obtained. The groups of automorphisms of the Sasakian structures and the groups of isometries of the underlying Riemannian metrics are determined. As a corollary, the Sasakian space forms are also determined.     

Two families of mixed finite elements for second order elliptic problems

Summary Two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. Error estimates inL ² () andH ^–5 () are derived for these elements. A hybrid version of the mixed method is also considered, and some superconvergence phenomena are discussed.     

Thermochemical properties of benzoic acid derivatives VIII. Enthalpies of combustion and formation of o-, m-, and p- t-butylbenzoic acids

The enthalpies of formation in the crystalline state at 298.15 K of o-, m-, and p-t-butyl-benzoic acids have been determined by static-bomb calorimetry. Vapour-pressure determinations were made by the Knudsen-effusion technique and the sublimation enthalpies at the mean temperatures of the measurement ranges have been derived for the three acids. The values obtained are:

     

10.

Reactions of tetracarbonylcobaltate(-I) with chlorosilanes in ether solvents     

Brian K. Nicholson  Jim Simpson 《Journal of organometallic chemistry》1978,155(2):237-244

The reactions of NaCo(CO)₄ with Me_nSiCl_4?n (n = 0–3) in diethylether (Et₂O) and in tetrahydrofuran (THF) have been studied. Three distinct reaction pathways were recognised which depend on the acidity of the chlorosilane and basicity of solvent. Attack at the silicon centre via the Co atom of Co(CO)₄^? leads to formation of a SiCo bond; reaction involving a CO ligand of Co(CO)₄^? gives clusters R₃SiOCCo₃(CO)₉; and chlorosilane induced attack of Co(CO)₄^? on the solvent gives products derived from THF molecules.     

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	$\text{ΔH}{}_{\mathrm{f}}{}^{\mathrm{o}}\text{(c, 298.15 K)/kJ mol}{}^{\mathrm{?1}}$	$\text{ΔH}{}_{\mathrm{s}}\text{/kJ mol}{}^{\mathrm{?1}}$
o-t-butylbenzoic acid	476.2 ± 1.9	99.8 ± 0.4	(at 314.6 K)
m-t-butylbenzoic acid	504.3 ± 1.6	103.0 ± 0.5	(at 326.5 K)
p-t-butylbenzoic acid	502.9 ± 1.7	103.8 ± 0.4	(at 334.1 K)

Reactions of tetracarbonylcobaltate(-I) with chlorosilanes in ether solvents

The reactions of NaCo(CO)₄ with Me_nSiCl_4?n (n = 0–3) in diethylether (Et₂O) and in tetrahydrofuran (THF) have been studied. Three distinct reaction pathways were recognised which depend on the acidity of the chlorosilane and basicity of solvent. Attack at the silicon centre via the Co atom of Co(CO)₄^? leads to formation of a SiCo bond; reaction involving a CO ligand of Co(CO)₄^? gives clusters R₃SiOCCo₃(CO)₉; and chlorosilane induced attack of Co(CO)₄^? on the solvent gives products derived from THF molecules.