Crystal and molecular structure of 1R,3S,5S,7R,10R-3,6,6,10,14-Pentamethyltricyclo[10.3.0.05,7]pentadeca-11,14-diene-1, 10-dihydroxy-2,13-dione (Japodagrol), C20H28O4

A new cytotoxic macrocyclic diterpenoid named Japodagrol, C₂₀H₂₈O₄, has been isolated from the ornamental plantJatropha podagrica, family Euphorbiaceae, grown in Nigeria. The structure of the title compound, C₂₀H₂₈O₄, was solved by X-ray analysis.M _r =332.44, monoclinic space groupC2,a=23.285(4),b=6.5105(12),c=12.505(3) Å,=98.504(17),V=1874.8 ų,Z=4,D _c =1.178 Mg/m³. CuK radiation (graphite crystal monochromator, =1.54184 A), (CuK)=6.13 cm^–1,F(000)=720,T=290 K. Final conventionalR factor=0.035,R _w =0.038 for 3349 observed reflections. The structure was solved with the programDirdif. The 5-membered ring is closed to a half-chair form. The compound contains inter- and intramolecular hydrogen bonds.     

On 2-spannedness for the adjunction mapping

LetL be a line bundle on a smooth connected projective manifold X of dimension n. We extend to any dimension the definition of k-spannedness forL; this is a notion of k-th order embedding which was recently given in the case of curves and surfaces. Then, by a reduction to the surfaces case, we prove that the adjoint bundle K_x+(n–1)L is 2-spanned ifL is (at least) 3-spanned.     

Intra- versus intermolecular hydrogen bonds in salicylamide derivatives

The crystal structures, solid-state infrared patterns, and thermal properties of two polymorphs of 4-nitrosalicylanilide are presented. In both polymorphs, intramolecular hydrogen bonds are found between the phenol oxygen and the amide proton, and intermolecular hydrogen bonds are found between the amide carbonyl oxygen and the phenol proton. These hydrogen bond patterns are compared to those found in other known salicylamide derivatives and an analysis is given of the factors contributing to preferences for intra- or intermolecular hydrogen bonds in these structures. Crystal data: polymorph, orthorhombic,Pbca,a=11.003(4),b=27.959(7),c=7.622(5) Å,Z=4,V=2345(3) ų, andR=0.038 (1351 reflections); polymorph, monoclinic,P2₁/a,a=28.36(1),b=11.64(1),c=7.293(8) Å,=90.68(6)°,Z=8,V=2408 ų, andR=0.043 (2425 reflections).     

On a characteristic of random matrices connected with unconditional convergence almost everywhere

В статье рассматрива ются множестваM _N , 1≦N<∞ всех систем функций Φ={?(x)} _j ^=1/N , заданных на [0,1] с где (ε _{i, j} ) _{i, j} ^=1/N — матрица с э лементами ± 1. Изучаетс я поведение наМ _N функц ии $$\alpha _N (\Phi ) = \mathop {\sup }\limits_\sigma \mathop {\sup }\limits_{\sum a_j^2 = 1} (\int\limits_0^1 {\mathop {\sup }\limits_{1 \leqq k \leqq N} (\sum\limits_{j = 1}^k {a_j \varphi _{\sigma (j)} (x)} } )^2 dx)^{1/2} $$ гдеσ: {1, ...,N}?{1, ...,N}. Дока зьгаается, что сущест вуют абсолютные постоянн ыеc ₃,c ₄>0,y ₀>1, такие, что для любог оN=1,2, ... иy>y ₀ $$\mu _N (\{ \Phi \in {\rm M}_{\rm N} :\alpha _N (\Phi )/\left\| \Phi \right\| > y\} ) \leqq c_3 \exp [ - \exp (c_4 y)N]$$ гдеμ _N — мера наM _N с µ _N ({Ф}) = 2^?N2 дл я любой системыΦ∈M     

Distribution density of the norm of a stable vector

Let B be a Banach space,X be a stable B -valued random vector with exponentd(0,2), and P(·) be the distribution density of the norm of X. In this paper we study the question of the boundedness of P. In particular, we construct examples of a space B with a symmetric stable vector X with exponentd(1,2) with unbounded P and prove that if X is a nondegenerate strictly stable vector with exponentd(0,1), then P is bounded.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 105–114, 1987.The author is grateful to Yu. A. Davydov, V. I. Paulauskas, V. Yu. Bentkus, and D. Pap for stimulating discussions of the subject of this paper. When the paper was finished the author learned that similar results are found in [9].     

Superbranching processes and projections of random Cantor sets

We study sequences (X ₀, X ₁, ...) of random variables, taking values in the positive integers, which grow faster than branching processes in the sense that , for m, n0, where the X _n (m, i) are distributed as X _n and have certain properties of independence. We prove that, under appropriate conditions, X _n ^1/n almost surely and in L ¹, where =sup E(X _n )^1/n . Our principal application of this result is to study the Lebesgue measure and (Hausdorff) dimension of certain projections of sets in a class of random Cantor sets, being those obtained by repeated random subdivisions of the M-adic subcubes of [0, 1] ^d . We establish a necessary and sufficient condition for the Lebesgue measure of a projection of such a random set to be non-zero, and determine the box dimension of this projection.Work done partly whilst visiting Cornell University with the aid of a Fulbright travel grant     

Influence of crystal-field on the thermal conductivity of PrNi5

The thermal conductivity of PrNi₅ in the temperature range 0·5 to 20 K is investigated. The analysis of crystalline electric field effect on the experimentally obtained temperature dependence of the thermal conductivity indicates that beside the main electronic component also other contributions (phonons, magnetic excitons) can take place in the heat transport in this intermetallic compound.The authors would like to thank Dr. G. Eska for lending the sample and Dr. . Jáno for his interest in the work and stimulating discussions.     

Three-body Coulomb effects in neutral-particle-exchange singularity

In a three-body model with Coulomb interactions the Faddeev equations for the Alt-Grassberger-Sandhas transition operators are used to find the leading term of the neutron-transfer amplitude near the exchange singularity in the cos plane. We derive formulae containing three-body Coulomb effects for the renormalization of the second-order exchange pole in the calculation of observables, such as the cross section and polarizations.