Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.     

Comparison between structural and residual error formulations of an optimum design mechanism problem

Summary The model formulation of the objective function is one of the most important steps for solving an optimization problem. Generally, the objective function of an optimal design mechanism problem can be mathematically formulated either with structural or residual errors. In this paper we have conducted some comparisons between the results obtained by the structural and residual error formulations utilized in solving the optimum design of a four-bar linkage. The optimization problem is defined as a nonlinear least-squares problem. The damped Gauss-Newton algorithm is utilized for computing the solution, which ensures a local convergence for almost all nonlinear least-squares problems.

---

Sommario La formulazione matematica della funzione obiettivo è uno degli aspetti più delicati nella soluzione di un problema di ottimizzazione. Generalmente la funzione obiettivo di un problema di progettazione ottima di un meccanismo può essere formulata sia mediante l'errore strutturale che residuo. In questo lavoro sono stati eseguiti dei confronti tra i risultati ottenuti mediante le due precedenti formulazioni, in riferimento al problema della progettazione ottima di un quadrilatero articolato. Il problema di ottimizzazione viene definito come un problema nonlineare ai minimi quadrati la cui soluzione numerica è ottenuta mediante l'algoritmo damped di Gauss-Newton.

---

---

This paper was partially discussed at theII Congegno di Meccanica Computazionale, Roma, 1987.     

Reducible Dupin submanifolds

Pinkall's standard constructions for obtaining a Dupin hypersurface W in ^N from a Dupin hypersurface M in ⁿ , N>n, are studied in the context of Lie sphere geometry. It is shown that a compact Dupin hypersurface W in ^N with g distinct principal curvatures at each point is reducible to a compact Dupin hypersurface M in ⁿ if and only if g=2.This research was supported by NSF Grant No. DMS 87-06015.     

Relaxation methods in control theory

Two different relaxed problems associated with a problem of optimal control theory, governed by an ODE, are considered: the first is obtained by Young's methods and the second by semicontinuity arguments. A formula which relates the two relaxed functionals to each other is given.     

Poisson structure of a periodic classical XYZ -chain

Classical variables ( -variables) are constructed for a periodic classical XYZ -chain (of the discrete Landau-Lifshitz equation). The connection of the quantum method of the inverse problem and the theory of finite-zone integration is discussed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 150, pp. 154–180, 1986.     

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.     

A note on the kernel of the\bar \partial -Neumann operator on strongly pseudo-convex domains

In this paper, we discuss the relations between a special Heisenberg coordinate system and a normalized Levi metric on strongly pseudo-convex domains in Cⁿ and see how they are related to the -Neumann operator.Work supported by MSRI, Berkeley, California.     

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.     

Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups

Let ( _t ) _t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent ₀ is the Haar measure on some compact subgroupK. Then all the measures ₁ are supported by theK-contraction groupC _K() of the topological automorphism ofG. We prove here the structure theoremC _K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.     

A proof of Freud's conjecture for exponential weights

LetW (x) be a function nonnegative inR, positive on a set of positive measure, and such that all power moments ofW ²(x) are finite. Let {p _n (W ²;x)} ₀ denote the sequence of orthonormal polynomials with respect to the weightW ²(x), and let {A _n } ₁ and {B _n } ₁ denote the coefficients in the recurrence relation