Cyclic torsion of elliptic curves

Let be an elliptic curve over a number field such that
and let denote the number of roots of unity in . Ross proposed a question: Is isogenous over to an elliptic curve such that is cyclic of order dividing ? A counter-example of this question is given. We show that is isogenous to such that . In case has complex multiplication and , we obtain certain criteria whether or not is isogenous to such that .

     

The effect of anhydrous ammonia on the crystalline-state deformation of nylons 6 and 6,6

The aliphatic polyamides nylon 6 and 6,6 have been cold drawn by using the new concept of reversible plasticization with NH₃. Two aspects were investigated: the effect of NH₃ plasticization on the stress-strain behavior of nylon 6,6, and the extent of NH₃ absorption as determined by x-ray analysis for the structurally simpler nylon 6. X-ray analysis shows that ammonia is absorbed preferentially by the amorphous phase and that the plasticization has a significant effect on the unit-cell orientation, the small-angle void scattering, and the interplanar spacings between sheets of hydrogen-bonded chains. The effect of plasticization was seen in the lower yield stress, the higher draw ratio (up to 8X) and tensile modulus (10 GPa) not attainable with unplasticized specimens.     

Residuenfreie Differentiale und der Cartier-Operator algebraischer Funktionenkörper

Ohne ZusammenfassungThe author acknowledges support received from the National Research Council of Canada, Grant A-7210.Herrn. Prof. E.Lamprecht und Herrn Dr. H.Mathieu dankt Verfasser für ihre Anmerkungen, die zu Verbesserungen der ursprünglichen Fassung führten.     

Concise three-component synthesis of defucogilvocarcin M

[reaction: see text] Concise synthesis of defucogilvocarcin M was achieved via the [2 + 2 + 2] approach to beta-phenylnaphthalene structure.     

Pseudo Approximation Algorithms with Applications to Optimal Motion Planning

We introduce a technique for computing approximate solutions to optimization problems. If $X$ is the set of feasible solutions, the standard goal of approximation algorithms is to compute $x\in X$ that is an $\varepsilon$-approximate solution in the following sense: $$d(x) \leq (1+\varepsilon)\, d(x^*),$$ where $x^* \in X$ is an optimal solution, $d\colon\ X\rightarrow {\Bbb R}_{\geq 0}$ is the optimization function to be minimized, and $\varepsilon>0$ is an input parameter. Our approach is first to devise algorithms that compute pseudo $\varepsilon$-approximate solutions satisfying the bound $$d(x) \leq d(x_R^*) + \varepsilon R,$$ where $R>0$ is a new input parameter. Here $x^*_R$ denotes an optimal solution in the space $X_R$ of $R$-constrained feasible solutions. The parameter $R$ provides a stratification of $X$ in the sense that (1) $X_R \subseteq X_{R}$ for $R < R$ and (2) $X_R = X$ for $R$ sufficiently large. We first describe a highly efficient scheme for converting a pseudo $\varepsilon$-approximation algorithm into a true $\varepsilon$-approximation algorithm. This scheme is useful because pseudo approximation algorithms seem to be easier to construct than $\varepsilon$-approximation algorithms. Another benefit is that our algorithm is automatically precision-sensitive. We apply our technique to two problems in robotics: (A) Euclidean Shortest Path (3ESP), namely the shortest path for a point robot amidst polyhedral obstacles in three dimensions, and (B) $d_1$-optimal motion for a rod moving amidst planar obstacles (1ORM). Previously, no polynomial time $\varepsilon$-approximation algorithm for (B) was known. For (A), our new solution is simpler than previous solutions and has an exponentially smaller complexity in terms of the input precision.     

Ruthenium catalyzed addition reaction of carboxylic acid across olefins without beta-hydride elimination

The cationic ruthenium catalyst (Cp*RuCl2)2/AgOTf/Ligand promotes the addition reaction of carboxylic acids across olefins without beta-hydride elimination.     

Determination of distance of intra-molecular hydrogen bonding in (Ala-Gly)15 with silk I form after removal of the effect of MAS frequency in REDOR experiment

It is important to know the structure of silk I (Bombyx mori silk structure before spinning in the solid state) in order to understand the mechanism of fiber formation at the atomic level. In this study, 15N-dephased, 13C-observe REDOR has been carried out to determine the atomic distance of intra-molecular hydrogen bond between the 13C=O carbon of the 14th Gly residue and the 15N nitrogen of the 17th Ala residue of (AG)(6)A[1-13C]GAG[15N]AG(AG)(6) with silk I form after removal of the effect of MAS frequency on the re-coupling. The distance was determined to be 4.3A, which confirmed the intra-molecular hydrogen bonding formation between these two atomic sites.     

60]fullerenoacetyl chloride as a versatile precursor for fullerene derivatives: efficient ester formation with various alcohols

[reaction: see text] [60]Fullerenoacetyl chloride, one of the reactive derivatives of [60]fullerenoacetic acid, was isolated and identified for the first time. This acid chloride was easily synthesized in good yield from tert-butyl [60]fullerenoacetate through two steps. In the presence of 4-(dimethylamino)pyridine as a base, the acid chloride smoothly reacted with various alcohols under mild conditions to give the corresponding esters including [60]fullerene-biomolecule hybrids in moderate to high yields.     

Some Geometry of the Cone of Nonnegative Definite Matrices and Weights of Associated X2 Distribution

Consider the test problem about matrix normal mean M with the null hypothesis M = O against the alternative that M is nonnegative definite. In our previous paper (Kuriki (1993, Ann. Statist., 21, 1379–1384)), the null distribution of the likelihood ratio statistic has been given in the form of a finite mixture of ² distributions referred to as X² distribution. In this paper, we investigate differential-geometric structure such as second fundamental form and volume element of the boundary of the cone formed by real nonnegative definite matrices, and give a geometric derivation of this null distribution by virtue of the general theory on the X² distribution for piecewise smooth convex cone alternatives developed by Takemura and Kuriki (1997, Ann. Statist., 25, 2368–2387).