Interior path following primal-dual algorithms. part II: Convex quadratic programming

We describe a primal-dual interior point algorithm for convex quadratic programming problems which requires a total of number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds an approximate Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea. The total number of arithmetic operations is shown to be of the order of O(n ³ L).     

Stereoselective preparation of dienyl zirconocene complexes via a tandem allylic C-H bond activation-elimination sequence

Several dienyl zirconocene derivatives were easily prepared, as unique geometrical isomers, from simple non-conjugated unsaturated enol ethers with (1-butene)ZrCp2 complexes. This new methodology is based on a tandem allylic C-H bond activation-elimination sequence and the mechanism has been mapped out by deuterium labeling experiments. The stereochemical outcome of this process was determined by addition of several electrophiles. Moreover, when the organometallic derivative is vinylic as well as allylic such as in 44-47Zr, an unexpected reversal of the stereochemistry has been found during the zirconium to copper transmetalation step.     

Stereoselective Access to Fully Substituted Aldehyde‐Derived Silyl Enol Ethers by Iridium‐Catalyzed Alkene Isomerization

An in situ generated cationic Ir‐catalyst isomerizes simple allylic silyl ethers into valuable, fully substituted aldehyde‐derived silyl enol ethers. Importantly, by judicious choice of substrate, either of the two possible stereoisomers of a given enolate derivative is accessible with complete stereoselectivity. One‐pot isomerization‐aldol and isomerization‐allylation processes illustrate the synthetic utility of this method.     

A Bragg grating embedded in a slab waveguide fabricated by the implantation of high-energy light ions in KLTN substrate

Electro-optically tunable transmission grating was imprinted in potassium lithium tantalate niobate by irreversible spatial patterning of the dielectric constant. While embedded into waveguided architecture, it provides a reliable and versatile building block for opto-electronic circuitry, capable of both active switching and multiplexing. Realization of such a block is critical for the fabrication of integrated photonic circuits in electro-optic substrates by means of Refractive Index Engineering by fast ion implantation.     

A note on conservative galaxies,Skolem systems,cyclic cycle decompositions,and Heffter arrays

The conservative number of a graph $G$ is the minimum positive integer $M$, such that $G$ admits an orientation and a labeling of its edges by distinct integers in $\{1,2,\dots ,M\}$, such that at each vertex of degree at least three, the sum of the labels on the in-coming edges is equal to the sum of the labels on the out-going edges. A graph is conservative if $M=\left|E\left(G\right)\right|$. It is worth noting that determining whether certain biregular graphs are conservative is equivalent to find integer Heffter arrays.In this work we show that the conservative number of a galaxy (a disjoint union of stars) of size $M$ is $M$ for $M\equiv 0$, $3(mod4)$, and $M+1$ otherwise. Consequently, given positive integers $m_1$, $m_2$, …, $m_n$ with $m_i\ge 3$ for $1\le i\le n$, we construct a cyclic $(m_1,m_2,\dots ,m_n)$-cycle system of infinitely many circulant graphs, generalizing a result of Bryant, Gavlas and Ling (2003). In particular, it allows us to construct a cyclic $(m_1,m_2,\dots ,m_n)$-cycle system of the complete graph $K_{2M+1}$, where $M={\sum }_{i=1}^n{m}_i$. Also, we prove necessary and sufficient conditions for the existence of a cyclic $(m_1,m_2,\dots ,m_n)$-cycle system of $K_{2M+2}?F$, where $F$ is a 1-factor. Furthermore, we give a sufficient condition for a subset of ${\mathbb{Z}}_v?\left\{0\right\}$ to be sequenceable.     

Diastero- and enantioselective intramolecular carbometalation reaction

The zinc-catalyzed addition of various alkynes to acylsilanes followed by a Zn-Brook rearrangement and either the Zn-ene-allene or Zn-yne-allene cyclization led to the enantio- and diastereoselective formation of carbocycles in a single-pot operation.