Heterogeneous platinum catalytic aerobic oxidation of cyclopentane-1,2-diols to cyclopentane-1,2-diones

A method for the aerobic oxidation of cyclopentane-1,2-diols to the corresponding diketones over a commercial heterogeneous Pt/C catalyst is described. Unsubstituted and 3- or 4-substituted cyclopentane-1,2-diols are oxidized to 1,2-dicarbonyl compounds in good yields under the reported optimized reaction conditions (atmospheric air, 1 mol % of catalyst, 1 equiv of LiOH, aqueous solvents and 60 °C temperature). The method is applicable for producing cyclopentane-1,2-diketones in a scalable manner.     

Torification and factorization of birational maps

Building on work of the fourth author and Morelli's work, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field of characteristic zero is a composite of blowings up and blowings down with nonsingular centers.

     

The lower bound of the quadratic spans of Debruijn sequences

It is proven that the quadratic span of DeBruijn sequence of spann is at leastn+2, forn>3.     

Microcomputer interfaced stopped-flow spectrometer with interactive graphics

One problem in the use of stopped-flow rapid-mixing systems is that data can be collected much more rapidly than they can be digitized and analyzed. Microprocessor based systems can overcome this problem, but until now they have been expensive and have required experts to assemble the appropriate components.     

Cone Dependence—A Basic Combinatorial Concept

We call A ? $ \mathbb{E} $ ⁿ cone independent of B ? $ \mathbb{E} $ ⁿ , the euclidean n-space, if no a = (a ₁,..., a _n ) ∈ A equals a linear combination of B \ {a} with non-negative coefficients. If A is cone independent of A we call A a cone independent set. We begin the analysis of this concept for the sets P(n) = {A ? {0, 1} ⁿ ? $ \mathbb{E} $ ⁿ : A is cone independent} and their maximal cardinalities c(n) ? max{|A| : A ∈ P(n)}. We show that lim _{n → ∞} $ \frac{{c\left( n \right)}}{{2^n }} $ > $\frac{1}{2}$ , but can't decide whether the limit equals 1. Furthermore, for integers 1 < k < ? ≤ n we prove first results about c _n (k, ?) ? max{|A| : A ∈ P _n (k, ?)}, where P _n (k, ?) = {A : A ? V ⁿ _k and V ⁿ _? is cone independent of A} and V ⁿ _k equals the set of binary sequences of length n and Hamming weight k. Finding c _n (k, ?) is in general a very hard problem with relations to finding Turan numbers.     

Total syntheses of (±)‐cis‐ and trans‐11‐methoxydeethyleburnamonine

The total syntheses of 11‐methoxydeethyleburnamonines ( 4 ) and ( 13 ) were carried out with use of 6‐methoxytryptophyl bromide ( 5 ) as starting material. Compound 5 was converted in three steps to trans‐ester 8 . Acid‐catalysed epimerization of 8 , lithium aluminum hydride reduction of the ester group, tosylation and substitution with cyanide gave the cis‐nitrile 12 . Acid‐induced cyclization of 12 yielded mainly (±)‐trans‐11‐methoxydeethyleburnamonine ( 13 ), whereas base‐induced cyclization gave (±)‐cis‐11‐methoxydeethyleburnamonine ( 4 ).     

Everywhere -repetitive sequences and Sturmian words

Local constraints on an infinite sequence that imply global regularity are of general interest in combinatorics on words. We consider this topic by studying everywhere α-repetitive sequences. Such a sequence is defined by the property that there exists an integer N≥2 such that every length-N factor has a repetition of order α as a prefix. If each repetition is of order strictly larger than α, then the sequence is called everywhere α⁺-repetitive. In both cases, the number of distinct minimal α-repetitions (or α⁺-repetitions) occurring in the sequence is finite.A natural question regarding global regularity is to determine the least number, denoted by M(α), of distinct minimalα-repetitions such that an α-repetitive sequence is not necessarily ultimately periodic. We call the everywhere α-repetitive sequences witnessing this property optimal. In this paper, we study optimal 2-repetitive sequences and optimal 2⁺-repetitive sequences, and show that Sturmian words belong to both classes. We also give a characterization of 2-repetitive sequences and solve the values of M(α) for 1≤α≤15/7.     

Isomer ratios for products of photonuclear reactions with middle-weight nuclei

The isomer ratios for nuclei ^104m,g Ag, ^110m,g In, ^108m,g In as products of the photonuclear reactions ¹⁰⁷Ag(γ, 3n)^104m,g Ag, ¹¹³In(γ, 3n)^110m,g In, ¹⁰⁹Ag(γ, 5n)^104m,g Ag, ¹¹⁵In)(γ, 5n)^110m,g In, ¹¹⁵In(γ, 7n)^108m,g In are obtained. The Bremsstrahlung of electrons with energies within 32–84 MeV from the LU-40 linear accelerator was used for the irradiation of targets. The energy resolution and mean current of the electron beam were ～1% and 5 μA, respectively. The induced activity was used to obtain experimental isomer ratios. An HPGe spectrometer with an energy resolution of 1.9 keV for ⁶⁰Co γ-line 1332 keV was used to acquire the instrumental γ-ray spectra of the activation products. A set of serial measurements with various acquisition times was performed. The cooling times varied from 5 seconds to several hours for Ag and up to tens of hours for In specimens. The obtained experimental isomer ratios are compared with the results from theoretical calculations.