Beyond Schmittel and Myers-Saito cyclizations: rearrangements of 4-heteroatom-1,2-hexa-diene-5-ynes

The thermal rearrangements of 4-heteroatom-1,2-hexadiene-5-ynes (2) were studied at the BLYP/6-311+G//BLYP/6-31G level of theory. Cyclization of 2 to heteroatom-containing cyclopentadienyl structures (6) competes with the Claisen-type rearrangement to acyclic, allenic structures. Cyclizations to cyclobutene (4)- and cyclohexadiene (8)-derived heterocycles are not feasible as a result of high reaction barriers and lower-lying alternative pathways. [structure: see text]     

Dioscorealides and dioscoreanone,novel cytotoxic naphthofuranoxepins,and 1,4-phenanthraquinone from Dioscorea membranacea Pierre

[structure: see text] Commonly used among ingredients in Thai traditional anticancer preparations, the rhizome of Dioscorea membranacea Pierre was found potently cytotoxic and possibly contributed to such a therapeutic effect. Bioassay-guided isolation resulted in two novel cytotoxic naphthofuranoxepins, dioscorealides A (1) and B (2), and a new 1,4-phenanthraquinone, dioscoreanone (3). The structure determination, achieved mainly by means of NMR and CD spectral and X-ray crystallographic analyses, and cytotoxicity are discussed here.     

Observations of high-energy electrons in the stratosphere

Summary To investigate the variation of the flux of cosmic radiation in the vicinity of the Earth, stratospheric balloon soundings are performed weekly at Campinas (Brazil). During some soundings, enhancements of the counting rates are detected. In this paper data from these excesses as well as their analysis are shown. It seems to indicate that possibly high-energy electrons are injected from the lower boundary of the radiation belt into the stratosphere.

---

Riassunto Per ricercare la variazione del flusso delle radiazioni cosmiche in prossimità della Terra, sono fatti funzionare settimanalmente palloni sonda a Campinas (Brasile). In alcune sonde si registrano aumenti delle frequenze di conteggio. In questo lavoro si mostrano dati da questi eccessi nonché le loro analisi. Ciò sembra indicare che gli elettroni ad alta energia sono probabilmente immessi dallo strato inferiore della fascia di radiazioni nella stratosfera.

---

Резюме для исследования изменения потока космического излучения в окрестности Земли еженедельно запускаются стратосферные шары-зонды в лаборатории Кампинас (Бразилия). Во время некоторых зондирований зарегистрированы увеличения интенсивности излучения. В этой статье приводятся данные измерений и их анализ. Проведенный анализ показывает, что эти случаи возможно связаны с электронами высоких энергий, инжектированными из нижней границы радиационного пояса в стратосферу.

     

An ant-based algorithm for coloring graphs

This paper presents an ant-based algorithm for the graph coloring problem. An important difference that distinguishes this algorithm from previous ant algorithms is the manner in which ants are used in the algorithm. Unlike previous ant algorithms where each ant colors the entire graph, each ant in this algorithm colors just a portion of the graph using only local information. These individual coloring actions by the ants form a coloring of the graph. Even with the lack of pheromone laying capacity by the ants, the algorithm performed well on a set of 119 benchmark graphs. Furthermore, the algorithm produced very consistent results, having very small standard deviations over 50 runs of each graph tested.     

Channel effect in isomeric ratio of 137m,gCe produced in different nuclear reactions

This work presents the experimental study of the isomeric ratio of ^137mCe–^137gCe produced in ¹³⁸Ce(γ, n) ^137m,gCe photonuclear reaction, in neutron capture reaction ¹³⁶Ce(n, γ) ^137m,gCe and in the two simultaneous reactions ¹³⁸Ce(γ, n) ^137m,gCe and ¹³⁶Ce(n, γ) ^137m,gCe in the mixed photon—neutron field by the activation method. The investigated samples were irradiated at the bremsstrahlung photon flux, in the epithermal and thermal-epithermal neutron beam and in the mixed photon-neutron field constructed at the electron accelerator Microtron MT-25 of the Flerov Laboratory of Nuclear Reaction, Joint Institute for Nuclear Research, Dubna, Russia. The results were analyzed, discussed and compared with those of other authors to examine the role of the channel effect in nuclear reaction and provide the nuclear data for theoretical model interpretation of nuclear reactions.

     

On Balazard,Saias, and Yor’s equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t)$S\left(t\right)$ in the theory of the Riemann zeta-function.     

Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions

Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.     

VMO Spaces Associated with Operators with Gaussian Upper Bounds on Product Domains

In this paper, we extend the well-known result “the predual of Hardy space \(H^1\) is VMO” to the product setting, associated with differential operators. Let \(L_i\), \(i = 1, 2\), be the infinitesimal generators of the analytic semigroups \(\{e^{-tL_i}\}\) on \(L^2({\mathbb {R}})\). Assume that the kernels of the semigroups \(\{e^{-tL_i}\}\) satisfy the Gaussian upper bounds. We introduce the VMO spaces VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) associated with operators \(L_1\) and \(L_2\) on the product domain \(\mathbb {R}\times \mathbb {R}\), then show that the dual space of VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) is the Hardy space \(H^1_{L_1^*, L_2^*}(\mathbb {R}\times \mathbb {R})\) associated with the adjoint operators \(L^*_1\) and \(L^*_2\).     

On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints

Motivated by our recent works on optimality conditions in discrete optimal control problems under a nonconvex cost function, in this paper, we study second-order necessary and sufficient optimality conditions for a discrete optimal control problem with a nonconvex cost function and state-control constraints. By establishing an abstract result on second-order optimality conditions for a mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.