Marine Toxins with Spiroimine Rings: Total Synthesis of Pinnatoxin A

This microreview provides a compilation of synthetic approaches and total syntheses of pinnatoxin A in a survey of the literature up to early 2010. Pinnatoxin A is the first discovered and representative member of a fascinating group of potent marine toxins that share a spiroimine subunit as a unifying structural element.     

On Path Factors of (3, 4)-Biregular Bigraphs

A (3, 4)-biregular bigraph G is a bipartite graph where all vertices in one part have degree 3 and all vertices in the other part have degree 4. A path factor of G is a spanning subgraph whose components are nontrivial paths. We prove that a simple (3,4)-biregular bigraph always has a path factor such that the endpoints of each path have degree three. Moreover we suggest a polynomial algorithm for the construction of such a path factor.     

Synthesis of derivatives of 4,5-dihydrofuran,furan, and hexahydrobenzofuran from conjugated alkenynes

The regiochemistry of the reaction of 1,2- and 1-substituted derivatives of 1-buten-3-yne and its 4- and 2,4-substituted derivatives of the isoprenoid type with acetoacetic ester and acetylacetone in the presence of the manganese(III) acetate-copper(II) acetate oxidative system was studied. Derivatives of 4,5-dihydrofuran, furan, and hexahydrobenzofuran were obtained.Communication 137 from the series Reactions of unsaturated compounds. See [1] for communication 136.Translated from Khimiya Geterotsiklicheskikh Soedinenii, Vol. 24, No. 3, pp. 317–323, March, 1988.     

Solid-phase synthesis of trisubsituted guanidines

The solid-phase library synthesis of trisubstituted guanidines was accomplished. Amines were loaded onto the 4-formyl-3,5-dimethoxyphenoxymethyl linker via reductive amination. Subsequent acylation with Fmoc-4-aminomethylbenzoic acid followed by Fmoc deprotection gave solid-supported primary amines. Alternatively, sulfonylation of resin-bound secondary amines with 4-cyanobenzenesulfonyl chloride followed by borane reduction also gave solid-supported primary amines. Both resins were acylated with isocyanates to furnish solid-supported ureas. Dehydration of ureas with p-toluenesulfonyl chloride in pyridine gave solid-supported carbodiimides. Nucleophilic addition of amines to the carbodiimide bond followed by cleavage off the solid support gave trisubstituted guanidines.     

The Crystal Structure of Kx(MgxIn1–x)F3 (x = 0.38): a New Magnéli‐Bronze Type Fluoride

K_x(Mg_xIn_1–x)F₃ (x = 0.38) is monoclinic, pseudo tetragonal: a = 12.781(2) Å, b = 12.787(2) Å, c = 7.930(1) Å, β = 90,00(1)°, Z = 20. The crystal structure was solved in the space group P2₁/a (No. 14), subgroup of the tetragonal space group P4/mbm (No. 127), from X‐ray single crystal data using 4302 unique reflections (1770 with F_o/σ(F_o) > 4). The final observed R factor is 0.053. K_x(Mg_xIn_1–x)F₃ has the Magnéli‐bronze structural type, which consists in a tridimensional framework of mixed [(Mg_xIn_1–x)F₆] octahedra linked together by corners. The potassium ions are mainly located in large almost fully occupied 15‐coordinated sites and in practically empty 12‐coordinated cavities.     

Divergence of the greedy algorithm in the Faber-Schauder system on a continuum cardinality set

The paper establishes that there exist a continuum cardinality set E ₀ ? [0, 1] and a function f ₀(x) ∈ C _[0,1], such that the greedy algorithm of f ₀(x) with respect to the Faber-Schauder system converges to +∞ at all points of E ₀.     

Stochastic Dissipative PDE's and Gibbs Measures

We study a class of dissipative nonlinear PDE's forced by a random force η^{omega( t} , ^x ), with the space variable x varying in a bounded domain. The class contains the 2D Navier–Stokes equations (under periodic or Dirichlet boundary conditions), and the forces we consider are those common in statistical hydrodynamics: they are random fields smooth in t and stationary, short-correlated in time t. In this paper, we confine ourselves to “kick forces” of the form

Quantum Non-Markovian Stochastic Equations

We derive quantum diffusion equations with transport coefficients explicitly depending on time from generalized non-Markovian Langevin equations and obtain generalized fluctuation-dissipation relations. We substantiate the axiomatic Lindblad approach in the microscopic model. For non-Markovian dynamics, we find sets of diffusion coefficients that ensure the purity of states at any instant. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 87–101, October, 2005.     

Adaptive homodyne measurement of optical phase

We present an experimental demonstration of the power of feedback in quantum metrology, confirming the predicted [H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)]] superior performance of an adaptive homodyne technique for single-shot measurement of optical phase. For measurements performed on weak coherent states with no prior knowledge of the signal phase, adaptive homodyne estimation approaches closer to the intrinsic quantum uncertainty than any previous technique. Our results underscore the importance of real-time feedback for reaching quantum limits in measurement and control.     

Ergodicity for the Randomly Forced 2D Navier–Stokes Equations

We study space-periodic 2D Navier–Stokes equations perturbed by an unbounded random kick-force. It is assumed that Fourier coefficients of the kicks are independent random variables all of whose moments are bounded and that the distributions of the first N ₀ coefficients (where N ₀ is a sufficiently large integer) have positive densities against the Lebesgue measure. We treat the equation as a random dynamical system in the space of square integrable divergence-free vector fields. We prove that this dynamical system has a unique stationary measure and study its ergodic properties.