A proposal for the mechanism-of-action of diazoparaquinone natural products

Treatment of the representative diazoparaquinone prekinamycin dimethyl ether with Bu3SnH/AIBN in aromatic solvents furnishes moderate-to-good yields of formal aryl adducts wherein a molecule of solvent is attached to the carbon (C(11)) previously bearing the diazo function. Substituent studies provide evidence in support of a radical aromatic substitution mechanism, in which radical addition to the diazoparaquinone function generates an intermediate C(11) vinylic radical.     

SEASONAL TRENDS IN ERYTHEMAL and CARCINOGENIC ULTRAVIOLET RADIATION AT MID-SOUTHERN LATITUDES1989–1991

A network of solar carcinogenic/erythemal ultraviolet radiometers has been established in New Zealand. Daily integrated irradiances of this biologically harmful ultraviolet radiation for 1989, 1990 and 1991 are reported from radiometers located at Wellington (41°S) and Christchurch (43.5°S) and for 1990 and 1991 from the Auckland (37°S) radiometer. Although the monitoring program has not been running sufficiently long to discern any long-term changes in levels of solar ultraviolet radiation, shorter term trends are apparent, which are attributed to a seasonal cycle in levels of ozone at midlatitudes and changes in atmospheric aerosols.     

Proof of the generalized expressions for the number of perfect matchings of polycube graphs

The number of perfect rnatchings for the linear 2 × 2 ×n cubic lattice was analytically derived by diagonalizing the skew—symmetric 4n × 4n determinant, whose non—zero off—diagonal elements are either ±1 or ±i (pure imaginary number). The basic formulation invoking the matrix manipulation follows that of Kasteleyn, but the result obtained in this paper is the first example of the analytical solution for a special case of the three-dimensional Ising model.received by the Publisher 20 September 1989     

The endomorphism spectrum of an ordered set

Theendomorphism spectrum of an ordered setP, spec(P)={|f(P)|:f End(P)} andspectrum number, sp(P)=max(spec(P)\{|P|}) are introduced. It is shown that |P|>(1/2)n(n – 1) ^{n – 1} implies spec(P) = {1, 2, ...,n} and that if a projective plane of ordern exists, then there is an ordered setP of size 2n ²+2n+2 with spec(P)={1, 2, ..., 2n+2, 2n+4}. Lettingh(n)=max{|P|: sp(P)n}, it follows thatc ₁ n ²h(n)c ₂ n ⁿ⁺¹ for somec ₁ andc ₂. The lower bound disproves the conjecture thath(n)2n. It is shown that if |P| – 1 spec(P) thenP has a retract of size |P| – 1 but that for all there is a bipartite ordered set with spec(P) = {|P| – 2, |P| – 4, ...} which has no proper retract of size|P| – . The case of reflexive graphs is also treated.Partially supported by a grant from the NSERC.Partially supported by a grant from the NSERC.     

LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL ₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW _m (D), with [0, 1] ⁿ D. We assume data of the formy _i =f(t _i )+ _i ,i=1,..., N with {t _i } _i=1 ^N D, the _i are errors withE( _i )=0, andf is assumed to be inW _m . An LAD smoothing spline is the solution,s , of the following optimization problem

Spin dynamics and spin correlations in the spinS=1 two-dimensional square-lattice Heisenberg antiferromagnet La2NiO4

The static and dynamic spin fluctuations in the spinS=1, two-dimensional (2D) square-lattice antiferromagnet La₂NiO₄ have been studied over a wide temperature range using neutron scattering techniques. The spin correlations in La₂NiO₄ exhibit a crossover from two- to three-dimensional (3D) behavior as the Néel temperature is approached from above. Critical slowing down of the low-energy spin fluctuations is also observed just aboveT _N . The correlation length, (T), and the static structure factor,S(0), have been measured and are compared with recent theoretical calculations for the quantum 2D Heisenberg antiferromagnet using microscopic parameters determined from previous spin-wave measurements. Good agreement for (T) is found with the exact low-temperature result of Hasenfratz and Niedermeyer provided that 2 p _s is renormalized by 20% from the spin-wave value.     

Galloyl-Derived Orthoquinones as Reactive Partners in Nucleophilic Additions and Diels-Alder Dimerizations: A Novel Route to the Dehydrodigalloyl Linker Unit of Agrimoniin-Type Ellagitannins

Orthochloranil-mediated oxidation of galloyl monoethers furnishes the derived orthoquinones in excellent yield. These reactive electrophiles participate in a variety of nucleophilic addition reactions with heteroatomic and carbanionic partners. In addition, Lewis acid-mediated dimerization of the orthoquinones provides an efficient route to dehydrodigalloyl-type diaryl ether units characteristic of several ellagitannin natural products. The implications for ellagitannin biosynthesis and gallotannin-protein covalent attachment are discussed.     

AnL 1 smoothing spline algorithm with cross validation

We propose an algorithm for the computation ofL ₁ (LAD) smoothing splines in the spacesW _M (D), with . We assume one is given data of the formy _i =(f(t _i ) + _i , i=1,...,N with {itt_i} _i=1 ^{N D} , the _i are errors withE( _i )=0, andf is assumed to be inW _M . The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s , of the optimization problem (1/N) _i=1 ^N ¦y _i –g(t _i ¦+J _M (g), whereJ _M (g) is the seminorm consisting of the sum of the squaredL ₂ norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s , would be expected to give robust smoothed estimates off in situations where the _i are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.