Minimax risk overl p -balls forl p -error

Summary Consider estimating the mean vector from dataN _n (, ² I) withl _q norm loss,q1, when is known to lie in ann-dimensionall _p ball,p(0, ). For largen, the ratio of minimaxlinear risk to minimax risk can bearbitrarily large ifp. Obvious exceptions aside, the limiting ratio equals 1 only ifp=q=2. Our arguments are mostly indirect, involving a reduction to a univariate Bayes minimax problem. Whenp, simple non-linear co-ordinatewise threshold rules are asymptotically minimax at small signal-to-noise ratios, and within a bounded factor of asymptotic minimaxity in general. We also give asymptotic evaluations of the minimax linear risk. Our results are basic to a theory of estimation in Besov spaces using wavelet bases (to appear elsewhere).     

Determination of the partition coefficients of the nonionic detergent C12E7 between lipid-detergent mixed membranes and water by means of Laurdan fluorescence spectroscopy

The membrane-water partition coefficient of the detergent C₁₂E₇ between water and C₁₂E₇/POPC mixed membranes has been determined by means of steady-state fluorescence spectroscopy. The emission spectra of the fluorescent probe Laurdan were used as an indicator of membrane composition at different membrane concentrations in the sample. The partition coefficient expressed as the ratio of the mole fractions of the detergent in the membrane and water phases is about 6^*10⁵ at low molar ratios of C₁₂E₇/POPC (R _c ) and decreases rapidly with increasingR _c . The limiting detergent content of the lamellar phase (R _c ^* >0.8) is indicated by a minimum ofP(R _c ).     

On a functional equation of Luce

Summary In a recent communication to J. Aczél, R. Duncan Luce asked about the functional equationU(x)U(G(x)F(y)) = U(G(x))U(xy) forx, y > 0, (1) which has arisen in his research on certainty equivalents of gambles. He was particularly interested in cases in which the unknowns (U, F andG) are strictly increasing functions from (0, + ) into (0, + ). In this paper we solve (1) in the case whereU, F andG are continuously differentiable with everywhere positive first derivatives. Our solution is perhaps novel in that in certain cases (1) reduces to a functional equation in a single variable and in other cases to a functional equation in several variables; see [1] for the terminology.     

On a problem of H. N. Gupta

It is shown that the axiom For any points x, y, z such that y is between x and z, there is a right triangle having x and z as endpoints of the hypotenuse and y as foot of the altitude to the hypotenuse, when added to three-dimensional Euclidean geometry over arbitrary ordered fields, is weaker than the axiom Every line which passes through the interior of a sphere intersects that sphere.     

A θ-stable approximations of abstract Cauchy problems

Summary We study the approximation of linear parabolic Cauchy problems by means of Galerkin methods in space andA -stable multistep schemes of arbitrary order in time. The error is evaluated in the norm ofL _t ² (H _x ¹ ) L _t (L _x ² ).     

Cyclic actions on some Klein bottle bundles over S1

Leth be a cyclic action of periodn onM, whereM is eitherS ¹×K, K is the Klein bottle or on , the twisted Klein bottle bundle overS ¹, such that there is a fiberingq:MS ¹ with fiber a Klein bottleK or a torusT with respect to which the action is fiber preserving. We classify all such actions and show that they might be distinguished by their fixed points or by their orbit spaces.     

Harmonic analysis in infinite dimension

We study the Hermite transform onL ²() where is a Gaussian measure on a Lusin locally convex spaceE. We are then lead to a Hilbert space () of analytic functions onE which is also a natural range for the Laplace transform. LetB be a convenient Hilbert-Schmidt operator on the Cameron-Martin spaceH of . There exists a natural sequence Cap _n of capacities onE associated toB. This implies the Kondratev-Yokoi theorem about positive linear forms on the Hida test-functions space.     

Visible light induced photocatalytic reaction of rhodamine B dye via 12-tungstosilicic acid in water

Using 12-tungstosilicic acid (SiW124-) as the catalyst, rhodamine B (RhB) dye in an aerated aqueous solution can undergo an effective photocatalytic stepwise N-deethylation process under visible light irradiation, and dioxygen is reduced to hydrogen peroxide by the reducedSiW12 4-. This provides the potential for moving polyoxometalate-based photocatalytic processes from the near-UV into the visible region of the spectrum.     

微波固相法合成钠快离子导体Na5YSi4O12

应用微波方法合固相反应难于制备的Ｎａ５ＹＳｉ４Ｏ１２纯相，讨论了微波合成条件对产物的影响，与溶胶－凝胶法相比，微波法反应速率快，选择性强，合成的样品具有特异的聚集态，缺陷和微结构，从而导致离子导电活化能下降。     

Novel design of a pentacyclic scaffold as structural mimic of saframycin A

The design, synthesis and evaluation of a pentacyclic scaffold, CWO-324 to mimic saframycin A is described. CWO-324 is readily synthesized in five steps from 1,4-diacetyl-piperazine-2,5-dione and 2,5-dimethoxybenzaldehyde. CWO-324 was found to scission DNA, binds to bases 69-83(5′-GCAGTCAGG CACCGT-3′) of Hind III/Rsa I from plasmid pBR322 DNA in a foot-printing study and possesses anti-tumor activity.