Regularized minimization under weaker hypotheses

LetV andW be two Banach spaces, withV reflexive, a bounded convex set ofV, A a linear mapping fromV intoW, and letF be a convex functional onW. We minimizeJ(v)=F(Av) on using hypotheses about particular sequences in IfV is uniformly convex, we prove existence and uniqueness of a solution of minimal norm minimizingJ. In the Hilbert space case, withF defined byF(w)=w–f ²,f given inW, we get existence and uniqueness of the projection off on A(), which generalizes the case where A() is a closed set ofW (taking closed andA continuous). Finally, we give examples, and we study an unbounded operator case.     

Effect of the twisted alignment on the liquid crystal wave‐front corrector

The effect of twisted alignment on the phase modulation of a liquid crystal wave‐front corrector was investigated. First, the effect of twisted alignment is discussed in terms of the modulation principle of the liquid crystal molecule. Only partial incident light can be modulated because of the effect of the twisted alignment. Other unmodulated light will affect the correction accuracy and the resolution of the image. The blazed grating method is proposed to solve this problem. Adaptive correction was performed without the blazed grating method and the correction results are poor. A similar adaptive correction experiment was performed with the blazed grating method and a better correction result is obtained. The residual averaged wave‐front errors are PV = 0.101λ and RMS = 0.015λ and a resolvable image is obtained.     

On the evaluation at (<Emphasis Type="Italic">j</Emphasis>, <Emphasis Type="Italic">j</Emphasis><Superscript>2</Superscript>) of the Tutte polynomial of a ternary matroid

F. Jaeger has shown that up to a ± sign the evaluation at (j, j ²) of the Tutte polynomial of a ternary matroid can be expressed in terms of the dimension of the bicycle space of a representation over GF(3). We give a short algebraic proof of this result, which moreover yields the exact value of ±, a problem left open in Jaeger's paper. It follows that the computation of t(j, j ²) is of polynomial complexity for a ternary matroid.E. Gioan: C.N.R.S., MontpellierM. Las Vergnas: C.N.R.S., Paris     

Coupling microscopic and mesoscopic scales to simulate chemical equilibrium between a nanometric carbon cluster and detonation products fluid

This paper presents a new method to obtain chemical equilibrium properties of detonation products mixtures including a solid carbon phase. In this work, the solid phase is modelled through a mesoparticle immersed in the fluid, such that the heterogeneous character of the mixture is explicitly taken into account. Inner properties of the clusters are taken from an equation of state obtained in a previous work, and interaction potential between the nanocluster and the fluid particles is derived from all-atoms simulations using the LCBOPII potential (Long range Carbon Bond Order Potential II). It appears that differences in chemical equilibrium results obtained with this method and the "composite ensemble method" (A. Hervouet et al., J. Phys. Chem. B, 2008, 112.), where fluid and solid phases are considered as non-interacting, are not significant, underlining the fact that considering the inhomogeneity of such system is crucial.     

Matricial logarithmic derivatives

If θ is a norm on Cⁿ, then the mapping $\text{A→}\text{lim}{}_{\mathrm{h\downarrow 0}}\text{6I+hA6}{}_{\mathrm{\theta }}\text{?1}\text{/h}$ from M_n(C) (=C^{n × n}) into R is called the logarithmic derivative induced by the vector norm θ. In this paper we generalize this concept to a mapping γ from M_n(C) into M_k(R), where k ? n. Denoting by α(B) the spectral abscissa of a square matrix B (the largest of the real parts of the eigenvalues), we show, in particular, that α(A) ?α(γ(A)). As a byproduct we obtain simple sufficient conditions for the stability of a matrix.     

Combinatorial approach to N-substituted aminocyclitol libraries by solution-phase parallel synthesis and preliminary evaluation as glucocerebrosidase inhibitors

Libraries of N-substituted aminocyclitol derivatives of the scyllo and racemic chiro series by means of parallel solution-phase methodology with the help of robotic technology are described. Chemical diversity has been introduced by reaction of selected scaffolds with a set of aldehydes, acyl chlorides, sulfonyl chlorides, chloroformates, and amines to afford the corresponding amines, amides, sulfonamides, carbamates and ureas, respectively. The optimized methodology has proven excellent, in terms of overall purities of the resulting libraries, for the production of amides. Sulfonamides and carbamates have been obtained in slightly lower purities, while amines afforded modest results. Selected library members have been evaluated as inhibitors of recombinant glucocerebrosidase with K(i) values ranging in the low micromolar scale for the most active members.     

Laser-driven shock experiments on precompressed water: Implications for "icy" giant planets

Laser-driven shock compression of samples precompressed to 1 GPa produces high-pressure-temperature conditions inducing two significant changes in the optical properties of water: the onset of opacity followed by enhanced reflectivity in the initially transparent water. The onset of reflectivity at infrared wavelengths can be interpreted as a semiconductor<-->electronic conductor transition in water, and is found at pressures above approximately 130 GPa for single-shocked samples precompressed to 1 GPa. Our results indicate that conductivity in the deep interior of "icy" giant planets is greater than realized previously because of an additional contribution from electrons.     

Adjacent q-Cycles in Permutations

We introduce a new permutation statistic, namely, the number of cycles of length q consisting of consecutive integers, and consider the distribution of this statistic among the permutations of {1, 2, . . . , n}. We determine explicit formulas, recurrence relations, and ordinary and exponential generating functions. A generalization to more than one fixed length is also considered.