Algorithmic Construction of the Subdifferential from Directional Derivatives

The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes algorithms to reconstruct a polyhedral subdifferential of a function from the computation of finitely many directional derivatives. We provide upper bounds on the required number of directional derivatives when the space is ?¹ and ?², as well as in ? ⁿ where subdifferential is known to possess at most three vertices.     

Smoothness of convolution powers of orbital measures on the symmetric space SU(n)/SO(n)

We prove that if m_a = m_K*d_a*m_K{\mu _{a}\,{=}\,m_{K}*\delta _{a}*m_{K}} is the K-bi-invariant measure supported on the double coset KaK í SU(n){KaK\subseteq SU(n)} , for K = SO(n), then m_a^k{\mu _{a}^{k}} is absolutely continuous with respect to the Haar measure on SU(n) for all a not in the normalizer of K if and only if k ≥ n. The measure, μ _a , supported on the minimal dimension double coset has the property that m_a^n-1{\mu _{a}^{n-1}} is singular to the Haar measure.     

Shock waves in molecular solids: ultrafast vibrational spectroscopy of the first nanosecond

A novel technique which uses a microfabricated shock target array assembly is described, where the passage of a shock front through a thin (0.5μm) polycrystalline layer and the subsequent unloading process is monitored in real time with ultrafast coherent Raman spectroscopy. Using a high repetition rate laser shock generation technique, high resolution, coherent Raman spectra are obtained in shocked anthracene and in a high explosive material, NTO, with time resolution of ∼ 50 ps. Spectroscopic measurements are presented which yield the shock pressure (up to 5 GPa), the shock velocity (∼ 4 km/s), the shock front risetime (t _r < 25 ps), and the temperature (∼ 400°C). A brief discussion is presented, how this new technique can be used to determine the Hugoniot, the equation of state, the entropy increase across the shock front, and monitor shock induced chemical reactions in real time. Received 28 October 1996 / Accepted 12 November 1996     

Posaconazole (Noxafil, SCH 56592), a new azole antifungal drug, was a discovery based on the isolation and mass spectral characterization of a circulating metabolite of an earlier lead (SCH 51048)

Posaconazole (SCH 56592) is a novel triazole antifungal drug that is marketed in Europe and the United States under the trade name 'Noxafil' for prophylaxis against invasive fungal infections. SCH 56592 was discovered as a possible active metabolite of SCH 51048, an earlier lead. Initial studies have shown that serum concentrations determined by a microbiological assay were higher than those determined by HPLC from animals dosed with SCH 51048. Subsequently, several animals species were dosed with (3)H-SCH 51048 and the serum was analyzed for total radioactivity, SCH 51048 concentration and antifungal activity. The antifungal activity was higher than that expected based on SCH 51048 serum concentrations, confirming the presence of active metabolite(s). Metabolite profiling of serum samples at selected time intervals pinpointed the peak that was suspected to be the active metabolite. Consequently, (3)H-SCH 51048 was administered to a large group of mice, the serum was harvested and the metabolite was isolated by extraction and semipreparative HPLC. LC-MS/MS analysis suggested that the active metabolite is a secondary alcohol with the hydroxyl group in the aliphatic side chain of SCH 51048. All corresponding monohydroxylated diastereomeric mixtures were synthesized and characterized. The HPLC retention time and LC-MS/MS spectra of the diastereomeric secondary alcohols of SCH 51048 were similar to those of the isolated active metabolite. Finally, all corresponding individual monohydroxylated diasteriomers were synthesized and evaluated for in vitro and in vivo antifungal potencies, as well as pharmacokinetics. SCH 56592 emerged as the candidate with the best overall profile.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-singular dichotomy for orbital measures of classical simple Lie algebras

We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie group satisfy a smoothness dichotomy: Either μ ^k is singular to Lebesgue measure or μ ^k ∈ L ². The minimum k for which μ ^k ∈ L ² is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure. S. K. Gupta appreciates the hospitality of the Department of Pure Mathematics at the University of Waterloo where some of this research was done. K. E. Hare was supported in part by NSERC.     

Quantification strategies for elemental imaging of biological samples using laser ablation-inductively coupled plasma-mass spectrometry

This review provides analysts with critical insights of current approaches for quantification by laser ablation-inductively coupled plasma-mass spectrometry in the field of elemental imaging. This encompasses both calibration strategies that have been used with success in imaging biological samples, as well as those with potential to improve analytical accuracy and precision if applied to imaging. Methods reviewed include the use of CRMs, laboratory prepared matrix matched standards, internal standardisation, online standard addition and a variety of novel approaches that makes elemental imaging accessible to a wider base of analysts. The importance of quantification and factors affecting its use in imaging will also be considered.     

Comparative study of the effect of various electrode membranes on biofouling and electrochemical measurements

Stability of sensors in biosamples is a critical issue and can be mitigated by membranes. The effect of different membranes (Nafion, cellulose acetate, chitosan, fibronectin, PSS/PL) on the electrochemistry of an outer-sphere redox couple (ruthenium II/III hexaammine) and on the electrocatalytic reduction of dissolved oxygen are described. Biofouling has been induced by albumin solutions. Results demonstrate good performances of fibronectin in all situations investigated. Other membranes do not provide a satisfactory protection from biofouling and some of them, PSS/PL in particular, seriously disturb electrochemical mechanisms.     

Electronic spectra and transitions of the fullerene C60

Absorption spectra of C₆₀ have been measured in the ranges (a) 190–700 nm in n-hexane solutions at 300 K, (b) 390–700 nm in n-hexane and in 3-methylpentane solutions at 77 K. 40 vibronic bands were observed. They exhibit a large range of bandwidths and intensities, whose significance is discussed. Assignment of electronic transitions has been carried out using the results of theoretical calculations. Vibronic structures have been analyzed within the framework of theories of electronic transitions of polyatomic molecules applied to the I_h symmetry group. Nine allowed ¹T_1u−¹A_g transitions have been assigned in the 190–410 nm region. Observed and calculated allowed transition energies and oscillator strengths are compared. Detailed vibronic analyses of the 1 ¹T_1u−1 ¹A_g and 2 ¹T_1u−1 ¹A_g transitions illustrate the role of Jahn-Teller couplings. Orbitally forbidden singlet-singlet transitions are observed between 410 and 620 nm. Their vibronic structures were analyzed in terms of concurrent Herzberg-Teller and Jahn-Teller vibronic interactions. The 77 K spectra provided useful information on hot bands and on other aspects of the analyses. Vibronic bands belonging to triplet←singlet transitions were detected between 620 and 700 nm.     

Computing the Principal Branch of log-Gamma

Thelog-Gammafunction is an important special function of mathematics, and its principal branch is required in many applications. We develop here the mathematics required to evaluate the principal branch to arbitrary precision, including a new bound for the error in Stirling's asymptotic series. We conclude with a discussion of the implementation of the principal branch of the log-Gamma function in the Maple symbolic algebra system, starting with version Maple V, Release 3.     

The energy of signed measures

We generalize the concept of energy to complex measures of finite variation. We show that although the energy dimension of a measure can exceed that of its total variation, it is always less than the Hausdorff dimension of the measure. As an application we prove a variant of the uncertainty principle.