On the theory of convolution equations of the third kind, II

Existence results of Part I of the paper are generalized to two types of autoconvolution equations of the third kind having free terms with nonzero values at x=0 like the well-known Bernstein-Doetsch equation for the Jacobian theta zero functions. Also uniqueness results for the linear convolution equations in Part I of the paper are extended to more general function spaces. Further, a special class of integro-differential equations with autoconvolution integral and two classes of the linear singular Abel-Volterra equations are dealt with.     

Hexafluoroacetone as a Protecting and Activating Reagent. N- and O-Glycosylation of Isoserine and Isocysteine

Starting from HFA-protected malic and thiomalic acid a series of O- and N-glycoconjugates suitable for peptide and depsipeptide modification has been synthesized.     

A new zero-finder for Tikhonov regularization

Tikhonov regularization with the regularization parameter determined by the discrepancy principle requires the computation of a zero of a rational function. We describe a cubically convergent zero-finder for this purpose. AMS subject classification (2000)  65F22, 65H05, 65R32     

The use of vector-valued martingales in risk theory

A completely dependent risk process with perturbation and phase-type distributed claim sizes is analyzed. Claim arrivals are modeled by a Markovian arrival process. Using a vector-valued martingale, the Laplace transform of the time to ruin is derived algorithmically. The conditional memoryless property of the phase-type distribution yields the distribution of the deficit at ruin as a corollary.     

Novel Osmium‐based Coordination Complexes as Photosensitizers for Panchromatic Photodynamic Therapy

Cancer remains a major global malaise requiring the advent of new, efficient and low‐cost treatments. Photodynamic therapy, which combines a photosensitizer and photons to produce cytotoxic reactive oxygen species, has been established as an effective cancer treatment but has yet to become mainstream. One of the main limitations has been the paucity of photosensitizers that are effective over a wide range of wavelengths, can exert their cytotoxic effects in hypoxia, are easily synthesized and produce few if any side effects. To address these shortfalls, three new osmium‐based photosensitizers (TLD1822, TLD1824 and TLD1829) were synthesized and their photophysical and photobiological attributes determined. These photosensitizers are panchromatic (i.e. black absorbers), activatable from 200 to 900 nm and have strong resistance to photobleaching. In vitro studies show photodynamic therapy efficacy with both red and near‐infrared light in normoxic and hypoxic conditions, which translated to good in vivo efficacy of TLD1829 in a subcutaneous murine colon cancer model.     

A Facile Route to Metal Nitride Clusterfullerenes by Using Guanidinium Salts: A Selective Organic Solid as the Nitrogen Source

Using guanidinium salts 1 and 2 as the new nitrogen sources, metal nitride clusterfullerenes (NCFs) based on a variety of metals (Dy, Sc, Y, Gd, Lu, and mixed metals Sc/Dy, Sc/Gd, Sc/Lu, and Lu/Ce) have been synthesized based on a new “selective organic solid” (SOS) route. The synthesis of Dy‐NCFs by using Dy/ 1 was studied in detail, and the optimum molar ratio of 1 /Dy/C has been determined to be 2.5:1:10. For several representative metals such as Sc, Y, Gd, Dy, and Sc/Dy, we quantitatively compared the yield of M₃N@C₈₀ synthesized by the SOS route with the reported “reactive gas atmosphere” route, thereby indicating that the yield of M₃N@C₈₀ by using 1 could be comparable to that obtained by the reactive gas atmosphere route. Three other nitrogen sources ( 3 – 5 ) were also studied for comparison, which were mixed with Dy metal but did not result in the formation of Dy‐NCF. A possible reaction scheme for the solid‐state reaction of 1 , metal, and graphite is proposed. The SOS route appears to be a general route for the synthesis of NCFs that promises both high selectivity of NCFs and high reproducibility of the fullerene yield. Another advantages of the SOS route compared to the reported “trimetallic nitride template” (TNT) process and the reactive gas atmosphere route is that no additional heating pretreatment is needed, thus simplifying the procedure and being much more facile.     

Crystallization of niobium germanosilicate glasses

Niobium germanosilicate glasses are potential candidates for the fabrication of transparent glass ceramics with interesting non-linear optical properties. A series of glasses in the (Ge,Si)O₂-Nb₂O₅-K₂O system were prepared by melting and casting and their characteristic temperatures were determined by differential thermal analysis. Progressive replacement of GeO₂ by SiO₂ improved the thermal stability of the glasses. Depending on the composition and the crystallization heat-treatment, different nanocrystalline phases—KNbSi₂O₇, K₃Nb₃Si₂O₁₃ and K_3.8Nb₅Ge₃O_20.4 could be obtained. The identification and characterization of these phases were performed by X-ray diffraction and Raman spectroscopy.The 40 GeO₂-10 SiO₂-25 Nb₂O₅-25 K₂O (mol%) composition presented the higher ability for volume crystallization and its nucleation temperature was determined by the Marotta's method. An activation energy for crystal growth of ∼529 kJ/mol and a nucleation rate of 9.7×10¹⁸ m⁻³ s⁻¹ was obtained, for this composition. Transparent glass ceramics with a crystalline volume fraction of ∼57% were obtained after a 2 h heat-treatment at the nucleation temperature, with crystallite sizes of ∼20 nm as determined by transmission electron microscopy.