Minkowski type theorems for convex sets in cones

Acta Mathematica Hungarica - Minkowski’s classical existence theorem provides necessary and sufficient conditions for a Borel measure on the unit sphere of Euclidean space to be the surface...     

Kinetic Analysis of the Hydrolysis of Pentose-1-phosphates through Apparent Nucleoside Phosphorolysis Equilibrium Shifts**

Herein, we report an addition to the toolbox for the monitoring and quantification of the hydrolytic decay of pentose-1-phosphates, which are known to be elusive and difficult to quantify. This communication describes how apparent equilibrium shifts of a nucleoside phosphorolysis reaction can be employed to calculate hydrolytic loss of pentose-1-phosphates based on the measurement of post-hydrolysis equilibrium concentrations of a nucleoside and a nucleobase. To demonstrate this approach, we assessed the stability of the relatively stable ribose-1-phosphate at 98 °C and found half-lives of 1.8–11.7 h depending on the medium pH. This approach can be extended to other sugar phosphates and related reaction systems to quantify the stability of UV-inactive and hard-to-detect reaction products and intermediates.     

Modular Synthetic Approach to Carboranyl‒Biomolecules Conjugates

The development of novel, tumor-selective and boron-rich compounds as potential agents for use in boron neutron capture therapy (BNCT) represents a very important field in cancer treatment by radiation therapy. Here, we report the design and synthesis of two promising compounds that combine meta-carborane, a water-soluble monosaccharide and a linking unit, namely glycine or ethylenediamine, for facile coupling with various tumor-selective biomolecules bearing a free amino or carboxylic acid group. In this work, coupling experiments with two selected biomolecules, a coumarin derivative and folic acid, were included. The task of every component in this approach was carefully chosen: the carborane moiety supplies ten boron atoms, which is a tenfold increase in boron content compared to the l-boronophenylalanine (l-BPA) presently used in BNCT; the sugar moiety compensates for the hydrophobic character of the carborane; the linking unit, depending on the chosen biomolecule, acts as the connection between the tumor-selective component and the boron-rich moiety; and the respective tumor-selective biomolecule provides the necessary selectivity. This approach makes it possible to develop a modular and feasible strategy for the synthesis of readily obtainable boron-rich agents with optimized properties for potential applications in BNCT.     

Intramolecular Hydroamination of Selenoalkynes to 2-Selenylindoles in the Absence of Catalyst

In this work, a series of 2-chalcogenylindoles was synthesized by an efficient methodology, starting from chalcogenoalkynes, including a previously unreported tellurium indole derivative. For the first time, these 2-substituted chalcogenylindoles were obtained in the absence of metal catalyst or base, under thermal conditions only. In addition, the results described herein represent a methodology with inverse regioselectivity for the chalcogen functionalization of indoles.     

Non-linear Stability of Modulated Fronts¶for the Swift–Hohenberg Equation

We consider front solutions of the Swift–Hohenberg equation ∂ _t u= -(1+ ∂ _x ²)² u + ɛ² u -u ³. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using renormalization techniques and a decomposition into Bloch waves, we show the non-linear stability of these solutions. It turns out that this problem is closely related to the question of stability of the trivial solution for the model problem ∂ _t u(x,t) = ∂ _x ² u (x,t)+(1+tanh(x-ct))u(x,t)+u(x,t) ^p with p>3. In particular, we show that the instability of the perturbation ahead of the front is entirely compensated by a diffusive stabilization which sets in once the perturbation has hit the bulk behind the front. Received: 23 February 2001 / Accepted: 27 August 2001     

Crystal structures of two ancylite modifications

The crystal structures of two ancylite specimens from Khibiny massif (the Kola Peninsula, Russia)—ancylite-(Ce) from alkali hydrothermalites (Sr_1.01Ca_0.02Ba_0.01)_Σ1.04(Ce_0.52La_0.28Nd_0.11Pr_0.04 Sm_0.01)_Σ0.96(CO₃)₂(OH_0.83F_0.13)_Σ0.96 · 0.9H₂O and ancylite-(Ce) from carbonatites—have (Sr_0.80Ca_0.05Ba_0.01)_Σ0.86(Ce_0.62La_0.40Nd_0.09Pr_0.03) _Σ1.14(CO₃)₂(OH_0.99F_0.15)_Σ1.14 · 1.0H₂O been refined by the Rietveld method. A focusing STOE-STADIP diffractometer with a bent Ge(111) primary monochromator was used (λ MoK _{α 1} radiation, 2.16° < 2θ < 54.98°; reflection number 237–437). All the computations for ancylite from alkali hydrothermalites were performed within the sp. gr. Pmc2₁, a = 5.0634(1) Å, b = 8.5898(1) Å, c = 7.2781(1) Å, V = 316.55(1) ų, R _wp = 1.90; the computations for ancylite from carbonatites were performed within the sp. gr. Pmcn, a = 5.0577(1) Å, b = 8.5665(2) Å, c = 7.3151(2) Å, V = 316.94(1) ų, R _wp = 2.38 in the anisotropic approximation of thermal vibrations of cations and oxygen atoms.