To develop solid-phase synthesis of phosphinic peptides, different FmocXaaPsi{PO(OAd)CH(2)}XaaOH building blocks have been prepared, where Fmoc is (fluorenylmethoxy)carbonyl. In this respect, the protection of the hydroxyphosphinyl function in these phosphinic dipeptides by the adamantyl group turns out to be convenient. The phosphinic adamantyl esters are completely stable in basic conditions and can be removed under relatively mild acidic conditions. Using these building blocks, despite the bulkiness of the adamantyl group, no particular problem of coupling was observed during the solid-phase synthesis of phosphinic peptides by the Fmoc strategy. The developed methodology is of particular interest to facilitate the development of potent inhibitors of zinc-metalloproteases. 相似文献
Using the natural equivalence relation in the set of flat Banach principal fibre bundles with group G and connected base B, we obtain a bisection between the corresponding equivalence classes and classes of similar homomorphisms of 1(B) into G. 相似文献
It is well known that if a scalar second order hyperbolic partial differential equation in two independent variables is Darboux integrable, then its local Cauchy problem may be solved by ordinary differential equations. In addition, such an equation has infinitely many non-trivial conservation laws. Moreover, Darboux integrable equations have properties in common with infinite dimensional completely integrable systems.
In this paper we employ a geometric object intrinsically associated with any hyperbolic partial differential equation, its hyperbolic structure, to study the Darboux integrability of the class of semilinear second order hyperbolic partial differential equations in one dependent and two independent variables. It is shown that the problem of classifying the Darboux integrable equations in contains, as a subproblem, that of classifying the manifolds of -hyperbolic type of rank 4 and dimension , ; .
In turn, it is shown that the problem of classifying these manifolds in the two (lowest) cases contains, as a subproblem, the classification problem for Lie groups. This generalizes classical results of E. Vessiot.
The main result is that if an equation in is (2,2)- or (2,3)-Darboux integrable on the -jets, , then its intrinsic hyperbolic structure admits a Lie group of symmetries of dimension or , respectively. It follows that part of the moduli space for the Darboux integrable equations in is determined by isomorphism classes of Lie groups.
The Lie group in question is the group of automorphisms of the characteristic systems of the given equation which leaves invariant the foliation induced by the characteristic (or, Riemann) invariants of the equation, the tangential characteristic symmetries. The isomorphism class of the tangential characteristic symmetries is a contact invariant of the corresponding Darboux integrable partial differential equation.
We study coupled systems of nonlinear wave equations from the point of view of their formal Darboux integrability. By making use of Vessiot's geometric theory of differential equations, it is possible to associate to each system of nonlinear wave equations a module of vector fields on the second-order jet bundle — the Vessiot distribution. By imposing certain conditions of the structure of the Vessiot distributions, we identify the so-called separable Vessiot distributions. By expressing the separable Vessiot distributions in a basis of singular vector fields, we show that there are, at most, 27 equivalence classes of such distributions. Of these, 14 classes are associated with Darboux integrable nonlinear systems. We take one of these Darboux integrable classes and show that it is in correspondence with the class of six-dimensional simply transitive Lie algebras. Finally, this later result is used to reduce the problem of constructing exact general solutions of the nonlinear wave equations understudy to the integration of Lie systems. These systems were first discovered by Sophus Lie as the most general class of ordinary differential equations which admit nonlinear superposition principles. 相似文献
Abstract The compression behaviour in a multi-anvil apparatus of pure NaCl and of a foil of Ni3Al embedded in a pressure medium of NaCl has been studied by energy-dispersive X-ray diffraction. At ambient temperature, the pressure and stresses, determined from line positions of NaCl, were constant throughout the sample chamber. Line positions and line widths of NaCl reflections were reversible on pressure release. A saturation of microstrains observed in NaCl at 2 GPa is thus attributed to brittle fracture setting in at uniaxial stresses of around 0.3 GPa. Ni3Al polycrystals, in contrast, undergo extensive (ductile) plastic deformation above 4 GPa. The compression behaviour of both Ni3Al and NaCl is identical to that previously determined in a diamond anvil cell. While a multi-anvil device thus has the advantage, compared with a diamond anvil cell, of constant pressure and stress throughout the sample chamber, microstrains in poly-crystalline samples arise in both devices. Samples in a multi-anvil apparatus thus need to be mixed with a pressure medium and to consist of essentially single crystals just as in a diamond anvil cell. Annealing experiments at high pressures confirm that the release of the uniaxial stress component in the pressure medium does not cause a release of microstrains in the embedded sample if the latter has been plastically deformed. Annealing for the purpose of attaining hydrostatic conditions in compression studies thus has to be carried out with care. 相似文献
Hypertension is one of the most common diseases nowadays and is still the major cause of premature death despite of the continuous discovery of novel therapeutics. The discovery of the Renin Angiotensin System (RAS) unveiled a path to develop efficient drugs to fruitfully combat hypertension. Several compounds that prevent the Angiotensin II hormone from binding and activating the AT1R, named sartans, have been developed. Herein, we report a comprehensive review of the synthetic paths followed for the development of different sartans since the discovery of the first sartan, Losartan. 相似文献
Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance. 相似文献