Design and Synthesis of New Withaferin A Inspired Hedgehog Pathway Inhibitors

Withanolides constitute a well-known family of plant-based alkaloids characterised by widespread biological properties, including the ability of interfering with Hedgehog (Hh) signalling pathway. Following our interest in natural products and in anticancer compounds, we report here the synthesis of a new class of Hh signalling pathway inhibitors, inspired by withaferin A, the first isolated member of withanolides. The decoration of our scaffolds was rationally supported by in silico studies, while functional evaluation revealed promising candidates, confirming once again the importance of natural products as inspiration source for the discovery of novel bioactive compounds. A stereoselective approach, based on Brown chemistry, allowed the obtainment and the functional evaluation of the enantiopure hit compounds.     

Raman study of SO2 at high pressure: aggregation,phase transformations,and photochemistry

We report Raman measurements made on SO₂ in a diamond cell up to 75 kbar showing two new phases, solid II and solid III, which differ from known, zero-pressure solid I. Spectra indicate that SO₂ molecules aggregate in solid III to possibly form a cyclical trimer; solid III is shown to be photochemically active to blue radiation.     

Group valued measures with the lyapunoff property

Dopo aver dato una definizione di parte convessa di un gruppo topologico, si stabilisce una condizione affinchè il condominio di una misura sia convesso.     

On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form

In the approximation of linear elliptic operators in mixed form, it is well known that the so-called inf-sup and ellipticity in the kernel properties are sufficient (and, in a sense to be made precise, necessary) in order to have good approximation properties and optimal error bounds. One might think, in the spirit of Mercier-Osborn-Rappaz-Raviart and in consideration of the good behavior of commonly used mixed elements (like Raviart-Thomas or Brezzi-Douglas-Marini elements), that these conditions are also sufficient to ensure good convergence properties for eigenvalues. In this paper we show that this is not the case. In particular we present examples of mixed finite element approximations that satisfy the above properties but exhibit spurious eigenvalues. Such bad behavior is proved analytically and demonstrated in numerical experiments. We also present additional assumptions (fulfilled by the commonly used mixed methods already mentioned) which guarantee optimal error bounds for eigenvalue approximations as well.

     

On mixtures of distributions of Markov chains

Let X be a chain with discrete state space I, and V be the matrix of entries V_i,n, where V_i,n denotes the position of the process immediately after the nth visit to i. We prove that the law of X is a mixture of laws of Markov chains if and only if the distribution of V is invariant under finite permutations within rows (i.e., the V_i,n's are partially exchangeable in the sense of de Finetti). We also prove that an analogous statement holds true for mixtures of laws of Markov chains with a general state space and atomic kernels. Going back to the discrete case, we analyze the relationships between partial exchangeability of V and Markov exchangeability in the sense of Diaconis and Freedman. The main statement is that the former is stronger than the latter, but the two are equivalent under the assumption of recurrence. Combination of this equivalence with the aforesaid representation theorem gives the Diaconis and Freedman basic result for mixtures of Markov chains.     

Direct evidence for the breakdown of the N = 8 shell closure in 12Be

We derive the formalism to obtain spatial distributions of collisional correlation times for macroscopic particles undergoing granular flow from pulsed gradient spin echo nuclear magnetic resonance diffusion data. This is demonstrated with an example of axial motion in the shear flow regime of a 3D granular flow in a horizontal rotating cylinder at one rotation rate.     

The simulation of infrared bands from the analyses of rotational spectra: the 2ν9-ν9 and ν5-ν9 hot bands of HNO3

The results of millimeter and submillimeter wave rotational spectroscopy are used to simulate the complex structure of the 2ν₉-ν₉ and ν₅-ν₉ hot bands. The comparison data were obtained with a high-resolution Bruker FTIR. The combination of the quality of these data and the complexity of the spectra of these interacting states represents a stringent test for the simulation. It is shown that the agreement is very good and that this approach is generally advantageous. From this simulation, the ratios of the transition dipole moments for the 2ν₉-ν₉ and ν₅-ν₉ hot bands with respect to the ν₉ fundamental band were found to be 1.38(11) and 0.67(20), respectively. Using these results, the calculated integrated band intensities for the hot bands at were determined to be and . These results were used to successfully simulate high-resolution stratospheric spectra obtained from a balloon flight of the FIRS-2 spectrometer. The more general problem of the rotation-vibration database and the optimal use of both microwave and infrared data to define it is discussed. It is concluded that it is best if the combination of data takes place at the level of the original spectra.