On the role of energy convexity in the web function approximation

For a given p > 1 and an open bounded convex set we consider the minimization problem for the functional over Since the energy of the unique minimizer u_p may not be computed explicitly, we restrict the minimization problem to the subspace of web functions, which depend only on the distance from the boundary δΩ. In this case, a representation formula for the unique minimizer v_p is available. Hence the problem of estimating the error one makes when approximating J_p(u_p) by J_p(v_p) arises. When Ω varies among convex bounded sets in the plane, we find an optimal estimate for such error, and we show that it is decreasing and infinitesimal with p. As p → ∞, we also prove that u_p − v_p converges to zero in for all m < ∞. These results reveal that the approximation of minima by means of web functions gains more and more precision as convexity in J_p increases.     

Imidazolone and Imidazolidinone Artifacts of a Pivotal Imidazolthione,Zyzzin, from the poecilosclerid sponge Zyzza massalis from the coral sea. The first thermochromic systems of marine origin

Dry acetone extracts of the freeze-dried, deep-red powder of the poecilosclerid sponge Zyzza massalis (DENDY ) from the Coral Sea gave the orange alkaloid zyzzin (= 4-(1H-indol-3-yl)-1,5-dihydro-5-thioxo-1H-imidazol-2-one 14 ), which underwent exchange of the 5-thioxo for the 5-oxo group during aqueous chromatographic workup, giving yellow 13 . Both 13 and 14 added hydroxylic solvents at C(4)=N giving colourless, racemic products, 3 and 8 , respectively, by incorporation of MeOH and 10 and 11 , respectively, by incorporation of H₂O. On warming 3 or 10 in DMSO, 13 was recovered, thus furnishing a novel thermochromic system. Optically active (+)- 12 , which may be viewed to derive from enzymatic reduction of 14 at C(4)=N followed by S→O exchange, was also isolated from this sponge, along with the linear amides 16 and 19 . Compound 3 proved to have antibacterial and antifungal activities.     

The Weierstrass factorization theorem for slice regular functions over the quaternions

The class of slice regular functions of a quaternionic variable has been recently introduced and is intensively studied, as a quaternionic analogue of the class of holomorphic functions. Unlike other classes of quaternionic functions, this one contains natural quaternionic polynomials and power series. Its study has already produced a rather rich theory having steady foundations and interesting applications. The main purpose of this article is to prove a Weierstrass factorization theorem for slice regular functions. This result holds in a formulation that reflects the peculiarities of the quaternionic setting and the structure of the zero set of such functions. Some preliminary material that we need to prove has its own independent interest, like the study of a quaternionic logarithm and the convergence of infinite products of quaternionic functions.     

Contrasting the denaturing effect of guanidinium chloride with the stabilizing effect of guanidinium sulfate

Guanidinium chloride, GdmCl, is a strong denaturing agent of globular proteins, whereas guanidinium sulfate, Gdm(2)SO(4), is a stabilizing agent of globular proteins. The stabilizing activity of Gdm(2)SO(4) is unexpected because the denaturant capability of GdmCl is due to direct interactions of Gdm(+) ions with protein surface groups. It is shown that the statistical thermodynamic approach devised to explain the molecular origin of cold denaturation [G. Graziano, Phys. Chem. Chem. Phys., 2010, 12, 14245-14252] can provide a rationalization of the different behaviour of GdmCl and Gdm(2)SO(4) towards globular proteins. The fundamental quantity is the reversible work to create in the aqueous solution a cavity suitable to host the D-state and a cavity suitable to host the N-state. In aqueous GdmCl solutions, this contribution is not large enough to overwhelm the conformational entropy gain upon unfolding and the direct attractions between Gdm(+) ions and protein surface groups; in aqueous Gdm(2)SO(4) solutions, it is so large that it overwhelms the two destabilizing contributions. Sulfate ions, due to their high charge density, interact strongly with water molecules producing a number density increase, that, in turn, renders the cavity creation process very costly, reversing the denaturing power of Gdm(+) ions and stabilizing the N-state of globular proteins.     

Reaction between Dichlorophosphines and Azoalkenes: A General Synthesis of 3,4-Dihydro-2H-1,2,3-diazaphosphole Derivatives

The reaction between dichlorophosphines and azoalkenes provides a smooth method for the preparation of 3,4-dihydro-2H-1,2,3-diazaphosphole-3-oxides. When R¹ ≠ H, the cis: trans ratio is strongly dependent on the nature of the R⁴ substituent. Compounds arising from phenylazoalkenes are stable for several months, whereas compounds arising from methylazoalkenes undergo modifications during silica gel chromatography. Trichlorosilane reduction of these oxides gives the corresponding phosphines with retention of configuration. In some cases, this process competes with stereomutation of the starting phosphine oxide. Aryl-substituted phosphines are much more stable than the corresponding alkyl-substituted phosphines.