Design, synthesis, evaluation, and structure of vitamin D analogues with furan side chains

Based on the crystal structures of human vitamin D receptor (hVDR) bound to 1α,25-dihydroxy-vitamin D(3) (1,25 D) and superagonist ligands, we previously designed new superagonist ligands with a tetrahydrofuran ring at the side chain that optimize the aliphatic side-chain conformation through an entropy benefit. Following a similar strategy, four novel vitamin D analogues with aromatic furan side chains (3a, 3b, 4a, 4b) have now been developed. The triene system has been constructed by an efficient stereoselective intramolecular cyclization of an enol triflate (A-ring precursor) followed by a Suzuki-Miyaura coupling of the resulting intermediate with an alkenyl boronic ester (CD-side chain, upper fragment). The furan side chains have been constructed by gold chemistry. These analogues exhibit significant pro-differentiation effects and transactivation potency. The crystal structure of 3a in a complex with the ligand-binding domain of hVDR revealed that the side-chain furanic ring adopts two conformations.     

Synthesis of Some Selectively N-Protected (1S,2S)-p-Nitrophenylserinol–Based Diamino-1,3-dioxanes and Tripodands

The unconventional methodology for the non-epimerizable cycloacetalization of optically active (1S,2S)-2-amino-1-(4-nitrophenyl)propane-1,3-diol (p-nitrophenylserinol) (condensed H₂SO₄ 96% as solvent and catalyst, i.e., sulfuric transacetalization) producing (2R,4S,5S) diamino-1,3-dioxanes was enlarged by the use of N-protected forms of 2,2-dimethoxyethylamine (DMEA, aminoacetaldehyde dimethylacetal). Conversely, N-protected derivatives of p-nitrophenylserinol were successfully cyclocondensed with DMEA in the same sulfuric conditions. N-Functionalization of DMEA upon treatment with trimesic acid trichloride and cyanuric chloride yielded the corresponding triple amide and melamine, respectively. Their adapted sulfuric transacetalization in triplicate in reaction with arylserinols (aryl: phenyl, p-nitrophenyl) afforded a new series of optically active tripodands.     

Production study of high specific activity NCA Re-186g by proton and deuteron cyclotron irradiation

Very high specific activity (A_S) ^186gRe could be produced by either proton or deuteron cyclotron irradiation on highly enriched ¹⁸⁶W target in no-carrier-added (NCA) form, leading to a A_S very close to the theoretical carrier free (CF) value of 6.88 GBq μg⁻¹. Thick Target Yields (TTYs), obtained irradiating both thick metal W targets of natural isotopic composition and highly enriched powdered ¹⁸⁶W targets, were measured at different particles energies taking into account high accuracy and precision. The evaluation of radionuclidic purities of ^186gRe obtained activating highly enriched ¹⁸⁶W by both p and d were also carried out and accurately compared. The thin-target excitation functions for all Re (A = 181, 182, 183, 184, 186 and their metastable levels), and W and Ta coproduced radionuclides will be presented elsewhere in deep details.     

Bi-Sobolev mappings with differential matrices in Orlicz Zygmund classes

Bi-Sobolev mappings have been defined as those homeomorphisms such that f and f−1 belong to . We deduce regularity properties of the distortion of f from the regularity of the differential matrix Df−1 and conversely.     

Radon measure-valued solutions of nonlinear strongly degenerate parabolic equations

We prove the existence of suitably defined weak Radon measure-valued solutions of the homogeneous Dirichlet initial-boundary value problem for a class of strongly degenerate quasilinear parabolic equations. We also prove that: \((i)\) the concentrated part of the solution with respect to the Newtonian capacity is constant; \((ii)\) the total variation of the singular part of the solution (with respect to the Lebesgue measure) is nonincreasing in time. Conditions under which Radon measure-valued solutions of problem \((P)\) are in fact function-valued (depending both on the initial data and on the strength of degeneracy) are also given.     

Carleson and Vanishing Carleson Measures on Radial Trees

We extend a discrete version of an extension of Carleson’s theorem proved in [5] to a large class of trees that have certain radial properties. We introduce the geometric notion of s-vanishing Carleson measure on such a tree T (with s ≥ 1) and give several characterizations of such measures. Given a measure σ on T and p ≥ 1, let L ^p (σ) denote the space of functions g defined on T such that |g| ^p is integrable with respect to σ and let L ^p (? T) be the space of functions f defined on the boundary of T such that |f| ^p is integrable with respect to the representing measure of the harmonic function 1.We prove the following extension of the discrete version of a classical theorem in the unit disk proved by Power. A finite measure σ on T is an s-vanishing Carleson measure if and only if for any real number p > 1, the Poisson operator P : L ^p (? T) → L ^sp (σ) is compact. Characterizations of weak type for the case p = 1 and in terms of the tree analogue of the extended Poisson kernel are also given. Finally, we show that our results hold for homogeneous trees whose forward probabilities are radial and whose backward probabilities are constant, as well as for semihomogeneous trees.     

Some classes of operators with symbol on the Lipschitz space of a tree

In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to \(\mathbf L^1\). We then study the properties of two useful operators \(\nabla \) and \(\Delta \) and use them (along with the multiplicative symbol \(\psi \)) to define the Toeplitz operator \(T_\psi \) on the space \(\mathbf L^p\) for \(1\le p \le \infty \). We give conditions for its boundedness and study its point spectrum.     

Composition Operators on the Lipschitz Space of a Tree

The Lipschitz space ${\mathcal{L}}$ of an infinite tree T rooted at o is defined as the space consisting of the functions ${f : T \rightarrow \mathbb{C}}$ such that $$\beta_f = {\rm sup}\{|f(v) - f(v^-)| : v \in T\backslash\{o\}, \,v^- {\rm parent \, of \,} v\}$$ is finite. Under the norm ${\|f\|_\mathcal{L} = |f(o)|+\beta_f,\mathcal{L}}$ is a Banach space. In this article, the functions φ mapping T into itself whose induced composition operator ${C_{\varphi} : f \mapsto f \circ \varphi}$ on the Lipschitz space is bounded, compact, or an isometry, are characterized. Specifically, it is shown that the symbols of the bounded composition operators are the Lipschitz maps of T into itself viewed as a metric space under the edge-counting distance. The symbols inducing compact operators have finite range while those inducing isometries on ${\mathcal{L}}$ are precisely the onto maps fixing the root and whose images of neighboring vertices coincide or are themselves neighboring vertices. Finally, the spectrum of the operators ${C_\varphi}$ that are isometries is studied in detail.