On certain spaces of lattice diagram determinants

The aim of this work is to study some lattice diagram determinants Δ_L(X,Y) as defined in (Adv. Math. 142 (1999) 244) and to extend results of Aval et al. (J. Combin. Theory Ser. A, to appear). We recall that M_L denotes the space of all partial derivatives of Δ_L. In this paper, we want to study the space M_i,j^k(X,Y) which is defined as the sum of M_L spaces where the lattice diagrams L are obtained by removing k cells from a given partition, these cells being in the “shadow” of a given cell (i,j) in a fixed Ferrers diagram. We obtain an upper bound for the dimension of the resulting space M_i,j^k(X,Y), that we conjecture to be optimal. This dimension is a multiple of n! and thus we obtain a generalization of the n! conjecture. Moreover, these upper bounds associated to nice properties of some special symmetric differential operators (the “shift” operators) allow us to construct explicit bases in the case of one set of variables, i.e. for the subspace M_i,j^k(X) consisting of elements of 0 Y-degree.     

Role of nitrogen in the mobility drop of electrons in modulation-doped GaAsN/AlGaAs heterostructures

We report transport properties of a 2 dimension electron gas (2DEG) in molecular beam epitaxy-grown GaAs_1−xN_x/AlGaAs modulation-doped heterostructures. Quantum oscillations in far infrared cyclotron resonance prove the efficient electron transfer and formation of the 2DEG. The 2DEG mobility strongly depends on the N concentration in the channel layer. It shows a drastic decrease as compared to N-free samples, even for the smallest amount of N (0.02%). For this N composition, the electron effective mass was found to be 0.073m₀. Reduced growth temperature (450 °C) was found to improve the mobility of N-containing channels. Examination of transport properties from 4 to 300 K and cyclotron resonance experiments give evidence of the presence of ionised impurity-like scattering centres in GaAsN.     

Carbon-13 nuclear magnetic resonance spectra of 1,2,3,4-tetrahydroquinazoline and some 3-benzyl derivatives

The concerted use of the ¹H/¹³C shift correlation with full ¹H/¹H decoupling and the modified COLOC sequence for long-range X/H correlation 2D nmr spectroscopy allows the total assignment of the ¹³C nmr resonances of 1,2,3,4-tetrahydroquinazoline and 3-benzyl-1,2,3,4-tetrahydroquinazoline. From these data, the ¹³C nmr chemical shifts of a series of 3-benzylsubstituted-1,2,3,4-tetrahydroquinazolines are deduced.     

Poly(N-vinylimidazole/ethylene glycol dimethacrylate) for the purification and isolation of phenolic acids

In this study we report the novel polymeric resin poly(N-vinyl imidazole/ethylene glycol dimethacrylate) for the purification and isolation of phenolic acids. The monomer to crosslinker ratio and the porogen composition were optimized for isolating phenolic acids diluted in acetonitrile at normal phase chromatography conditions, first. Acetonitrile serves as polar, aprotic solvent, dissolving phenolic acids but not interrupting interactions with the stationary phase due to the approved Hansen solubility parameters. The optimized resin demonstrated high loading capacities and adsorption abilities particularly for phenolic acids in both, acetonitrile and aqueous solutions. The adsorption behavior of aqueous standards can be attributed to ion exchange effects due to electrostatic interactions between protonated imidazole residues and deprotonated phenolic acids. Furthermore, adsorption experiments and subsequent curve fittings provide information of maximum loading capacities of single standards according to the Langmuir adsorption model. Recovery studies of the optimized polymer in the normal-phase and ion-exchange mode illustrate the powerful isolation properties for phenolic acids and are comparable or even better than typical, commercially available solid phase extraction materials. In order to prove the applicability, a highly complex extract of rosemary leaves was purified by poly(N-vinyl imidazole/ethylene glycol dimethacrylate) and the isolated compounds were identified using UHPLC–qTOF-MS.     

Positive block matrices and numerical ranges

Any positive matrix M partitioned in four n-by-n blocks satisfies the unitarily invariant norm inequality $6M6\le 6M_{1,1}+M_{2,2}+\omega I6$, where ω is the width of the numerical range of $M_{1,2}$. Some related inequalities and a reverse Lidskii majorization are given.     

Convergence of the Two‐Dimensional Dynamic Ising‐Kac Model to

The Ising‐Kac model is a variant of the ferromagnetic Ising model in which each spin variable interacts with all spins in a neighborhood of radius γ ^{? 1} for around its base point. We study the Glauber dynamics for this model on a discrete two‐dimensional torus for a system size and for an inverse temperature close to the critical value of the mean field model. We show that the suitably rescaled coarse‐grained spin field converges in distribution to the solution of a nonlinear stochastic partial differential equation. This equation is the dynamic version of the quantum field theory, which is formally given by a reaction‐diffusion equation driven by an additive space‐time white noise. It is well‐known that in two spatial dimensions such equations are distribution valued and a Wick renormalization has to be performed in order to define the nonlinear term. Formally, this renormalization corresponds to adding an infinite mass term to the equation. We show that this need for renormalization for the limiting equation is reflected in the discrete system by a shift of the critical temperature away from its mean field value.© 2016 by the authors. Communications on Pure and Applied Mathematics is published by Wiley Periodicals, Inc., on behalf of the Courant Institute of Mathematics.     

Electrochemistry and spectroelectrochemistry of bismanganese porphyrin-corrole dyads

A series of homobimetallic manganese cofacial porphyrin-corrole dyads were synthesized and investigated as to their electrochemistry, spectroelectrochemistry, and ligand binding properties in nonaqueous media. Four dyads were investigated, each of which contained a Mn(III) corrole linked in a face-to-face arrangement with a Mn(III) porphyrin. The main difference between compounds in the series is the type of spacer, 9,9-dimethylxanthene, anthracene, dibenzofuran, or diphenylether, which determines the distance and interaction between the metallomacrocycles. Each redox process of the porphyrin-corrole dyads was assigned on the basis of spectroscopic and electrochemical data and by comparison with reactions and properties of the monocorrole and the monoporphyrin which were examined under the same solution conditions. The Mn(III) porphyrin part of the dyad undergoes two major one-electron reductions in pyridine and benzonitrile, the first of which involves a Mn(III)/Mn(II) process and the second the addition of an electron to the conjugated π-ring system of the macrocycle. The Mn(III) corrole part of the dyads also exhibits two major redox processes, one involving Mn(III)/Mn(II) and the other Mn(III) to Mn(IV) under the same solution conditions. The potentials and reversibility of each electron transfer reaction were shown to depend upon the solvent, type of spacer separating the two macrocycles, and the presence or absence of axial ligation, the latter of which was investigated in detail for the case of acetate ion which was found to bind within the cavity of the dyad to both manganese centers, both before and after the stepwise electroreduction to the Mn(II) forms of the two macrocycles. An intramolecular chloride ion exchange between the porphyrin part of the dyads which contain Mn(III)Cl and the singly oxidized corrole in the dyad is observed after the Mn(III)/Mn(IV) reaction of the corrole, suggesting that chloride is coordinated inside the cavity in the neutral compound.     

Modulating the photophysical properties of azamacrocyclic europium complexes with charge-transfer antenna chromophores

Two europium complexes with bis(bipyridine) azamacrocyclic ligands featuring pendant arms with or without π-conjugated donor groups are synthesized and fully characterized by theoretical calculations and NMR spectroscopy. Their photophysical properties, including two-photon absorption, are investigated in water and in various organic solvents. The nonfunctionalized ligand gives highly water-stable europium complexes featuring bright luminescence properties but poor two-photon absorption cross sections. On the other hand, the europium complex with an extended conjugated antenna ligand presents a two-photon absorption cross section of 45 GM at 720 nm but is poorly luminescent in water. A detailed solvent-dependent photophysical study indicates that this luminescence quenching is not due to the direct coordination of O-H vibrators to the metal center but to the increase of nonradiative processes in a protic solvent induced by an internal isomerization equilibrium.     

Asymmetric total synthesis of (+)-luciduline: toward a general approach to related Lycopodium alkaloids

As part of a research program directed toward the synthesis of Lycopodium alkaloids, a multigram scale asymmetric synthesis of intermediate 11 was achieved in 11 steps from pyridine (17). In addition to our alkene metathesis strategy, a key feature of this synthetic approach consists of a Fukuyama's Diels-Alder cycloaddition between 1,2-dihydropyridine and acrolein using MacMillan's catalyst (18) on a 50 g scale. This led to a 12-step catalytic asymmetric synthesis of (+)-luciduline (1). A broader subset of Lycopodium alkaloids could also be obtained, as demonstrated by the derivatization of 11 into advanced intermediates for the synthesis of some of these natural products.