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.     

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.     

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.     

Quantitative and sensitive detection of rare mutations using droplet-based microfluidics

Somatic mutations within tumoral DNA can be used as highly specific biomarkers to distinguish cancer cells from their normal counterparts. These DNA biomarkers are potentially useful for the diagnosis, prognosis, treatment and follow-up of patients. In order to have the required sensitivity and specificity to detect rare tumoral DNA in stool, blood, lymph and other patient samples, a simple, sensitive and quantitative procedure to measure the ratio of mutant to wild-type genes is required. However, techniques such as dual probe TaqMan(?) assays and pyrosequencing, while quantitative, cannot detect less than ～1% mutant genes in a background of non-mutated DNA from normal cells. Here we describe a procedure allowing the highly sensitive detection of mutated DNA in a quantitative manner within complex mixtures of DNA. The method is based on using a droplet-based microfluidic system to perform digital PCR in millions of picolitre droplets. Genomic DNA (gDNA) is compartmentalized in droplets at a concentration of less than one genome equivalent per droplet together with two TaqMan(?) probes, one specific for the mutant and the other for the wild-type DNA, which generate green and red fluorescent signals, respectively. After thermocycling, the ratio of mutant to wild-type genes is determined by counting the ratio of green to red droplets. We demonstrate the accurate and sensitive quantification of mutated KRAS oncogene in gDNA. The technique enabled the determination of mutant allelic specific imbalance (MASI) in several cancer cell-lines and the precise quantification of a mutated KRAS gene in the presence of a 200,000-fold excess of unmutated KRAS genes. The sensitivity is only limited by the number of droplets analyzed. Furthermore, by one-to-one fusion of drops containing gDNA with any one of seven different types of droplets, each containing a TaqMan(?) probe specific for a different KRAS mutation, or wild-type KRAS, and an optical code, it was possible to screen the six common mutations in KRAS codon 12 in parallel in a single experiment.     

Numerical spectral analysis of a grid: Application to strain measurements

We present a nondestructive and noncontact extensometry technique, which has been developed in order to study the behavior of different materials such as polycarbonate, araldite, urethane, etc. A spectral analysis of a crossed grating marked on the surface of a specimen and recorded by a charge coupled device camera is presented. The procedure is based on the use of a bidimensional fast Fourier transform algorithm coupled with an interpolation process. It leads to the accurate determination of frequencies. Numerical simulations have been made to evaluate the strain sensitivity; it depends on both the initial phase and the number of cycles characterizing the grid. Theoretically, the strain sensitivity can reach 10^-5 in best cases, but practically it is notbetter than 10^-4. Several applications on different materials are presented: polyurethane, paper and cloth.