Unusual sum rule for Clebsch–Gordan coefficients

Letters in Mathematical Physics - We present a new sum rule for Clebsch–Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is...     

The Glycolytic Pathway as a Target for Novel Onco-Immunology Therapies in Pancreatic Cancer

Pancreatic ductal adenocarcinoma (PDA) is one of the most lethal forms of human cancer, characterized by unrestrained progression, invasiveness and treatment resistance. To date, there are limited curative options, with surgical resection as the only effective strategy, hence the urgent need to discover novel therapies. A platform of onco-immunology targets is represented by molecules that play a role in the reprogrammed cellular metabolism as one hallmark of cancer. Due to the hypoxic tumor microenvironment (TME), PDA cells display an altered glucose metabolism—resulting in its increased uptake—and a higher glycolytic rate, which leads to lactate accumulation and them acting as fuel for cancer cells. The consequent acidification of the TME results in immunosuppression, which impairs the antitumor immunity. This review analyzes the genetic background and the emerging glycolytic enzymes that are involved in tumor progression, development and metastasis, and how this represents feasible therapeutic targets to counteract PDA. In particular, as the overexpressed or mutated glycolytic enzymes stimulate both humoral and cellular immune responses, we will discuss their possible exploitation as immunological targets in anti-PDA therapeutic strategies.     

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.     

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.     

Chemical Processes Involving 18-Crown-6-Ether in Activated Noncovalent Complexes with Protonated Peptides

These last decades, it has been widely assumed that 18-crown-6-ether (CE) plays a spectator role during the chemical processes occurring in isolated host-guest complexes between peptides or proteins and CE after activation in mass spectrometers. Our present experimental and theoretical results challenge this hypothesis by showing that CE can abstract a proton or a protonated molecule from protonated peptides after activation by collisions in argon or electron capture/transfer. Furthermore, thanks to comparison between experimental and calculated values of collision cross-sections, we demonstrate that CE can change binding site after electron transfer. We also propose detailed mechanisms for these processes.     

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.