3He Transverse Electron Scattering Response Function with �� Degrees of Freedom

A calculation of the ³He transverse (e, e??) inclusive response function, R _T , which includes ?? degrees of freedom is performed using the Lorentz integral transform method. The resulting coupled equations are treated in impulse approximation, where the NNN and NN?? channels are solved separately. R _T is calculated for the breakup threshold region at a momentum transfer of q?=?862 MeV/c.     

On Riesz means of the coefficients of spinor zeta functions in genus two

Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp ₂(?) of genus 2. The Fourier coefficients of the spinor zeta function Z _F (s) are denoted by c _n . Let D _ρ (x;Z _F ) be the Riesz mean of c _n . In this paper, we obtain the truncated Voronoï-type formula of D _ρ (x;Z _F ) under the Ramanujan–Petersson conjecture.     

Magnetic silyl scaffold enables efficient recycling of protecting groups

A novel organic/inorganic hybrid material comprising carboncoated cobalt nanoparticles and a poly(benzylchloride)styrene shell is the first magnetic support that complies with important requirements for immobilized reagents and scavengers, that is, stability under harsh conditions (e.g., acids), sufficient loading (up to 2 mmol g(-1)), and satisfying magnetization. The durability of the scaffold was demonstrated by immobilization of a trialkylsilane reagent, which served as a "magnetic" protecting group for a number of primary and secondary alcohols. Importantly, the scaffold could be efficiently separated, recycled, and reused after alcohol cleavage (HF·pyridine) via regeneration of the silyl chloride moiety with BCl(3).     

Reducing Neuronal Networks to Discrete Dynamics

We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [W. Just, S. Ahn, D. Terman. Minimal attractors in digraph system models of neuronal networks (preprint)], we analyse the discrete model.