Improving Site‐Directed RNA Editing In Vitro and in Cell Culture by Chemical Modification of the GuideRNA

Adenosine‐to‐inosine deamination can be re‐addressed to user‐defined mRNAs by applying phosphothioate/2′‐methoxy‐modified guideRNAs. Dense chemical modification of the guideRNA clearly improves performance of the covalent conjugates inside the living cell. Furthermore, careful positioning of a few modifications controls editing selectivity in vitro and was exploited for the challenging repair of the Factor 5 Leiden missense mutation.     

Effective Control of the Electron-donating Ability of Phosphines by using Phosphazenyl and Phosphoniumylidyl Substituents

Phosphoniumylidyl and phosphazenyl groups are effective substituents to increase the electron-donating ability of tertiary phosphines. However, the influence of structural variations among those substituents on the electronic properties of the phosphines is little explored. Herein, we show that protonation of the ylidic carbon atom of phosphoniumylidyl phosphines increases the Tolman electronic parameter (TEP) by ΔTEP = 16.0–18.8 cm^–1. Furthermore, phosphazenyl phosphines were synthesized with isopropyl groups (NP{iPr}₃) and tetramethylguanidino groups (NP{tmg}₃) at the phosphonium center. Determination of their TEP values reveals a remarkable low substituent parameter of χ = –18.5 cm^–1 for the NP(tmg)₃ group. In addition, we prepared the corresponding gold(I) complexes and determined their solid-state structures using single-crystal X-ray diffraction studies to analyze the steric profile of the new phosphine ligands.     

Semi-internal Stabilization for a Non-linear Bernoulli–Euler Equation

We consider a non-linear plate equation of Bernoulli–Euler type with a locally distributed damping term. Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially. The method we use is a combination of multiplier techniques and of a compactness-uniqueness argument.     

Dual Description of the Superconducting Phase Transition

The dual approach to the Ginzburg-Landau theory of a Bardeen-Cooper-Schrieffer superconductor is reviewed. The dual theory describes a grand canonical ensemble of fluctuating closed magnetic vortices, of arbitrary length and shape, which interact with a massive vector field representing the local magnetic induction. When the critical temperature is approached from below, the magnetic vortices proliferate. This is signaled by the disorder field, which describes the loop gas, developing a non-zero expectation value in the normal conducting phase. It therby breaks a global U(1) symmetry. The ensuing Goldstone field is the magnetic scalar potential. The superconducting-to-normal phase transition is studied by applying renormalization group theory to the dual formulation. In the regime of a second-order transition, the critical exponents are given by those of a superfluid with a reversed temperature axis.     

Chaotic synchronization of memristive neurons: Lyapunov function versus Hamilton function

Nonlinear Dynamics - In this paper, we consider a 5-dimensional Hindmarsh–Rose neuron model. This improved version of the original model shows rich dynamical behaviors, including a chaotic...     

Isolated singularities of polyharmonic inequalities

We study nonnegative classical solutions u of the polyharmonic inequality

     

Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces

In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and B^{-\frac12,\frac12}₄{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS _ν ) has a unique global solution with initial data u₀ = (u₀^h, u₀³){u_0 = (u_0^h, u_0^3)} which satisfies ||u₀^h||_B exp(\fracCn⁴ ||u₀³||_B⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or ||u₀^h||_{B^{-\frac12,\frac12}4} exp(\fracCn⁴ ||u₀³||_{B^{-\frac12,\frac12}4}⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c ₀ sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner type spaces, [(L^p_t)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L²_{t, f})\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L ¹ function f(t).     

Multivariate Hierarchical Copulas with Shocks

A transformation to obtain new multivariate hierarchical copulas, starting with an arbitrary copula, is introduced. In addition to the hierarchical structure, the presented construction principle explicitly supports singular components. These may be interpreted as the effect of local or global shocks to the underlying random variables. A large spectrum of dependence patterns can be achieved by the presented transformation, which seems promising for practical applications. Moreover, copulas arising from this construction are similarly admissible with respect to analytical tractability and sampling routines as the original copula. Finally, several well-known families of copulas may be interpreted as special cases.     

Weighted Estimations from a Conjugate Operator

In this Letter we develop a general procedure leading from a Mourre-type estimation for a given self-adjoint operator H to a Hardy-type weighted inequality. We use this method in order to prove exponential decay for eigenvectors of a large class of perturbations of operators of convolution with bounded analytic functions.