Transition-Metal-Free Heterocyclic Carbon-Boron Bond Formation

Heteroaryl boronic acids and esters are extremely important and valuable intermediates because of their wide application in the synthesis of marketed drugs and bioactive compounds. Over the last couple of decades, the construction of highly important heteroaryl carbon-boron bonds has created huge attention. The transition-metal-free protocols are more green, less sensitive to air and moisture, and also economically advantageous over the transition-metal-based protocols. The transition-metal-free C−H borylation of heteroarenes and C−X (X=halogen) borylation of heteroaryl halides represents an excellent approach for their synthesis. Also, various cyclization and alkyne activation protocols have been recently established for their synthesis. The goal of this review article is to summarize the existing literature and the current state of the art for transition-metal-free synthesis of heteroaryl boronic acid and esters.     

Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether $\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}$ takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range $0?\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}?1$. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.     

基于Kronecker型替换的黑盒多项式稀疏插值

本文基于新的Kronecker型替换,给出两个由黑盒表示的稀疏多项式的新确定性插值算法.令f∈R[x1,……,xn]是一个稀疏黑盒多项式,其次数上界为D.当R是C或者是有限域时,相对于已有算法,新算法具有更好的计算复杂度或者关于D的复杂度更低.特别地,对于一般黑盒模型,D是复杂度中的主要因素,而在所有的确定性算法中,本文的第二个算法的复杂度关于D是最低的.     

Sterically Facilitated Intramolecular Nucleophilic NMe2 Group Substitution in the Synthesis of Fused Isoxazoles: Theoretical Study

The influence of steric repulsion between the NMe₂ group and a second ortho-(peri-)substituent in the series of 1-dimethylaminonaphthalene and N,N-dimethylanilene ortho-oximes on the ease of the NMe₂ group’s intramolecular nucleophilic substitution is studied. Possible reaction intermediates for three mechanisms are calculated (ωB97xd/def-2-TZVP), and their free Gibbs energies are compared to model reaction profiles. Supporting experiments have proved the absence of studied reactivity in the case of simple 2-dimethylaminobenzaldoxime, which allowed us to establish reactivity limits. The significant facilitation of NMe₂ group displacement in the presence of bulky substituents is demonstrated. The possibility of fused isoxazoles synthesis via the intramolecular nucleophilic substitution of a protonated NMe₂ group in the aniline and naphthalene series is predicted.     

Existence and Uniqueness of Solution for a Class of Nonlinear Degenerate Elliptic Equations

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations■,in the setting of the weighted Sobolev spaces.     

On the Generalized Porous Medium Equation in Fourier-Besov Spaces

We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.