We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation (−∆)γ/2, 0 < γ ≤ 1). We show in this paper that if θ ∈ C((0, T ); C1−γ), or θ ∈ Lr((0, T ); Cα) with α = 1−γ+ γ r is a weak solution of the 2D quasi-geostrophic equation, then θ is a classical solution in (0, T ]× R2. This result improves our previous result in [18].

This paper describes a new method for the transannular functionalization of γ-C−H bonds in alicyclic amines to install C(sp3)−halogen, oxygen, nitrogen, boron, and sulfur bonds. The key challenge this transformation is controlling relative rate Cγ−H versus Cα−H functionalization. We demonstrate that selectivity can be achieved by pre-complexation substrate with Pd prior addition oxidant. approa...

We point out that the remarkable Knutson and Tao Saturation Theorem [9] and polynomial time algorithms for linear programming [14] have together an important, immediate consequence in geometric complexity theory [15, 16]: The problem of deciding positivity of Littlewood-Richardson coefficients belongs to P ; cf.[10]. Specifically, for GLn(C), positivity of a Littlewood-Richardson coefficient cα...

In this article we present 1H and 13C chemical shift assignments, secondary structural propensity data and normalized temperature coefficient data for N-terminal peptides of Connexin 26 (Cx26), Cx26G12R and Cx32G12R mutants seen in syndromic deafness and Charcot Marie Tooth Disease respectively, published in "Structural Studies of N-Terminal Mutants of Connexin 26 and Connexin 32 Using 1H NMR S...

We prove that the following two statements are equiconsistent: there exists a greatly Mahlo cardinal; there exists a regular uncountable cardinal κ such that no stationary subset of κ+ ∩ cof(κ) carries a partial square. A famous theorem in set theory is the result that the failure of the square principle κ, for a regular uncountable cardinal κ, is equiconsistent with a Mahlo cardinal. Solovay p...

Predicting one-dimensional structure properties has played an important role to improve prediction of protein three-dimensional structures and functions. The most commonly predicted properties are secondary structure and accessible surface area (ASA) representing local and nonlocal structural characteristics, respectively. Secondary structure prediction is further complemented by prediction of ...