We study the system curl (a(x) curlu) = 0, divu = 0 with a bounded measurable coefficient a(x). The main result of this paper is the Hölder continuity of weak solutions of the system above. As an application, we prove the Cα regularity of weak solutions of the Maxwell’s equations in a quasi-stationary electromagnetic field.

Aib α-Aminoisobutyric acid or Cα-methylalanine (αMe)Phe Cα-methylphenylalanine (αMe)Val Cα-methylvaline BOP (Benzotriazol-1-yloxy)tris(dimethylamino)phosphonium CIP 2-Chloro-1,3-dimethylimidazolidium phosphate Db z g Cα,α-dibenzylglycine Deg Cα,α-diethylglycine Dφg Cα,α-diphenylglycine Dp n g Cα,α-di-n-propylglycine EDC 1-(3-Dimethylamino)propyl-3-ethylcarbodiimide HATU 2-(1H-7-aza-1,2,3-benzot...

We study the problem of estimating surface area boundary ∂S a sufficiently smooth set S⊂Rd when available information is only finite subset Xn⊂S. propose two estimators. The first makes use Devroye–Wise support estimator and based on Crofton’s formula, which, roughly speaking, states that (d−1)-dimensional enough mean number intersections randomly chosen lines. For purpose, we an such lines wit...

We study polynomial identities of algebras with involution nonassociative over a field characteristic zero. prove that the growth sequence ⁎-codimensions finite-dimensional algebra is exponentially bounded. construct series fractional ⁎-PI-exponent. also family infinite-dimensional Cα such exp⁎(Cα) does not exist.

where p > 0, c > 0, and λ > 0 are parameters and Ω is an open bounded region with boundary ∂Ω in class C2 in Rn for n ≥ 1. Here g :Ω→ R is a Cα function while h :Ω→ R is a nonnegative Cα function with ‖h‖∞ = 1. When p = 1, (1.1) arises in population dynamics where 1/λ is the diffusion coefficient and ch(x) represents the constant yield harvesting. In this case (p = 1), when g(x) is a positive c...

This paper is concerned with palindromes occurring in characteristic Sturmian words cα of slope α, where α ∈ (0, 1) is an irrational. As cα is a uniformly recurrent infinite word, any (palindromic) factor of cα occurs infinitely many times in cα with bounded gaps. Our aim is to completely describe where palindromes occur in cα. In particular, given any palindromic factor u of cα, we shall estab...

MOTIVATION Solvent exposure of amino acid residues of proteins plays an important role in understanding and predicting protein structure, function and interactions. Solvent exposure can be characterized by several measures including solvent accessible surface area (ASA), residue depth (RD) and contact numbers (CN). More recently, an orientation-dependent contact number called half-sphere exposu...

We give upper and lower bounds for the consistency strength of the failure of a combinatorial principle introduced by Jensen, Square on singular cardinals. A combinatorial principle of great importance in set theory is the Global principle of Jensen [6]: Global : There exists 〈Cα | α a singular ordinal 〉 such that for each α, Cα is a closed unbounded subset of α of ordertype less than α, the li...

In this paper, we study the planar Lp-Minkowski problem(0.1)uθθ+u=fup−1,θ∈S1 for all p∈R, which was introduced by Lutwak [21]. A detailed exploration of (0.1) on solvability will be presented. More precisely, prove that p∈(0,2), there exists a positive function f∈Cα(S1),α∈(0,1) such admits nonnegative solution vanishes somewhere S1. case p∈(−1,0], surprising a-priori upper/lower bound establish...

Chain Fold It is a usual way to tabulate the torsion (dihedral) angles for each residue to reconstruct protein structure using standard covalent bond length and angles. The backbone can be further represented by virtual bond between Cα-atoms. The mainchain is fully described by the virtual dihedral angle αi defined by four successive Cα atoms and the virtual bond angle. This description is used...