In this paper, we define a new, special second order cone as type-$k$ cone. We focus on the case of $k=2$, which can be viewed SOCO with an additional {\em complicating variable}. For new problem, develop necessary prerequisites, based previous work for traditional SOCO. then primal-dual interior point algorithm solving type-2 conic optimization (SOCO) family kernel functions suitable finally d...

Let Ω be a convex domain in ℂn satisfying certain restrictions, and let f function holomorphic continuous $$ \overline{\Omega},\kern0.5em f\kern0.5em \in \kern0.5em {H}^{r+\omega}\left(\overline{\Omega}\right) for an appropriate modulus of continuity ω. Then there exist polynomials PN, deg PN ≤ N, such that \left|f(z)-{P}_N(z)\right|\le {cN}^{-r}\omega \left(\frac{1}{N}\right),z\kern0.5em \over...

Abstract Let K be a number field which is multiquadratic or quartic cyclic. We prove several results about the Kummer extensions of , namely concerning intersection between and cyclotomic . For G finitely generated subgroup × we consider cyclotomic-Kummer K ( ? </m:mro...

In this paper, we study the Cauchy problem for nonlinear Schrödinger equations with Coulomb potential $${\rm{i}}{\partial _t}u + \Delta u {K \over {\left| x \right|}}u = \lambda \right|^{p - 1}}u$$ $$1 < p \le 5\,\,{\rm{on}}\,\,{\mathbb{R}^3}$$ . Our results reveal influence of long range K∣x∣−1 on existence and scattering theories equations. particular, prove global when is attractive, i.e., K...

Induction step. Let n 2 and suppose that the lemma holds for all insertion permutations of size strictly less than n. Let π = (π(1), . . . , π(n)) be a permutation drawn uniformly at random from Sn. The rst element π(1) will become the root of the tree Tπ. Since the distribution of π(1) is u.a.r. from [n], the root of the tree is chosen uniformly at random, as required by the construction of ~ ...

Ionophore complexes of K(TCNQ˙ − )(TCNQ 0 ) n adopt a variety stacking motifs such as wave-like infinite TCNQ columns separated by K + -cryptates (left) and -π-dimerised cation slipped stacks (right).

We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group A(K) has such a subgroup if its defining graph K contains an n-hole (i.e. an induced cycle of length n) with n ≥ 5. We construct another eight “forbidden” graphs and show that every graph K on ≤ 8 vertices either contains one of our examples, or co...

After the ring theoretic study of diierential operators in positive characteristic by S.U. Chase and S.P. Smith, B. Haastert started investigation of D-modules on smooth varieties in positive characteristic, and the work of R. BBgvad followed. The purpose of this paper is to complement some basics for further study. We x an algebraically closed eld k of positive characteristic p. All the variet...

We show how k-grams can be used to extend classes of terminal distinguishable right-linear languages (k-TDRL). Moreover, we present an efficient identification algorithm for k-TDRL languages. Our approach not only generalizes the class TDRL, but also the k-testable languages, as well as the k-reversible languages.

Hypoxia-inducible factor 2a regulates key neutrophil functions in humans, mice, and zebrafish A. A. Roger Thompson, Philip M. Elks, Helen M. Marriott, Suttida Eamsamarng, Kathryn R. Higgins, Amy Lewis, Lynne Williams, Selina Parmar, Gary Shaw, Emmet E. McGrath, Federico Formenti, Fredericus J. Van Eeden, Vuokko L. Kinnula, Christopher W. Pugh, Ian Sabroe, David H. Dockrell, Edwin R. Chilvers, P...