On the spectrum of the Cesàro operator C 1 on b\bar v_0 \cap \ell _\infty

In this paper we have investigated the spectrum of the Cesàro operator C ₁ which is regarded as an operator on the sequence space $b\bar v_0 \cap \ell _\infty $ the space of statistically null bounded variation sequences.     

On $$\gamma $$ γ - and local $$\gamma $$ γ -vectors of the interval subdivision

Journal of Algebraic Combinatorics - We show that the $$\gamma $$ -vector of the interval subdivision of a simplicial complex with a nonnegative and symmetric h-vector is nonnegative. In...     

Limits on an extension of Carleson’s\bar \partial - Theorem

We study a theorem essentially due to Carleson about solving the $\bar \partial - equation$ on the unit disk. We show that this theorem generalizes to bordered Riemann surfaces with finitely generated fundamental groups. However, our main result is that the constant appearing in the generalized theorem cannot be taken to be independent of the bordered Riemann surface in question. We exhibit a sequence of (topologically equivalent) Riemann surfaces on which the constant tends to ∞. Since Carleson’s $\bar \partial - theorem$ depends on the notion of a Carleson measure, we also discuss Carleson measures at some length in order to define them appropriately on arbitrary Riemann surfaces.     

Limq → ∞ \frac{c(G)}{r(G)} for Simple Groups

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. For a given finite group G, let c(G) denote the minimal degree of a faithful representation of G by complex quasi-permutation matrices and let r(G) denote the minimal degree of a faithful rational valued character of G. Also let G denote one of the symbols A_l, B_l, C_l, D_l, E₆, E₇, E₈, G₂, F₄, ²B₂, ²E₄, ²G₂, and ³D₄. Let G(q) denote simple group of type G over GF(q). Let c(q) = c(G(q)) and r(q) = r(G(q)). Then we will show that lim Lim_q = 1.     

Positive\partial \bar \partial - closed currents and non-Kähler geometrycurrents and non-Kähler geometry

In this paper some new results on positive \(\partial \bar \partial - closed\) currents are applied to modifications \(f:\bar M \to M\) . The main result in this topic is that every smooth proper modification of a compact Kähler manifoldM is balanced. Moreover, under suitable hypotheses on the map, the Kähler degrees of \(\bar M\) corresponds to homological properties of the exceptional set of the modification. More examples ofp-Kähler manifolds are discussed in the last section of the paper.     

Volterra-type operators from weighted Bergman–Orlicz space to $$\beta $$-Zygmund–Orlicz and $$\gamma $$γ-Bloch–Orlicz spaces

We find the conditions to ensure the boundedness and compactness of the Volterra-type operators acting from weighted Bergman–Orlicz space to \(\beta \)-Zygmund–Orlicz and \(\gamma \)-Bloch–Orlicz spaces, respectively.     

Randregularität des\bar \partial -Problems für die Halbkugel in ℂn

Let f be a -closed (0, q+1)-form defined on the half ball B₊ in ⁿ, which is of class C^k on ¯B. We prove the existence with C^k-estimates of a solution u of the equation .

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Die Anregung zu dieser Arbeit verdanke ich auch Herrn Piotr Jakóbczak aus Krakau, der sich eine gewisse Zeit am Max-Planck-Institut für Mathematik in Bonn aufhielt. Während dieser Zeit untersuchten wir die C⁰-Abschätzungen für die Halbkugel in ⁿ     

Solving ax+b=c

PicturingtheSolvingofax+b=cSupposethereisabalance-scalepictureoftheequation3w+5=14.Onthescale,threeboxesofequalunknownweightand5one-kilogramweightsbalancewith14one-kilogramweights.Youcanfindtheweightwofoneboxintwosteps.Eachstepkeepsthescalebalanced.Step1Remove5one-kilogramweightsfromeachside.Step2Distributetheremainingweightequallyamongtheboxes.     

Global solutions to the Navier–Stokes-{\bar \omega} and related models with rough initial data

We establish the global well-posedness of the Navier–Stokes- ${\bar \omega}$ model with initial data ${u_0 \in H^{1-s}(\mathbb{R}^3)}$ with ${0 < s < \frac{1}{2}}$ which improves the existence results in Fan and Zhou (Appl Math Lett 24:1915–1918, 2011), Layton et al. (Commun Pure Appl Anal 10:1763–1777, 2011) where the initial data are required belonging to ${H^2(\mathbb{R}^3)}$ . We also obtain the similar results for a family of Navier–Stokes-α-like and magnetohydrodynamic-α models.     

Solvability of the\bar \partial problem withC ∞ regularity up to the boundary on wedges of ℂNproblem withC ∞ regularity up to the boundary on wedges of ℂN

For awedge W of ?^N, we introduce an intrinsic condition of weakq-pseudoconvexity which can be expressed in terms ofq-subharmonicity both of a defining function or an exhaustion function. Under this condition we prove solvability of the $\bar \partial $ system for forms withC ^∞ (W)-coefficients of degree ≥q+1. Our method relies on theL ²-estimates by Hörmander. ForC ^∞(W) solvability we refer to Hörmander (if ?W∈C ²), and to Zampieri (for general wedgesW). ForC ^∞ (W) solvability and with ?W∈C ², we 025 refer to Dufresnoy (ifq=0), Michel (if the number of negative Levieigenvalues of ?W is constant), and finally Zampieri (for more generalq-pseudoconvexity).     

不等式(a b)(b c)(c a)》=8abc(a,b,c∈R~ )的引伸

不等式（ａ＋ｂ）（ｂ＋ｃ）（ｃ＋ａ）８ａｂｃ（ａ，ｂ，ｃ∈Ｒ＋）的引伸周才凯（湖南省长沙市雅礼中学４１０００７）高中《代数》（必修）下册Ｐ１１上有这样一道习题：已知ａ，ｂ，ｃ＞０，求证（ａ＋ｂ）（ｂ＋ｃ）（ｃ＋ａ）８ａｂｃ（１）对ａ，ｂ，ｃ中每两...     

Hölder andL p -estimates for the\bar \partial -equation on non-smooth strictlyq-convex domainson non-smooth strictlyq-convex domains

A solution operator for the \(\bar \partial \) -equation on strictlyq-convex domains with nonsmooth boundary is constructed. It is proved that the solution satisfies optimal 1/2-Hölder andL ^p estimates.     

所有形如a2=b+c的勾股数组(a,b,c)

本刊文[1](第17页)给出了勾股数组(3,4,5),(5,12,13)满足的规律:32=4 5,52=12 13.能否求出所有形如a2=b c的勾股数组(a,b,c)呢?这是一个有趣的问题.     

On the\bar \partial equation in weightedL 2 norms in ℂ1equation in weightedL 2 norms in ℂ1

For a large class of subharmonicφ, the equation is studied in . Pointwise upper bounds are derived for the distribution kernels of the canonical solution operator and of the orthogonal projection onto the space of entire functions inH. Existence theorems inL ^p norms are derived as a corollary. A class of counterexamples, related to the failure of to be analytic-hypoelliptic on certain CR manifolds, is discussed. Communicated by Steven Krantz     

Absolutely monotonic functions related to Euler’s gamma function and Barnes’ double and triple gamma function

It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler’s gamma function are Laplace transformations of positive multiples of absolutely monotonic functions. Applications concerning positivity of sums involving Bernoulli numbers are given.     

Optimal Lp estimates for the\bar \partial -equation on complex ellipsoids in ℂn-equation on complex ellipsoids in ℂn

In this paper we prove the best possible L^p estimates for the-equation on complex ellipsoids in ℂⁿ, and provide examples to show why they cannot be improved.