scholarly journals TOWERS IN FILTERS, CARDINAL INVARIANTS, AND LUZIN TYPE FAMILIES

2018 ◽  
Vol 83 (3) ◽  
pp. 1013-1062 ◽  
Author(s):  
JÖRG BRENDLE ◽  
BARNABÁS FARKAS ◽  
JONATHAN VERNER
Keyword(s):  
List Type ◽  
Type Number ◽  
Cardinal Invariants ◽  
Regular Cardinals ◽  
Image Position

AbstractWe investigate which filters onωcan contain towers, that is, a modulo finite descending sequence without any pseudointersection (in${[\omega ]^\omega }$). We prove the following results:(1)Many classical examples of nice tall filters contain no towers (in ZFC).(2)It is consistent that tall analytic P-filters contain towers of arbitrary regular height (simultaneously for many regular cardinals as well).(3)It is consistent that all towers generate nonmeager filters (this answers a question of P. Borodulin-Nadzieja and D. Chodounský), in particular (consistently) Borel filters do not contain towers.(4)The statement “Every ultrafilter contains towers.” is independent of ZFC (this improves an older result of K. Kunen, J. van Mill, and C. F. Mills).Furthermore, we study many possible logical (non)implications between the existence of towers in filters, inequalities between cardinal invariants of filters (${\rm{ad}}{{\rm{d}}^{\rm{*}}}\left( {\cal F} \right)$,${\rm{co}}{{\rm{f}}^{\rm{*}}}\left( {\cal F} \right)$,${\rm{no}}{{\rm{n}}^{\rm{*}}}\left( {\cal F} \right)$, and${\rm{co}}{{\rm{v}}^{\rm{*}}}\left( {\cal F} \right)$), and the existence of Luzin type families (of size$\ge {\omega _2}$), that is, if${\cal F}$is a filter then${\cal X} \subseteq {[\omega ]^\omega }$is an${\cal F}$-Luzin family if$\left\{ {X \in {\cal X}:|X \setminus F| = \omega } \right\}$is countable for every$F \in {\cal F}$.

SHARP WEIGHTED BOUNDS FOR GEOMETRIC MAXIMAL OPERATORS

2016 ◽  
Vol 59 (3) ◽  
pp. 533-547 ◽  
Author(s):  
ADAM OSȨKOWSKI
Keyword(s):  
Maximal Operator ◽  
General Setting ◽  
Maximal Operators ◽  
List Type ◽  
Type Number ◽  
Type Estimate ◽  
Formula Group ◽  
Probability Spaces ◽  
Image Position

AbstractLet $\mathcal{M}$ and G denote, respectively, the maximal operator and the geometric maximal operator associated with the dyadic lattice on $\mathbb{R}^d$. (i)We prove that for any 0 < p < ∞, any weight w on $\mathbb{R}^d$ and any measurable f on $\mathbb{R}^d$, we have Fefferman–Stein-type estimate $$\begin{equation*} ||G(f)||_{L^p(w)}\leq e^{1/p}||f||_{L^p(\mathcal{M}w)}. \end{equation*} $$ For each p, the constant e1/p is the best possible.(ii)We show that for any weight w on $\mathbb{R}^d$ and any measurable f on $\mathbb{R}^d$, $$\begin{equation*} \int_{\mathbb{R}^d} G(f)^{1/\mathcal{M}w}w\mbox{d}x\leq e\int_{\mathbb{R}^d} |f|^{1/w}w\mbox{d}x \end{equation*} $$ and prove that the constant e is optimal. Actually, we establish the above estimates in a more general setting of maximal operators on probability spaces equipped with a tree-like structure.

Questions on data and the input to GEN

2016 ◽  
Vol 19 (5) ◽  
pp. 889-890 ◽  
Author(s):  
LUIS LÓPEZ
Keyword(s):  
Code Switching ◽  
List Type ◽  
Type Number ◽  
Image Position

The keynote article (Goldrick, Putnam & Schwartz, 2016) discusses doubling phenomena occasionally found in code-switching corpora. Their analysis focuses on an English–Tamil sentence in which an SVO sequence in English is followed by a verb in Tamil, resulting in an apparent VOV structure: (1)

Derivations Tangential to Compact Group Actions: Spectral Conditions in the Weak Closure

1985 ◽  
Vol 37 (1) ◽  
pp. 160-192 ◽  
Author(s):  
Ola Bratteli ◽  
Frederick M. Goodman
Keyword(s):  
Finite Elements ◽  
Common Core ◽  
Dimensional Space ◽  
List Type ◽  
Finite Dimensional Space ◽  
Type Number ◽  
Compact Lie Group ◽  
Parameter Group ◽  
Finite Dimensional ◽  
Image Position

Let G be a compact Lie group and a an action of G on a C*-algebra as *-automorphisms. Let denote the set of G-finite elements for this action, i.e., the set of those such that the orbit {αg(x):g ∊ G} spans a finite dimensional space. is a common core for all the *-derivations generating one-parameter subgroups of the action α. Now let δ be a *-derivation with domain such that Let us pose the following two problems:Is δ closable, and is the closure of δ the generator of a strongly continuous one-parameter group of *-automorphisms?If is simple or prime, under what conditions does δ have a decompositionwhere is the generator of a one-parameter subgroup of α(G) and is a bounded, or approximately bounded derivation?

scholarly journals Solar X radiation

1965 ◽  
Vol 23 ◽  
pp. 45-52 ◽  
Author(s):  
C. de Jager
Keyword(s):  
Electromagnetic Radiation ◽  
Gamma Rays ◽  
Electronic Transitions ◽  
List Type ◽  
X Rays ◽  
Type Number ◽  
X Ray ◽  
Image Position ◽  
Electron Shells

X-ray bursts are defined as electromagnetic radiation originating from electronic transitions involving the lowest electron shells; gamma rays are of nuclear origin. Solar gamma rays have not yet been discovered.According to the origin we have : 1.Quasi thermal X-rays, emitted by (a) the quiet corona, (b) the activity centers without flares, and (c) the X-ray flares.2.Non-thermal X-ray bursts; these are always associated with flares.The following subdivision is suggested for flare-associated bursts :

The definition of a multi-dimensional generalization of shot noise

1971 ◽  
Vol 8 (01) ◽  
pp. 128-135 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Stochastic Process ◽  
Probability Distribution ◽  
Absolute Convergence ◽  
List Type ◽  
Type Number ◽  
Homogeneous Poisson Process ◽  
Cauchy Principal ◽  
Principal Value ◽  
Definition Of ◽  
Image Position

The paper studies the formally defined stochastic process where {tj } is a homogeneous Poisson process in Euclidean n-space En and the a.e. finite Em -valued function f(·) satisfies |f(t)| = g(t) (all |t | = t), g(t) ↓ 0 for all sufficiently large t → ∞, and with either m = 1, or m = n and f(t)/g(t) =t/t. The convergence of the sum at (*) is shown to depend on (i) (ii) (iii) . Specifically, finiteness of (i) for sufficiently large X implies absolute convergence of (*) almost surely (a.s.); finiteness of (ii) and (iii) implies a.s. convergence of the Cauchy principal value of (*) with the limit of this principal value having a probability distribution independent of t when the limit in (iii) is zero; the finiteness of (ii) alone suffices for the existence of this limiting principal value at t = 0.

scholarly journals IDEAL PROJECTIONS AND FORCING PROJECTIONS

2014 ◽  
Vol 79 (4) ◽  
pp. 1247-1285 ◽  
Author(s):  
SEAN COX ◽  
MARTIN ZEMAN
Keyword(s):  
Set Theory ◽  
Negative Answer ◽  
Large Cardinals ◽  
Normal Ideal ◽  
List Type ◽  
Type Number ◽  
Inner Model ◽  
Image Position ◽  
Open Question ◽  
Woodin Cardinal

AbstractIt is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman–Magidor–Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove:(1)If${\cal I}$is a normal ideal on$\omega _2 $which satisfiesstationary antichain catching, then there is an inner model with a Woodin cardinal;(2)For any$n \in \omega $, it is consistent relative to large cardinals that there is a normal ideal${\cal I}$on$\omega _n $which satisfiesprojective antichain catching, yet${\cal I}$is not saturated (or even strong). This provides a negative answer to Open Question number 13 from Foreman’s chapter in the Handbook of Set Theory ([7]).

scholarly journals USING ALMOST-EVERYWHERE THEOREMS FROM ANALYSIS TO STUDY RANDOMNESS

2016 ◽  
Vol 22 (3) ◽  
pp. 305-331 ◽  
Author(s):  
KENSHI MIYABE ◽  
ANDRÉ NIES ◽  
JING ZHANG
Keyword(s):  
Integrable Function ◽  
Lebesgue Point ◽  
Algorithmic Randomness ◽  
List Type ◽  
Type Number ◽  
Random Real ◽  
Computably Enumerable Set ◽  
Almost Everywhere ◽  
Image Position ◽  
Nondecreasing Functions

AbstractWe study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable functions. The corresponding randomness notions are slightly stronger than Martin–Löf (ML) randomness.We establish several equivalences. Given a ML-random realz, the additional randomness strengths needed for the following are equivalent.(1)all effectively closed classes containingzhave density 1 atz.(2)all nondecreasing functions with uniformly left-c.e. increments are differentiable atz.(3)zis a Lebesgue point of each lower semicomputable integrable function.We also consider convergence of left-c.e. martingales, and convergence in the sense of Birkhoff’s pointwise ergodic theorem. Lastly, we study randomness notions related to density of${\rm{\Pi }}_n^0$and${\rm{\Sigma }}_1^1$classes at a real.

Stability Theorems for Solutions to the Optimal Inventory Equation

1969 ◽  
Vol 6 (01) ◽  
pp. 211-217 ◽  
Author(s):  
S. Edward Boylan
Keyword(s):  
Distribution Function ◽  
List Type ◽  
Type Number ◽  
Stability Theorems ◽  
Image Position ◽  
Uniformly Continuous

In a previous paper, [1] it was shown that a solution, f(x) will exist for the optimal inventory equation (where f(y − z) = f(0), y &lt; z) provided: 1. g(x) ≧ 0, x ≧ 0; 2. 0 &lt; a &lt; 1; 3. h(x) is monotonically nondecreasing, h(0) = 0; 4. F is a distribution function on [0, ∞); (In [1], 1–4 were denoted collectively as (A).) and either 5a. g(x) is continuous for all x ≧ 0; 5b. lim x→∞ g(x) = ∞; 5c h(x) is continuous for all x &gt; 0 (Theorem 2 of [1]); or 6. g(x) is uniformly continuous for all x ≧ 0 (Theorem 3 of [1]).

scholarly journals Selection effects in the discovery of NEAs

2012 ◽  
Vol 10 (H16) ◽  
pp. 490-491
Author(s):  
G. B. Valsecchi ◽  
G. D'Abramo ◽  
A. Boattini
Keyword(s):  
List Type ◽  
Selection Effects ◽  
Type Number ◽  
Formula Group ◽  
Image Position

To highlight discovery selection effects, we consider four NEA subpopulations: (a)“Taurid asteroids”, the Apollos with orbits similar to those of 2P/Encke and of the Taurid meteoroid complex;(b)Atens, to which we add the Inner Earth Objects;(c)non-Taurid Apollos;(d)Amors. The “Taurid asteroids“ are identified by Asher et al. (1993) with a reduced version of the D-criterion (Southworth and Hawkins 1963), involving only a, e and i: \begin{displaymath} D=\sqrt{\left(\frac{a-2.1}{3}\right)^2+(e-0.82)^2+\left(2\sin{\frac{i-4^\circ}{2}}\right)^2}\leq0.25. \end{displaymath} It turns out that the distribution of the longitudes of perihelion ϖ of NEAs with D<0.25 is significantly non-random, due to the existence of two groups whose apse lines are approximately aligned with those of 2P/Encke and of (2212) Hephaistos.

The definition of a multi-dimensional generalization of shot noise

1971 ◽  
Vol 8 (1) ◽  
pp. 128-135 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Stochastic Process ◽  
Probability Distribution ◽  
Absolute Convergence ◽  
List Type ◽  
Type Number ◽  
Homogeneous Poisson Process ◽  
Cauchy Principal ◽  
Principal Value ◽  
Definition Of ◽  
Image Position

The paper studies the formally defined stochastic process where {tj} is a homogeneous Poisson process in Euclidean n-space En and the a.e. finite Em-valued function f(·) satisfies |f(t)| = g(t) (all |t | = t), g(t) ↓ 0 for all sufficiently large t → ∞, and with either m = 1, or m = n and f(t)/g(t) =t/t. The convergence of the sum at (*) is shown to depend on (i)(ii)(iii). Specifically, finiteness of (i) for sufficiently large X implies absolute convergence of (*) almost surely (a.s.); finiteness of (ii) and (iii) implies a.s. convergence of the Cauchy principal value of (*) with the limit of this principal value having a probability distribution independent of t when the limit in (iii) is zero; the finiteness of (ii) alone suffices for the existence of this limiting principal value at t = 0.

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