Search results for "OMEGA"
showing 10 items of 1174 documents
Presenting signs and patient co-variables in Gaucher disease: outcome of the Gaucher Earlier Diagnosis Consensus (GED-C) Delphi initiative.
2019
Background: Gaucher disease (GD) presents with a range of signs and symptoms. Physicians can fail to recognise the early stages of GD owing to a lack of disease awareness, which can lead to significant diagnostic delays and sometimes irreversible but avoidable morbidities. Aim: The Gaucher Earlier Diagnosis Consensus (GED-C) initiative aimed to identify signs and co-variables considered most indicative of early type 1 and type 3 GD, to help non-specialists identify ‘at-risk’ patients who may benefit from diagnostic testing. Methods: An anonymous, three-round Delphi consensus process was deployed among a global panel of 22 specialists in GD (median experience 17.5 years, collectively managin…
Upper bounds for the tightness of the $$G_\delta $$-topology
2021
We prove that if X is a regular space with no uncountable free sequences, then the tightness of its $$G_\delta $$ topology is at most the continuum and if X is, in addition, assumed to be Lindelof then its $$G_\delta $$ topology contains no free sequences of length larger then the continuum. We also show that, surprisingly, the higher cardinal generalization of our theorem does not hold, by constructing a regular space with no free sequences of length larger than $$\omega _1$$ , but whose $$G_\delta $$ topology can have arbitrarily large tightness.
Backward production of mesons associated with? ++(1232) in? + p interactions at 20 GeV/c
1991
We have analyzed backward meson production inπ + p reactions at 20GeV/c, which were measured in the CERN Ω spectrometer triggered by a fast proton (p f ), in experiment WA56. Production via baryon exchange of quasi-two-body final statesΔ ++ (1232)ρ 0 (770),Δ ++ (1232)f 2 (1270), andΔ ++ (1232)ρ 3 0 (1690) is clearly identified. The density matrix elements of meson resonances and ofΔ ++ (1232) are analyzed. We have observed also the reactionsπ + p→Δ ++ (1232)π 0 andπ + p→Δ ++ (1232)ω in thep f π + π 0 andp f π + π + π − π 0 final states.
Validity and reliability of the Turkish version of the orthognathic quality of life questionnaire in patients with dentofacial deformity
2021
Due to the lack of a specific quality of life (QoL) survey on dentofacial deformities (DFD) for Turkish speakers, the present research aimed to perform a translation of the English version of the Orthognathic Quality of Life Questionnaire (OQLQ) into Turkish (the OQLQ-TR) and provide cultural adaptation to the Turkish population. The process of this cross-cultural adaptation followed the six stages given in the guidelines that were proposed by Beaton et al. (2000), which comprised the following: 1) performing the initial translation, 2) synthesizing the translation, 3) performing the back translation, 4) presenting it to the expert committee, and 5) testing the prefinal version. Throughout …
Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data
2018
We prove boundedness and continuity for solutions to the Dirichlet problem for the equation $$ - {\rm{div}}(a(x,\nabla u)) = h(x,u) + \mu ,\;\;\;\;\;{\rm{in}}\;{\rm{\Omega }} \subset \mathbb{R}^{N},$$ where the left-hand side is a Leray-Lions operator from $$- {W}^{1,p}_0(\Omega)$$ into W−1,p′(Ω) with 1 < p < N, h(x,s) is a Caratheodory function which grows like ∣s∣p−1 and μ is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Holder-continuous far from the support of μ.
The Dirichlet problem for the total variation flow
2001
Suppose that Ω is an open bounded domain with a Lipschitz boundary. The purpose of this chapter is to study the Dirichlet problem $$ \left\{ \begin{gathered} \frac{{\partial u}} {{\partial t}} = div\left( {\frac{{Du}} {{\left| {Du} \right|}}} \right)in Q = \left( {0,\infty } \right) \times \Omega , \hfill \\ u\left( {t,x} \right) = \phi \left( x \right)on S = \left( {0,\infty } \right) \times \partial \Omega , \hfill \\ u\left( {0,x} \right) = u_0 \left( x \right)in x \in \Omega \hfill \\ \end{gathered} \right. $$ (5.1) where u0 ∈ L1(Ω) and ϕ ∈ L1 (∂Ω). This evolution equation is related to the gradient descent method used to solve the problem $$ \begin{gathered} Minimize \int {_\Omega \lef…
Elliptic equations having a singular quadratic gradient term and a changing sign datum
2012
In this paper we study a singular elliptic problem whose model is \begin{eqnarray*} - \Delta u= \frac{|\nabla u|^2}{|u|^\theta}+f(x), in \Omega\\ u = 0, on \partial \Omega; \end{eqnarray*} where $\theta\in (0,1)$ and $f \in L^m (\Omega)$, with $m\geq \frac{N}{2}$. We do not assume any sign condition on the lower order term, nor assume the datum $f$ has a constant sign. We carefully define the meaning of solution to this problem giving sense to the gradient term where $u=0$, and prove the existence of such a solution. We also discuss related questions as the existence of solutions when the datum $f$ is less regular or the boundedness of the solutions when the datum $f \in L^m (\Omega)$ with …
VECTOR-VALUED FUNCTIONS INTEGRABLE WITH RESPECT TO BILINEAR MAPS
2008
Let $(\Omega, \Sigma, \mu)$ be a $\sigma-$finite measure space, $1\le p \lt \infty$, $X$ be a Banach space $X$ and ${\cal B} :X\times Y \to Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p-$integrable with respect to ${\cal B}$ whenever $\sup\{\int_\Omega\|{\cal B}(f(w),y)\|^pd\mu: \|y\|=1\}$ is finite. We identify the spaces of functions integrable with respect to the bilinear maps arising from H\"older's and Young's inequalities. We apply the theory to give conditions on $X$-valued kernels for the boundedness of integral operators $T_{{\cal B}}(f) (w)=\int_{\Omega'}{{\cal B}}(k(w,w'),$ $f(w'))d\mu'(w')$ from ${\mathrm L}^p(Y)$ into ${\mathrm L}^p(Z)$, extending t…
Subgroups of $$SF(\omega )$$ S F ( ω ) and the relation of almost containedness
2016
The relations of almost containedness and orthogonality in the lattice of groups of finitary permutations are studied in the paper. We define six cardinal numbers naturally corresponding to these relations by the standard scheme of $$P(\omega )$$P(ź). We obtain some consistency results concerning these numbers and some versions of the Ramsey theorem.
Estimates of Jacobians by subdeterminants
2002
Let ƒ: Ω → ℝn be a mapping in the Sobolev space W1,n−1(Ω,ℝn), n ≥ 2. We assume that the determinant of the differential matrix Dƒ (x) is nonnegative, while the cofactor matrix D#ƒ satisfies\(|D^\sharp f|^{\frac{n}{{n - 1}}} \in L^P (\Omega )\), where Lp(Ω) is an Orlicz space. We show that, under the natural Divergence Condition on P, see (1.10), the Jacobian lies in Lloc1 (Ω). Estimates above and below Lloc1 (Ω) are also studied. These results are stronger than the previously known estimates, having assumed integrability conditions on the differential matrix.