Frequently hypercyclic semigroups

We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis integral. This criterion can be verified in certain cases in terms of the infinitesimal generator of semigroup. Applications are given for semigroups generated by Ornstein-Uhlenbeck operators, and especially for translation semigroups on weighted spaces of $p$-integrable functions, or continuous functions that, multiplied by the weight, vanish at infinity

Frequently hypercyclic translation semigroups

Frequent hypercyclicity for translation $C_0$-semigroups on weighted spaces of continuous functions is investigated. The results are achieved by establishing an analogy between frequent hypercyclicity for the translation semigroup and for weighted pseudo-shifts and by characterizing frequent hypercyclic weighted pseudo-shifts in spaces of vanishing sequences. Frequent hypercylic translation semigroups in weighted $L^p$-spaces are also characterized

Analyticity of a class of degenerate evolution equations on the canonical simplex of Rd\R^d arising from Fleming--Viot processes

We study the analyticity of the semigroups generated by a class of degenerate second order differential operators in the space $C(S_d)$, where $S_d$ is the canonical simplex of $\R^d$. The semigroups arise from the theory of Fleming--Viot processes in population genetics.Comment: 32 page

Associated weights for spaces of p-integrable entire functions

[EN] In analogy to the notion of associated weights for weighted spaces of analytic functions with sup-norms, p-associated weights are introduced for spaces of entire p-integrable functions, 1 <= p < infinity. As an application, necessary conditions for the boundedness of composition operators acting between general Fock type spaces are provedThe research of Bonet was partially supported by the projects MTM2016-76647-P and GV Prometeo/2017/102 (Spain).Bonet Solves, JA.; Mangino, EM. (2020). Associated weights for spaces of p-integrable entire functions. Quaestiones Mathematicae. 43(5/6):747-760. https://doi.org/10.2989/16073606.2019.1605420S747760435/

Generation of semigroups associated to strongly coupled elliptic operator in Lp(Rd;Rm)L^p(\mathbb R^d;\mathbb R^m)

A class of vector-valued elliptic operators with unbounded coefficients, coupled up to the second-order is investigated in the Lebesgue space $L^p(\mathbb R^d;\mathbb R^m)$ with $p \in (1,\infty)$, providing sufficient conditions for the generation of an analytic $C_0$-semigroup $T(t)$. Under further assumptions, a characterization of the domain of the infinitesimal generator is given

Platelet Activating Factor Synthesis and Metabolism in Intestinal Ischaemia-Reperfusion Injury

The object of this study was to characterize the synthesis and metabolism of platelet activating factor (PAF) by intestinal mucosa subjected to ischaemia–reperfusion injury. Canine intestinal mucosa produced 16:0-PAF, 18:0-PAF, and high levels of the corresponding lyso- PAF metabolites. Three h of intestinal ischaemia and ischaemia followed by 1 h of reperfusion did not affect the synthesis or metabolism of PAF by intestinal mucosa. Intestinal mucosa elaborated a factor that rapidly hydrolyzes PAF to lyso-PAF. The observed hydrolysis rate was not altered by ischaemia or ischaemia and reperfusion. In conclusion, this study suggests that intestinal mucosa produces PAF and rapidly hydrolyzes PAF. The PAF synthesis and metabolism rates of intestinal mucosa is not altered by ischaemia reperfusion in this model under the imposed conditions

Missing Data and IRT Item Parameter Estimation

Non-randomly missing data has theoretically different implications for item parameter estimation depending on whether joint maximum likelihood or marginal maximum likelihood methods are used in the estimation. The objective of this paper is to illustrate what potentially can happen, under these estimation procedures, when there is an association between ability and the absence of response. In this example, data is missing because some students, particularly low-ability students, did not complete the test

Heritability of insulin sensitivity and lipid profile depend on BMI: evidence for gene–obesity interaction

Evidence from candidate gene studies suggests that obesity may modify genetic susceptibility to type 2 diabetes and dyslipidaemia. On an aggregate level, gene-obesity interactions are expected to result in different heritability estimates at different obesity levels. However, this hypothesis has never been tested. The present study included 2,180 British female twins. BMI was used as an index of general obesity. Outcome measures were insulin sensitivity (indexed by quantitative insulin-sensitivity check index [QUICKI]) and fasting plasma lipid profile. Structural equation modelling was used to test whether BMI interacted with latent genetic and environmental effects to impact on the outcome measures. Genetic influences on triacylglycerol increased with BMI (p <0.001) whereas the unique environmental influence on QUICKI decreased with BMI (p <0.001), resulting in a higher heritability estimate for both measures at higher BMI levels. This was further illustrated by stratified analysis in twin pairs concordant for normal weight and twin pairs concordant for overweight. Heritability was 19 percentage points higher for triacylglycerol (p <0.001) and 31 percentage points higher for QUICKI (p <0.01) among twins concordant for overweight than among twins concordant for normal weight. BMI had no moderator effect on the latent genetic and environmental factors for total cholesterol and HDL-cholesterol. Our results suggest that the expression of genes influencing triacylglycerol and insulin sensitivity can vary as a function of obesity status. The substantial increases in the genetic contribution to the total variance in insulin sensitivity and triacylglycerols at higher BMIs may prove extremely valuable in the search for candidate genes