Marcinkiewicz–Zygmund Strong Laws for Infinite Variance Time Series

We study rate of convergence in the strong law of large numbers for finite and infinite variance time series in both contexts of weak and strong dependence.     

Some multivariate inequalities with applications

Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>{\cal {X}}_{n} =(X_1,\ldots,X_n)$ be a random vector. Suppose that the random variables $(X_i)_{1\leq i\leq n}$ are stationary and fulfill a suitable dependence criterion. Let $f$ be a real valued function defined on $\mathbbm{R}^n$ having some regular properties. Let ${\cal {Y}}_{n}$ be a random vector, independent of ${\cal {X}}_{n}$, having independent and identically distributed components. We control $\left|\mathbbm{E}(f({\cal {X}}_{n}))-\mathbbm{E} (f({\cal {Y}}_{n}))\right|$. Suitable choices of the function $f$ yield, under minimal conditions, to rates of convergence in the central limit theorem, to some moment inequalities or to bounds useful for Poisson approximation. The proofs are derived from multivariate extensions of Taylor's formula and of the Lindeberg decomposition. In the univariate case and in the mixing setting the method is due to Rio (1995).     

Finite Rank Commutators and Semicommutators of Quasihomogeneous Toeplitz Operators

We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols. We show that in this context, the situation is different from the case of harmonic Toeplitz operators. Submitted: July 23, 2007. Accepted: December 4, 2007.     

Functional Convergence of Linear Processes with Heavy-Tailed Innovations

We study convergence in law of partial sums of linear processes with heavy-tailed innovations. In the case of summable coefficients, necessary and sufficient conditions for the finite dimensional convergence to an \(\alpha \)-stable Lévy Motion are given. The conditions lead to new, tractable sufficient conditions in the case \(\alpha \le 1\). In the functional setting, we complement the existing results on \(M_1\)-convergence, obtained for linear processes with nonnegative coefficients by Avram and Taqqu (Ann Probab 20:483–503, 1992) and improved by Louhichi and Rio (Electr J Probab 16(89), 2011), by proving that in the general setting partial sums of linear processes are convergent on the Skorokhod space equipped with the \(S\) topology, introduced by Jakubowski (Electr J Probab 2(4), 1997).     

Powers and roots of Toeplitz operators

We study the commutativity of two Toeplitz operators whose symbols are quasihomogeneous functions. We give a relationship between this commutativity and the roots (or powers) of the Toeplitz operators. We use this to characterize Toeplitz operators with symbols in which commute with Toeplitz operators whose symbols are of the form .

     

Cupressus sempervirens Essential Oil: Exploring the Antibacterial Multitarget Mechanisms,Chemcomputational Toxicity Prediction,and Safety Assessment in Zebrafish Embryos

Nowadays, increasing interest has recently been given to the exploration of new food preservatives to avoid foodborne outbreaks or food spoilage. Likewise, new compounds that substitute the commonly used synthetic food preservatives are required to restrain the rising problem of microbial resistance. Accordingly, the present study was conducted to examine the chemical composition and the mechanism(s) of action of the Cupressus sempervirens essential oil (CSEO) against Salmonella enterica Typhimuriumand Staphyloccocus aureus. The gas chromatography analysis revealed α-pinene (38.47%) and δ-3-carene (25.14%) are the major components of the CSEO. By using computational methods, such as quantitative structure–activity relationship (QSAR), we revealed that many CSEO components had no toxic effects. Moreover, findings indicated that α-pinene, δ-3-carene and borneol, a minor compound of CSEO, could inhibit the AcrB-TolC and MepR efflux pump activity of S. enterica Typhimurium and S. aureus, respectively. In addition, our molecular docking predictions indicated the high affinity of these three compounds with active sites of bacterial DNA and RNA polymerases, pointing to plausible impairments of the pathogenic bacteria cell replication processes. As well, the safety profile was developed through the zebrafish model. The in vivo toxicological evaluation of (CSEO) exhibited a concentration-dependent manner, with a lethal concentration (LC₅₀) equal to 6.6 µg/mL.     

Computing reachable sets for uncertain nonlinear monotone systems

We address nonlinear reachability computation for uncertain monotone systems, those for which flows preserve a suitable partial orderings on initial conditions. In a previous work Ramdani (2008) [22], we introduced a nonlinear hybridization approach to nonlinear continuous reachability computation. By analysing the signs of off-diagonal elements of system’s Jacobian matrix, a hybrid automaton can be obtained, which yields component-wise bounds for the reachable sets. One shortcoming of the method is induced by the need to use whole sets for addressing mode switching. In this paper, we improve this method and show that for the broad class of monotone dynamical systems, component-wise bounds can be obtained for the reachable set in a separate manner. As a consequence, mode switching no longer needs to use whole solution sets. We give examples which show the potentials of the new approach.     

The central limit theorem for stationary associated sequences

We study the problem of convergence in distribution of a suitably normalized sum of stationary associated random variables. We focus on the infinite variance case. New results are announced. This revised version was published online in June 2006 with corrections to the Cover Date.     

On Toeplitz operators with quasihomogeneous symbols

In this paper, we give some basic results concerning Toeplitz operators whose symbol is of the form e^{i p θ}ϕ, where ϕ is a radial function, then use these results to characterize all Toeplitz operators which commute with them.Received: 12 June 2004; revised: 27 January 2005