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When for the first time, in 1987, a Banach space X and a bounded operator T: X → X without nontrivial invariant subspaces was constructed, one of the many tools used was a series of estimates on the norm of a product of polynomials. Here, we continue this study of estimates on the norm of a product of polynomials by, on the one hand, extending some results due to Beauzamy and Enflo and, on the other, observing that an inequality by Borwein and Erdelyi holds in a more general context. [ABSTRACT FROM AUTHOR]

We construct a Generalized p value for testing statistical hypotheses on the comparison of mean vectors in the sequential observation of two continuous time multidimensional Gaussian processes. The mean vectors depend linearly on two multidimensional parameters and with different conditions about their covariance structures. The invariance of the generalized p value considered is proved under certain linear transformations. We report results of a simulation study showing power and errors probabilities for them. Finally, we apply our results to a real data set. [ABSTRACT FROM AUTHOR]

In this paper, we study well-posedness for the following third-order in time equation with delay (0.1)α(Mu′)″(t)+(Nu′)′(t)=βAu(t)+γBu′(t)+Gut′+Fut+f(t),t∈[0,2π] where α, β, γ are real numbers, A and B are linear operators defined on a Banach space X with domains D(A) and D(B) such that D(A)∩D(B)⊂D(M)∩D(N);u(t)is the state function taking values in X and ut: (−∞, 0] → X defined as ut(θ) = u(t+θ) for θ < 0 belongs to an appropriate phase space where F and G are bounded linear operators. Using operator-valued Fourier multiplier techniques we provide optimal conditions for well-posedness of equation (0.1) in periodic Lebesgue-Bochner spaces Lp(T,X), periodic Besov spaces Bp,qs(T,X) and periodic Triebel-Lizorkin spaces Fp,qs(T,X). A novel application to an inverse problem is given. [ABSTRACT FROM AUTHOR]

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, ). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth. [ABSTRACT FROM AUTHOR]

We show that there exists an infinite dimensional vector space every non–zero element of which is a non–measurable function. Moreover, this vector space can be chosen to be closed and to have dimension β for any cardinality β. Some techniques involving measure theory and density characters of Banach spaces are used. [ABSTRACT FROM AUTHOR]