Curves in Banach spaces which allow a C2C^2 parametrization

We give a complete characterization of those $f: [0,1] \to X$ (where $X$ is a Banach space which admits an equivalent Fr\'echet smooth norm) which allow an equivalent $C^2$ parametrization. For $X=\R$, a characterization is well-known. However, even in the case $X=\R^2$, several quite new ideas are needed. Moreover, the very close case of parametrizations with a bounded second derivative is solved.Comment: 22 pages; We split the original paper into two parts. This is the first part ($C^2$ paths), the second part (paths with finite convexity) will appear late

BXP Investment Report Draft

This is a draft of my investment report which still needs some refining. It demonstrates a buy rating on BXP, a REIT focusing primarily in the office sector

Second order differentiability of paths via a generalized 12-variation

AbstractWe find an equivalent condition for a continuous vector-valued path to be Lebesgue equivalent to a twice differentiable function. For that purpose, we introduce the notion of a VBG12 function, which plays an analogous role for the second order differentiability as the classical notion of a VBG∗ function for the first order differentiability. In fact, for a function f:[a,b]→X, being Lebesgue equivalent to a twice differentiable function is the same as being Lebesgue equivalent to a differentiable function g with a pointwise Lipschitz derivative such that g″(x) exists whenever g′(x)≠0. We also consider the case when the first derivative can be taken non-zero almost everywhere

KONCEPCJA PARAMETRYCZNO-SEMANTYCZNEJ OTWARTEJ PLATFORMY INTELIGENTNYCH URZĄDZEŃ SENSOROWYCH

The parametric and semantic model of open platform of intelligent devices and sensor technologies based on tomography in cyber-physical self-monitoring system contains: new techniques of conducting measurements and construction of novel intelligent measurement devices, system's structure along with communication interface, unique algorithms for data optimization and analysis, algorithms for image reconstruction and technological processes monitoring, cyber-physical system's prototype.Parametryczno-semantyczny model otwartej platformy inteligentnych urządzeń sensorowych został oparty na technologiach tomograficznych. W samo-monitorującym się systemie cyber-fizycznym zastosowano nowe techniki pomiarowe i konstrukcje inteligentnych urządzeń pomiarowych. Proponowane rozwiązanie prototypu systemu cyber-fizycznego składa się z interfejsu komunikacyjnego, unikalnych algorytmów do optymalizacji i analizy danych oraz systemu monitoringu procesów logistyczno-technologicznych