Facile synthesis of novel indolo[3,2-b]carbazole derivatives and a chromogenic-sensing 5,12-dihydroindolo[3,2-b]carbazole

Novel indolo[3,2-b]carbazole derivatives and a chromogenic-sensing 5,12-dihydroindolo[3,2-b]carbazole have been synthesized starting from tetra-tert-butylated 6,12-diaryl-5,11-dihydroindolo[3,2-b]carbazoles, which were prepared via an efficient tert-butylation of 6,12-diaryl-5,11-dihydroindolo[3,2-b]carbazoles.     

The electronic spectrum of the C(s)-C11H3 radical

The electronic gas-phase absorption spectrum of the bent carbon-chain radical, HC(4)CHC(6)H with C(s) symmetry, is recorded in the 595 nm region by cavity ring-down spectroscopy through an expanding hydrogen plasma. An unambiguous spectroscopic identification becomes possible from a systematic deuterium labeling experiment. A comparison of the results with recently reported spectra of the nonlinear HC(4)CHC(4)H and HC(4)C(C(2)H)C(4)H radicals with C(2v) symmetry provides a more comprehensive understanding of the molecular behavior of π-conjugated bent carbon-chain systems upon electronic excitation. We find that the electronic excitation in the bent carbon-chain HC(4)CHC(2n)H (n = 1-4) series exhibits a similar trend as in the linear HC(2n+1)H (n = 3-6) series, shifting optical absorptions towards longer wavelengths for increasing overall bent chain lengths. The π-conjugation in bent HC(4)CHC(2n)H (n = 1-4) chains is found to be generally smaller than in the linear HC(2n+1)H (n = 3-6) case for equivalent numbers of C-atoms. The addition of an electron-donating group to the bent chain causes a slight decrease of the effective conjugation.     

On constructing a Green’s function for a semi-infinite beam with boundary damping

The main aim of this paper is to contribute to the construction of Green’s functions for initial boundary value problems for fourth order partial differential equations. In this paper, we consider a transversely vibrating homogeneous semi-infinite beam with classical boundary conditions such as pinned, sliding, clamped or with a non-classical boundary conditions such as dampers. This problem is of important interest in the context of the foundation of exact solutions for semi-infinite beams with boundary damping. The Green’s functions are explicitly given by using the method of Laplace transforms. The analytical results are validated by references and numerical methods. It is shown how the general solution for a semi-infinite beam equation with boundary damping can be constructed by the Green’s function method, and how damping properties can be obtained.     

A novel ultrasonic strain gauge for single-sided measurement of a local 3D strain field

A novel method is introduced for the measurement of a 3D strain field by exploiting the interaction between ultrasound waves and geometrical characteristics of the insonified specimen. First, the response of obliquely incident harmonic waves to a deterministic surface roughness is utilized. Analysis of backscattered amplitudes in Bragg diffraction geometry then yields a measure for the in-plane strain field by mapping any shift in angular dependency. Secondly, the analysis of the reflection characteristics of normal incident pulsed waves in frequency domain provides a measure of the out-of-plane normal strain field component, simply by tracking any change in the stimulation condition for a thickness resonance. As such, the developed ultrasonic strain gauge yields an absolute, contactless and single-sided mapping of a local 3D strain field, in which both sample preparation and alignment procedure are needless. Results are presented for cold-rolled DC06 steel samples onto which skin passing of the work rolls is applied. The samples have been mechanically loaded, introducing plastic strain levels ranging from 2 % up to 35 %. The ultrasonically measured strains have been validated with various other strain measurement techniques, including manual micrometer, longitudinal and transverse mechanical extensometer and optical mono- and stereovision digital image correlation. Good agreement has been obtained between the ultrasonically determined strain values and the results of the conventional methods. As the ultrasonic strain gauge provides all three normal strain field components, it has been employed for the extraction of Lankford ratios at different applied longitudinal plastic strain levels, revealing a strain dependent plastic anisotropy of the investigated DC06 steel sheet.     

Kripke submodels and universal sentences

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with (homo)morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms (including ? and ⊥) using ∧, ∨, ?, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model‐consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using delays and time-varying gains to improve the static output feedback stabilizability of linear systems: a comparison

We address the output feedback stabilization problem of linearfinite-dimensional SISO systems. Limitations of static time-invariantoutput feedback on stabilizability are well known. We investigateand compare the possibilities of two recently proposed simplemodifications/generalizations of static time-invariant outputfeedback to remove such limitations. The first approach consistsof introducing a time-delay in the control law, which can betreated as an additional control parameter. The second approachconsists of making the gain time-varying. We show that bothapproaches are complementary. Existing theoretical results arebrought together in a unifying framework. Numerical proceduresfor the construction of the controllers are provided. Robustnessw.r.t. both parametric and delay uncertainty are dealt with.As an illustration the stabilizability of all second-order systemsis completely determined.     

Interpretation of “the wave function of the Universe”

Hawking and Hartle interpreted their wave function of the universe as giving the probability for the universe to appear from nothing. However, this is not a correct interpretation, since the normalization presupposes a universe, not nothing. Transition probabilities require a measure on the initial state and a physical result requires a physical initial state.