Photogenerated cumulenic structure of adamantyl endcapped linear carbon chains: an experimental and computational investigation based on infrared spectroscopy

The infrared (IR) spectrum of an adamantyl endcapped α, ω-polyyne (the hexayne, Ad-C(12)-Ad) is investigated both experimentally and computationally. A new IR band is observed upon UV photoexcitation of the compound (embedded in a poly methyl methacrylate matrix at 78 K), thus, revealing the existence of new photogenerated molecular structure trapped at low temperature. Complete reversibility is found, thus, demonstrating that the photoexcitation is responsible for the generation of metastable excited states of the molecule. Density functional theory and time dependent density functional theory calculations indicate that these metastable states result from the forbidden singlet (S(1)) or triplet (T(1)) excited states, and geometry optimizations of the polyyne trapped in either S(1) and/or T(1) states demonstrate that the carbon chain takes on a cumulenic structure. Comparison of the experimental and the computed IR spectra for the molecule trapped in the forbidden states confirms that the new IR features are clear markers of cumulenic species. The temperature and time dependent behavior of the new IR band is analyzed, while the experimentally determined value of the activation energy highlights the low stability of these molecular structures.     

3-(Hydroxy(phenyl)methyl)azetidin-2-ones obtained via catalytic asymmetric hydrogenation or by biotransformation

The catalytic asymmetric reduction of ethyl-2-(benzamidomethyl)-3-oxo-phenylpropanoate was realized with high enantiomeric and diastereoisomeric excesses via biotransformation using whole cells of different yeasts and asymmetric hydrogenation with Ru(II) complexes prepared from different chiral diphosphine ligands.With these combined approaches it was possible to prepare both enantiomers of the syn-stereoisomers in almost enantiomerically pure form; one of the enantiomers of the anti-stereoisomer was obtained in high ee with selected yeast while the other enantiomer of the anti was prepared in low ee and de. With three of the four epimers we were able to prepare the corresponding azetidinones.     

Variational approach for a general financial equilibrium problem: The Deficit Formula,the Balance Law and the Liability Formula. A path to the economy recovery

Without using a technical language, but using the universal language of mathematics, we provide simple but significant laws, as Deficit Formula, Balance Law and Liability Formula, for the management of the world economy. Decisions, under these laws, for the recovery of the economy and for the good governance clearly appear. Further a simple but useful economical indicator E(t)$E(t)$ is provided and the results are illustrated with a significant example.     

Single and Multi Camera Simultaneous Localization and Mapping Using the Extended Kalman Filter

Simultaneous Localization and Mapping (SLAM) has received quite a lot of attention in the last decades because of its relevance for many applications centered on a mobile observer, such as service robotics and intelligent transportation systems. This paper focuses on the use of recursive Bayesian filtering, as implemented by the Extendend Kalman Filter (EKF), to face the Visual SLAM problem, i.e., when using data from visual sources. In Monocular SLAM, which uses a single camera as unique source of information, it is not possible to directly estimate the depth of a feature from a single image. To handle the severely non-normal distribution representing such uncertainty, inverse parametrizations were developed, capable to deal with such uncertainty and still relying on Gaussian variables. In the paper, after an introduction to EKF-SLAM, we provide a review of different inverse parametrizations, and we introduce a novel proposal, the Framed Inverse Depth (FID) parametrization, which, in terms of consistency, performs similarly to state of the art Monocular SLAM parametrizations, but at a reduced computational cost. All these parametrizations can be used in a stereo and multi camera setting too. An extensive analysis is presented for both Monocular and stereo SLAM, for a simulated environment widely used in the literature as well as on a widely used real dataset.     

Universal Properties of Łukasiewicz Consequence

Boolean logic deals with {0, 1}-observables and yes–no events, as many-valued logic does for continuous ones. Since every measurement has an error, continuity ensures that small measurement errors on elementary observables have small effects on compound observables. Continuity is irrelevant for {0, 1}-observables. Functional completeness no longer holds when n-ary connectives are understood as [0, 1]-valued maps defined on [0, 1] ⁿ . So one must envisage suitable selection criteria for [0, 1]-connectives. ?ukasiewicz implication has a well known characterization as the only continuous connective ${\Rightarrow}$ satisfying the following conditions: (i) ${x\Rightarrow(y\Rightarrow z)= y\Rightarrow(x\Rightarrow z)}$ and (ii) ${x\Rightarrow y=1\, \, {\rm iff} x\leq y}$ . Then syntactic consequence can be defined purely algorithmically using the ?ukasiewicz axioms and Modus Ponens. As discussed in this paper, to recover a strongly complete semantics one may use differential valuations.     

Mean field bipartite spin models treated with mechanical techniques

Inspired by a continuously increasing interest in modeling and framing complex systems in a thermodynamic rationale, in this paper we continue our investigation in adapting well-known techniques (originally stemmed in fields of physics and mathematics far from the present) for solving for the free energy of mean field spin models in a statistical mechanics scenario. Focusing on the test cases of bipartite spin systems embedded with all the possible interactions (self and reciprocal), we show that both the fully interacting bipartite ferromagnet, as well as the spin glass counterpart, at least at the replica symmetric level, can be solved via the fundamental theorem of calculus, trough an analogy with the Hamilton-Jacobi theory and lastly with a mapping to a Fourier diffusion problem. All these technologies are shown symmetrically for ferromagnets and spin-glasses in full details and contribute as powerful tools in the investigation of complex systems.     

Bicomplex holomorphic functional calculus

In this paper we introduce and study a functional calculus for bicomplex linear bounded operators. The study is based on the decomposition of bicomplex numbers and of linear operators using the two nonreal idempotents. We show that, due to the presence of zero divisors in the bicomplex numbers, the spectrum of a bounded operator is unbounded. We therefore introduce a different spectrum (called reduced spectrum) which is bounded and turns out to be the right tool to construct the bicomplex holomorphic functional calculus. Finally we provide some properties of the calculus.     

A new necessary and sufficient condition for the strong duality and the infinite dimensional Lagrange multiplier rule

Throughout this paper, the authors introduce a new condition, defined by Assumption  S^′$S^{\prime }$, which establishes a necessary and sufficient condition for the validity of the strong duality between a convex optimization problem and its Lagrange dual. This work will be focused on the context of emptiness of the interior of the ordering cone and convexity of the equality constraints. Moreover, this new condition will be necessary and sufficient for the infinite dimensional Lagrange multiplier rule. This new principle will find application to the elastic–plastic torsion problem, to the continuum model of transportation and to a problem with quadratic equality constraint with connected to evolutionary illumination and visibility problems.