A genetic algorithm based determination of the ground and excited (1Lb) state structure and the orientation of the transition dipole moment of benzimidazole

The structure of benzimidazole has been determined in the electronic ground and excited states using rotationally resolved electronic spectroscopy. The rovibronic spectra of four isotopomers and subsequently the structure of benzimidazole have been automatically assigned and fitted using a genetic algorithm based fitting strategy. The lifetimes of the deuterated isotopomers have been shown to depend on the position of deuteration. The angle of the transition dipole moment with the inertial a-axis could be determined to be -30 degrees. Structures and transition dipole moment orientation have been calculated at various levels of theory and were compared to the experimental results.     

An efficient method for calculation of the MM fiber frequency response in the presence of mode coupling

We present a more efficient and less time consuming method for calculating the mode coupling effects in multimode fibers. Instead of solving the power transfer equation, we solve the system of coupled equations. It is shown that this method is much faster, more accurate and easier to implement. It allows defining the fiber transfer function in the matrix formalism. The convergence of the power transfer equation to our method is investigated.     

Sharp <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> Bound for Holomorphic Functions on the Unit Disc

For any 1 < p < ∞ and any \({X, Y\in \mathbb{R}}\) satisfying \({|X|\leq Y}\) , we determine the optimal constant C _p (X,Y) such that the following holds. If F is a holomorphic function on the unit disc satisfying ReF(0) = X and \({||{\rm Re}F||_{L^{p}(\mathbb{T})}=Y}\) , then

$$||F||_{L^p(\mathbb{T})}\geq C_p(X,Y).$$

This can be regarded as a reverse version of the classical estimates of Riesz and Essén. The proof rests on the exploitation of certain families of special subharmonic functions on the plane.

     

Anti-Cancer Potential of Synthetic Oleanolic Acid Derivatives and Their Conjugates with NSAIDs

Naturally occurring pentacyclic triterpenoid oleanolic acid (OA) serves as a good scaffold for additional modifications to achieve synthetic derivatives. Therefore, a large number of triterpenoids have been synthetically modified in order to increase their bioactivity and their protective or therapeutic effects. Moreover, attempts were performed to conjugate synthetic triterpenoids with non-steroidal anti-inflammatory drugs (NSAIDs) or other functional groups. Among hundreds of synthesized triterpenoids, still the most promising is 2-cyano-3,12-dioxooleana-1,9(11)-dien-28-oic acid (CDDO), which reached clinical trials level of investigations. The new group of synthetic triterpenoids are OA oximes. The most active among them is 3-hydroxyiminoolean-12-en-28-oic acid morpholide, which additionally improves the anti-cancer activity of standard NSAIDs. While targeting the Nrf2 and NF-κB signaling pathways is the main mechanism of synthetic OA derivatives′ anti-inflammatory and anti-cancer activity, most of these compounds exhibit multifunctional activity, and affect cross-talk within the cellular signaling network. This short review updates the earlier data and describes the new OA derivatives and their conjugates in the context of modification of signaling pathways involved in inflammation and cell survival and subsequently in cancer development.     

Sharp inequalities for dyadic A 1 weights

We show how the Bellman function method can be used to obtain sharp inequalities for the maximal operator of a dyadic A ₁ weight on ${\mathbb{R}^n}$ R n . Using this approach, we determine the optimal constants in the corresponding weak-type estimates. Furthermore, we provide an alternative, simpler proof of the related maximal L ^p -inequalities, originally shown by Melas.     

The 41Σ+ electronic state of LiCs molecule

The 4¹Σ⁺ state of LiCs molecule is observed experimentally for the first time. The inverted perturbation approach (IPA) method is used to derive the potential energy curve of the state from the measured spectra. The experiment is accompanied by theoretical calculations of adiabatic potentials for excited states in LiCs including 4¹Σ⁺, performed with the MOLPRO program package. The irregular shape of the 4¹Σ⁺ state potential predicted by theory is confirmed in the experiment.     

On fixed points of a linear operator of polynomial form of order 3

Let X be a complex linear space, endowed with an extended (that is, admitting infinite values) norm. We prove a fixed point theorem for operators of the form \(p_3 \mathcal {L}^3 + p_2 \mathcal {L}^2 +p_1\mathcal {L}\), where \( \mathcal {L}:X\rightarrow X\) is linear and \(p_1,p_2,p_3\) are fixed scalars. That result has been motivated by some issues arising in Ulam stability. One of the tools is the Diaz-Margolis fixed point alternative.