The challenge in managing new financial risks: adopting an heuristic or theoretical approach

The financial crisis began with the collapse of Lehman Brothers and the subprime asset backed securities debacle. Credit risk was turned into liquidity risk, resulting in a lack of confidence among financial institutions. In this article, we will propose a way to model liquidity risk and the credit risk in best practices. We will show that liquidity risk is a new type of risk and the current way to deal with it is based solely on observed variables without any theoretical link. We propose an heuristic approach to combine the numerous liquidity risk indicators with a logistic regression for the first time. In regards to credit risk, several articles prove that the best practice is to use an option model to appreciate this risk. We will present our methodology using stochastic diffusion for the interest rate because currently the yield curves aren’t liquid. This approach is more relevant because the basis model in prior publications has a constant interest rate or a forward rate. Both models allow a better understanding of liquidity and credit risks and the further development of research deals with the link between these two financial risks.     

Orthogonal polynomials on the unit circle and their derivatives

We characterize the sequences of orthogonal polynomials on the unit circle whose derivatives are also orthogonal polynomials on the unit circle. Some relations for the sequences of derivatives of orthogonal polynomials are provided. Finally, we pose some problems about orthogonality-preserving maps and differential equations for orthogonal polynomials on the unit circle.     

Conical stochastic maximal L^p-regularity for 1\leqslant p<\infty

Let \(A = -\mathrm{div} \,a(\cdot ) \nabla \) be a second order divergence form elliptic operator on \({\mathbb R}^n\) with bounded measurable real-valued coefficients and let \(W\) be a cylindrical Brownian motion in a Hilbert space \(H\) . Our main result implies that the stochastic convolution process $$\begin{aligned} u(t) = \int _0^t e^{-(t-s)A}g(s)\,dW(s), \quad t\geqslant 0, \end{aligned}$$ satisfies, for all \(1\leqslant p<\infty \) , a conical maximal \(L^p\) -regularity estimate $$\begin{aligned} {\mathbb E}\Vert \nabla u \Vert _{ T_2^{p,2}({\mathbb R}_+\times {\mathbb R}^n)}^p \leqslant C_p^p {\mathbb E}\Vert g \Vert _{ T_2^{p,2}({\mathbb R}_+\times {\mathbb R}^n;H)}^p. \end{aligned}$$ Here, \(T_2^{p,2}({\mathbb R}_+\times {\mathbb R}^n)\) and \(T_2^{p,2}({\mathbb R}_+\times {\mathbb R}^n;H)\) are the parabolic tent spaces of real-valued and \(H\) -valued functions, respectively. This contrasts with Krylov’s maximal \(L^p\) -regularity estimate $$\begin{aligned} {\mathbb E}\Vert \nabla u \Vert _{L^p({\mathbb R}_+;L^2({\mathbb R}^n;{\mathbb R}^n))}^p \leqslant C^p {\mathbb E}\Vert g \Vert _{L^p({\mathbb R}_+;L^2({\mathbb R}^n;H))}^p \end{aligned}$$ which is known to hold only for \(2\leqslant p<\infty \) , even when \(A = -\Delta \) and \(H = {\mathbb R}\) . The proof is based on an \(L^2\) -estimate and extrapolation arguments which use the fact that \(A\) satisfies suitable off-diagonal bounds. Our results are applied to obtain conical stochastic maximal \(L^p\) -regularity for a class of nonlinear SPDEs with rough initial data.     

Spin and Majorana polarization in topological superconducting wires

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.     

The Kinematics and the Full Minimal Dynamic Model of a 6-DOF Parallel Robot Manipulator

In this paper we present a particular architecture of parallel robots which has six-degrees-of-freedom (6-DOF) with only three limbs. The particular properties of the geometric and kinematic models with respect to that of a classical parallel robot are presented. We show that inverse problems have an analytical solution. However, to solve the direct problems, an efficient numerical procedure which needs to inverse only a 3 × 3 passive Jacobian matrix is proposed. In a second step, dynamic equations are derived using the Lagrangian formalism where the joint variables are passive and active joint coordinates. Based on the geometrical properties of the robot, the equations of motion are derived in terms of only nine coordinates related by three kinematic constraints instead of 18 joint coordinates. The computational cost of the dynamic model obtained is reduced by using a minimum set of base inertial parameters.     

Controlled pinewood fractionation with supercritical ethanol: A prerequisite toward pinewood conversion into chemicals and biofuels

The objective of this work was to investigate the ability of supercritical (SC) ethanol conditions to attack preferentially the lignin fraction against the carbohydrate fraction and their effects on the product distribution among gases, light products, bio-oils, and chars. In this study, the conversion of each pinewood component was determined by the analysis of solid residues to quantify cellulose, hemicellulose, lignin, and char contents. It is shown that, by tuning the temperature, hemicellulose and lignin are already transformed in subcritical ethanol conditions, lignin being more reactive than hemicellulose. In contrast, native wood cellulose is recalcitrant to liquefaction in SC ethanol near the critical point (T_c = 241 °C and P_c = 61 bar), but 20% of native wood cellulose is converted in SC ethanol at 280 °C. Besides, the severity of the conditions, in terms of temperature and treatment time, does not significantly influence the yields of gases, light products, and bio-oils but strongly enhances char formation. Interestingly, the increase in SC ethanol density does not change the conversion of biomass components but has a marked effect on bio-oil yield and prevents char formation. The optimum fractionation conditions to convert the lignin component, while keeping unattacked the cellulose fraction with a minimum formation of char, are dense SC ethanol, at 250 °C for 1 h, in batch conditions. However, although lignin is more reactive than hemicellulose under these conditions, these fractions are converted, in a parallel way, to around 50% and 60%, respectively.     

Luminescent Graphene-Based Materials via Europium Complexation on Dipyridylpyridazine-Functionalized Graphene Sheets

Graphene-based materials exhibit outstanding physical properties and so are potentially applicable in a great variety of fields. Unlike their corresponding oxides, graphite and graphene are not prone to functionalization. Diels–Alder reactions are among the scarce reactions that they can occur without disrupting their conjugated sp² systems. Herein, the reaction between graphite and 3,6-di(2-pyridyl)-1,2,4,5-tetrazine under different conditions affords several graphene-based materials consisting of dipyridylpyridazine-functionalized few-layer graphene, multilayer graphene and graphite, the sheets of which act as ligands for the grafting of a europium complex. These three materials show strong red emission under 365 nm UV radiation. Their emitting particles can be visualized by confocal microscopy. The rich coordination chemistry of dipyridylpyridazine ligands has potential novel properties for similarly functionalized graphene-based materials grafted with other metal complexes.     

Excited-State Dynamics of Thienoguanosine,an Isomorphic Highly Fluorescent Analogue of Guanosine

Thienoguanosine (^thG) is an isomorphic analogue of guanosine with promising potentialities as fluorescent DNA label. As a free probe in protic solvents, ^thG exists in two tautomeric forms, identified as the H1, being the only one observed in nonprotic solvents, and H3 keto–amino tautomers. We herein investigate the photophysics of ^thG in solvents of different polarity, from water to dioxane, by combining time-resolved fluorescence with PCM/TD-DFT and CASSCF calculations. Fluorescence lifetimes of 14.5–20.5 and 7–13 ns were observed for the H1 and H3 tautomers, respectively, in the tested solvents. In methanol and ethanol, an additional fluorescent decay lifetime (≈3 ns) at the blue emission side (λ≈430 nm) as well as a 0.5 ns component with negative amplitude at the red edge of the spectrum, typical of an excited-state reaction, were observed. Our computational analysis explains the solvent effects observed on the tautomeric equilibrium. The main radiative and nonradiative deactivation routes have been mapped by PCM/TD-DFT calculations in solution and CASSCF in the gas phase. The most easily accessible conical intersection, involving an out-of plane motion of the sulfur atom in the five-membered ring of ^thG, is separated by a sizeable energy barrier (≥0.4 eV) from the minimum of the spectroscopic state, which explains the large experimental fluorescence quantum yield.     

On-Surface Synthesis and Characterization of Acene-Based Nanoribbons Incorporating Four-Membered Rings

A bottom up method for the synthesis of unique tetracene-based nanoribbons, which incorporate cyclobutadiene moieties as linkers between the acene segments, is reported. These structures were achieved through the formal [2+2] cycloaddition reaction of ortho-functionalized tetracene precursor monomers. The formation mechanism and the electronic and magnetic properties of these nanoribbons were comprehensively studied by means of a multitechnique approach. Ultra-high vacuum scanning tunneling microscopy showed the occurrence of metal-coordinated nanostructures at room temperature and their evolution into nanoribbons through formal [2+2] cycloaddition at 475 K. Frequency-shift non-contact atomic force microscopy images clearly proved the presence of bridging cyclobutadiene moieties upon covalent coupling of activated tetracene molecules. Insight into the electronic and vibrational properties of the so-formed ribbons was obtained by scanning tunneling microscopy, Raman spectroscopy, and theoretical calculations. Magnetic properties were addressed from a computational point of view, allowing us to propose promising candidates to magnetic acene-based ribbons incorporating four-membered rings. The reported findings will increase the understanding and availability of new graphene-based nanoribbons with high potential in future spintronics.