Oxygen-related band gap state in single crystal rubrene

A molecular exciton signature is established and investigated under different ambient conditions in rubrene single crystals. An oxygen-related band gap state is found to form in the ambient atmosphere. This state acts as an acceptor center and assists in the fast dissociation of excitons, resulting in a higher dark and photoconductivity of oxidized rubrene. The band gap state produces a well-defined photoluminescence band at an energy 0.25 eV below the energy of the 0-0 molecular exciton transition. Two-photon excitation spectroscopy shows that the states are concentrated near the surface of naturally oxidized rubrene.     

A Raman and infrared spectroscopic study of the uranyl silicates--weeksite, soddyite and haiweeite

Raman spectroscopy has been used to study the molecular structure of a series of selected uranyl silicate minerals, including weeksite K2[(UO2)2(Si5O13)].H2O, soddyite [(UO2)2SiO4.2H2O] and haiweeite Ca[(UO2)2(Si5O12(OH)2](H2O)3 with UO2(2+)/SiO2 molar ratio 2:1 or 2:5. Raman spectra clearly show well resolved bands in the 750-800 cm-1 region and in the 950-1000 cm-1 region assigned to the nu1 modes of the (UO2)2+ units and to the (SiO4)4- tetrahedra. For example, soddyite is characterized by Raman bands at 828.0, 808.6 and 801.8 cm-1 (UO2)2+ (nu1), 909.6 and 898.0 cm-1 (UO2)2+ (nu3), 268.2, 257.8 and 246.9 cm-1 are assigned to the nu2 (delta) (UO2)2+. Coincidences of the nu1 (UO2)2+ and the nu1 (SiO4)4- is expected. Bands at 1082.2, 1071.2, 1036.3, 995.1 and 966.3 cm-1 are attributed to the nu3 (SiO4)4-. Sets of Raman bands in the 200-300 cm-1 region are assigned to nu2 (delta) (UO2)2+ and UO ligand vibrations. Multiple bands indicate the non-equivalence of the UO bonds and the lifting of the degeneracy of nu2 (delta) (UO2)2+ vibrations. The (SiO4)4- tetrahedral are characterized by bands in the 470-550 cm-1 and in the 390-420 cm-1 region. These bands are attributed to the nu4 and nu2 (SiO4)4- bending modes. The minerals show characteristic OH stretching bands in the 2900-3500 cm-1 and 3600-3700 cm-1.     

Stretching of polymer chains by fluctuating flow fields

We investigate polymer stretching by fluctuating flow fields via numerical solutions of the Brownian dynamics of multibead polymer chains taking into account nonlinear elasticity, hydrodynamic interactions and good solvent, excluded volume interaction effects. By varying the scaling exponent of the energy spectrum whilst keeping the same Reynolds and Deborah numbers, as well as microscale length and turnover times, we show that steeper spectra are associated with stronger stretching. We compute the probability density functions of chain length, and explain their main features by examining explicit molecular histories. We quantify the interaction between strain rate tensor structure and chain geometry as a means of understanding better the different stretching mechanisms in mild, moderate and strong polymer stretching regimes.     

Feynman-Diagrammatic Description of the Asymptotics of the Time Evolution Operator in Quantum Mechanics

We describe the “Feynman diagram” approach to nonrelativistic quantum mechanics on \({\mathbb{R}^n}\), with magnetic and potential terms. In particular, for each classical path γ connecting points q ₀ and q ₁ in time t, we define a formal power series V _γ (t, q ₀, q ₁) in \({\hbar}\), given combinatorially by a sum of diagrams that each represent finite-dimensional convergent integrals. We prove that exp(V _γ ) satisfies Schrödinger’s equation, and explain in what sense the \({t \to 0}\) limit approaches the δ distribution. As such, our construction gives explicitly the full \({\hbar\to 0}\) asymptotics of the fundamental solution to Schrödinger’s equation in terms of solutions to the corresponding classical system. These results justify the heuristic expansion of Feynman’s path integral in diagrams.     

Dark-field optical coherence microscopy

Dark-field illumination is known to enhance scattering contrast in optical microscopy. We combined this concept with Fourier domain optical coherence microscopy (OCM). The detection and illumination paths are decoupled, and only the scattered light originating from the sample generates the tomogram signal, whereas any specular reflection is highly suppressed. We analyze and discuss this dark-field OCM concept and present its superior imaging quality on live cell samples.     

Strengthening the security of authenticated key exchange against bad randomness

Recent history has revealed that many random number generators (RNGs) used in cryptographic algorithms and protocols were not providing appropriate randomness, either by accident or on purpose. Subsequently, researchers have proposed new algorithms and protocols that are less dependent on the RNG. One exception is that all prominent authenticated key exchange (AKE) protocols are insecure given bad randomness, even when using good long-term keying material. We analyse the security of AKE protocols in the presence of adversaries that can perform attacks based on chosen randomness, i.e., attacks in which the adversary controls the randomness used in protocol sessions. We propose novel stateful protocols, which modify memory shared among a user’s sessions, and show in what sense they are secure against this worst case randomness failure. We develop a stronger security notion for AKE protocols that captures the security that we can achieve under such failures, and prove that our main protocol is correct in this model. Our protocols make substantially weaker assumptions on the RNG than existing protocols.     

Easy knapsacks and the complexity of energy allocation problems in the smart grid

Motivated by the growing interest in the smart grid and intelligent energy management mechanisms we study two classes of domestic energy allocation problems. In the first case we work with a system that is tasked with scheduling the work on a number of appliances over a given time window. In the second one a collection of air conditioning appliances is used to control the temperature of a given domestic environment. Our framework for this case includes a simplified mechanism for modelling the heat exchange between the interior and the exterior of the given environment. We present various polynomial time algorithms and NP-hardness proofs. In particular the main result of the paper is a proof that although it is NP-hard to schedule the operation of a single air-conditioning unit, working at various temperature levels in a variable energy price regime, there is a polynomial time algorithm for controlling one such device working at a single temperature level, for houses with low thermal inertia. The algorithm analysis hinges on the properties of a polynomial time variant of the minimisation version of the knapsack problem which may be of independent interest.     

A note on the nucleolus for 2-convex TU games

For 2-convex n-person cooperative TU games, the nucleolus is determined as some type of constrained equal award rule. Its proof is based on Maschler, Peleg, and Shapley’s geometrical characterization for the intersection of the prekernel with the core. Pairwise bargaining ranges within the core are required to be in equilibrium. This system of non-linear equations is solved and its unique solution agrees with the nucleolus.     

Exact categories

We survey the basics of homological algebra in exact categories in the sense of Quillen. All diagram lemmas are proved directly from the axioms, notably the five lemma, the 3×3$3\times 3$-lemma and the snake lemma. We briefly discuss exact functors, idempotent completion and weak idempotent completeness. We then show that it is possible to construct the derived category of an exact category without any embedding into abelian categories and we sketch Deligne's approach to derived functors. The construction of classical derived functors with values in an abelian category painlessly translates to exact categories, i.e., we give proofs of the comparison theorem for projective resolutions and the horseshoe lemma. After discussing some examples we elaborate on Thomason's proof of the Gabriel–Quillen embedding theorem in an appendix.     

Fast Algorithms for Nonparametric Curve Estimation

Abstract

Naive implementations of local polynomial fits and kernel estimators require almost O(n ²) operations. In this article two fast O(n) algorithms for nonparametric local polynomial fitting are presented. They are based on updating normal equations. Numerical stability is guaranteed by controlling ill-conditioned situations for small bandwidths and data-tuned restarting of the updating procedure. Restarting at every output point results in a moderately fast but highly stable O(n ^7/5) algorithm. Applicability of algorithms is evaluated for estimation of regression curves and their derivatives. The idea is also applied to kernel estimators of regression curves and densities.