On the basic algebraic operations in solvable Lie groups

Summary For a simply connected solvable Lie group we specify the structure of the product, the inverse and the exponential map expressed in suitable coordinates (canonical coordinates of the second kind), and point out that in these coordinates the product and inverse are expressed entirely in terms of polynomials, exponential functions and trigonometric functions. We devise algorithms for computing the product, the inverse and the exponential map.     

Identifying assembly maps in K- and L-theory

In this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in K- and L-theory, and C^*-theory.Partially supported by NSERC grant A4000 and NSF grant DMS 9104026. The authors also wish to thank the SFB für Geometrie und Analysis, Münster, and the Max Planck Institut für Mathematik, Bonn, for their hospitality and support.Received: 7 May 2001     

On systematic scan for sampling H‐colorings of the path

We show that systematic scan for H‐colorings of the n‐vertex path mixes in O(log n) scans for any fixed H using block dynamics. For a restricted family of H we furthermore show that systematic scan mixes in O(log n) scans for any scan order. For completeness we show that a random update Markov chain mixes in O(nlog n) updates for any fixed H. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Global Existence and Blowup for a Parabolic Equation with a Non-Local Source and Absorption

In this paper we consider a double fronts free boundary problem for a parabolic equation with a non-local source and absorption. The long time behaviors of the solutions are given and the properties of the free boundaries are discussed. Our results show that if the initial value is sufficiently large, then the solution blows up in finite time, while the global fast solution exists for sufficiently small initial data, and the intermediate case with suitably large initial data gives the existence of the global slow solution.     

Some mildly wild circles in Sn arising from algebraic K-Theory

We study wild embeddings of S ¹ in S ⁿ which are tame in a sense introduced by Quinn. We show that if is a finitely presented group with H ₁()=H ₂()=0, then any finiteness obstruction K ₀() can be realized on the complement of such an embedded S ¹. We also realize trivially symmetric K _–1() obstructions on the complements of such embeddings. For trivially symmetric , the embeddings constructed are shown to be isotopy homogeneous.     

Estimates of Entire Functions of Exponential Type Less than π in Terms of Logarithmic Sums over Real Duffin and Schaeffer Sequences

We give uniform estimates of entire functions of exponential type less than having sufficiently small logarithmic sums over real sequences { _n } satisfying | _n –n|L and _n+1– _n for fixed positive constants L and . We thereby generalize results about logarithmic sums over the set of integers and so-called relatively h-dense sequences.     

Analytical gradients of the second‐order Møller–Plesset energy using Cholesky decompositions

An algorithm for computing analytical gradients of the second‐order Møller–Plesset (MP2) energy using density fitting (DF) is presented. The algorithm assumes that the underlying canonical Hartree–Fock reference is obtained with the same auxiliary basis set, which we obtain by Cholesky decomposition (CD) of atomic electron repulsion integrals. CD is also used for the negative semidefinite MP2 amplitude matrix. Test calculations on the weakly interacting dimers of the S22 test set (Jure?ka et al., Phys. Chem. Chem. Phys. 2006, 8, 1985) show that the geometry errors due to the auxiliary basis set are negligible. With double‐zeta basis sets, the error due to the DF approximation in intermolecular bond lengths is better than 0.1 pm. The computational time is typically reduced by a factor of 6–7. © 2013 Wiley Periodicals, Inc.     

Side-chain liquid crystalline polyesters for optical information storage

Azobenzene side-chain liquid crystalline polyester structures suitable for permanent optical storage are described. The synthesis and characterization of the polyesters together with differential scanning calorimetry and X-ray investigations are discussed. Optical anisotropic investigations and holographic storage in one particular polyester are described in detail and polarized Fourier transform infrared spectroscopic data complementing the optical data are presented. Optical and atomic force microscope investigations point to a laser-induced aggregation as responsible for permanent optical storage.     

Quantitation of pressure-sensitive film using digital image scanning

An experimental technique is presented for measurement of contact stress distribution using Fuji Pressensor film. The development of packets of Pressensor disks for use in small areas or surfaces of complex curvature is explained. A digital-image-scanning procedure has been developed to substantially increase the spatial resolution with which stress distributions can be constructed from stained Fuji Pressensor film. The technique is developed for small, discrete disks as well as for larger, continuous sheets of Pressensor. As an illustration, sealed packets of small Pressensor disks are used to measure the stress distribution across a cadaveric juvenile femoral head under load.