On the near periodicity of eigenvalues of Toeplitz matrices

Let $A$ be an infinite Toeplitz matrix with a real symbol $f$ defined on $[-\pi, \pi]$. It is well known that the sequence of spectra of finite truncations $A_N$ of $A$ converges to the convex hull of the range of $f$. Recently, Levitin and Shargorodsky, on the basis of some numerical experiments, conjectured, for symbols $f$ with two discontinuities located at rational multiples of $\pi$, that the eigenvalues of $A_N$ located in the gap of $f$ asymptotically exhibit periodicity in $N$, and suggested a formula for the period as a function of the position of discontinuities. In this paper, we quantify and prove the analog of this conjecture for the matrix $A^2$ in a particular case when $f$ is a piecewise constant function taking values $-1$ and $1$.

Asymmetric phase-transfer-catalyzed synthesis of five-membered cyclic gamma-Amino acid precursors

The first example of an intramolecular enantioselective Michael addition of nitronates onto conjugated systems utilizing a chiral phase-transfer catalyst is described. A range of five-membered gamma-nitro esters with up to three stereocentres have been prepared and the relative and absolute configurations proven by chemical and crystallographic methods. The products are rapidly obtained and are precursors to five-membered cyclic gamma-amino acids.

The full-spectrum correlated-k method for longwave atmospheric radiative transfer using an effective Planck function

The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas and performing a monochromatic radiation calculation for each point. In this presentation it is shown that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K/day due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such that they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide, and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K/day can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K/day for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

Knowledge transfer processes in PFI: identification of barriers and enablers

Increasingly, the UK’s Private Finance Initiative has created a demand for construction companies to transfer knowledge from one organization or project to another. Knowledge transfer processes in such contexts face many challenges, due to the many resulting discontinuities in the involvement of organisations, personnel and information flow. This paper empirically identifies the barriers and enablers that hinder or enhance the transfer of knowledge in PFI contexts, drawing upon a questionnaire survey of construction firms. The main findings show that knowledge transfer processes in PFIs are hindered by time constraints, lack of trust, and policies, procedures, rules and regulations attached to the projects. Nevertheless, the processes of knowledge transfer are enhanced by emphasising the value and importance of a supportive leadership, participation/commitment from the relevant parties, and good communication between the relevant parties. The findings have considerable relevance to understanding the mechanism of knowledge transfer between organizations, projects and individuals within the PFI contexts in overcoming the barriers and enhancing the enablers. Furthermore, practitioners and managers can use the findings to efficiently design knowledge transfer frameworks that can be used to overcome the barriers encountered while enhancing the enablers to improve knowledge transfer processes.

The full-spectrum correlated k method for longwave atmospheric radiative transfer: treatment of gaseous overlap

The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models, and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas, and performing a pseudo-monochromatic radiation calculation for each point. In this paper it is first argued that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer pseudo-monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K d−1 due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K d−1 can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K d−1 for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

Molecular t-matrices for low-energy electron diffraction (TMOL v1.1)*1

We describe a FORTRAN-90 program that computes scattering t-matrices for a molecule. These can be used in a Low-Energy Electron Diffraction program to solve the molecular structural problem very efficiently. The intramolecular multiple scattering is computed within a Dyson-like approach, using free space Green propagators in a basis of spherical waves. The advantage of this approach is related to exploiting the chemical identity of the molecule, and to the simplicity to translate and rotate these t-matrices without performing a new multiple-scattering calculation for each configuration. FORTRAN-90 routines for rotating the resulting t-matrices using Wigner matrices are also provided.

Spectrally-invariant behavior of zenith radiance around cloud edges simulated by radiative transfer

In a previous paper, we discovered a surprising spectrally-invariant relationship in shortwave spectrometer observations taken by the Atmospheric Radiation Measurement (ARM) program. The relationship suggests that the shortwave spectrum near cloud edges can be determined by a linear combination of zenith radiance spectra of the cloudy and clear regions. Here, using radiative transfer simulations, we study the sensitivity of this relationship to the properties of aerosols and clouds, to the underlying surface type, and to the finite field-of-view (FOV) of the spectrometer. Overall, the relationship is mostly sensitive to cloud properties and has little sensitivity to other factors. At visible wavelengths, the relationship primarily depends on cloud optical depth regardless of cloud phase function, thermodynamic phase and drop size. At water-absorbing wavelengths, the slope of the relationship depends primarily on cloud optical depth; the intercept, by contrast, depends primarily on cloud absorbing and scattering properties, suggesting a new retrieval method for cloud drop effective radius. These results suggest that the spectrally-invariant relationship can be used to infer cloud properties near cloud edges even with insufficient or no knowledge about spectral surface albedo and aerosol properties.

Charge transfer in Cr adsorption and reaction at the rutile TiO2(110) surface

The rutile TiO2(110) surface has been doped with sub-monolayer metallic Cr, which oxidises and donates charge to specific surface Ti ions. X-Ray and ultra violet photoemission spectroscopy and first principles density functional theory with Hubbard U are used to assign the oxidation states of Cr and surface Ti and we find that Cr2+ forms on bridging oxygen ions and a 5-fold coordinated surface Ti atom is reduced to Ti3+ and the Cr ions readily react with oxygen (to Cr3+), which leads to depletion of surface Ti3+ 3d electrons.

Photochromic switches incorporated in bridging ligands: a new tool to modulate energy-transfer processes

The thoughtful construction of molecular switches has led to a gamut of supramolecular systems that can be used in molecular electronics. These include molecules based on thienylethenes, spiropyrans, fulgides, dithienylphenanthrolines, and diazafluorenes. This article reviews the recent developments made in the synthesis and characterization of all these systems, thereby allowing a comparative study to validate the viability of these switchable molecules on a nanoscale. Also, the drawbacks of each class are demonstrated and, at the same time, the remedies for further improvisation are prescribed. We have made an honest attempt to present at? exhaustive account of all the different photochromic switches developed by us hitherto.

Electronic energy transfer in a dinuclear Ru/Os complex containing a photoresponsive dithienylethene derivative as bridging ligand

In order to build up a multicomponent system able to perform useful light-induced functions, a dithienylethene-bridged heterodinuclear metal complex (Ru/Os) has been prepared. The compound was characterized and its photophysical properties studied in detail.

Using the Cayley-Hamilton theorem with N-partitioned matrices

A definition is given for the characteristic equation of anN-partitioned matrix. It is then proved that this matrix satisfies its own characteristic equation. This can then be regarded as a version of the Cayley-Hamilton theorem, of use withN-dimensional systems.

Knowledge transfer processes in PFI/PPP: critical success factors

Successful knowledge transfer is an important process which requires continuous improvement in today’s knowledge-intensive economy. However, improving knowledge transfer processes represents a challenge for construction practitioners due to the complexity of knowledge acquisition, codification and sharing. Although knowledge transfer is context based, understanding the critical success factors can lead to improvements in the transfer process. This paper seeks to identify and evaluate the most significant critical factors for improving knowledge transfer processes in Public Private Partnerships/Private Finance Initiatives (PPP/PFI) projects. Drawing upon a questionnaire survey of 52 construction firms located in the UK, data is analysed using Severity Index (SI) and Coefficient of Variation (COV), to examine and identify these factors in PPP/PFI schemes. The findings suggest that a supportive leadership, participation/commitment from the relevant parties, and good communication between the relevant parties are crucial to improving knowledge transfer processes in PFI schemes. Practitioners, managers and researchers can use the findings to efficiently design performance measures for analysing and improving knowledge transfer processes.

Commuting, CO2 and the location of offices

This paper investigates the extent to which office activity contributes to travel-related CO2 emission. Using ‘end-user’ figures[1], travel accounts for 32% of UK CO2 emission (Commission for Integrated Transport, 2007) and commuting and business travel accounts for a fifth of transport-related CO2 emissions, equating to 6.4% of total UK emissions (Building Research Establishment, 2000). Figures from the Department for Transport (2006) report that 70% of commuting trips were made by car, accounting for 73% of all commuting miles travelled. In assessing the environmental performance of an office building, the paper questions whether commuting and business travel-related CO2 emission is being properly assessed. For example, are office buildings in locations that are easily accessible by public transport being sufficiently rewarded? The de facto method for assessing the environmental performance of office buildings in the UK is the Building Research Establishment’s Environmental Assessment Method (BREEAM). Using data for Bristol, this paper examines firstly whether BREEAM places sufficient weight on travel-related CO2 emission in comparison with building operation-related CO2 emission, and secondly whether the methodology for assigning credits for travel-related CO2 emission efficiency is capable of discerning intra-urban differences in location such as city centre and out-of-town. The results show that, despite CO2 emission per worker from building operation and travel being comparable, there is a substantial difference in the credit-weighting allocated to each. Under the current version of BREEAM for offices, only a maximum of 4% of the available credits can be awarded for ensuring the office location is environmentally sustainable. The results also show that all locations within the established city centre of Bristol will receive maximum BREEAM credits. Given the parameters of the test there is little to distinguish one city centre location from another and out of town only one office location receives any credits. It would appear from these results that the assessment method is not able to discern subtle differences in the sustainability of office locations