On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Application to argon ions of a new technique to measure the two-electron contribution to the ground state energy of helium-like ions

We have measured the two-electron contribution of the ground state energy of helium-like argon ions using an electron beam ion trap (EBIT). A two-dimensional map was measured showing the intensity of x-rays from the trap passing through a krypton-filled absorption cell. The independent axes of this map were electron beam energy and x-ray energy. From this map, we deduced the two-electron contribution of the ground state of helium-like argon. This experimentally determined Value (312.4 +/- 9.5 eV) was found to be in good agreement with our calculated values (about 303.35 eV) and previous calculations of the same quantity. Based on these measurements, we have shown that a ten-day absorption spectroscopy run with a super-EBIT should be sufficient to provide a new benchmark value for the two-electron contribution to the ground state of helium-like krypton. Such a measurement would then constitute a test of quantum electrodynamics to second order.

Sustainable Value Added - ein neues Maß des Nachhaltigkeitsbeitrags von Unternehmen am Beispiel der Henkel KGaA

This article introduces a new approach to measure corporate contributions to sustainability called Sustainable Value Added. Existing approaches to measure sustainability are based on a comparative assessment of environmental and social burdens and can thus be characterised as burden-based approaches. However, these approaches suffer from severe limitations as a comparative assessment and aggregation of all relevant environmental and social burdens fails in practice. In contrast to these burden-based approaches Sustainable Value Added is value-based. It determines the value that is created by the reduced or increased use of different environmental and social resources. For this purpose the use of environmental and social resources is valued at their opportunity cost. Sustainable Value Added allows an integrated assessment of the economic, environmental, and social performance of a company and expresses the corporate contribution to sustainability in a single monetary indicator. This article explains the theoretical background of Sustainable Value Added, relates it to existing approaches to measure sustainability, and - using the example of Henkel KGaA - demonstrates its practical applicability.

Environmental Value Added - Ein neues Maß zur Messung der Öko-Effizienz. (Environmental Value Added. A new measure for the measurement of eco-efficiency)

To increase eco-efficiency environmental information needs to be integrated into corporate decision making. For decision makers the interpretation of eco-efficiency as a ratio can however be quite difficult in practice. One of the reasons for this is, that eco-efficiency as a ratio is measured in a unit, that is difficult to interpret. This article therefore suggests an alternative measure for eco-efficiency. The Environmental Value Added, the measure proposed in this paper, reflects the excess economic benefit, resulting from the difference between the eco-efficiency under consideration and a benchmark eco-efficiency. It is measured in a purely monetary unit and is thus easier to interpret and integrate than eco-efficiency as a ratio.

Generation of entangled coherent states via cross-phase-modulation in a double electromagnetically induced transparency regime

The generation of an entangled coherent state is one of the most important ingredients of quantum information processing using coherent states. Recently, numerous schemes to achieve this task have been proposed. In order to generate travelling-wave entangled coherent states, cross-phase-modulation, optimized by optical Kerr effect enhancement in a dense medium in an electromagnetically induced transparency (EIT) regime, seems to be very promising. In this scenario, we propose a fully quantized model of a double-EIT scheme recently proposed [D. Petrosyan and G. Kurizki, Phys. Rev. A 65, 33 833 (2002)]: the quantization step is performed adopting a fully Hamiltonian approach. This allows us to write effective equations of motion for two interacting quantum fields of light that show how the dynamics of one field depends on the photon-number operator of the other. The preparation of a Schrodinger cat state, which is a superposition of two distinct coherent states, is briefly exposed. This is based on nonlinear interaction via double EIT of two light fields (initially prepared in coherent states) and on a detection step performed using a 50:50 beam splitter and two photodetectors. In order to show the entanglement of an entangled coherent state, we suggest to measure the joint quadrature variance of the field. We show that the entangled coherent states satisfy the sufficient condition for entanglement based on quadrature variance measurement. We also show how robust our scheme is against a low detection efficiency of homodyne detectors.

Electronic cell counting to measure total cell numbers in bronchoalveolar lavage fluid

Cell counting of bronchoalveolar lavage (BAL) fluid is performed manually in routine practice. This has both methodological and inherent errors; however, the accuracy and suitability of automated counting devices have been questioned. In this study, a Coulter(R) Counter D Industrial model was calibrated and then used to measure the total cell count in unprocessed bronchoalveolar lavage fluid, and compared to a standard manual method.

House value as an indicator of cumulative wealth is strongly related to morbidity and mortality risk in older people: a census-based cross-sectional and longitudinal study

Background: There has been relatively little research into health inequalities in older populations. This may be partly explained by the difficulty in identifying appropriate indicators of socio-economic status for older people. Ideally, indicators of socio-economic status to be used in studies of health inequalities in older populations should incorporate some measure of life-time socio-economic standing, and house value may fill this role. This study examined whether an indicator of accumulated wealth based on a combination of housing tenure and house value was a strong predictor of ill-health in older populations.
Methods: A total of 191 848 people aged =65 years and not living in communal establishments were identified from the 2001 Northern Ireland Census and followed for 5 years. Self-reported health and mortality risk by housing tenure/house value groupings were examined while controlling for a range of other demographic and socio-economic characteristics.
Results: Housing tenure/house value was highly correlated with other indicators of socio-economic status. Public-sector renters had worse self-reported health and higher mortality rates than owner occupiers but significant gradients were also found between those living in the highest-and lowest-valued owner-occupier properties. The relationship between housing tenure and value was unchanged by adjustment for indicators of social support and quality of the physical environment. Adjustment for limiting long-term illness and self-reported health at baseline narrowed but did not eliminate the health gains associated with living in more expensive housing.
Conclusions: House value of residence is an accessible and powerful indicator of accumulated wealth that is highly correlated with current health status and predictive of future mortality risk in older populations.

Small volume laboratory on a chip measurements incorporating the quartz crystal microbalance to measure the viscosity-density product of room temperature ionic liquids

A microfluidic glass chip system incorporating a quartz crystal microbalance (QCM) to measure the square root of the viscosity-density product of room temperature ionic liquids (RTILs) is presented. The QCM covers a central recess on a glass chip, with a seal formed by tightly clamping from above outside the sensing region. The change in resonant frequency of the QCM allows for the determination of the square root viscosity-density product of RTILs to a limit of similar to 10 kg m(-2) s(-0.5). This method has reduced the sample size needed for characterization from 1.5 ml to only 30 mu l and allows the measurement to be made in an enclosed system.