Group theoretic approach to the screened Coulomb problem

Perturbation method based on the group theory is developed for the radial solution of the Schrödinger equation with screened Coulomb potential. It may be treated as an alternative to the analytic perturbation theory proposed recently by McEnnan, Kissel, and Pratt (Phys. Rev. A, 2 (1976), 532) and is based on the expansion of the potential of the following form $\text{V(r) = ?(}\text{a}\text{r}\text{) × (1 + λV}{}_1\text{r + λ}{}^2\text{V}{}_2\text{r}{}^2\text{+ …)}$. Corrections to the point-Coulomb energy levels are given as series in λ and also the screened Coulomb eigenstates are given in the form of expansions in powers of λ. The method is applied also to the continuous spectrum and similar expansions are found. The problem of the normalization of both discrete and continuous spectrum eigenstates is discussed and we find some differences in the case of the scattering states. Origin of this discrepancy is explained.     

Error Estimates for Orthogonal Matching Pursuit and?Random Dictionaries

In this paper we investigate the efficiency of the Orthogonal Matching Pursuit algorithm (OMP) for random dictionaries. We concentrate on dictionaries satisfying the Restricted Isometry Property. We also introduce a stronger Homogenous Restricted Isometry Property which we show is satisfied with overwhelming probability for random dictionaries used in compressed sensing. For these dictionaries we obtain upper estimates for the error of approximation by OMP in terms of the error of the best n-term approximation (Lebesgue-type inequalities). We also present and discuss some open problems about OMP. This is a development of recent results obtained by D.L. Donoho, M. Elad and V.N. Temlyakov.     

Greedy wavelet projections are bounded on BV

Let be the space of functions of bounded variation on with . Let , , be a wavelet system of compactly supported functions normalized in , i.e., , . Each has a unique wavelet expansion with convergence in . If is the set of indicies for which are largest (with ties handled in an arbitrary way), then is called a greedy approximation to . It is shown that with a constant independent of . This answers in the affirmative a conjecture of Meyer (2001).

     

Imaging cytoplasmic cAMP in mouse brainstem neurons

Background  

cAMP is an ubiquitous second messenger mediating various neuronal functions, often as a consequence of increased intracellular Ca²⁺ levels. While imaging of calcium is commonly used in neuroscience applications, probing for cAMP levels has not yet been performed in living vertebrate neuronal tissue before.     

Generation of squeezed states in a homogeneous magnetic field

It is shown that a homogeneous magnetic field acting on a charged harmonic oscillator in the ground state may produce a state with reduced fluctuation of one of the quadrature phase amplitudes. The amount of squeezing in the final state depends on the time during which the magnetic field was switched on.     

Stable isotopic studies of earthworm feeding ecology in tropical ecosystems of Puerto Rico

Feeding strategies of earthworms and their influence on soil processes are often inferred from morphological, behavioral and physiological traits. We used (13)C and (15)N natural abundance in earthworms, soils and plants to explore patterns of resource utilization by different species of earthworms in three tropical ecosystems in Puerto Rico. In a high altitude dwarf forest, native earthworms Trigaster longissimus and Estherella sp. showed less (15)N enrichment ((15)N = 3-6 per thousand) than exotic Pontoscolex corethrurus ((15)N =7-9 per thousand) indicating different food sources or stronger isotopic discrimination by the latter. Conversely, in a lower altitude tabonuco forest, Estherella sp. and P. corethrurus overlapped completely in (15)N enrichment ((15)N = 6-9 per thousand), suggesting the potential for interspecific competition for N resources. A tabonuco forest converted to pasture contained only P. corethrurus which were less enriched in (15)N than those in the forest sites, but more highly enriched in (13)C suggesting assimilation of C from the predominant C(4) grass. These results support the utility of stable isotopes to delineate resource partitioning and potential competitive interactions among earthworm species. Copyright 1999 John Wiley & Sons, Ltd.     

Design and Synthesis of a Fluorescently End-Labeled Poly(β-amino ester): Application to the Characterization of Degradable Polyelectrolyte Multilayers

We report the synthesis of a fluorescently end-labeled analog of a synthetic and degradable cationic poly(β-amino ester) (PBAE; polymer 1) used in past studies for the delivery of DNA and the layer-by-layer assembly of erodible polyelectrolyte multilayers (PEMs). The synthesis of an analog of polymer 1 having acrylate functionalized end groups provided a platform for the introduction of fluorescent labels by post-polymerization conjugate addition of amine-functionalized fluorophores. This approach enabled the synthesis of fluorescently end-labeled polymer (polymer 1(FL)) with molecular weights and polydispersities (M(n) = 18,000; PDI ~1.8) similar to those used in past studies for the fabrication of PEMs using polymer 1. Layer-by-layer assembly of PEMs using polymer 1(FL) and poly(styrene sulfonate) enabled characterization of film erosion and, for the first time, direct observation of the release of cationic polymer from these assemblies using fluorescence microscopy and fluorometry. Our results shed new light on the behaviors of the cationic components of these PEMs and could prove useful for the design of thin films for a range of different controlled release applications. Our results also provide new fluorescent cationic polymer probes that could be useful for characterization of the behaviors of PBAEs in other fundamental or applied biotechnological contexts.     

Wavelet Approximation of Distributions with Bounded Variation Derivatives

Let BV ^r denote the space of distributions f such that the distributional derivatives D ^α f with |α|≤r exist as measures of bounded variation. This paper discusses estimates for wavelet coefficients of BV ^r distributions, direct (Jackson) and inverse (Bernstein) inequalities for n-term approximation of elements of BV ^r in the L _p spaces using compactly supported wavelets. In particular, optimal rates of approximation are established. Linear approximation in similar contexts is also considered for comparison. This research was supported by the 2003–2007 Academic Grant of Prof. P. Wojtaszczyk awarded by the Foundation for Polish Science. Part of this research was supported within the HASSIP framework.     

Product line optimization in the presence of preferences for compromise alternatives

Recent advances in customer choice analysis demonstrated the strong impact of compromise alternatives on the behaviour of decision-makers in a wide range of decision situations. Compromise alternatives are characterized by an intermediate performance on some of the relevant attributes. For instance, price compromises are well known in the sense that customers tend to buy neither the cheapest, nor the most expensive alternative, but the mid-priced one. However, thus far, the literature on product line optimization has not considered such context effects.In this paper, we propose a model-based approach for optimal product line selection which incorporates customers’ preferences for compromise alternatives. We consider customer choice in a realistic, sophisticated fashion by applying an established utility model that integrates compromise variables into a multinomial logit model. We formulate the resulting optimization problem as a mixed-integer linear program. The challenging feature for modelling – making the formulation substantially more complicated than existing ones without compromises – are the endogenous effects of selected products on other alternatives’ utilities that need to be adequately captured via compromise variables. Based on data we collected by a stated choice experiment in a retail setting, we perform a computational study and demonstrate the superiority of our product line selection approach compared to a reference model that does not take compromises into account. Even under uncertainty of the estimated utility parameters, profit gains of, on average, 23% can be achieved in our experimental setting.