Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

EPR of a novel high-spin component in activated hydrogenase from Desulfovibrio vulgaris (Hildenborough)

The EPR of reoxidized hydrogenase from Desulfovibrio vulgaris (H.) has been reinvestigated. In contrast to other workers [(1984) Proc. Natl. Acad. Sci. USA 81, 3728-3732] we find the axial signal with g = 2.06; 2.01 to be only a minor component of concentration 0.03 spin/mol. In the spectrum of fully active reoxidized enzyme this signal is overshadowed by a rhombic signal (0.1 spin/mol) with g = 2.11; 2.05; 2.00 reminiscent of the only signal found for other oxidized bidirectional hydrogenases. In addition, a novel signal has been detected with geff = 5.0 which, under the assumptions that S = 2 and |[Delta]ms|= 2, quantitates to roughly one spin/mol. Ethylene glycol affects the relative intensity of the different signals. It is suggested that O2 sensitization parallels a spin-state transition of an iron-sulfur cluster.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26169/1/0000246.pd

Phenotypic Plasticity and Contemporary Evolution in Introduced Populations: Evidence from Translocated Populations of White Sands Pupfish (Cyrpinodon tularosa)

Contemporary evolution has been shown in a few studies to be an important component of colonization ability, but seldom have researchers considered whether phenotypic plasticity facilitates directional evolution from the invasion event. In the current study, we evaluated body shape divergence of the New Mexico State-threatened White Sands pupfish (Cyprinodon tularosa) that were introduced to brackish, lacustrine habitats at two different time in the recent past (approximately 30 years and 1 year previously) from the same source population (saline river environment). Pupfish body shape is correlated with environmental salinity: fish from saline habitats are characterized by slender body shapes, whereas fish from fresher, yet brackish springs are deep-bodied. In this study, lacustrine populations consisted of an approximately 30-year old population and several 1-year old populations, all introduced from the same source. The body shape divergence of the 30-year old population was significant and greater than any of the divergences of the 1-year old populations (which were for the most part not significant). Nonetheless, all body shape changes exhibited body deepening in less saline environments. We conclude that phenotypic plasticity potentially facilitates directional evolution of body deepening for introduced pupfish populations

A 750 mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+ ions

We present a solid-state laser system that generates 750 mW of continuous-wave single-frequency output at 313 nm. Sum-frequency generation with fiber lasers at 1550 nm and 1051 nm produces up to 2 W at 626 nm. This visible light is then converted to UV by cavity-enhanced second-harmonic generation. The laser output can be tuned over a 495 GHz range, which includes the 9Be+ laser cooling and repumping transitions. This is the first report of a narrow-linewidth laser system with sufficient power to perform fault-tolerant quantum-gate operations with trapped 9Be+ ions by use of stimulated Raman transitions.Comment: 9 pages, 4 figure

Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions

We review the most important experimental results from the first three years of nucleus-nucleus collision studies at RHIC, with emphasis on results from the STAR experiment, and we assess their interpretation and comparison to theory. The theory-experiment comparison suggests that central Au+Au collisions at RHIC produce dense, rapidly thermalizing matter characterized by: (1) initial energy densities above the critical values predicted by lattice QCD for establishment of a Quark-Gluon Plasma (QGP); (2) nearly ideal fluid flow, marked by constituent interactions of very short mean free path, established most probably at a stage preceding hadron formation; and (3) opacity to jets. Many of the observations are consistent with models incorporating QGP formation in the early collision stages, and have not found ready explanation in a hadronic framework. However, the measurements themselves do not yet establish unequivocal evidence for a transition to this new form of matter. The theoretical treatment of the collision evolution, despite impressive successes, invokes a suite of distinct models, degrees of freedom and assumptions of as yet unknown quantitative consequence. We pose a set of important open questions, and suggest additional measurements, at least some of which should be addressed in order to establish a compelling basis to conclude definitively that thermalized, deconfined quark-gluon matter has been produced at RHIC.Comment: 101 pages, 37 figures; revised version to Nucl. Phys.

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev.

Measurement of the Neutron Spin Structure Function g1ng_1^n with a Polarized ^3He Target

Results are reported from the HERMES experiment at HERA on a measurement of the neutron spin structure function $g_1^n(x,Q^2)$ in deep inelastic scattering using 27.5 GeV longitudinally polarized positrons incident on a polarized $^3$He internal gas target. The data cover the kinematic range $0.023<x<0.6$ and $1 (GeV/c)^2 < Q^2 <15 (GeV/c)^2$. The integral $\int_{0.023}^{0.6} g_1^n(x) dx$ evaluated at a fixed $Q^2$ of $2.5 (GeV/c)^2$ is $-0.034\pm 0.013(stat.)\pm 0.005(syst.)$. Assuming Regge behavior at low $x$, the first moment $\Gamma_1^n=\int_0^1 g_1^n(x) dx$ is $-0.037\pm 0.013(stat.)\pm 0.005(syst.)\pm 0.006(extrapol.)$.Comment: 4 pages TEX, text available at http://www.krl.caltech.edu/preprints/OAP.htm

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec

Reasonable potential for GHG savings by anaerobic biomethane in Germany and UK derived from economic and ecological analyses

This study introduces a new approach to estimate biomethane market potential by analysing biogas markets and their relative environmental and economic advantages. This potential is then combined with greenhouse gas emission values for different feedstock shares (farm-fed and waste-fed systems) and different application share to determine the possible contribution of biomethane to national greenhouse gas emission saving goals. Markets that are considered are Germany and the UK being the biggest emitters of CO2eq in the European Union. The current use was compared with the scenarios (i) market projection, derived from literature study and (ii) reasonable potential, derived from environmental and economic calculations. The current market status is presented to show the past market development until the present date and associated greenhouse gas savings. Additionally the potential of biomethane to contribute to greenhouse gas emission savings is extensively described. Results indicate that the share of application in Germany is more environmental beneficial than the one in the UK achieving higher greenhouse gas savings at comparable feed-in level. In contrast, the UK has a higher share of waste-fed systems to produce biomethane. The use of biomethane in CHP plants achieves the highest GHG emission savings and if organic waste is used as feedstock the possible savings are even higher. With an increase of biomethane used in CHP plants and a decrease of biomethane used for direct heating the savings in the UK could increase up to 52%. Current savings of 2446 kt CO2eq (Germany) and 606 kt CO2eq (UK) can be extended to 4483 kt CO2eq (Germany) and 1443 kt CO2eq (UK) respectively. Scenario results were determined based on the environmental and economic advantageousness development of the existing biogas market. In this way positive future market development as well as improved shares of feedstock and application can contribute to further greenhouse gas emission savings of Germany and the UK

Measurements of the observed cross sections for exclusive light hadron production in e^+e^- annihilation at \sqrt{s}= 3.773 and 3.650 GeV

By analyzing the data sets of 17.3 pb$^{-1}$ taken at $\sqrt{s}=3.773$ GeV and 6.5 pb$^{-1}$ taken at $\sqrt{s}=3.650$ GeV with the BESII detector at the BEPC collider, we have measured the observed cross sections for 12 exclusive light hadron final states produced in $e^+e^-$ annihilation at the two energy points. We have also set the upper limits on the observed cross sections and the branching fractions for $\psi(3770)$ decay to these final states at 90% C.L.Comment: 8 pages, 5 figur