Stability of Coalescence Hidden variable Fractal Interpolation Surfaces

In the present paper, the stability of Coalescence Hidden variable Fractal Interpolation Surfaces(CHFIS) is established. The estimates on error in approximation of the data generating function by CHFIS are found when there is a perturbation in independent, dependent and hidden variables. It is proved that any small perturbation in any of the variables of generalized interpolation data results in only small perturbation of CHFIS. Our results are likely to be useful in investigations of texture of surfaces arising from the simulation of surfaces of rocks, sea surfaces, clouds and similar natural objects wherein the generating function depends on more than one variable

A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Mott-Kondo Insulator Behavior in the Iron Oxychalcogenides

We perform a combined experimental-theoretical study of the Fe-oxychalcogenides (FeO$\emph{Ch}$) series La$_{2}$O$_{2}$Fe$_{2}$O\emph{M}$_{2}$ (\emph{M}=S, Se), which is the latest among the Fe-based materials with the potential \ to show unconventional high-T$_{c}$ superconductivity (HTSC). A combination of incoherent Hubbard features in X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS) spectra, as well as resitivity data, reveal that the parent FeO$\emph{Ch}$ are correlation-driven insulators. To uncover microscopics underlying these findings, we perform local density approximation-plus-dynamical mean field theory (LDA+DMFT) calculations that unravel a Mott-Kondo insulating state. Based upon good agreement between theory and a range of data, we propose that FeO$\emph{Ch}$ may constitute a new, ideal testing ground to explore HTSC arising from a strange metal proximate to a novel selective-Mott quantum criticality

Exploring quantum criticality based on ultracold atoms in optical lattices

Critical behavior developed near a quantum phase transition, interesting in its own right, offers exciting opportunities to explore the universality of strongly-correlated systems near the ground state. Cold atoms in optical lattices, in particular, represent a paradigmatic system, for which the quantum phase transition between the superfluid and Mott insulator states can be externally induced by tuning the microscopic parameters. In this paper, we describe our approach to study quantum criticality of cesium atoms in a two-dimensional lattice based on in situ density measurements. Our research agenda involves testing critical scaling of thermodynamic observables and extracting transport properties in the quantum critical regime. We present and discuss experimental progress on both fronts. In particular, the thermodynamic measurement suggests that the equation of state near the critical point follows the predicted scaling law at low temperatures.Comment: 15 pages, 6 figure

Sedimentary inputs to the Nankai subduction zone: The importance of dispersed ash

We examine the importance of dispersed volcanic ash as a critical component of the aluminosilicate sediment entering the Nankai Trough, located south of Japan’s island of Honshu, via the subducting Philippine Sea plate. Multivariate statistical analyses of an extensive major, trace, and rare earth element data set from bulk sediment and discrete ash layers at Integrated Ocean Drilling Program (IODP) Sites C0011 and C0012 quantitatively determine the abundance and accumulation of multiple aluminosilicate inputs to the Nankai subduction zone. We identify the eolian input of continental material to both sites, and we further find that there are an additional three ash sources from Kyushu and Honshu, Japan and other regions. Some of these ash sources may themselves represent mixtures of ash inputs, although the final compositions appear statistically distinct. The dispersed ash comprises 38 ± 7 weight percent (wt%) of the bulk sediment at Site C0011, and 34 ± 4 wt% at Site C0012. When considering the entire sediment thickness at Site C0011, the dispersed ash component supplies 38000 ± 7000 g/cm2 of material to the Nankai subduction system, whereas Site C0012 supplies 20000 ± 3000 g/cm2. These values are enormous compared to the ~2500 g/cm2 (C0011) and ~1200 g/cm2 (C0012) of ash in the discrete ash layers. Therefore, the mass of volcanic ash and chemically equivalent alteration products (e.g., smectite) that are dispersed throughout the stratigraphic succession of bulk sediment appears to be up to 15–17 times greater than the mass of discrete ash layers. The composition of the dispersed ash component at Site C0011 appears linked to that of the discrete layers, and the mass accumulation rate for dispersed ash correlates best with discrete ash layer thickness. In contrast, at Site C0012 the mass accumulation rate for dispersed ash correlates better with the number of ash layers. Together, the discrete ash layers, dispersed ash, and clay-mineral assemblages present a complete record of volcanism and erosion of volcanic sources; and indicate that mass balances and subduction factory budgets should include the mass of dispersed ash for a more accurate assessment of volcanic contributions to large-scale geochemical cycling

Spanning trees on the Sierpinski gasket

We obtain the numbers of spanning trees on the Sierpinski gasket $SG_d(n)$ with dimension $d$ equal to two, three and four. The general expression for the number of spanning trees on $SG_d(n)$ with arbitrary $d$ is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4$ are also obtained.Comment: 20 pages, 8 figures, 1 tabl

Electro-Magnetic Nucleon Form Factors and their Spectral Functions in Soliton Models

It is demonstrated that in simple soliton models essential features of the electro-magnetic nucleon form factors observed over three orders of magnitude in momentum transfer $t$ are naturally reproduced. The analysis shows that three basic ingredients are required: an extended object, partial coupling to vector mesons, and relativistic recoil corrections. We use for the extended object the standard skyrmion, one vector meson propagator for both isospin channels, and the relativistic boost to the Breit frame. Continuation to timelike $t$ leads to quite stable results for the spectral functions in the regime from the 2- or 3-pion threshold to about two rho masses. Especially the onset of the continuous part of the spectral functions at threshold can be reliably determined and there are strong analogies to the results imposed on dispersion theoretic approaches by the unitarity constraint.Comment: 24 pages, (RevTeX), 5 PS-figures; Data points in fig.2 and corresponding references added. Final version, to be published in Z.Physik

Inclusive Electron-Nucleus Scattering at Large Momentum Transfer

Inclusive electron scattering is measured with 4.045 GeV incident beam energy from C, Fe and Au targets. The measured energy transfers and angles correspond to a kinematic range for Bjorken $x > 1$ and momentum transfers from $Q^2 = 1 - 7 (GeV/c)^2$. When analyzed in terms of the y-scaling function the data show for the first time an approach to scaling for values of the initial nucleon momenta significantly greater than the nuclear matter Fermi-momentum (i.e. $> 0.3$ GeV/c).Comment: 5 pages TEX, 5 Postscript figures also available at http://www.krl.caltech.edu/preprints/OAP.htm

Measurement of the Proton's Neutral Weak Magnetic Form Factor

We report the first measurement of the parity-violating asymmetry in elastic electron scattering from the proton. The asymmetry depends on the neutral weak magnetic form factor of the proton which contains new information on the contribution of strange quark-antiquark pairs to the magnetic moment of the proton. We obtain the value $G_M^Z= 0.34 \pm 0.09 \pm 0.04 \pm 0.05$ n.m. at $Q^2=0.1$ (GeV/c)${}^2$.Comment: 4 pages TEX, text available at http://www.krl.caltech.edu/preprints/OAP.htm

Systemic Injection of RPE65-Programmed Bone Marrow-Derived Cells Prevents Progression of Chronic Retinal Degeneration

Bone marrow stem and progenitor cells can differentiate into a range of non-hematopoietic cell types, including retinal pigment epithelium (RPE)-like cells. In this study, we programmed bone marrow-derived cells (BMDCs) ex vivo by inserting a stable RPE65 transgene using a lentiviral vector. We tested the efficacy of systemically administered RPE65-programmed BMDCs to prevent visual loss in the superoxide dismutase 2 knockdown (Sod2 KD) mouse model of age-related macular degeneration. Here, we present evidence that these RPE65-programmed BMDCs are recruited to the subretinal space, where they repopulate the RPE layer, preserve the photoreceptor layer, retain the thickness of the neural retina, reduce lipofuscin granule formation, and suppress microgliosis. Importantly, electroretinography and optokinetic response tests confirmed that visual function was significantly improved. Mice treated with non-modified BMDCs or BMDCs pre-programmed with LacZ did not exhibit significant improvement in visual deficit. RPE65-BMDC administration was most effective in early disease, when visual function and retinal morphology returned to near normal, and less effective in late-stage disease. This experimental paradigm offers a minimally invasive cellular therapy that can be given systemically overcoming the need for invasive ocular surgery and offering the potential to arrest progression in early AMD and other RPE-based diseases