Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Temperature dependence of the crystal structure and g-values of [(HC(Ph2PO)(3))(2)Cu] (ClO4)(2)center dot 2H(2)O: Influence of dynamic Jahn-Teller coupling and lattice strain interactions

The temperature dependence of the X-ray crystal structure and powder EPR spectrum of [(HC(Ph2PO)(3))(2)CU]-(ClO4)(2)center dot 2H(2)O is reported, and the structure at room temperature confirms that reported previously. Below similar to 100 K, the data imply a geometry with near elongated tetragonal symmetry for the [(HC(Ph2PO)(3))(2)Cu](2+) complex, but on warming the two higher Cu-O bond lengths and g-values progressively converge, and by 340 K the bond lengths correspond to a compressed tetragonal geometry. The data may be interpreted satisfactorily assuming an equilibrium among the energy levels of a Cu-O-6 polyhedron subjected to Jahn-Teller vibronic coupling and a lattice strain. However, agreement with the experiment is obtained only if the orthorhombic component of the lattice strain decreases to a negligible value as the temperature approaches 340 K.

Influence of lattice interactions on the jahn-teller distortion of the [Cu(H2O)(6)](2+) ion: Dependence of the crystal structure of K-2[Cu(H2O)(6)](SO4)(2x)(SeO4)(2-2x) upon the sulfate/selenate ratio

The temperature dependence of the structure of the mixed-anion Tutton salt K-2[Cu(H2O)(6)](SO4)(2x)(SeO4)(2-2x) has been determined for crystals with 0, 17, 25, 68, 78, and 100% sulfate over the temperature range of 85-320 K. In every case, the [Cu(H2O)(6)](2+) ion adopts a tetragonally elongated coordination geometry with an orthorhombic distortion. However, for the compounds with 0, 17, and 25% sulfate, the long and intermediate bonds occur on a different pair of water molecules from those with 68, 78, and 100% sulfate. A thermal equilibrium between the two forms is observed for each crystal, with this developing more readily as the proportions of the two counterions become more similar. Attempts to prepare a crystal with approximately equal amounts of sulfate and selenate were unsuccessful. The temperature dependence of the bond lengths has been analyzed using a model in which the Jahn-Teller potential surface of the [Cu(H2O)(6)](2+) ion is perturbed by a lattice-strain interaction. The magnitude and sign of the orthorhombic component of this strain interaction depends on the proportion of sulfate to selenate. Significant deviations from Boltzmann statistics are observed for those crystals exhibiting a large temperature dependence of the average bond lengths, and this may be explained by cooperative interactions between neighboring complexes.

Purification and crystallization of the hydroxylase component of the methanesulfonate monooxygenase from Methylosulfonomonas methylovora strain M2

The aim of the work described in this paper was two-fold: (1) the purification of the hydroxylase component of the MSAMO to electrophoretic homogeneity using a four-step chromatographic strategy and (2) the crystallization of the two-component hydroxylase of the MSAMO in order to enhance our understanding of the precise three-dimensional structure of the MSAMO, thus yielding an insight into the nature of the active site of this enzyme. Optimised crystallization conditions were identified allowing growth of crystals of the hydroxylase component of the MSAMO within five days. Crystals exhibited a brown colour suggesting the presence on an intact Rieske-iron sulfur centre and diffracted to 7.0 Å when a few degrees of data were evaluated on a beam line X11. © 2006 Elsevier Inc. All rights reserved.

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.

A Characterization of Varieties of Associative Algebras of Exponent two

∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233.

New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10

∗ This work has been partially supported by the Bulgarian NSF under Contract No. I-506/1995.

Groups of Order 32 as Galois Groups

2000 Mathematics Subject Classification: 12F12.

A precise measurement of the two -photon exchange effect

The two-photon exchange phenomenon is believed to be responsible for the discrepancy observed between the ratio of proton electric and magnetic form factors, measured by the Rosenbluth and polarization transfer methods. This disagreement is about a factor of three at Q 2 of 5.6 GeV2. The precise knowledge of the proton form factors is of critical importance in understanding the structure of this nucleon. The theoretical models that estimate the size of the two-photon exchange (TPE) radiative correction are poorly constrained. This factor was found to be directly measurable by taking the ratio of the electron-proton and positron-proton elastic scattering cross sections, as the TPE effect changes sign with respect to the charge of the incident particle. A test run of a modified beamline has been conducted with the CEBAF Large Acceptance Spectrometer (CLAS) at Thomas Jefferson National Accelerator Facility. This test run demonstrated the feasibility of producing a mixed electron/positron beam of good quality. Extensive simulations performed prior to the run were used to reduce the background rate that limits the production luminosity. A 3.3 GeV primary electron beam was used that resulted in an average secondary lepton beam of 1 GeV. As a result, the elastic scattering data of both lepton types were obtained at scattering angles up to 40 degrees for Q2 up to 1.5 GeV2. The cross section ratio displayed an &epsis; dependence that was Q2 dependent at smaller Q2 limits. The magnitude of the average ratio as a function of &epsis; was consistent with the previous measurements, and the elastic (Blunden) model to within the experimental uncertainties. Ultimately, higher luminosity is needed to extend the data range to lower &epsis; where the TPE effect is predicted to be largest.

Fabrication of a two-terminal super conducting device with a poled ferroelectric control layer

The discovery of High-Temperature Superconductors (HTSCs) has spurred the need for the fabrication of superconducting electronic devices able to match the performance of today's semiconductor devices. While there are several HTSCs in use today, YBaCuO7-x (YBCO) is the better characterized and more widely used material for small electronic applications. This thesis explores the fabrication of a Two-Terminal device with a superconductor and a painted on electrode as the terminals and a ferroelectric, BaTiO 3 (BTO), in between. The methods used to construct such a device and the challenges faced with the fabrication of a viable device will be examined. The ferroelectric layer of the devices that proved adequate for use were poled by the application of an electric field. Temperature Bias Poling used an applied field of 105V/cm at a temperature of approximately 135*C. High Potential Poling used an applied field of 106V/cm at room temperature (20*C). The devices were then tested for a change in their superconducting critical temperature, Tc. A shift of 1-2K in the Tc(onset) of YBCO was observed for Temperature Bias Poling and a shift of 2-6K for High Potential Poling. These are the first reported results of the field effect using BTO on YBCO. The mechanism involved in the shifting of Tc will be discussed along with possible applications.

(Supplementary Material 2) Landmark coordinates of the analyzed specimens with associated metadata

The use of planktonic foraminifera in paleoceanographic studies relies on the assumption that morphospecies represent biological species with ecological preferences that are stable through time and space. However, genetic surveys unveiled a considerable level of diversity in most morphospecies of planktonic foraminifera. This diversity is significant for paleoceanographic applications because cryptic species were shown to display distinct ecological preferences that could potentially help refine paleoceanographic proxies. Subtle morphological differences between cryptic species of planktonic foraminifera have been reported, but so far their applicability within paleoceanographic studies remains largely unexplored. Here we show how information on genetic diversity can be transferred to paleoceanography using Globorotalia inflata as a case study. The two cryptic species of G. inflata are separated by the Brazil-Malvinas Confluence (BMC), a major oceanographic feature in the South Atlantic. Based on this observation, we developed a morphological model of cryptic species detection in core top material. The application of the cryptic species detection model to Holocene samples implies latitudinal oscillations in the position of the confluence that are largely consistent with reconstructions obtained from stable isotope data. We show that the occurrence of cryptic species in G. inflata, can be detected in the fossil record and used to trace the migration of the BMC. Since a similar degree of morphological separation as in G. inflata has been reported from other species of planktonic foraminifera, the approach presented in this study can potentially yield a wealth of new paleoceanographical proxies.

(Table 2) Radiocarbon ages of selected southern Baja California sediment cores

Piston, gravity, and multicores as well as hydrographic data were collected along the Pacific margin of Baja California to reconstruct past variations in the intensity of the oxygen-minimum zone (OMZ). Gravity cores collected from within the OMZ north of 24°N did not contain laminated surface sediments even though bottom water oxygen (BWO) concentrations were close to 5 µmol/kg. However, many of the cores collected south of 24°N did contain millimeter- to centimeter-scale, brown to black laminations in Holocene and older sediments but not in sediments deposited during the Last Glacial Maximum. In addition to the dark laminations, Holocene sediments in Soledad Basin, silled at 290 m, also contain white coccolith laminae that probably represent individual blooms. Two open margin cores from 430 and 700 m depth that were selected for detailed radiocarbon dating show distinct transitions from bioturbated glacial sediment to laminated Holocene sediment occurring at 12.9 and 11.5 ka, respectively. The transition is delayed and more gradual (11.3-10.0 ka) in another dated core from Soledad Basin. The observations indicate that bottom-water oxygen concentrations dropped below a threshold for the preservation of laminations at different times or that a synchronous hydrographic change left an asynchronous sedimentary imprint due to local factors. With the caveat that laminated sections should therefore not be correlated without independent age control, the pattern of older sequences of laminations along the North American western margin reported by this and previous studies suggests that multiple patterns of regional productivity and ventilation prevailed over the past 60 kyr.

(Table 2) Age determination of sediment cores from the continental shelf of Mac Roberston Land, East Antarctica

Geochemical records are presented for five sediment cores from basins on the continental shelf of Mac. Robertson Land, East Antarctica. The cores contain 2-4 m thick sequences of hemipelagic, siliceous mud and ooze (SMO) deposited under seasonally open marine conditions. The inner and middle shelf SMO sequences are massive dark olive green material, whereas the outer shelf SMO sequences are dark olive material interspersed with light olive green layers ~1-10 cm thick. The biogenic material is dominated by marine diatoms including Fragilariopsis curta, Fragilariopsis cylindrus, and Chaetoceros spp. in the dark-colored SMO and Corethron criophilum in the light-colored layers. Radiocarbon dates suggest that the cores provide continuous accumulation records extending from < 1 kyr before present (B.P.) back as far as 4-15 kyr B.P., with estimated accumulation rates of 0.07-5 mm/yr. The three core records from the middle and outer shelf suggest six episodes of increased accumulation of biogenic material at ~5.5 kyr B.P. (all three cores), 1, 2, and 6.2 kyr B.P. (two of the three cores), and 3.8 and 10.8 kyr B.P. (one core), most of which coincide with Corethron layers. We interpret these features as the result of enhanced diatom production over the outer shelf, possibly related to climatic warm periods. The absence of such features in the inner shelf core records is thought to reflect a relatively constant level of seasonal diatom production in adjacent waters maintained by a coastal polynya.

(Table 2) Age determination of Aegean Sea sediments

The modern Aegean Sea is an important source of deep water for the eastern Mediterranean. Its contribution to deep water ventilation is known to fluctuate in response to climatic variation on a decadal timescale. This study uses marine micropalaeontological and stable isotope data to investigate longer-term variability during the late glacial and Holocene, in particular that associated with the deposition of the early Holocene dysoxic/anoxic sapropel S1. Concentrating on the onset of sapropel-forming conditions, we identify the start of 'seasonal' stratification and highlight a lag in d18O response of the planktonic foraminifer N. pachyderma to termination T1b as identified in the d18O record of G. ruber. By use of a simple model we determine that this offset cannot be a function of bioturbation effects. The lag is of the order of 1 kyr and suggests that isolation of intermediate/deep water preceded the start of sapropel formation by up to 1.5 kyr. Using this discovery, we propose an explanation for the major unresolved problem in sapropel studies, namely, the source of nutrient supply required for export productivity to reach levels needed for sustained sapropel deposition. We suggest that nutrients had been accumulating in a stagnant basin for 1-1.5 kyr and that these accumulated resources were utilized during the deposition of S1. In addition, we provide a first quantitative estimate of the diffusive (1/e) mixing timescale for the eastern Mediterranean in its "stratified" sapropel mode, which is of the order of 450 years.