A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Convexity around the Unit of a Banach Algebra

2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.

A Note About the Nowicki Conjecture on Weitzenböck Derivations

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.

45°-TFG based in-fiber polarizer at 800nm by UV inscription

We show in-fiber polarizers at 800nm range with polarization extinction ratio (PER) up to 37dB, fabricated by UV-inscribing grating structures tilted at 45° in standard single mode fiber. The results show that the PER of such polarizers increases linearly with the grating length. © OSA 2012.

UV-Inscribed optical fiber gratings in Mid-IR range and their laser applications

We have UV-inscribed fiber Bragg gratings (FBGs), long-period gratings (LPGs), and tilted fiber gratings (TFGs) into mid-IR 2μm range using three common optical fiber grating fabrication techniques (two-beam holographic, phase mask, and point-by-point). The fabricated FBGs have been evaluated for thermal and strain response. It has been revealed that the FBG devices with responses in mid-IR range are much more sensitive to temperature than that in near-IR range. To explore the unique cladding mode coupling function, we have investigated the thermal and refractive index sensitivities of LPGs and identified that the coupled cladding modes in mid-IR range are also much more sensitive to temperature and surrounding medium refractive index change. The 45° tilted fiber gratings (45°-TFGs) as polarizing devices in mid-IR have been investigated for their polarization extinction characteristics. As efficient reflection filters and in-cavity polarizers, the mid-IR FBGs and 45°-TFGs have been employed in fiber laser cavity to realize multi-wavelength 2 μm Tm-doped CW and mode locked fiber lasers, respectively.

Sea-floor images during POLARSTERN cruise ANT-XIII/3 to the Weddell Sea, Antarctica

Transects of a Remotely Operated Vehicle (ROV) providing sea-bed videos and photographs were carried out during POLARSTERN expedition ANT-XIII/3 focussing on the ecology of benthic assemblages on the Antarctic shelf in the South-Eastern Weddell Sea. The ROV-system sprint 103 was equiped with two video- and one still camera, lights, flash-lights, compass, and parallel lasers providing a scale in the images, a tether-management system (TMS), a winch, and the board units. All cameras used the same main lense and could be tilted. Videos were recorded in Betacam-format and (film-)slides were made by decision of the scientific pilot. The latter were mainly made under the aspect to improve the identification of organisms depicted in the videos because the still photographs have a much higher optical resolution than the videos. In the photographs species larger than 3 mm, in the videos larger than 1 cm are recognisable and countable. Under optimum conditions the transects were strait; the speed and direction of the ROV were determined by the drift of the ship in the coastal current, since both, the ship and the ROV were used as a drifting system; the option to operate the vehicle actively was only used to avoide obstacles and to reach at best a distance of only approximately 30 cm to the sea-floor. As a consequence the width of the photographs in the foreground is approximately 50 cm. Deviations from this strategy resulted mainly from difficult ice- and weather conditions but also from high current velocity and local up-welling close to the sea-bed. The sea-bed images provide insights into the general composition of key species, higher systematic groups and ecological guilds. Within interdisciplinary approaches distributions of assemblages can be attributed to environmental conditions such as bathymetry, sediment characteristics, water masses and current regimes. The images also contain valuable information on how benthic species are associated to each other. Along the transects, small- to intermediate-scaled disturbances, e.g. by grounding icebergs were analysed and further impact to the entire benthic system by local succession of recolonisation was studied. This information can be used for models predicting the impact of climate change to benthic life in the Southern Ocean. All these approaches contribute to a better understanding of the fiunctioning of the benthic system and related components of the entire Antarctic marine ecosystem. Despite their scientific value the imaging methods meet concerns about the protection of sensitive Antarctic benthic systems since they are non-invasive and they also provide valuable material for education and outreach purposes.

Sea-floor images from ROV transects during POLARSTERN cruise ANT-XVII/3 (EASIZ III) to the Weddell Sea, Antarctica

Transects of a Remotely Operated Vehicle (ROV) providing sea-bed videos and photographs were carried out during POLARSTERN expedition ANT-XVII/3 focussing on the ecology of benthic assemblages on the Antarctic shelf in the South-Eastern Weddell Sea. The ROV-system sprint 103 was equiped with two video- and one still camera, lights, flash-lights, compass, and parallel lasers providing a scale in the images, a tether-management system (TMS), a winch, and the board units. All cameras used the same main lense and could be tilted. Videos were recorded in Betacam-format and (film-)slides were made by decision of the scientific pilot. The latter were mainly made under the aspect to improve the identification of organisms depicted in the videos because the still photographs have a much higher optical resolution than the videos. In the photographs species larger than 3 mm, in the videos larger than 1 cm are recognisable and countable. Under optimum conditions the transects were strait; the speed and direction of the ROV were determined by the drift of the ship in the coastal current, since both, the ship and the ROV were used as a drifting system; the option to operate the vehicle actively was only used to avoide obstacles and to reach at best a distance of only approximately 30 cm to the sea-floor. As a consequence the width of the photographs in the foreground is approximately 50 cm. Deviations from this strategy resulted mainly from difficult ice- and weather conditions but also from high current velocity and local up-welling close to the sea-bed. The sea-bed images provide insights into the general composition of key species, higher systematic groups and ecological guilds. Within interdisciplinary approaches distributions of assemblages can be attributed to environmental conditions such as bathymetry, sediment characteristics, water masses and current regimes. The images also contain valuable information on how benthic species are associated to each other. Along the transects, small- to intermediate-scaled disturbances, e.g. by grounding icebergs were analysed and further impact to the entire benthic system by local succession of recolonisation was studied. This information can be used for models predicting the impact of climate change to benthic life in the Southern Ocean. All these approaches contribute to a better understanding of the fiunctioning of the benthic system and related components of the entire Antarctic marine ecosystem. Despite their scientific value the imaging methods meet concerns about the protection of sensitive Antarctic benthic systems since they are non-invasive and they also provide valuable material for education and outreach purposes.

Ultrasonic measurement of anisotropic reflectivity from Water-Phenolic CE Interface

In this contribution, we experimentally test the effects of azimuth and tilt angle on the acoustic reflectivity of a liquid- anisotropic solid interface. For this study, we are using a large source transducer, and acquired data for samples with different tilt angles. We use Phenolic CE material, which is known to have orthorhombic symmetry. Our results show that changes of the tilt angle produce important variations on the reflectivity that are larger as the tilt increases. The most remarkable feature is the change of the critical angle with the azimuth, which shows a larger spread for larger tilts. The spectral components of the acquired waveforms also show characteristic features linked to the location of the critical angle, we particularly observed a drop in the peak frequency. These observations suggest that care must be taken about the interpretation and inversion of observed incidence and azimuth dependent seismic reflectivities and critical angles in obtaining information on a formation's anisotropy. Zip archive contains four segy files: - LAB_TI00, is not tilted sample in contact with water, - LAB_TI30, is 30degrees tilted sample in contact with water, - LAB_TI45, is 45 degrees tilted sample in contact with water, - LAB_TI90, is 90 degrees tilted sample in contact with water.

Técnicas en análisis lineal (y no lineal) y aplicaciones

La presente tesis est a centrada en dos temas principales: el primero abarca el primer cap tulo y el segundo se divide entre los cap tulos dos y tres. En el primer cap tulo estudio un problema que apareci o como tal hace relativamente poco tiempo (aunque ya en la segunda mitad del pasado siglo se publicaron una serie de resultados que, con la terminolog a adecuada, estar an englobados dentro de esta teor a). Nos interesaremos en la b usqueda de estructuras algebraicas (como espacios vectoriales, algebras, espacios de Banach) contenidas en subconjuntos de funciones cuyos elementos (con la posible excepci on del elemento nulo) veri can ciertas propiedades anti-intuitivas (propiedades de dif cil visualizaci on). Ello nos puede conducir a la idea de c omo la intuci on puede enga~narnos, y sugerir que, aunque se haya dedicado una ingente cantidad de esfuerzo y tiempo para encontrar un unico ejemplo que veri que tales propiedades, y dicho trabajo pueda dar la idea de que no existen muchos m as espec menes de similares caracter sticas, de hecho existen ejemplares su cientes como para construir espacios \grandes" cuyos elementos (salvo el cero) satisfacen las mismas propiedades. M as espec camente, decimos que un subconjunto de un espacio vectorial topol ogico es -lineable (dado un numero cardinal ) si podemos garantizar la existencia de un espacio vectorial de dimensi on contenido en el conjunto (uni on el elemento cero, en caso de que cero no forme parte del conjunto de partida). Si el espacio vectorial es cerrado, nos referiremos a este conjunto como - espaciable (y la propiedad que trataremos ser a la de -espaciabilidad) y si la estructura en cuesti on es un algebra de Banach, entonces diremos que el conjunto es ( ; )-algebrable (donde aqu es la cardinalidad de un conjunto minimal de generadores del algebra)...

A planar reconfigurable linear rigid-body motion linkage with two operation modes

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Mg/Ca ratio of Globorotalia tumida and subsurface temperature reconstruction for ODP Site 130-806

The tropical Pacific thermocline strength, depth, and tilt are critical to tropical mean state and variability. During the early Pliocene (~3.5 to 4.5 Ma), the Eastern Equatorial Pacific (EEP) thermocline was deeper and the cold tongue was warmer than today, which resulted in an mean state with a reduced zonal sea surface temperature gradient, or El Padre. However, it is unclear whether the deep thermocline was a local feature of the EEP or a basin-wide condition with global implications. Our measurements of Mg/Ca of Globorotalia tumida in a western equatorial Pacific site indicate Pliocene subsurface temperatures warmer than today; thus, El Padre included a basin-wide thermocline that was relatively warm, deep, and weakly tilted. At ~4 Ma, thermocline steepening was coupled to cooling of the cold tongue. Since ~4 Ma, the basin-wide thermocline cooled/shoaled gradually, with implications for thermocline feedbacks in tropical dynamics and the interpretation of TEX86-derived temperatures.

Characterization of New Carbosilane Liquid Crystalline Monomers and Dimers

‘De Vries-like’ smectic liquid crystals exhibit low layer contraction of approximately 1% on transitions from the SmA to the SmC phase. These materials have received considerable attention as potential solutions for problems affecting liquid crystal displays using surface-stabilized ferroelectric liquid crystals (SSFLC). In SSFLCs, layer contraction of 710% is normally observed during the SmA to SmC phase transition. A study by the Lemieux group has shown that liquid crystals with nanosegregating carbosilane segments exhibit enhanced ‘de Vries-like’ properties through the formation of smectic layers and by lengthening the nanosegregating carbosilane end-groups from monocarbosilane to tricarbosilane. This observed enhancement is assumed to be due to an increase in the cross-section of the free volume in the hydrocarbon sub-layer. To test this hypothesis, it is assumed that dimers with a tricarbosilane linking group have smaller cross-sections on time average. In his thesis, this hypothesis is tested through the characterization of new liquid crystalline monomers (QL39-n) and dimers (QL40-n) with 2-phenylpyrimidine cores and tricarbosilane end-groups and spacers, respectively. The thesis describes the synthesis of two homologous series of liquid crystals and their characterization using a variety of techniques, including polarized optical microscopy, differential scanning calorimetry and X-ray diffraction. The results show that the monomers QL39-n form a tilted SmC phase only, whereas the dimers QL40-n form an orthogonal SmA phase. These results are discussed in the context of our hypothesis.

Classifying Rational G-Spectra for Finite G

We give a new proof that for a finite group G, the category of rational G-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G, as H runs over the conjugacy classes of subgroups of G. Furthermore, the Quillen equivalences of our proof are all symmetric monoidal. Thus we can understand categories of algebras or modules over a ring spectrum in terms of the algebraic model.

Spectrally isometric elementary operators

We present criteria for unital elementary operators (of small length) on unital semisimple Banach algebras to be spectral isometries. The surjective ones among them turn out to be algebra automorphisms.