Symmetric representation of an integral domain over a subdomain

Let F(θ) be a separable extension of degree n of a field F. Let Δ and D be integral domains with quotient fields F(θ) and F respectively. Assume that Δ ᴝ D. A mapping φ of Δ into the n x n D matrices is called a Δ/D rep if (i) it is a ring isomorphism and (ii) it maps d onto dI_n whenever d ϵ D. If the matrices are also symmetric, φ is a Δ/D symrep.

Every Δ/D rep can be extended uniquely to an F(θ)/F rep. This extension is completely determined by the image of θ. Two Δ/D reps are called equivalent if the images of θ differ by a D unimodular similarity. There is a one-to-one correspondence between classes of Δ/D reps and classes of Δ ideals having an n element basis over D.

The condition that a given Δ/D rep class contain a Δ/D symrep can be phrased in various ways. Using these formulations it is possible to (i) bound the number of symreps in a given class, (ii) count the number of symreps if F is finite, (iii) establish the existence of an F(θ)/F symrep when n is odd, F is an algebraic number field, and F(θ) is totally real if F is formally real (for n = 3 see Sapiro, “Characteristic polynomials of symmetric matrices” Sibirsk. Mat. Ž. 3 (1962) pp. 280-291), and (iv) study the case D = Z, the integers (see Taussky, “On matrix classes corresponding to an ideal and its inverse” Illinois J. Math. 1 (1957) pp. 108-113 and Faddeev, “On the characteristic equations of rational symmetric matrices” Dokl. Akad. Nauk SSSR 58 (1947) pp. 753-754).

The case D = Z and n = 2 is studied in detail. Let Δ’ be an integral domain also having quotient field F(θ) and such that Δ’ ᴝ Δ. Let φ be a Δ/Z symrep. A method is given for finding a Δ’/Z symrep ʘ such that the Δ’ ideal class corresponding to the class of ʘ is an extension to Δ’ of the Δ ideal class corresponding to the class of φ. The problem of finding all Δ/Z symreps equivalent to a given one is studied.

Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

A Poética de Adélia Prado: espaço de articulação entre língua portuguesa e língua literária

A tese estuda a obra poética de Adélia Prado sob o ponto de vista da Estilística. Mostra que a metáfora é o recurso mais afeito a construir a língua literária e, no caso da poetisa, modelá-la em português. O estudo atesta que a linguagem conotativa da poetisa alcança os três níveis da língua e promove o inesperado e o distante da expressão comum. Afirma a importância da polifonia e da intertextualidade , além da excelência do discurso indireto livre na criação literária, não só da poetisa, mas de todo uso da língua portuguesa como ferramenta de expressão poética, principalmente se a intenção do autor é criar o discurso surrealista. A pesquisa mostra que há, na obra, um grande número de poemas em que predomina a linguagem religiosa católica. Ocorre a expressão da alma feminina , marcada com orgulho pela poetisa. A autora cria prosodemas, inaugura neologismos ,aproveitando todos os processos de criação vocabular. Assim, a obra se notabiliza pelo aproveitamento da sonoridade das palavras, pela escolha lexical inédita, por uma estrutura frasal apositiva, evocativa, sucinta e nominal, não escravizada às regras do registro culto como padrão literário. A tese reconhece que a autora lida eficientemente com as classes de palavras, com a construção nominal e com uma estruturação sintática peculiar, em que sobressai a oração adjetiva com função de sujeito, apesar de conter verbo: a oração adjetiva subjetivada. A essência da pesquisa são os conjuntos metafóricos, verdadeiros modelos universais, que permitem reconhecer a possível existência de uma língua literária em português. No mesmo contexto, focaliza um grupo de poemas chamados de telegráficos, curtos e de teor filosófico. Tal qualidade metafórica mostra a importância da poetisa Adélia Prado para a articulação da língua literária em língua portuguesa

Reggeization of some unequal mass processes involving higher spins : the reactions pion-nucleon going to (V,Nucleon), pion-nucleon going to (V,delta-hyperon), and photon-proton going to (positive pion,neutron)

Recent theoretical developments in the reggeization of inelastic processes involving particles with high spin are incorporated into a model of vector meson production. A number of features of experimental differential cross sections and density matrices are interpreted in terms of this model.

The method chosen for reggeization of helicity amplitudes first separates kinematic zeros and singularities from the parity-conserving amplitudes and then applies results of Freedman and Wang on daughter trajectories to the remaining factors. Kinematic constraints on helicity amplitudes at t = 0 and t = (M – M_Δ)² are also considered.

It is found that data for reactions of types πN→VN and πN→VΔ are consistent with a model of this type in which all kinematic constraints at t = 0 are satisfied by evasion (vanishing of residue functions). As a quantitative test of the parametrization, experimental differential cross sections of vector meson production reactions dominated by pion trajectory exchange are compared with the theory. It is found that reduced residue functions are approximately constant, once the kinematic behavior near t = (M – M_Δ)² has been removed.

The alternative possibility of conspiracy between amplitudes is also discussed; and it is shown that unless conspiracy is present, some amplitudes allowed by angular momentum conservation will not contribute with full strength in the forward direction. An example, γp→π⁺n in which the data for dσ/dt indicate conspiracy, is studied in detail.

Part I. Approximate Hartree-Fock wavefunctions one-electron properties and electronic structure of the water molecule. Part II. Perturbation-variational calculation of the nuclear spin-spin isotope coupling constant in HD

Part I

Several approximate Hartree-Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann-Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p-orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.

Part II

The perturbation-variational theory of R. M. Pitzer for nuclear spin-spin coupling constants is applied to the HD molecule. The zero-order molecular orbital is described in terms of a single 1s Slater-type basis function centered on each nucleus. The first-order molecular orbital is expressed in terms of these two functions plus one singular basis function each of the types e^-r/r and e^-r ln r centered on one of the nuclei. The new kinds of molecular integrals were evaluated to high accuracy using numerical and analytical means. The value of the HD spin-spin coupling constant calculated with this near-minimal set of basis functions is J_HD = +96.6 cps. This represents an improvement over the previous calculated value of +120 cps obtained without using the logarithmic basis function but is still considerably off in magnitude compared with the experimental measurement of J_HD = +43 0 ± 0.5 cps.

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

The analytical description and experiments of the optical bottle generated by an axicon and a lens

Based on the interferential theory, we deduce a new type of analytic expression suitable for describing the evolutions of the optical bottle beam generated from the axicon-lens optical system illuminated by the Gaussian beam for the first time. The theory does not use much approximation in the process of mathematical analysis and can better illustrate the optical bottle beam evolutions at any positions. With the derived expression, the three-dimensional (3D) longitudinal and transverse intensity profiles of the optical bottle beam are simulated numerically. The numerical calculations have been confirmed by the experimental results.

Electronic properties of graphene grain boundaries

Grain boundaries and defect lines in graphene are intensively studied for their novel electronic and magnetic properties. However, there is not a complete comprehension of the appearance of localized states along these defects. Graphene grain boundaries are herein seen as the outcome of matching two semi-infinite graphene sheets with different edges. We classify the energy spectra of grain boundaries into three different types, directly related to the combination of the four basic classes of spectra of graphene edges. From the specific geometry of the grains, we are able to obtain the band structure and the number of localized states close to the Fermi energy. This provides a new understanding of states localized at grain boundaries, showing that they are derived from the edge states of graphene. Such knowledge is crucial for the ultimate tailoring of electronic and optoelectronic applications.

Report on the analysis of salmon scale samples returned by anglers on the Rivers Ribble and Hodder

Fisheries technical staff from the North West Central Area of the National Rivers Authority (NRA) currently provide a service for the ageing of salmon scales from fish caught by anglers on the Rivers Ribble and Hodder in order to gather information on the biological characteristics of the salmon population on the River Ribble system in terms of weight, freshwater age and sea age. At the beginning of each fishing season, scale envelopes are distributed by the NRA to angling clubs and some individual anglers. Scales taken from salmon caught on the rivers are returned to the NRA Central Area Office by the anglers, or more often, by NRA bailiffs. The age of each fish caught is then determined by the identification and counting of annuli for both the river and sea zones on the scale. Information is provided by the angler on the scale packet concerning the length and weight of the fish caught, and the date, location and method of capture. Both this information and the age of the fish is recorded on a database. These data can be used to investigate the distribution, and exploitation patterns of the different age classes of the salmon stock within the river system. This report is principally concerned with the scale samples received in 1994, although comparison is also made with samples from 1993 and 1992. References to data will all relate to that received in 1994 unless an alternate year is stated.

Otolith morphometrics and population structure of Pacific sardine (Sardinops sagax) along the west coast of North America

The broad distribution of Pacific sardine (Sardinops sagax) along the Pacif ic coast of North America makes it difficult for fisheries managers to identify regional stocks of this dominant small pelagic species. An investigation of morphometric characteristics of otoliths of Pacific sardine across most of their range revealed regional differences in populations. In a survey of over 2000 otoliths, all ages (with an emphasis on age-1 recruits) were compared. Principal components analysis, multivariate analysis of variance, and a novel method derived from regression and residuals calculations, termed perimeter-weight profiles (PWPs), revealed otolith similarities and differences. The results of the different approaches to statistical comparisons did not always agree. Sardine otoliths from Mexican waters were generally lighter and more lobate than those from U.S. and Canadian populations. Age-1 otoliths from northern California in 2006–07 tended to be heavier and smoother than those from other areas, including year-class cohorts from southern California. Comparisons of age-groups and year-classes of northern California otoliths with the use of the PWP models indicated signif icant trends in year-to-year patterns. In conjunction with other established indices of population structure, otolith PWPs are a useful tool for identifying local and regional stocks of Pacific sardine and may help distinguish populations of other fish species as well.

Variation in movement patterns of red drum (Sciaenops ocellatus) inferred from conventional tagging and ultrasonic telemetry

We used 25 years of conventional tagging data (n= 6173 recoveries) and 3 years of ultrasonic telemetry data (n=105 transmitters deployed) to examine movement rates and directional preferences of four age classes of red drum (Sciaenops ocellatus) in estuarine and coastal waters of North Carolina. Movement rates of conventionally tagged red drum were dependent on the age, region, and season of tagging. Age-1 and age-2 red drum tagged along the coast generally moved along the coast, whereas fish tagged in oligohaline waters far from the coast were primarily recovered in coastal regions in fall months. Adult (age-4+) red drum moved from overwintering grounds on the continental shelf through inlets into Pamlico Sound in spring and summer months and departed in fall. Few tagged red drum were recovered in adjacent states (0.6% of all recoveries); however, some adult red drum migrated seasonally from overwintering grounds in coastal North Carolina northward to Virginia in spring, returning in fall. Age-2 transmitter-tracked red drum displayed seasonal emigration from a small tributary, but upstream and downstream movements within the tributary were correlated with fluctuating salinity regimes and not season. Large-scale conventional tagging and ultrasonic telemetry programs can provide valuable insights into the complex movement patterns of estuarine fish.

Abundance, condition, and diet of juvenile Pacific ocean perch (Sebastes alutus) in the Aleutian Islands

T he relative value of pelagic habitat for three size classes of juvenile Pacific ocean perch (Sebastes alutus) was investigated by comparing their abundance and condition in two areas of the Aleutian Islands. Diet, zooplankton biomass, and water column temperatures were examined as potential factors affecting observed differences. Juvenile Pacific ocean perch abundance and condition, and zooplankton biomass varied significantly between areas, whereas juvenile Pacific ocean perch diet varied only by size class. Observed differences in fish condition may have been due to the quantity or quality of pelagic prey items consumed. For the delineation of essential demersal fish habitat, important ecological features of the pelagic habitat must therefore be considered.

Degeneration of postovulatory follicles in the Iberian sardine Sardina pilchardus: structural changes and factors affecting resorption

Inaccuracy in the aging of postovulatory follicles (POFs) and in estimating the effect of temperature on the resorption rate of POFs may introduce bias in the determination of the daily spawning age classes with the daily egg production method (DEPM). To explore the above two bias problems with f ield-collected European pilchard (Sardina pilchardus, known regionally as the Iberian sardine), a method was developed in which the time elapsed from spawning (POF age) was estimated from the size of POFs (i.e., from the cross-sectional area in histological sections). The potential effect of the preservative type and embedding material on POF size and the effect of ambient water temperature on POF resorption rate are taken into account with this method. A highly significant loglinear relationship was found between POF area and age; POF area shrank by approximately 50% per day. POFs were also shown to shrink faster at higher temperatures (approximately 3% per degree), but this temperature effect is unlikely to be an important source of bias in the assignment of females to daily spawning classes. The embedding material was also shown to influence the size of POFs, the latter being significantly larger in resin than in paraffin sections. In conclusion, the size of POFs provides an indirect, reliable estimation of the time elapsed from spawning and may thus be used to test both the validity of POF staging criteria for identifying daily classes of spawners and the effect of other factors (such as temperature and laboratory processing) in applications of the DEPM to S. pilchardus and other fish species.

Estimating consumption rates of juvenile sandbar sharks (Carcharhinus plumbeus) in Chesapeake Bay, Virginia, using a bioenergetics model*

Using a bioenergetics model, we estimated daily ration and seasonal prey consumption rates for six age classes of juvenile sandbar sharks (Carcharhinus plumbeus) in the lower Chesapeake Bay summer nursery area. The model, incorporating habitat and species-specific data on growth rates, metabolic rate, diet composition, water temperature (range 16.8−27.9°C), and population structure, predicted mean daily rations between 2.17 ±0.03 (age-0) and 1.30 ±0.02 (age-5) % body mass/day. These daily rations are higher than earlier predictions for sandbar sharks but are comparable to those for ecologically similar shark species. The total nursery population of sandbar sharks was predicted to consume ~124,000 kg of prey during their 4.5 month stay in the Chesapeake Bay nursery. The predicted consumption rates support the conclusion that juvenile sandbar sharks exert a lesser top-down effect on the Chesapeake Bay ecosystem than do teleost piscivores and hu

Application of two methods for determining diet of northern fur seals (Callorhinus ursinus)

Examination of hard parts recovered from scats (feces) is currently the most common method for determining the diet of pinnipeds. However, large or sharp prey remains may be spewed (regurgitated) biasing prey composition and size estimations in diet studies based on scats. Percent frequency of occurrence (FO%) and age or size of selected prey remains recovered from northern fur seal (Callorhinus ursinus) scat (n=3444) and spew samples (n=267) collected from rookeries on St. George Island and St. Paul Island, Alaska, between 1990 and 2000 were compared to determine if a bias in prey composition and age or size estimations existed between scats and spews. Overall prey composition was similar between sample type and location, but the relative FO% of primary prey (≥5%) varied by sample type and location. Age or size estimates of walleye pollock (Theragra chalcogramma) and of two species of gonatid squids (Gonatopsis borealis and Berryteuthis magister) were significantly larger in spews than in scats. Observed differences in FO% and estimated age or size of prey species whose remains were found in scats and spews likely result from size-selective digestion of prey remains. Scats were biased toward smaller prey remains, whereas spews were biased toward larger prey remains and cephalopod beaks. The percent overlap between age classes of walleye pollock caught by the commercial trawl fishery and age classes of walleye pollock consumed by northern fur seals varied noticeably between sample types for both islands (scats: St. George=15. 5%; St. Paul=4.1%; spews: St. George=94.6%; St. Paul=89.6%). These results demonstrate that the inclusion of multiple sampling methods allows for a more accurate assessment of northern fur seal prey occurrence and prey age and size.