2,568 research outputs found
DETERMINANT COMPUTATIONS FOR SOME CLASSES OF TOEPLITZ-HANKEL MATRICES
No full textThe purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of the form (a(i-j) +/- a(i+j+1-k))(i,j=0...N-1) with k fixed. We will show that this example as well as some general classes of operators have expansions that are similar to those that appear in the Strong Szego Limit Theorem. We also obtain exact identitities for some of the determinants that are analogous to the one derived independently by Geronimo and Case and by Borodin and Okounkov for finite Toeplitz matrices. These problems were motivated by certain statistical quantities that appear in random matrix theory.X1110sciescopu
Trace conditions for regular spectral behavior of vector-valued analytic functions
No full textA new class of Banach algebra valued functions is identified for which the logarithmic residue with respect to a Cauchy domain Delta vanishes (if and) only if the functions take invertible values in Delta. Trace conditions and the extraction of elementary factors of the type e - p + (lambda - alpha)p play an important role. The class contains the Fredholm operator valued functions and the Banach algebra valued functions possessing a simply meromorphic resolvent as special instances. An example is given to show that new ground is covered and a long standing open problem is discussed from a fresh angle. (C) 2008 Elsevier Inc. All rights reserved.X1157sciescopu
Arnold A. T. Ehrhardt, Politische Metaphysik von Solon bis Augustin. 3. Band : Civitas Dei. Tübingen, J. C. Β. Mohr, 1969
No full textSchwartz Jacques. Arnold A. T. Ehrhardt, Politische Metaphysik von Solon bis Augustin. 3. Band : Civitas Dei. Tübingen, J. C. Β. Mohr, 1969. In: Revue d'histoire et de philosophie religieuses, 50e année n°1,1970. p. 79
Contribution à l'histoire des Idées politiques. A propos de Arnold A. T. Ehrhardt, Politische Metaphysik von Solon bis Augustin, 1959.
No full textFreund Julien. Contribution à l'histoire des Idées politiques. A propos de Arnold A. T. Ehrhardt, Politische Metaphysik von Solon bis Augustin, 1959. In: Revue d'histoire et de philosophie religieuses, 40e année n°1,1960. Le Problème de la Tradition. pp. 58-64
Topramezone and its primary metabolite, topramezone-desmethyl as proposed by Grossman and Ehrhardt (2007).
No full text<p>Topramezone and its primary metabolite, topramezone-desmethyl as proposed by Grossman and Ehrhardt (2007).</p
Vector valued logarithmic residues and the extraction of elementary factors
No full textAn analysis is presented of the circumstances under which, by the extraction of elementary factors, an analytic Banach algebra valued function can be transformed into one taking invertible values only. Elementary factors are generalizations of the simple scalar expressions λ – α, the building blocks of scalar polynomials. In the Banach algebra situation they have the form e – p + (λ – α)p with p an idempotent. The analysis elucidates old results (such as on Fredholm operator valued functions) and yields new insights which are brought to bear on the study of vector-valued logarithmic residues. These are contour integrals of logarithmic derivatives of analytic Banach algebra valued functions. Examples illustrate the subject matter and show that new ground is covered. Also a long standing open problem is discussed from a fresh angle.analytic vector-valued function;annihilating family of idempotents;elementary factor;generalizations of analytic functions;idempotent;integer combination of idempotents;logarithmic residue;plain function;resolving family of traces;topological algebras
Chris T. H. R. Ehrhardt and the Ancient Greek and Roman coins in the Auckland Museum’s numismatic collection
No full textChristoph Traugott Hermann Rudolph Ehrhardt (1937–2001), Associate Professor in Classics at the University of Otago Ōtākou Whakaihu Waka and Honorary Curator for the Greek and Roman coins at Tūhura Otago Museum, was one of the most important figures in the study of ancient numismatics in Aotearoa. Among the many activities of his academic career, Ehrhardt sought to make a record of all the ancient Greek and Roman coins in public collections across the country. As part of this project, Ehrhardt produced a series of unpublished documents describing and identifying 1,285 ancient Greek and Roman coins in the Auckland Museum, completed in 1991 after a nine-year period of sporadic work. Ehrhardt’s extensive contribution in this regard, though previously little known, has recently come to light thanks to the Museum’s ongoing project to further develop its extensive numismatic collections, which comprise approximately 30,000 coins, medals, and other objects from a wide range of historical and cultural contexts. Although Ehrhardt’s specialist focus concerned only a small portion of the overall numismatic collection, his meticulous work left the ancient Greek and Roman coin collection in an excellent position to become the starting point for developing the Auckland Museum’s future management of its numismatic holdings. This article details Ehrhardt’s background, life, and career before moving to focus on his work on the Greek and Roman coin collection, recording the legacy of an important contributor to the study of numismatics at the Auckland Museum
The marine biogeochemistry of dissolved organic carbon and dissolved organic nutrients in the Atlantic Ocean
No full textThe marine biogeochemistry of dissolved organic carbon (DOC) has come underincreased scrutiny because of its involvement in the global carbon cycle andconsequently climate change. Dissolved organic nitrogen (DON) and phosphorus(DOP), which have historically been ignored because of their suggested “biologicalunavailability”, have now received greater attention due to their importance in nutrientcycling, particularly in oligotrophic ecosystems. DOM, a byproduct of photosyntheticproduction, has important ecological significance as a substrate that supportsheterotrophic bacterial growth, thereby causing oxygen consumption and regeneratinginorganic nutrients. In the open ocean the net production of DOC is ultimately due tothe decoupling of biological production and consumption processes. Concentrations ofDOM in the surface oceans, therefore, are controlled by both physical and biologicalprocesses. This research investigates the biological factors that control the distributionsof DOC, DON and DOP in surface waters, the importance of DOC degradation tooxygen consumption, the importance of DON and DOP degradation to remineraliseddissolved inorganic nitrogen (DIN) and dissolved inorganic phosphorus (DIP), and theC:N:P stoichiometry of DOM pool in the Atlantic Ocean. Samples were collected on Atlantic Meridional Transects (AMT) cruise 16 and 17, which crossed the southerntemperate region, the southern subtropical gyre, the equatorial region, the northernsubtropical gyre, and the northern temperate region. This work described here wasperformed as a component of the AMT programme.Concentrations of DOC and TDN were determined using a high-temperature catalyticcombustion technique, and TDP concentrations were determined using a UV oxidationmethod. Concentrations of DON and DOP were estimated as the difference betweenthe independent measurements of TDN and TDP. The results showed that the highestDOM concentrations were found in surface (0-30 m) waters, ranging from 70-80 µMDOC, 4.8-6.5 µM DON and 0.2-0.3 µM DOP, and decreased with increasing waterdepth to 45-55 µM DOC, 2.6-4.0 µM DON and 0.04-0.05 µM DOP at 300 m. Thelowest DOM concentrations were observed in the deep (>1000 m) ocean, averaging 44µM DOC, 2.3 µM DON and 0.02 µM DOP. In the upper 300 m, the concentrations ofsemilabile (and labile) DOC decreased by 45-95% from the surface values. DON andDOP were the dominant components of the total dissolved nutrient pools in the upper50 m, accounting for up to 99% and 80% of the TDN and TDP pools, respectively. Inthe upper 300 m, semilabile (and labile) DON and DOP decreased by 50-65% and90-95% from the surface values, respectively.The decoupled correlations between DOC/DON/DOP and chlorophyll-a and rates ofcarbon fixation suggested that phytoplankton biomass and rates of primary productionwere not the important controls of the cumulative DOC, DON and DOP. Zooplanktongrazing was hypothesised to be an important factor in regulating the distributions ofDOC, DON and DOP in surface waters. Poor correlations between DOC/DON/DOPand DIN/DIP suggested that inorganic nutrients were not the significant controls inDOC, DON and DOP distributions. N and P were probably retained mainly in theorganic pool in the surface waters due to a hypothesised insufficient functioning of the microbial degradation. If the vertical migration of zooplankton was significant inbringing new nutrients into the surface waters, strong correlations between dissolvedorganic and inorganic nutrients should not be anticipated. Prochlorococcus spp.abundance was statistically linked with the concentrations of DOC, DON and DOP.The significant correlations may reflect the ability of Prochlorococcus to assimilate thelabile forms of dissolved organic nutrients (including DOC), which may bequantitatively significant in surface waters of the Atlantic Ocean.The C:N, N:P and C:P stoichiometry of the bulk DOM pool deviated from the Redfieldratio of 6:1, 16:1 and 106:1, ranging from 12-18, 20-100 and 300-1400, respectively, inthe upper 300 m, suggesting that the cumulative DOM was rich in C relative to N and P,and N relative to P compared to the Redfield trajectories. The offsets of the C:N:Pstoichiometry relatively to the Redfield ratio were due to nutrient limitations thatimposed on prokaryotic and eukaryotic microbial populations. The C:N:Pstoichiometry of the bulk DOM pool showed an increased trend, with C:N = 12-16,N:P = 20-25, and C:P = 300-350 in the upper 30 m, C:N = 12-18, N:P = 50-100, andC:P = 700-1400 at 300 m, and C:N = 17-24, N:P = 79-132; C:P = 1791-2442 at 1000 m.The differences in the C:N:P stoichiometry of the bulk DOM pool between the upperand deep waters suggested preferential remineralisation of P relative to C and N, and Nrelative to C. A greater remineralisation length scale for DOC relative to DON andDOP produced a long-term, steady flux of C from the surface to the deep ocean.Therefore, CO2 fixed in the upper ocean during planktonic photosynthesis wascontinuously “pumped” into the ocean interior, and stored in the deep ocean up tothousands of years. The C:N, N:P and C:P stoichiometry of the semilabile (and labile)DOM pool generally agreed with the Redfield ratio (C:N = 6; N:P = 16; C:P = 106) inthe upper 30 m. At 100 m C:N ratio was 5-12, C:P ratio was 20-30, and C:P ratio was100-150. At 300 m, C:N ratio was 5-12, N:P ratio was 25-100, and C:P ratio was150-500. The findings suggested that in the upper 300 m, there was no preferential remineralisation between the semilabile (and labile) DOC and DON, however, thesemilabile (and labile) DOP seemed to be preferentially remineralised relative to thesemilabile (and labile) DOC and DON.In the upper thermocline (i.e. above 300 m), DOC degradation was important withrespect to oxygen consumption, contributing to as much as 25% of the apparentoxygen utilization (AOU). The remaining of 75% was attributable to POCdecomposition. However, the AOU contributable to DOC showed a function of latitude,with 15-55% found in the central subtropical Atlantic gyres and 15-25% in theequatorial region. The most likely explanation for the variation of DOC relative toPOC degradation with respect to AOU was the regional variability in the export ofPOC, which was suggested to be highest in the high nutrient regions of the equator andat the poleward margins of the subtropical gyres. As a result, DOC formed animportant contribution to AOU in oligotrophic regions, while POC was the dominantcontrol of AOU in upwelling regions. Some freshly-produced fractions of DON and DOP with turnover times of months toyears were capable of escaping rapid microbial degradation in surface waters andbecame entrained into deep waters via diffusive mixing. Subsequent microbialdegradation of these DON and DOP took place in the thermocline, regeneratinginorganic nutrients. Statistically significant correlations were observed between theDON-to-DIN and DOP-to-DIP relationships. Calculations of the fluxes of dissolvedorganic nutrients relative to inorganic nutrients suggested that in the upper thermocline(i.e. above 300 m), the downward fluxes of DON and DOP contributed to a total of 4%and 5% of the upward fluxes of DIN and DIP, respectively, into the euphotic zone. Theremaining of 95% of the upward dissolved inorganic nutrients fell out of the euphoticzone as particles in order to prevent nutrient accumulation and to maintain nutrientintegrity of the pelagic ecosystem
Inversion of centroskewsymmetric Toeplitz-plus-Hankel Bezoutians
No full textIn this paper, the inverse of a nonsingular, centroskewsymmetric Toeplitz-plus-Hankel Bezoutian B of (even) order n are computed, and a representation of B^(−1) as a sum of a Toeplitz and a Hankel matrix is found. Two possibilities are discussed. In the first one, the problem is reduced to the inversion of two skewsymmetric Toeplitz Bezoutians of order n. In the second one, the problem is tackled via the inversion of two Hankel Bezoutians of half the order n/2. The inversion of Toeplitz or Hankel Bezoutians is the subject of a previous paper [T. Ehrhardt and K. Rost. Resultant matrices and inversion of Bezoutians. Linear Algebra Appl., 439:621–639, 2013.]. Both approaches lead to fast O(n^2) inversion algorithms
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