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Academic literature on the topic 'Real ternary forms'

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Published: 10 March 2023

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Journal articles on the topic "Real ternary forms"

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Harris, William R. "Real Even Symmetric Ternary Forms." Journal of Algebra 222, no. 1 (December 1999): 204–45. http://dx.doi.org/10.1006/jabr.1998.8012.

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Michałek, Mateusz, Hyunsuk Moon, Bernd Sturmfels, and Emanuele Ventura. "Real rank geometry of ternary forms." Annali di Matematica Pura ed Applicata (1923 -) 196, no. 3 (August 23, 2016): 1025–54. http://dx.doi.org/10.1007/s10231-016-0606-3.

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CHAN, Wai-kiu, Myung-Hwan KIM, and S. RAGHAVAN. "Ternary universal integral quadratic forms over real quadratic fields." Japanese journal of mathematics. New series 22, no. 2 (1996): 263–73. http://dx.doi.org/10.4099/math1924.22.263.

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Raka, Madhu. "Inhomogeneous minima of a class of ternary quadratic forms." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 55, no. 3 (December 1993): 334–54. http://dx.doi.org/10.1017/s144678870003408x.

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AbstractLet denote the kth successive inhomogeneous minima for positive values of real indefinite ternary quadratic forms of type (2, 1). Here it is proved that for the class of zero forms, All the critical forms have also been obtained. is already known. For non-zero forms it is proved that .
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Krásenský, Jakub, Magdaléna Tinková, and Kristýna Zemková. "There are no universal ternary quadratic forms over biquadratic fields." Proceedings of the Edinburgh Mathematical Society 63, no. 3 (August 2020): 861–912. http://dx.doi.org/10.1017/s001309152000022x.

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AbstractWe study totally positive definite quadratic forms over the ring of integers $\mathcal {O}_K$ of a totally real biquadratic field $K=\mathbb {Q}(\sqrt {m}, \sqrt {s})$. We restrict our attention to classic forms (i.e. those with all non-diagonal coefficients in $2\mathcal {O}_K$) and prove that no such forms in three variables are universal (i.e. represent all totally positive elements of $\mathcal {O}_K$). Moreover, we show the same result for totally real number fields containing at least one non-square totally positive unit and satisfying some other mild conditions. These results provide further evidence towards Kitaoka's conjecture that there are only finitely many number fields over which such forms exist. One of our main tools are additively indecomposable elements of $\mathcal {O}_K$; we prove several new results about their properties.
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Chan, Wai Kiu, and Maria Ines Icaza. "Positive definite almost regular ternary quadratic forms over totally real number fields." Bulletin of the London Mathematical Society 40, no. 6 (September 2, 2008): 1025–37. http://dx.doi.org/10.1112/blms/bdn085.

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BENNETT, MICHAEL A., SANDER R. DAHMEN, MAURICE MIGNOTTE, and SAMIR SIKSEK. "Shifted powers in binary recurrence sequences." Mathematical Proceedings of the Cambridge Philosophical Society 158, no. 2 (January 8, 2015): 305–29. http://dx.doi.org/10.1017/s0305004114000681.

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AbstractLet {uk} be a Lucas sequence. A standard technique for determining the perfect powers in the sequence {uk} combines bounds coming from linear forms in logarithms with local information obtained via Frey curves and modularity. The key to this approach is the fact that the equation uk = xn can be translated into a ternary equation of the form ay2 = bx2n + c (with a, b, c ∈ ℤ) for which Frey curves are available. In this paper we consider shifted powers in Lucas sequences, and consequently equations of the form uk = xn+c which do not typically correspond to ternary equations with rational unknowns. However, they do, under certain hypotheses, lead to ternary equations with unknowns in totally real fields, allowing us to employ Frey curves over those fields instead of Frey curves defined over ℚ. We illustrate this approach by showing that the quaternary Diophantine equation x2n±6xn + 1 = 8y2 has no solutions in positive integers x, y, n with x, n > 1.
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Fuller, Carl W., Shiv Kumar, Mintu Porel, Minchen Chien, Arek Bibillo, P. Benjamin Stranges, Michael Dorwart, et al. "Real-time single-molecule electronic DNA sequencing by synthesis using polymer-tagged nucleotides on a nanopore array." Proceedings of the National Academy of Sciences 113, no. 19 (April 18, 2016): 5233–38. http://dx.doi.org/10.1073/pnas.1601782113.

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DNA sequencing by synthesis (SBS) offers a robust platform to decipher nucleic acid sequences. Recently, we reported a single-molecule nanopore-based SBS strategy that accurately distinguishes four bases by electronically detecting and differentiating four different polymer tags attached to the 5′-phosphate of the nucleotides during their incorporation into a growing DNA strand catalyzed by DNA polymerase. Further developing this approach, we report here the use of nucleotides tagged at the terminal phosphate with oligonucleotide-based polymers to perform nanopore SBS on an α-hemolysin nanopore array platform. We designed and synthesized several polymer-tagged nucleotides using tags that produce different electrical current blockade levels and verified they are active substrates for DNA polymerase. A highly processive DNA polymerase was conjugated to the nanopore, and the conjugates were complexed with primer/template DNA and inserted into lipid bilayers over individually addressable electrodes of the nanopore chip. When an incoming complementary-tagged nucleotide forms a tight ternary complex with the primer/template and polymerase, the tag enters the pore, and the current blockade level is measured. The levels displayed by the four nucleotides tagged with four different polymers captured in the nanopore in such ternary complexes were clearly distinguishable and sequence-specific, enabling continuous sequence determination during the polymerase reaction. Thus, real-time single-molecule electronic DNA sequencing data with single-base resolution were obtained. The use of these polymer-tagged nucleotides, combined with polymerase tethering to nanopores and multiplexed nanopore sensors, should lead to new high-throughput sequencing methods.
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Lin, Yixin, Qin Fu, Jie Zhu, Julie M. Miller, and Jennifer E. Van Eyk. "Development of a Qualitative Sequential Immunoassay for Characterizing the Intrinsic Properties of Circulating Cardiac Troponin I." Clinical Chemistry 56, no. 8 (August 1, 2010): 1307–19. http://dx.doi.org/10.1373/clinchem.2009.135186.

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BACKGROUND With myocardial infarction (MI), cardiac troponin is released from the heart into circulation, where it can be detected with immunoassays independently quantifying cardiac troponin I (cTnI) or cTnT. There is, however, no single immunoassay that sequentially probes the posttranslational modification status of cTnI or directly characterizes whether circulating cTnI is bound to cTnC and/or cTnT. Here we describe the development of a qualitative immunoassay to directly probe the primary and ternary structure of circulating cTnI through diffractive optics technology (dotLab® System, Axela). METHODS Anti-cTnI antibody 8I-7 was immobilized on a patterned sensor to capture cTnI. One or more detector antibodies were sequentially introduced to probe for amino acid sequence integrity or phosphorylation status of cTnI, or its association with cTnC and/or cTnT. Respective immunocaptures were recorded as real-time diffractive intensities (DIs), and the DI differences were analyzed. Each immunodetection was independent of the others but was done in a single sequential assay. RESULTS This diffraction-based immunoassay successfully characterized cTnI. The unamplified assay determined whether cTnI was degraded at N-terminus and/or C-terminus or phosphorylated. Sequential application of multiple detector antibodies without an antibody-stripping step enables real-time interrogation of 5 different epitopes of cTnI, or direct detection of the cTn complex (cTnI–cTnC–cTnT) in a single sequential assay. Finally, this assay was optimized with amplification to directly detect circulating cTnI bound to cTnC and cTnT in serum from an MI patient. CONCLUSIONS The dot® Immunoassay is the first qualitative sequential immunoassay to address the direct interactions of the troponin subunits and various modified forms of cTnI.
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Koyama, Toshiyuki, and Hidehiro Onodera. "Phase-Field Modeling of the Microstructure Evolutions in Fe-Cu Base Alloys." Materials Science Forum 539-543 (March 2007): 2383–88. http://dx.doi.org/10.4028/www.scientific.net/msf.539-543.2383.

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The phase transformations and the microstructure developments in Fe-Cu base alloys during isothermal aging are simulated based on the phase-field method. Since the chemical free energy used in this simulation is obtained from the thermodynamic database of phase diagrams, the calculated microstructure changes are directly related to the phase diagram of the real alloy system. Firstly the phase decomposition and the microstructure changes in the Fe-Cu binary alloy system are demonstrated as the simple example of the phase-field modeling, i.e., the phase decomposition in bcc phase where the Cu-rich phase forms, the structural phase transformation from bcc to fcc phase in the Cu-rich nano-particle, and the shape change of fcc-Cu precipitates from sphere to rod. Secondly, the phase decomposition in bcc phase of the multi-component alloys such as the Fe-Cu-X (X=Mn,Ni) ternary system and the Fe-Cu-Mn-Ni quaternary alloy is simulated. At the early stage of aging, the Cu-rich zone with bcc structure begins to nucleate, and the component X (=Mn, Ni) is partitioned to the Cu-rich phase. When the Cu composition in the precipitate reaches equilibrium, the component X inside the precipitates moves toward to the interface region between the precipitate and matrix. Finally, there appears the shell structure that the Cu precipitates surrounded by the thin layer with high concentration of component X.
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Dissertations / Theses on the topic "Real ternary forms"

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BANCHI, MAURIZIO. "Typical Ranks of ternary cubic forms over R." Doctoral thesis, 2013. http://hdl.handle.net/2158/808076.

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In this thesis we consider the problem of the classification of real ternary cubics, that is, plane cubic curves with real coefficients, with respect to an arithmetic invariant, the rank, and we give the decomposition of each real ternary cubic form. We prove a theorem that characterizes the reducible cubic which factors as a product of imaginary conic and a real line with respect to rank and this is a new result in the theory of real plane cubic curves.
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MACCIONI, MAURO. "Tensor rank and eigenvectors." Doctoral thesis, 2017. http://hdl.handle.net/2158/1077336.

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I investigate on the number t of real eigenvectors of a real symmetric tensor. In particular, given a homogeneous polynomial f of degree d in 3 variables, I prove that t is greater or equal than 2c+1, if d is odd, and t is greater or equal than max(3,2c+1), if d is even, where c is the number of ovals in the zero locus of f. About binary forms, I prove that t is greater or equal than the number of real roots of f. Moreover, the above inequalities are sharp for binary forms of any degree and for cubic and quartic ternary forms. Previously, I worked on the computation of the real ranks of real binary forms of degree four and five with assigned complex rank.
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Conference papers on the topic "Real ternary forms"

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Dickey, F. M., B. V. K. Vijaya Kumar, L. A. Romero, and J. M. Connelly. "Complex ternary matched filters yielding high signal-to-noise ratios." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.mff6.

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Matched spatial filters provide the highest output signal-to-noise ratio in pattern recognition applications but have not become practicable due to the complex nature of the spatial filters required. Lately much research effort has been devoted to methods of avoiding complex filters. This research has suggested binary and ternary real valued approximations to the phase-only filter. Dickey and Hansche1 suggested a quad-phase-only filter that does not suffer from having the simple symmetry of real valued filters and can have improved signal-to-noise ratio. The authors suggest a complex ternary matched filter (CTMF). This CTMF filter function has the form: where IR1 and IR2 are support functions, sr and S1 are the real and imaginary parts of the object function Fourier transform, and β is the threshold line angle. The algorithm introduced by Kumar and Bahri2 can be used to optimize this filter. The optimized CTMF produces signal-to-noise ratios very near the optimal phase-only filter and does not suffer from having the simple symmetry of real valued filters.
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Malerba, Lorenzo, Eric van Walle, Christophe Domain, Stephanie Jumel, and Jean-Claude Van Duysen. "State of Advancement of the International REVE Project: Computational Modelling of Irradiation-Induced Hardening in Reactor Pressure Vessel Steels and Relevant Experimental Validation Programme." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22260.

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The REVE (REactor for Virtual Experiments) project is an international joint effort aimed at developing multiscale modelling computational toolboxes capable of simulating the behaviour of materials under irradiation at different time and length scales. Well grounded numerical techniques such as molecular dynamics (MD) and Monte Carlo (MC) algorithms, as well as rate equation (RE) and dislocation-defect interaction theory, form the basis on which the project is built. The goal is to put together a suite of integrated codes capable of deducing the changes in macroscopic properties starting from a detailed simulation of the microstructural changes produced by irradiation in materials. To achieve this objective, several European laboratories are closely collaborating, while exchanging data with American and Japanese laboratories currently pursuing similar approaches. The material chosen for the first phase of this project is reactor pressure vessel (RPV) steel, the target macrosocopic magnitude to be predicted being the yield strenght increase (Δσy) due, essentially, to irradiation-enhanced formation of intragranular solute atom precipitates or clouds, as well as irradiation induced defects in the matrix, such as point defect clusters and dislocation loops. A description of the methodological approach used in the project and its current state is given in the paper. The development of the simulation tools requires a continuous feedback from ad hoc experimental data. In the framework of the REVE project SCK·CEN has therefore performed a neutron irradiation campaign of model alloys of growing complexity (from pure Fe to binary and ternary systems and a real RPV steel) in the Belgian test reactor BR2 and is currently carrying on the subsequent materials characterisation using its hot cell facilities. The paper gives the details of this experimental programme — probably the first large-scale one devoted to the validation of numerical simulation tools — and presents and discusses the first available results, with a view to their use as feedback for the improvement of the computational modelling.
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