Academic literature on the topic 'Q-z curve'

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Journal articles on the topic "Q-z curve"

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Dujella, Andrej, and Juan Carlos Peral. "High-rank elliptic curves with torsion induced by Diophantine triples." LMS Journal of Computation and Mathematics 17, no. 1 (2014): 282–88. http://dx.doi.org/10.1112/s1461157014000023.

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AbstractWe construct an elliptic curve over the field of rational functions with torsion group$\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/4\mathbb{Z}$and rank equal to four, and an elliptic curve over$\mathbb{Q}$with the same torsion group and rank nine. Both results improve previous records for ranks of curves of this torsion group. They are obtained by considering elliptic curves induced by Diophantine triples.
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Kim, Seon-Hong. "The number of connected components of certain real algebraic curves." International Journal of Mathematics and Mathematical Sciences 25, no. 11 (2001): 693–701. http://dx.doi.org/10.1155/s0161171201010481.

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For an integern≥2, letp(z)=∏k=1n(z−αk)andq(z)=∏k=1n(z−βk), whereαk,βkare real. We find the number of connected components of the real algebraic curve{(x,y)∈ℝ2:|p(x+iy)|−|q(x+iy)|=0}for someαkandβk. Moreover, in these cases, we show that each connected component contains zeros ofp(z)+q(z), and we investigate the locus of zeros ofp(z)+q(z).
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Heer, Henriette, Gary McGuire, and Oisín Robinson. "JKL-ECM: an implementation of ECM using Hessian curves." LMS Journal of Computation and Mathematics 19, A (2016): 83–99. http://dx.doi.org/10.1112/s1461157016000231.

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We present JKL-ECM, an implementation of the elliptic curve method of integer factorization which uses certain twisted Hessian curves in a family studied by Jeon, Kim and Lee. This implementation takes advantage of torsion subgroup injection for families of elliptic curves over a quartic number field, in addition to the ‘small parameter’ speedup. We produced thousands of curves with torsion$\mathbb{Z}/6\mathbb{Z}\oplus \mathbb{Z}/6\mathbb{Z}$and small parameters in twisted Hessian form, which admit curve arithmetic that is ‘almost’ as fast as that of twisted Edwards form. This allows JKL-ECM to compete with GMP-ECM for finding large prime factors. Also, JKL-ECM, based on GMP, accepts integers of arbitrary size. We classify the torsion subgroups of Hessian curves over$\mathbb{Q}$and further examine torsion properties of the curves described by Jeon, Kim and Lee. In addition, the high-performance curves with torsion$\mathbb{Z}/2\mathbb{Z}\oplus \mathbb{Z}/8\mathbb{Z}$of Bernsteinet al. are completely recovered by the$\mathbb{Z}/4\mathbb{Z}\oplus \mathbb{Z}/8\mathbb{Z}$family of Jeon, Kim and Lee, and hundreds more curves are produced besides, all with small parameters and base points.
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DELBOURGO, DANIEL, and ANTONIO LEI. "Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction." Mathematical Proceedings of the Cambridge Philosophical Society 160, no. 1 (October 15, 2015): 11–38. http://dx.doi.org/10.1017/s0305004115000535.

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AbstractLet$E_{/{\mathbb{Q}}}$be a semistable elliptic curve, andp≠ 2 a prime of bad multiplicative reduction. For each Lie extension$\mathbb{Q}$FT/$\mathbb{Q}$with Galois groupG∞≅$\mathbb{Z}$p⋊$\mathbb{Z}$p×, we constructp-adicL-functions interpolating Artin twists of the Hasse–WeilL-series of the curveE. Through the use of congruences, we next prove a formula for the analytic λ-invariant over the false Tate tower, analogous to Chern–Yang Lee's results on its algebraic counterpart. If one assumes the Pontryagin dual of the Selmer group belongs to the$\mathfrak{M}_{\mathcal{H}}$(G∞)-category, the leading terms of its associated Akashi series can then be computed, allowing us to formulate a non-commutative Iwasawa Main Conjecture in the multiplicative setting.
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Elahi, Kashif, Ali Ahmad, and Roslan Hasni. "Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices." Mathematics 6, no. 12 (December 4, 2018): 301. http://dx.doi.org/10.3390/math6120301.

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Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this paper we discuss eccentric topological indices of zero divisor graphs of commutative rings Z p 1 p 2 × Z q , where p 1 , p 2 , and q are primes. To enhance the importance of these indices a construction algorithm is also devised for zero divisor graphs of commutative rings Z p 1 p 2 × Z q .
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Hile, G. N., and W. E. Pfaffenberger. "Idempotents in Complex Banach Algebras." Canadian Journal of Mathematics 39, no. 3 (June 1, 1987): 625–30. http://dx.doi.org/10.4153/cjm-1987-030-1.

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The concept of the spectrum of A relative to Q, where A and Q commute and are elements in a complex Banach algebra with identity I, was developed in [1]. A complex number z is in the Q-resolvent set of A if and only if is invertible in otherwise, z is in the Q-spectrum of A, or spectrum of A relative to Q. One result from [1] was the following.THEOREM. Suppose no points in the ordinary spectrum of Q have unit magnitude. Let C be a simple closed rectifiable curve which lies in the Q-resolvent of A, and let*where P is defined asxs•
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Howe, Lawrence. "Twisted Hasse-Weil L-Functions and the Rank of Mordell-Weil Groups." Canadian Journal of Mathematics 49, no. 4 (August 1, 1997): 749–71. http://dx.doi.org/10.4153/cjm-1997-037-7.

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AbstractFollowing a method outlined by Greenberg, root number computations give a conjectural lower bound for the ranks of certain Mordell–Weil groups of elliptic curves. More specifically, for PQn a PGL2(Z/pnZ)–extension of Q and E an elliptic curve over Q, define the motive E ⊗ ρ, where ρ is any irreducible representation of Gal(PQn /Q). Under some restrictions, the root number in the conjectural functional equation for the L-function of E ⊗ ρ is easily computable, and a ‘–1’ implies, by the Birch and Swinnerton–Dyer conjecture, that ρ is found in E(PQn) ⊗ C. Summing the dimensions of such ρ gives a conjectural lower bound ofp2n–p2n–1–p–1for the rank of E(PQn).
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Vitenti, Sandro D. P., and Mariana Penna-Lima. "How well can the evolution of the scale factor be reconstructed by the current data?" Proceedings of the International Astronomical Union 10, S306 (May 2014): 219–22. http://dx.doi.org/10.1017/s1743921314011004.

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AbstractDistance measurements are currently the most powerful tool to study the expansion history of the universe without assuming its matter content nor any theory of gravitation. In general, the reconstruction of the scale factor derivatives, such as the deceleration parameter q(z), is computed using two different methods: fixing the functional form of q(z), which yields potentially biased estimates, or approximating q(z) by a piecewise nth-order polynomial function, whose variance is large. In this work, we address these two methods by reconstructing q(z) assuming only an isotropic and homogeneous universe. For this, we approximate q(z) by a piecewise cubic spline function and, then, we add to the likelihood function a penalty factor, with scatter given by σrel. This factor allows us to vary continuously between the full n knots spline, σrel → ∞, and a single linear function, σrel → 0. We estimate the coefficients of q(z) using the Monte Carlo approach, where the realizations are generated considering ΛCDM as a fiducial model. We apply this procedure in two different cases and assuming four values of σrel to find the best balance between variance and bias. First, we use only the Supernova Legacy Survey 3-year (SNLS3) sample and, in the second analysis, we combine the type Ia supernova (SNeIa) likelihood with those of baryonic acoustic oscillations (BAO) and Hubble function measurements. In both cases we fit simultaneously q(z) and 4 nuisance parameters of the supernovae, namely, the magnitudes $\mathcal{M}$1 and $\mathcal{M}$2 and the light curve parameters α and β.
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Dujella, Andrej, Ivica Gusić, and Petra Tadić. "The rank and generators of Kihara’s elliptic curve with torsion $\mathbf{Z}/4\mathbf{Z}$ over $\mathbf{Q}(t)$." Proceedings of the Japan Academy, Series A, Mathematical Sciences 91, no. 8 (August 2015): 105–9. http://dx.doi.org/10.3792/pjaa.91.105.

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BHAVE, AMALA, and LACHIT BORA. "ON THE SELMER GROUP OF A CERTAIN -ADIC LIE EXTENSION." Bulletin of the Australian Mathematical Society 100, no. 2 (February 27, 2019): 245–55. http://dx.doi.org/10.1017/s0004972719000108.

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Let $E$ be an elliptic curve over $\mathbb{Q}$ without complex multiplication. Let $p\geq 5$ be a prime in $\mathbb{Q}$ and suppose that $E$ has good ordinary reduction at $p$. We study the dual Selmer group of $E$ over the compositum of the $\text{GL}_{2}$ extension and the anticyclotomic $\mathbb{Z}_{p}$-extension of an imaginary quadratic extension as an Iwasawa module.
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Dissertations / Theses on the topic "Q-z curve"

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Forni, Fabio. "Investigating the axial response of pile foundations for offshore wind turbines." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017.

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I crescenti problemi legati ai cambiamenti climatici rendono l'impiego delle energie rinnovabili sempre più interessante. In questa ottica, in Germania si sta pianificando di aumentare la produzione di energia pulita attraverso lo sfruttamento dell’energia eolica. Nuovi impianti di turbine eoliche sono previsti nel Mare del Nord in acque medio profonde (25-45m) dove la parte immersa della struttura della turbina eolica (chiamata sottostruttura) è spesso costituita da una struttura jacket (traliccio) o tripod (a treppiedi). Questo tipo di sottostrutture trasmettono principalmente carichi assiali alle fondazioni (in genere fondazioni su palo), e il carico a trazione è la forza che maggiormente ne influenza il dimensionamento. Molte compagnie energetiche tedesche sono interessate a migliorare l’efficienza e i costi dei loro impianti eolici e, per questo, incaricano università ed istituti di ricerca (come il Fraunhofer IWES) per indagarne gli aspetti, come ad esempio il comportamento delle fondazioni offshore. All’autore di questa tesi è stata data l’opportunità di studiare e lavorare al Fraunhofer IWES e perciò questa tesi tratterà del compramento di pali caricati assialmente e staticamente pensati per sottostrutture jacket o tripod per turbine eoliche. Nello studio effettuato per questa tesi, i dati seprimentali, ottenuti da una campagna sperimentale condotta (in larga scala 1:10 1:5) su pali infissi in terreno sabbioso, sono confrontati attraverso l’impiego delle load-transfer curves (funzioni che descrivono il comportamento d’interfaccia palosuolo) usando sia un’approccio classico (fornito dal metodo di calcolo API Main Text) sia approcci più recenti (dati dai metodi di calcolo CPT). Uno script Matlab creato appositamente dall’autore di questa tesi riesce ad implementare 11 diversi tipi di load-transfer curves. Il lavoro di tesi si conclude con un esempio pratico in grado di fornire un’idea di come questo script può essere usato nella progettazione.
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Pan, Cheng-Chan, and 潘成展. "A Study of the t-z and q-z Curves of Shaft Socketed in Soft Rock." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/68691280664675960778.

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碩士
義守大學
土木與生態工程學系碩士班
95
The bearing capacity of pile socketed into soft rock was still not understood well nowadays. In this thesis, compression and tension pile loading tests of the instrumented bored piles were conducted at the soft rock formation site. The unconfined compression strength of soft rock range from 441 kPa to 1297 kPa, its average is about 903 kPa. The test site was located at Hsinchu County, Taiwan. The test data of those two load tests, tensile and compressive loading, were used to investigate the bearing capacity and mechanism of shaft socketed into soft rock. The compression and tension test piles dimension are 800 mm in diameter and 24 m in length. The results of those two pile tests show that the instrumented data of rebar stressmeter of pile sockted into soft rock were significant difference under tension and compression loading conditions. Beside, the elastic modulus of concrete Ec of pile were discussed in detail. Strain-dependent Ec were recommended to calculate the load transfer of pile. The unit skin friction is conducted based on the load distribution along the pile shaft. These curves are the so called t-z curves. The analysis results of the compression pile showed that the unit skin friction of the soft rock could be divided into three distinct phases: a linear phase, nonlinear phase (transition phase) and strain hardening phase. The maximum unit skin friction of this soft rock was about 16 t/m2. According to the q-z curve, a significant mobilization of the base resistance was observed in this test pile. A maximum end resistance of 749 t/m2 was observed under the maximum applied load of 1000 ton. The tension pile analysis results indicated that the t-z curves were with the similar trend. The maximum unit tension skin friction of this soft rock was about 17.4 t/m2.
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Book chapters on the topic "Q-z curve"

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Jia, Junbo. "Axial Force–Displacement of Piles: t-z and Q-z Curve." In Soil Dynamics and Foundation Modeling, 521–57. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-40358-8_17.

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Adam, John A. "Diffraction Catastrophes." In Rays, Waves, and Scattering. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691148373.003.0006.

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This chapter discusses the mathematics of diffraction catastrophes, focusing on the wavefront associated with a monochromatic wave with Q(x, y, f (x, y)) as a point on the wavefront surface and P (X, Y, Z) as a movable observation point. Optical caustics refer to surfaces (in space) and curves (in the plane) where light rays are focused. Caustics can be classified mathematically as the elementary catastrophes of singularity theory. In the plane, the classification gives two singularities: smooth caustic curves, which are “fold” catastrophes, and points where two fold caustics meet on opposite sides of a common tangent, which are “cusp” catastrophes. After providing an overview of the basic geometry of the fold and cusp catastrophes, the chapter considers the Fresnel integrals and the fold diffraction catastrophe. In particular, it examines the rainbow as a fold catastrophe, Airy integral in the complex plane, and the nature of the notation Ai(X).
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Conference papers on the topic "Q-z curve"

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Li, Hui, Muk Chen Ong, Bernt J. Leira, and Dag Myrhaug. "Dynamic Analysis of Offshore Monopile Wind Turbine Including the Effect of Scour." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83721.

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An engineering approach to dynamic analysis of an offshore monopile wind turbine is presented in this paper. The interactions between the foundation and the soil are simulated by nonlinear springs, which stiffnesses are obtained from the axial load transfer (t-z) curve, the tip load-displacement (Q-z) curve and the lateral load-deflection (p-y) curve. Three types of soil conditions are considered in the simulations; 100% sand layer, 50% sand layer (top) and 50% clay layer (bottom), as well as 100% clay layer. Wind, wave and current loads on the wind turbine in operational conditions are taken into account. The variation of the dynamic responses of the wind turbine due to the effect of scour is investigated by comparing the results between the cases with and without scour.
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Ong, Muk Chen, Hui Li, Bernt J. Leira, and Dag Myrhaug. "Dynamic Analysis of Offshore Monopile Wind Turbine Including the Effects of Wind-Wave Loading and Soil Properties." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10527.

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An engineering approach to dynamic analysis of an offshore monopile wind turbine is presented in this paper. The wind-wave coupling for shallow water conditions is considered. Different wind, wave and current loads on the wind turbine within the cut-in and cut-off conditions are taken into account. The hydrodynamic loading is computed based on the corresponding sea-states. The interaction between the foundation and the soil is simulated by nonlinear springs, which stiffness properties are obtained from the axial load transfer (t-z) curve, the tip load-displacement (Q-z) curve and the lateral load-deflection (p-y) curve. Three types of soil conditions are considered in the simulations, i.e., 100% sand layer, 50% sand layer (top) and 50% clay layer (bottom), as well as 100% clay layer. For a given current speed, the variations of the static and the dynamic responses of the wind turbine due to the effects of different wind-wave load combinations and soil conditions have been investigated and discussed.
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Yawen, Han, Wang Yang, Yuan Shouqi, Zhao Lifeng, and Zhu Xinxin. "Optimization Design on Performance of Self-Priming Jet Pump Based on Orthogonal Test." In ASME/JSME/KSME 2015 Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/ajkfluids2015-1617.

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This paper study on a JSW10 Self-priming jet pump, in order to improve the performance of the pump, using the method of orthogonal test design test [1–2] and selecting the ejector throat diameter D1, outlet diameter of the diffusion tube D2, the outlet width of impeller b2, the number of blades z as the impact factors. Then design orthogonal test of four factors and three levels. Using the k–ε turbulence model provided by CFD on the whole flow field numerical calculation. According to the Q-H curves of the tests. Only judge by the standard of head, the optimal solution is test7, followed by test2;while if only judge by the efficiency test2 is the optimal scheme, test7 is the sub-optimal solution. Application analysis of range obtained that the best level combination for head curves is A1B1C3D1 and the best level combination for hydraulic efficiency is A1B1C3D1. Then through numerical results prove the correctness.Analyzing the test data at the rated flow point.Get the order of the factor affecting on head is C>D>B>A while the order on the efficiency is C>A>B>D. This analysis method has a certain reference value for the structure optimization of self-priming jet pumps to make ejector and centrifugal impeller fit perfect to improve the performance.
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Agheshlui, Hossein. "Effect of Bracing Configurations on the Lateral Behavior of Jacket Type Offshore Platforms, Considering Pile-Soil-Structure Interaction." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20010.

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The configuration of braces has a considerable influence in the lateral behavior of pile supported steel jacket type offshore platforms. In this paper nonlinear static push over analyses and hysteresis curves are used to investigate lateral behavior of a jacket type offshore platform considering different configurations for vertical bracings of the jacket. One sample platform, constructed in Persian Gulf, is precisely modeled using the finite element program Opensees. Since the lateral response of offshore platforms is completely dependent on their foundations’ behavior, an accurate model is used for modeling the foundation of this structure. Soil-pile-structure interaction is considered using Beam on Nonlinear Winkler Foundation model (BNWF). Lateral and vertical soil stiffness and end bearing were considered using p-y, t-z and q-z nonlinear models, respectively. Moreover, the buckling behavior of the braces is considered in the simulation of the platform to consider the behavior of the platform after buckling, and redistribution of the shear forces in the structure due to the bracings failures. The structure was modeled using nonlinear beam-column elements which have the ability to consider the spread of plasticity along the elements. The sections used for elements are fiber sections which are suitable for considering composite section of pile-grout-leg. Displacement controlled nonlinear static pushover analysis and cyclic loading analysis are conducted applying lateral load which its pattern is according to the predominant vibration modes. Three different configurations for lateral bracings are assumed and the behavior of the platform using these three bracing forms is investigated. The first configuration considered is the original bracing of the platform which is a combination of X and chevron braces; the second one is a case in that X braces were used in all of the bays of the jacket; and in the third form chevron braces are used for all of the bays. According to the push over and hysteresis curves, it is concluded that in the jacket modeled using X vertical braces, lateral load capacity, ductility, residual strength ratio and the absorbed energy in cyclic loadings are considerably more than the jackets which were modeled using a combination of chevron and X braces or just chevron braces. In comparison with the jacket modeled using only chevron braces, the jacket constructed using a combination of X and chevron bracings presents better lateral behavior and capacity.
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Luan, B. F., R. S. Qiu, Z. Zhou, K. L. Murty, J. Zhou, and Q. Liu. "Characterization of Hot Deformation Behavior of Zr-1.0Sn-0.3Nb-0.3Fe-0.1Cr Using Processing Map." In 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icone21-15186.

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Hot deformation characteristics of forged and β-quenched Zr-1.0Sn-0.3Nb-0.3Fe-0.1Cr (N18 alloy) in the temperature range 625–950°C and in the strain rate range 0.005–5 s−1 have been studied by uniaxial compression testing of Gleeble 3500. For this study, the approach of processing maps has been adopted and their interpretation done using the Dynamic Materials Model (DMM). Based on a series of true stress-true strain curves on various temperatures and strain rates, the flow stress has been summarized and both the strain rate sensitivity index (m) and deformation activation energy (Q) have been calculated by the constitutive equations that flow stress and the relationship of Z parameter and flow stress have been established subsequently. Furthermore, the efficiency of power dissipation (⬜) given by [2m/(m+1)] and improved by Murty has been plotted as a function of temperature and strain rate to obtain different processing maps at different true strain rates ranging from 0.1–0.7. Subsequently, the microstructures of the specimens after compression testing were characterized by electron channeling contrast (ECC) imaging techniques used an FEI Nova 400 field emission gun scanning electron microscopy (FEG-SEM). The results showed that: (i) The hyperbolic sine constitutive equation can describe the flow stress behavior of zirconium alloy, and the deformation activation energy and flow stress equation were calculated under the different temperature stages which insists that the deformation mechanism is not dynamic recovery. (ii) The hot processing maps and its validation were analyzed, which indicated that the DMM theory was reliable and could be adopted as useful tool for optimizing hot workability of Zr. The optimum parameters for extrusion and hammer forging were revealed on the processing maps of 830–950°C, 0.048–2.141 s−1 and 916–950°C, 2.465–5 s−1. (iii) The microstructure of the ingot exhibits a typical lamellar Widmanstatten structure. Under the different strain rates, the grains formed by dynamic recrystallization existed normally in the central zone of the compression samples while the no uniformity of grain size increased with the increasing of strain rate. Meanwhile, due to the dynamic recrystallization as a thermal activation process, the grains size and uniformity increased with the increasing of temperature. In brief, microstructure analysis showed that continuous dynamic recrystallization and geometric dynamic recrystallization operated concurrently during the isothermal compressive deformation.
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