Relevant bibliographies by topics / Cubic

Academic literature on the topic 'Cubic'

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Published: 4 June 2021
Last updated: 4 March 2023

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Journal articles on the topic "Cubic"

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Odehnal, Boris. "Distance Product Cubics." KoG, no. 24 (2020): 29–40. http://dx.doi.org/10.31896/k.24.3.

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The locus of points that determine a constant product of their distances to the sides of a triangle is a cubic curve in the projectively closed Euclidean triangle plane. In this paper, algebraic and geometric properties of these distance product cubics shall be studied. These cubics span a pencil of cubics that contains only one rational and non-degenerate cubic curve which is known as the Bataille acnodal cubic determined by the product of the actual trilinear coordinates of the centroid of the base triangle. Each triangle center defines a distance product cubic. It turns out that only a small number of triangle centers share their distance product cubic with other centers. All distance product cubics share the real points of inflection which lie on the line at infinity. The cubics' dual curves, their Hessians, and especially those distance product cubics that are defined by particular triangle centers shall be studied.
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Shiue, Peter J. S., Anthony G. Shannon, Shen C. Huang, and Jorge E. Reyes. "Notes on efficient computation of Ramanujan cubic equations." Notes on Number Theory and Discrete Mathematics 28, no. 2 (June 14, 2022): 350–75. http://dx.doi.org/10.7546/nntdm.2022.28.2.350-375.

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This paper considers properties of a theorem of Ramanujan to develop properties and algorithms related to cubic equations. The Ramanujan cubics are related to the Cardano cubics and Padovan recurrence relations. These generate cubic identities related to heptagonal triangles and third order recurrence relations, as well as an algorithm for finding the real root of the relevant Ramanujan cubic equation. The algorithm is applied to, and analyzed for, some of the earlier examples in the paper.
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Woo, Sung Sik. "CUBIC FORMULA AND CUBIC CURVES." Communications of the Korean Mathematical Society 28, no. 2 (April 30, 2013): 209–24. http://dx.doi.org/10.4134/ckms.2013.28.2.209.

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Rossi, Laura, Stefano Sacanna, William T. M. Irvine, Paul M. Chaikin, David J. Pine, and Albert P. Philipse. "Cubic crystals from cubic colloids." Soft Matter 7, no. 9 (2011): 4139–42. http://dx.doi.org/10.1039/c0sm01246g.

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Mavron, V. C., and W. D. Wallis. "Cubic arcs in cubic nets." Designs, Codes and Cryptography 3, no. 2 (May 1993): 99–104. http://dx.doi.org/10.1007/bf01388408.

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Dresden, Greg, Prakriti Panthi, Anukriti Shrestha, and Jiahao Zhang. "Cubic Polynomials, Linear Shifts, and Ramanujan Simple Cubics." Mathematics Magazine 92, no. 5 (October 20, 2019): 374–81. http://dx.doi.org/10.1080/0025570x.2019.1655310.

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Zhang, Erchuan, and Lyle Noakes. "The cubic de Casteljau construction and Riemannian cubics." Computer Aided Geometric Design 75 (November 2019): 101789. http://dx.doi.org/10.1016/j.cagd.2019.101789.

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Ha, Sangtae, Injong Rhee, and Lisong Xu. "CUBIC." ACM SIGOPS Operating Systems Review 42, no. 5 (July 2008): 64–74. http://dx.doi.org/10.1145/1400097.1400105.

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Wright, David J. "Cubic character sums of cubic polynomials." Proceedings of the American Mathematical Society 100, no. 3 (March 1, 1987): 409. http://dx.doi.org/10.1090/s0002-9939-1987-0891136-3.

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Huybrechts, Daniel. "The K3 category of a cubic fourfold." Compositio Mathematica 153, no. 3 (March 2017): 586–620. http://dx.doi.org/10.1112/s0010437x16008137.

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Smooth cubic hypersurfaces $X\subset \mathbb{P}^{5}$ (over $\mathbb{C}$) are linked to K3 surfaces via their Hodge structures, due to the work of Hassett, and via a subcategory ${\mathcal{A}}_{X}\subset \text{D}^{\text{b}}(X)$, due to the work of Kuznetsov. The relation between these two viewpoints has recently been elucidated by Addington and Thomas. In this paper, both aspects are studied further and extended to twisted K3 surfaces, which in particular allows us to determine the group of autoequivalences of ${\mathcal{A}}_{X}$ for the general cubic fourfold. Furthermore, we prove finiteness results for cubics with equivalent K3 categories and study periods of cubics in terms of generalized K3 surfaces.
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Dissertations / Theses on the topic "Cubic"

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Ahmad, Qadeer. "CUBIC CONGRUENCE EQUATIONS." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-19506.

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Let Nm(f(x)) denote the number of solutions of the congruence equation f(x)≡0 (modm), where m≥2 is any composite integer and f(x) is a cubic polynomial. In this thesis, we use different theorems and corollaries to find a number of solutions of the congruence equations without solving then we also construct the general expression of corresponding congruence equations to demonstrate the solutions of the equations. In this thesis, we use Mathematica software as a tool.
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Biswass, Richard Swarup. "Singular cubic hypersurfaces." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240934.

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Cooley, Jenny. "Cubic surfaces over finite fields." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/66304/.

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It is well-known that the set of rational points on an elliptic curve forms an abelian group. When the curve is given as a plane cubic in Weierstrass form the group operation is defined via tangent and secant operations. Let S be a smooth cubic surface over a field K. Again one can define tangent and secant operations on S. These do not give S(K) a group structure, but one can still ask for the size of a minimal generating set. In Chapter 2 of the thesis I show that if S is a smooth cubic surface over a field K with at least 4 elements, and if S contains a skew pair of lines defined over K, then any non-Eckardt K-point on either line generates S(K). This strengthens a result of Siksek [20]. In Chapter 3, I show that if S is a smooth cubic surface over a finite field K = Fq with at least 8 elements, and if S contains at least one K-line, then there is some point P > S(K) that generates S(K). In Chapter 4, I consider cubic surfaces S over finite fields K = Fq that contain no K-lines. I find a lower bound for the proportion of points generated when starting with a non-Eckardt point P > S(K) and show that this lower bound tends to 1/6 as q tends to infinity. In Chapter 5, I define c-invariants of cubic surfaces over a finite field K = Fq with respect to a given K-line contained in S, give several results regarding these c-invariants and relate them to the number of points SS(K)S. In Chapter 6, I consider the problem of enumerating cubic surfaces over a finite field, K = Fq, with a given point, P > S(K), up to an explicit equivalence relation.
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Xia, Honggang. "On zeros of cubic L-functions." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1148497121.

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Atilhan, Mert. "A new cubic equation of state." Thesis, Texas A&M University, 2004. http://hdl.handle.net/1969.1/352.

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Thermodynamic properties are essential for the design of chemical processes, and they are most useful in the form of an equation of state (EOS). The motivating force of this work is the need for accurate prediction of the phase behavior and thermophysical properties of natural gas for practical engineering applications. This thesis presents a new cubic EOS for pure argon. In this work, a theoretically based EOS represents the PVT behavior of pure fluids. The new equation has its basis in the improved Most General Cubic Equation of State theory and forecasts the behavior of pure molecules over a broad range of fluid densities at both high and low pressures in both single and multiphase regions. With the new EOS, it is possible to make accurate estimations for saturated densities and vapor pressures. The density dependence of the equation results from fitting isotherms of test substances while reproducing the critical point, and enforcing the critical point criteria. The EOS includes analytical functions to fit the calculated temperature dependence of the new EOS parameters.
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Yoo, Jeewon. "Minimal indices of pure cubic fields." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/58308.

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Determining whether a number field admits a power integral basis is a classical problem in algebraic number theory. It is well known that every quadratic number field is monogenic, that is they admit power bases. However, when we talk about cubic or higher degree number fields we may discover fields without power integral bases. In 1878, Dedekind gave the first example of a cubic field without a power integral basis. It is known that a number field is monogenic if and only if the minimal index is one. In 1937, Hall proved that the minimal index of pure cubic fields can be arbitrarily large. We extend this result by showing that the minimal index of a family of infinitely many pure cubic fields have an element of index n but no element of index less than n for a positive integer n.
Irving K. Barber School of Arts and Sciences (Okanagan)
Mathematics, Department of (Okanagan)
Graduate
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Jackson, Stacey Michael. "Optical characterisation of cubic silicon carbide." Thesis, University of Surrey, 1998. http://epubs.surrey.ac.uk/842961/.

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The varied properties of Silicon Carbide (SiC) are helping to launch the material into many new applications, particularly in the field of novel semiconductor devices. In this work, the cubic form of SiC is of interest as a basis for developing integrated optical components. Here, the formation of a suitable SiO2 buried cladding layer has been achieved by high dose oxygen ion implantation. This layer is necessary for the optical confinement of propagating light, and hence optical waveguide fabrication. Results have shown that optical propagation losses of the order of 20 dB/cm are obtainable. Much of this loss can be attributed to mode leakage and volume scattering. Mode leakage is a function of the effective oxide thickness, and volume scattering related to the surface layer damage. These parameters have been shown to be controllable and so suggests that further reduction in the waveguide loss is feasible. Analysis of the layer growth mechanism by RBS, XTEM and XPS proves that SiO2 is formed, and that the extent of formation depends on implant dose and temperature. The excess carbon generated is believed to exit the oxide layer by a number of varying mechanisms. The result of this appears to be a number of stable Si-C-O intermediaries that form regions to either depth extreme of the SiO2 layer. Early furnace tests suggest a need to anneal at temperatures approaching the melting point of the silicon substrate, and that the quality of the virgin material is crutial in controlling the resulting oxide growth.
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Kolossovski, Kazimir Mathematics &amp Statistics Australian Defence Force Academy UNSW. "Parametric solitons due to cubic nonlinearities." Awarded by:University of New South Wales - Australian Defence Force Academy. School of Mathematics and Statistics, 2001. http://handle.unsw.edu.au/1959.4/38711.

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The main subject of this thesis is solitons due to degenerate parametric four-wave mixing. Derivation of the governing equations is carried out for both spatial solitons (slab waveguide) and temporal solitons (optical fibre). Higher-order effects that are ignored in the standard paraxial approximation are discussed and estimated. Detailed analysis of conventional solitons is carried out. This includes discovery of various solitons families, linear stability analysis of fundamental and higher-order solitons, development of theory describing nonlinear dynamics of higher-order solitons. The major findings related to the stationary problem are bifurcation of a two-frequency soliton family from an asymptotic family of infinitely separated one-frequency solitons, jump bifurcation and violation of the bound state principle. Linear stability analysis shows a rich variety of internal modes of the fundamental solitons and existence of a stability window for higher-order solitons. Theory for nonlinear dynamics of higher-order solitons successfully predicts the position and size of the stability window, and various instability scenarios. Equivalence between direct asymptotic approach and invariant based approach is demonstrated. A general analytic approach for description of localised solutions that are in resonance with linear waves (quasi-solitons and embedded solitons) is given. This includes normal form theory and approximation of interacting particles. The main results are an expression for the amplitude of the radiating tail of a quasi-soliton, and a two-fold criterion for existence of embedded solitons. Influence of nonparaxiality on soliton stability is investigated. Stationary instability threshold is derived. The major results are shift and decreasing of the size of the stability window for higher-order solitons. The latter is the first demonstration of the destabilizing influence of nonparaxiality on higher-order solitons. Analysis of different aspects of solitons is based on universal approaches and methods. This includes Hamiltonian formalism, consideration of symmetry properties of the model, development of asymptotic models, construction of perturbation theory, application of general theorems etc. Thus, the results obtained can be extended beyond the particular model of degenerate four-wave mixing. All theoretical predictions are in good agreement with the results of direct numerical modeling.
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Inacio, Helder. "Convex relaxations for cubic polynomial problems." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/47563.

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This dissertation addresses optimization of cubic polynomial problems. Heuristics for finding good quality feasible solutions and for improving on existing feasible solutions for a complex industrial problem, involving cubic and pooling constraints among other complicating constraints, have been developed. The heuristics for finding feasible solutions are developed based on linear approximations to the original problem that enforce a subset of the original problem constraints while it tries to provide good approximations for the remaining constraints, obtaining in this way nearly feasible solutions. The performance of these heuristics has been tested by using industrial case studies that are of appropriate size, scale and structure. Furthermore, the quality of the solutions can be quantified by comparing the obtained feasible solutions against upper bounds on the value of the problem. In order to obtain these upper bounds we have extended efficient existing techniques for bilinear problems for this class of cubic polynomial problems. Despite the efficiency of the upper bound techniques good upper bounds for the industrial case problem could not be computed efficiently within a reasonable time limit (one hour). We have applied the same techniques to subproblems with the same structure but about one fifth of the size and in this case, on average, the gap between the obtained solutions and the computed upper bounds is about 3%. In the remaining part of the thesis we look at global optimization of cubic polynomial problems with non-negative bounded variables via branch and bound. A theoretical study on the properties of convex underestimators for non-linear terms which are quadratic in one of the variables and linear on the other variable is presented. A new underestimator is introduced for this class of terms. The final part of the thesis describes the numerical testing of the previously mentioned underestimators together with approximations obtained by considering lifted approximations of the convex hull of the (x x y) terms. Two sets of instances are generated for this test and the descriptions of the procedures to generate the instances are detailed here. By analyzing the numerical results we can conclude that our proposed underestimator has the best behavior in the family of instances where the only non-linear terms present are of the form (x x y). Problems originating from least squares are much harder to solve than the other class of problems. In this class of problems the efficiency of linear programming solvers plays a big role and on average the methods that use these solvers perform better than the others.
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Papanikolopoulos, Stafanos. "Rational points on smooth cubic hypersurfaces." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/67565/.

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Let S be a smooth n-dimensional cubic variety over a field K and suppose that K is finitely generated over its prime subfield. It is a well-known fact that whenever we have a set of K-points on S, we may obtain new ones, using secant and tangent constructions. A Mordell-Weil generating set B ⊆ S(K) is a subset of minimal cardinality that generates S(K) via these operations; we define the Mordell-Weil rank as r(S,K) = #B. The Mordell-Weil theorem asserts that in the case of an elliptic curve E defined over a number field K, we have that r(E,K) < 1. Manin [11] asked whether this is true or not for surfaces. Our goal is to settle this question for higher dimensions, and for as many fields as possible. We prove that when the dimension of the cubic hypersurface is big enough, if a point can generate another point, then it can generate all the points in the hypersurface that lie in its tangent plane. This gives us a powerful tool, yet a simple one, for generating sets of points starting with a single one. Furthermore, we use this result to prove that if K is a finite field and the dimension of the hypersurface is at least 5, then r(S,K) = 1. On the other hand, it is natural to ask whether r(S,K) can be bounded by a constant, depending only on the dimension of S. It is conjectured that such a constant does not exist for the elliptic curves (the unboundedness of ranks conjecture for elliptic curves). In the case of cubic surfaces, Siksek [16] has proven that such a constant does not exist when K = Q. Our goal is to generalise this for cubic threefolds. This is achieved via an abelian group HS(K), which holds enough information about the Mordell-Weil rank r(S,K) in the following manner; if HS(K) becomes large, so does r(S,K). Then, by using a family of cubic surfaces that is known to have an unbounded number of Mordell-Weil generators over Q, we prove that the number of Mordell-Weil generators is unbounded in the case of threefolds too.
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Books on the topic "Cubic"

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Knott, Gary D. Interpolating Cubic Splines. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8.

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Ernő, Rubik, ed. Rubik's Cubic Compendium. Oxford: Oxford University Press, 1987.

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The cubic curriculum. London: Routledge, 1997.

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Hambleton, Samuel A., and Hugh C. Williams. Cubic Fields with Geometry. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01404-9.

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United States. National Aeronautics and Space Administration., ed. Accurate monotone cubic interpolation. [Washington, DC]: National Aeronautics and Space Administration, 1991.

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Pollock, S. Smoothing with cubic splines. London: London University, Queen Mary and Westfield College, Department of Economics, 1993.

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Lutstorf, Heinz Theo. Zur Geschichte der Gleichungen dritten Grades mit einer Unbekannten (16. Jahrhundert). Zürich: ETH-Bibliothek, 1996.

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Center, Ames Research, ed. Higher order B £ezier circles. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1993.

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Center, Ames Research, ed. Higher order Bʹezier circles. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1993.

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Baniasadi, Pouya, Vladimir Ejov, Jerzy A. Filar, and Michael Haythorpe. Genetic Theory for Cubic Graphs. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-19680-0.

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Book chapters on the topic "Cubic"

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Gooch, Jan W. "Cubic." In Encyclopedic Dictionary of Polymers, 185–86. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_3169.

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Knott, Gary D. "Rational Cubic Splines." In Interpolating Cubic Splines, 157–58. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_14.

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Knott, Gary D. "Mathematical Preliminaries." In Interpolating Cubic Splines, 1–29. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_1.

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Knott, Gary D. "Smoothing Splines." In Interpolating Cubic Splines, 123–32. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_10.

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Knott, Gary D. "Geometrically Continuous Cubic Splines." In Interpolating Cubic Splines, 133–38. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_11.

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Knott, Gary D. "Quadratic Space Curve Based Cubic Splines." In Interpolating Cubic Splines, 139–42. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_12.

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Knott, Gary D. "Cubic Spline Vector Space Basis Functions." In Interpolating Cubic Splines, 143–55. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_13.

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Knott, Gary D. "Two Spline Programs." In Interpolating Cubic Splines, 159–91. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_15.

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Knott, Gary D. "Tensor Product Surface Splines." In Interpolating Cubic Splines, 193–209. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_16.

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Knott, Gary D. "Boundary Curve Based Surface Splines." In Interpolating Cubic Splines, 211–16. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8_17.

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Conference papers on the topic "Cubic"

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Chuan, Ming-Yuan, and Chun-Wang Sun. "Cubic Tragedy." In the ACM SIGGRAPH 05 electronic art and animation catalog. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1086057.1086152.

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Chand, A. K. B., and P. Viswanathan. "Cubic hermite and cubic spline fractal interpolation functions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756439.

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Cesare, Bernardo, Fabrizio Nestola, Tim E. Johnson, Enrico Mugnaioli, Giancarlo Della Ventura, Luca Peruzzo, Omar Bartoli, Cecilia Viti, and Timmons M. Erickson. "GARNET, THE ARCHETYPAL CUBIC MINERAL, DOES NOT GROW CUBIC." In GSA Annual Meeting in Phoenix, Arizona, USA - 2019. Geological Society of America, 2019. http://dx.doi.org/10.1130/abs/2019am-334208.

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Liu, Qingge, and Guangwen Yan. "Cubic Prime Sequences." In 2010 6th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM). IEEE, 2010. http://dx.doi.org/10.1109/wicom.2010.5600224.

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Mogos, Gabriela. "Cubic Quantum Security." In 2014 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2014. http://dx.doi.org/10.1109/csci.2014.130.

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Fröhlich, Bernd, and John Plate. "The cubic mouse." In the SIGCHI conference. New York, New York, USA: ACM Press, 2000. http://dx.doi.org/10.1145/332040.332491.

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Peng, Gan Chew, Pooi Ah Hin, and C. K. Ho. "Cubic-normal distribution." In INNOVATION AND ANALYTICS CONFERENCE AND EXHIBITION (IACE 2015): Proceedings of the 2nd Innovation and Analytics Conference & Exhibition. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4937089.

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Cramer, M., and C. Webb. "A Zabolotskaya-Khokhlov equation for cubic and near-cubic nonlinearity." In 2nd AIAA, Theoretical Fluid Mechanics Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1998. http://dx.doi.org/10.2514/6.1998-2957.

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Mukherjee, S., A. Pradhan, S. Mukherjee, T. Maitra, A. Nayak, and S. Bhunia. "Growth and characterization of cubic and non-cubic Ge nanocrystals." In INTERNATIONAL CONFERENCE ON CONDENSED MATTER AND APPLIED PHYSICS (ICC 2015): Proceeding of International Conference on Condensed Matter and Applied Physics. Author(s), 2016. http://dx.doi.org/10.1063/1.4946162.

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Cao, Ning, and Wei Zhang. "Cubic with Faster Convergence: An Improved Cubic Fast Convergence Mechanism." In 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013). Paris, France: Atlantis Press, 2013. http://dx.doi.org/10.2991/iccsee.2013.211.

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Reports on the topic "Cubic"

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Kahan, W. To Solve a Real Cubic Equation. Fort Belvoir, VA: Defense Technical Information Center, November 1986. http://dx.doi.org/10.21236/ada206859.

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Rhee, I., L. Xu, S. Ha, A. Zimmermann, L. Eggert, and R. Scheffenegger. CUBIC for Fast Long-Distance Networks. RFC Editor, February 2018. http://dx.doi.org/10.17487/rfc8312.

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Rice, Anthony, and Mary Crawford. Chemical Vapor Deposition of Cubic Boron Nitride. Office of Scientific and Technical Information (OSTI), September 2021. http://dx.doi.org/10.2172/1821316.

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Spooner, Chad M., and William A. Gardner. Cubic Frequency-Shift Filtering for Cochannel Interference Removal,. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada290369.

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Verrill, Steve P., Victoria L. Herian, and Henry N. Spelter. Estimating the board foot to cubic foot ratio. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, 2004. http://dx.doi.org/10.2737/fpl-rp-616.

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Fearon, M. Finding the cubic smoothing spline function by scale invariants. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1990. http://dx.doi.org/10.4095/128121.

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7

Kleiner, Kevin Gordon, Daniel Blaschke, and Saryu Jindal Fensin. Modeling Dislocation Dynamics Near Sound Speeds in Cubic Crystals. Office of Scientific and Technical Information (OSTI), July 2019. http://dx.doi.org/10.2172/1544661.

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Molian, Arul, Madhav Rao, and P. Molian. Laser Deposition of Cubic Boron Nitride on Electronic Materials. Fort Belvoir, VA: Defense Technical Information Center, July 1991. http://dx.doi.org/10.21236/ada238313.

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Wills, Ann Elisabet, Aidan P. Thompson, and Sumathy Raman. An Atomistic Introduction to Orientation Relations Between Phases in the Face-centered Cubic to Body-centered Cubic Phase Transition in Iron and Steel. Office of Scientific and Technical Information (OSTI), January 2017. http://dx.doi.org/10.2172/1505395.

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10

Perkins, Leslie. Diffusion of adatoms on face-centered cubic transition metal surfaces. Office of Scientific and Technical Information (OSTI), May 1994. http://dx.doi.org/10.2172/10161694.

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