Showing papers on "Quintic function published in 2013"
TL;DR: In this paper, new classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry using vector bundle techniques for finding equations of Secant varieties in general.
Abstract: New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry Some old modules of equations (catalecticant minors) are revisited to determine when they are sufficient to give scheme-theoretic defining equations An algorithm to decompose a general ternary quintic as the sum of seven fifth powers is given as an illustration of our methods Our new equations and results about them are put into a larger context by introducing vector bundle techniques for finding equations of secant varieties in general We include a few homogeneous examples of this method
141 citations
TL;DR: In this paper, the power emitted in scalar modes for a binary system, including binary pulsars, with a conformal coupling to the most general Galileon effective field theory by considering perturbations around a static, spherical background is calculated.
Abstract: We calculate the power emitted in scalar modes for a binary system, including binary pulsars, with a conformal coupling to the most general Galileon effective field theory by considering perturbations around a static, spherical background While this method is effective for calculating the power in the cubic Galileon case, here we find that if the quartic or quintic Galileon dominate, for realistic pulsar systems the classical perturbative expansion about spherically symmetric backgrounds breaks down (although the quantum effective theory is well defined) The basic reason is that the equations of motion for the fluctuations are then effectively one dimensional This leads to many multipoles radiating with equal strength, as opposed to the normal Minkowski spacetime and cubic Galileon cases, where increasing multipoles are suppressed by increasing powers of the orbital velocity We consider the following two cases where perturbation theory gives trustworthy results: (1) when there is a large hierarchy between the masses of two orbiting objects and (2) when we choose scales such that the quartic Galileon only begins to dominate at distances smaller than the inverse pulsar frequency Implications for future calculations with the full Galileon that account for the Vainshtein mechanism are considered
82 citations
TL;DR: In this paper, the exact solution of the cubic-quintic Duffing oscillator was derived based on the use of Jacobi elliptic functions and the exact angular frequency was given in terms of the complete elliptic integral of the first kind.
70 citations
TL;DR: From the numerical experiments, it can be found that the present scheme possesses high accuracy and efficiency, and the numerical results are in good agreement with the exact solutions.
43 citations
TL;DR: In this paper, the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams with nonlinear nonlinearity is discussed, and the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution.
40 citations
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TL;DR: In this article, the existence of a compact global attractor for the solution semigroup of the dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered.
Abstract: The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.
37 citations
TL;DR: The Galerkin method with quintic B-splines as basis functions is presented to solve a fourth order boundary value problem with two different cases of boundary conditions.
Abstract: Abstract: In this paper, Galerkin method with quintic B-splines as basis functions is presented to solve a fourth order boundary value problem with two different cases of boundary conditions. In the method, the basis functions are redefined into a new set of basis functions which vanish at the boundary where the Dirichlet type of boundary conditions are prescribed. The proposed method is tested on several numerical examples of fourth order linear and nonlinear boundary value problems. Numerical results obtained by the proposed method are in good agreement with the exact solutions available in the literature.
33 citations
TL;DR: In this article, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by the method based on collocation of quintic B-splines over the finite elements.
Abstract: In this work, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by the method based on collocation of quintic B-splines over the finite elements. A linear stability analysis shows that the numerical scheme based on Von Neumann approximation theory is unconditionally stable. Test problems including the solitary wave motion, the interaction of two and three solitary waves and the Maxwellian initial condition are solved to validate the proposed method by calculating error norms L2 and L∞ that are found to be marginally accurate and efficient. The three invariants of the motion have been calculated to determine the conservation properties of the scheme. The obtained results are compared with other earlier results. MSC: 97N40; 65N30; 65D07; 76B25; 74S05
32 citations
TL;DR: In this article, the authors study the damped Navier-stokes equations in the whole 2D space and verify the global well-posedness, dissipativity and further regularity of weak solutions of this problem in the uniformly local spaces.
Abstract: We study the so-called damped Navier-Stokes equations in the whole 2D space. The global well-posedness, dissipativity and further regularity of weak solutions of this problem in the uniformly-local spaces are verified based on the further development of the weighted energy theory for the Navier-Stokes type problems. Note that any divergent free vector field u0 ∈ L ∞ (R 2 ) is allowed and no assumptions on the spatial decay of solutions as |x |→∞ are posed. In addition, applying the developed theory to the case of the classical Navier-Stokes problem in R2, we show that the properly defined weak solution can grow at most polynomially (as a quintic polynomial) as time goes to infinity. Mathematics Subject Classification (2010). 35Q30 · 35Q35.
32 citations
TL;DR: Modifications of the quasilinearization method with higher-order convergence for solving nonlinear differential equations are constructed and are applied to bifurcation problems and to obtain critical parameter values for the existence and uniqueness of solutions.
Abstract: In this paper, modifications of the quasilinearization method with higher-order convergence for solving nonlinear differential equations are constructed. A general technique for systematically obtaining iteration schemes of order m (Â?>Â?2) for finding solutions of highly nonlinear differential equations is developed. The proposed iterative schemes have convergence rates of cubic, quartic and quintic orders. These schemes were further applied to bifurcation problems and to obtain critical parameter values for the existence and uniqueness of solutions. The accuracy and validity of the new schemes is tested by finding accurate solutions of the one-dimensional Bratu and Frank-Kamenetzkii equations.
25 citations
TL;DR: In this article, the spin-5 Casimir operator was obtained in the coset model based on the second-order pole in the operator product expansion (OPE) between spin-3 and spin-4 Casimir operators, and the three-point functions with two scalars were obtained by analyzing the zero-mode eigenvalue equations carefully.
Abstract: By calculating the second-order pole in the operator product expansion (OPE) between the spin-3 Casimir operator and the spin-4 Casimir operator known previously, the spin-5 Casimir operator is obtained in the coset model based on (A_{N-1}^{(1)} \oplus A_{N-1}^{(1)}, A_{N-1}^{(1)}) at level (k,1). This spin-5 Casimir operator consisted of the quintic, quartic (with one derivative) and cubic (with two derivatives) WZW currents contracted with SU(N) invariant tensors. The three-point functions with two scalars for all values of 't Hooft coupling in the large N limit were obtained by analyzing the zero-mode eigenvalue equations carefully. These three-point functions were dual to those in AdS_3 higher spin gravity theory with matter. Furthermore, the exact three-point functions that hold for any finite N and k are obtained. The zero mode eigenvalue equations for the spin-5 current in CFT coincided with those of the spin-5 field in asymptotic symmetry algebra of the higher spin theory on the AdS_3. This paper also describes the structure constant appearing in the spin-4 Casimir operator from the OPE between the spin-3 Casimir operator and itself for N=4, 5 in the more general coset minimal model with two arbitrary levels (k_1, k_2).
TL;DR: In this paper, a class of quasi-quintic trigonometric Bezier curves with two shape parameters, based on newly constructed trigonometric basis functions, is presented.
Abstract: In this paper, a class of quasi-quintic trigonometric Bezier curve with two shape parameters, based on newly constructed trigonometric basis functions, is presented. The new basis functions share the properties with Bernstein basis functions, so the generated curves inherit many properties of traditional Bezier curves. The presence of shape parameters provides a local control on the shape of the curve which enables the designer to control the curve more than the ordinary Bezier curve.
TL;DR: In this article, the influence of the quintic nonlinear term on the ideal 1D pure cigar-like shape model for attractive and repulsive atom-atom interaction in Bose-Einstein condensates was explored.
Abstract: By means of a new variational method we report a direct solution for quintic and cubic-quintic nonlinear 1D Gross-Pitaeskii equations (GPE) in a harmonic confined potential. We explore the influence of the quintic nonlinear term on the ideal 1D pure cigar-like shape model for attractive and repulsive atom-atom interaction in Bose-Einstein condensates (BEC). Also, we offer a closed analytical expression to evaluate the error produced when solely the cubic nonlinear GPE is considered in the description of 1D BEC.
TL;DR: In this article, the quintic nonlinear Schrodinger equa- tion on the circle was solved in a nonlinear nonlinear way. But it was not shown how to solve the nonlinear version of the problem.
Abstract: We construct solutions to the quintic nonlinear Schrodinger equa- tion on the circle i@tu + @ 2 xu = � j uj
TL;DR: An efficient split-step compact finite difference method for the cubic–quintic complex Ginzburg–Landau (CQ CGL) equations both in one dimension and in multi-dimensions is proposed, which is convergent of second- order in time and fourth-order in space.
TL;DR: In this article, a nonlinear equation for the squared wave amplitude is derived, which allows the exact representation of periodic patterns as well as localized bright and dark pulses in terms of elliptic and their classical hyperbolic limits.
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TL;DR: In this article, it was shown that these Calabi-Yau threefolds Y are naturally paired with Reye congruence X, and X and Y have several interesting properties from the view of mirror symmetry and projective geometry.
Abstract: We consider Calabi-Yau threefolds Y defined as smooth linear sections of the double cover of the quintic symmetric determinantal hypersurface in P^{14}. In our previous works, we have shown that these Calabi-Yau threefolds Y are naturally paired with Reye congruence Calabi-Yau threefolds X, and X and Y have several interesting properties from the view point of mirror symmetry and projective geometry. In this paper, we prove the derived equivalence between Y and X.
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Abstract: We obtain homological properties of the second symmetric product of P^4 and the double cover of the symmetric determinantal quintic hypersurface in P^{14} (the double quintic symmetroids), which indicate the homological projective duality between (suitable noncommutative resolutions of) them. Among other things, we construct their good desingularizations and also (dual) Lefschetz collections in the derived categories of the desingularizations. These are expected to give (dual) Lefschetz decompositions of suitable noncommutative resolutions. The desingularization of the double quintic symmetroids also contains its interesting birational geometries.
TL;DR: This work rigorously proves that the PH interpolant it selects doesn’t depend on the unit pure vector chosen for representing its hodograph in quaternion form, and evaluates the corresponding interpolation scheme from a theoretical point of view, proving with the help of symbolic computation that it has fourth approximation order.
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TL;DR: The GIT compactification for the moduli space of smooth quintic surfaces in projective space has been studied in this article, where it is shown that a normal quintic surface with at worst an isolated double point or a minimal elliptic singularity is stable.
Abstract: We describe the GIT compactification for the moduli space of smooth quintic surfaces in projective space. In particular, we show that a normal quintic surface with at worst an isolated double point or a minimal elliptic singularity is stable. We also describe the boundary of the GIT quotient, and we discuss the stability of the nonnormal surfaces.
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TL;DR: The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.
Abstract: Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.
TL;DR: This work presents a construction of nested spaces of C^2 macro-elements of degree 5 on triangulations of a polygonal domain obtained by uniform refinements of an initial triangulation and a Powell-Sabin-12 split.
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TL;DR: In this paper, the limiting zero distribution of orthogonal polynomials with respect to some particular exponential weights exp(nV(z)) along contours in the complex plane was studied.
Abstract: We study the limiting zero distribution of orthogonal polynomials with respect to some particular exponential weights exp(-nV(z)) along contours in the complex plane. We are especially interested in the question under which circumstances the zeros of the orthogonal polynomials accumulate on a single analytic arc (one cut case), and in which cases they do not. In a family of cubic polynomial potentials V(z) = - iz^3/3 + iKz, we determine the precise values of K for which we have the one cut case. We also prove the one cut case for a monomial quintic V(z) = - iz^5/5 on a contour that is symmetric in the imaginary axis.
TL;DR: An alternative box-spline filter for the body-centered cubic (BCC) lattice is presented that has the same approximation order as the eight-direction quintic box- Spline M8 but a lower polynomial degree, smaller support, and is computationally more efficient.
Abstract: This paper presents an alternative box-spline filter for the body-centered cubic (BCC) lattice, the seven-direction quartic box-spline M7 that has the same approximation order as the eight-direction quintic box-spline M8 but a lower polynomial degree, smaller support, and is computationally more efficient. When applied to reconstruction with quasi-interpolation prefilters, M7 shows less aliasing, which is verified quantitatively by integral filter metrics and frequency error kernels. To visualize and analyze distributional aliasing characteristics, each spectrum is evaluated on the planes and lines with various orientations.
TL;DR: In this paper, the authors give a new Classic method for solving a fourth degree polynomial equation (Quartic) and show how the quartic formula can be presented easily at the precalculus level.
Abstract: Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level.
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TL;DR: In this article, a version of the Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic was shown to be equivalent to the Gromov-Witten theory of the Fermat quintic polynomial.
Abstract: We prove a version of the Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic. In particular we calculate the genus-zero FJRW theory for the pair (W, G) where W is the Fermat quintic polynomial and G = SL(W). We identify it with the Gromov-Witten theory of the mirror quintic three-fold via an explicit analytic continuation and symplectic transformation. In the process we prove a mirror theorem for the corresponding Landau-Ginzburg model (W,G).
TL;DR: By blossoming Marsden’s identity, local quasi-interpolation schemes for C 2 -continuous quintic Powell–Sabin splines represented with a normalized B-spline basis are investigated and various families of discrete and differential quasi-Interpolants reproducing quintic polynomials are presented.
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TL;DR: In this article, an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schrodinger equation in the supercritical regime has been proved, that is, below the critical space (H^1(mathbb T^3) ).
Abstract: In this paper we prove an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schrodinger equation in the supercritical regime, that is below the critical space $H^1(\mathbb T^3)$.
TL;DR: The scalar-vector representation is used to derive a simple algorithm to obtain the roots of a quadratic quaternion polynomial, which is illustrated by computed examples, and used to analyze the root structure of quadratically quaternions polynomials that generate quintic curves with rational rotation-minimizing frames (RRMF curves).
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TL;DR: A result characterising the covariants for these models in terms of their restrictions to the family of curves parametrised by the modular curve X(5) is proved.
Abstract: A genus one curve C of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We prove a result characterising the covariants for these models in terms of their restrictions to the family of curves parametrised by the modular curve X(5). We then construct covariants describing the covering map of degree 25 from C to its Jacobian and give a practical algorithm for evaluating them.