Showing papers on "Quintic function published in 2004"

A topological view of Gromov-Witten theory

Abstract: We study relative Gromov-Witten theory via universal relations provided by the interaction of degeneration and localization. We find relative Gromov-Witten theory is completely determined by absolute Gromov-Witten theory. The relationship between the relative and absolute theories is guided by a strong analogy to classical topology. As an outcome, we present a mathematical determination of the Gromov-Witten invariants (in all genera) of the Calabi-Yau quintic 3-fold in terms of known theories.

Fractional Branes in Landau-Ginzburg Orbifolds

Abstract: We construct fractional branes in Landau-Ginzburg orbifold categories and study their behavior under marginal closed string perturbations. This approach is shown to be more general than the rational boundary state construction. In particular we find new D-branes on the quintic -- such as a single D0-brane -- which are not restrictions of bundles on the ambient projective space. We also exhibit a family of deformations of the D0-brane in the Landau-Ginzburg category parameterized by points on the Fermat quintic.

Calabi-Yau manifolds over finite fields. 2.

Abstract: We study ζ-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The ζ-function for the quintic family involves factors that correspond to a certain pair of genus 4 Riemann curves. The appearance of these factors is intriguing since we have been unable to ‘see’ these curves in the geometry of the quintic. Having these ζ-functions to hand we are led to comment on their form in the light of mirror symmetry. That some residue of mirror symmetry survives into the ζ-functions is suggested by an application of the Weil conjec- tures to Calabi–Yau threefolds: the ζ-functions are rational functions and the degrees of the numerators and denominators are exchanged between the ζ-functions for the manifold and its mirror. It is clear nevertheless that the ζ-function, as classically defined, makes an essential distinction between Kahler parameters and the coefficients of the defining polynomial. It is an interesting question whether there is a ‘quantum modification’ of the ζ-function that restores the symmetry between the Kahler and complex structure param- eters. We note that the ζ-function seems to manifest an arithmetic analogue of the large complex structure limit which involves 5-adic expansion.

An example of non-normal quintic automorphic induction and modularity of symmetric powers of cusp forms of icosahedral type

Abstract: Due to the work of Arthur and Clozel [AC], the automorphic induction for cyclic Galois extensions of prime degree is well understood in great generality. It is not the case for non-normal extensions, even for monomial representations, i.e., the ones induced from grossencharacters. The only examples we have at the moment are: first, non-normal cubic automorphic induction due to Jacquet, Piatetski-Shapiro and Shalika [JPSS]. They obtained the automorphic induction as a consequence of the converse theorem on GL3. The second example is that of Harris [H]. He constructed automorphic induction for special class of algebraic Hecke characters of (suitable) non-normal extensions with solvable Galois closure. In this note, we give an example of automorphic induction for nonnormal quintic extension whose Galois closure is not solvable (Theorem 6.3). In fact, the Galois group is A5, the alternating group on 5 letters. The key observation due to Ramakrishnan is that symmetric fourth of the two dimensional icosahedral representation is equivalent to a suitable twist (by a character) of the five dimensional monomial representation of A5 . Our result follows immediately by combining results of K. Buzzard, M. Dickinson, N. Shepherd-Barron and R. Taylor [BDST] or R. Taylor’s result [Ta2] on modularity of certain icosahedral representations and our result on the functoriality of symmetric fourth [Ki]. We also prove the modularity of all symmetric powers of cuspidal representations of icosahedral type (Theorem 6.4).

Bifurcations of limit cycles from infinity for a class of quintic polynomial system

Abstract: In this work, we use an indirect method to investigate bifurcations of limit cycles at infinity for a class of quintic polynomial system, in which the problem for bifurcations of limit cycles from infinity be transferred into that from the origin. By the computation of singular point values, the conditions of the origin (correspondingly, infinity) to be the highest degree fine focus are derived. Consequently, we construct a quintic system with a small parameter and eight normal parameters, which can bifurcates 1 to 8 limit cycles from infinity respectively, when let normal parameters be suitable values. The positions of these limit cycles without constructing Poincare cycle fields can be pointed out exactly.

C 1 Quintic Splines on Type-4 Tetrahedral Partitions

Abstract: Starting with a partition of a rectangular box into subboxes, it is shown how to construct a natural tetrahedral (type-4) partition and associated trivariate C1 quintic polynomial spline spaces with a variety of useful properties, including stable local bases and full approximation power. It is also shown how the spaces can be used to solve certain Hermite and Lagrange interpolation problems.

Shape-Preserving Approximation of Spatial Data

Abstract: We present a new method for the construction of shape-preserving curves approximating a given set of 3D data, based on the space of “quintic like” polynomial splines with variable degrees recently introduced in [7]. These splines – which are C3 and therefore curvature and torsion continuous – possess a very simple geometric structure, which permits to easily handle the shape-constraints.

On a cubic-quintic Ginzburg-Landau equation with global coupling

Abstract: We study standing wave solutions in a Ginzburg-Landau equation which consists of a cubic-quintic equation stabilized by global coupling At = ΔA + μA + cA 3 - A 5 - kA (∫ Rn A 2 dx). We classify the existence and stability of all possible standing wave solutions.

G 2 ph quintic spiral transition curves and their applications

Abstract: A method for family of G 2 Pythagorean hodograph (PH) quintic spiral transition from straight line to circle is discussed in this paper. This method is then extended to a pair of spirals between two straight lines or two circles. We derive a family of quintic transition spiral curves joining them. Due to exibilit y and wide range of shape control parameters, our method can be easily applied for practical applications like high way designing, blending in CAD, consumer products such as ping-pong paddles, rounding corners, or designing a smooth path that avoids obstacles. 1 Introduction and Description of Method A method for smooth G 2 planar PH quintic spiral transition from straight line to circle is developed. This method is then ex- tended to a pair of spirals transition between two circles or between two non-parallel straight lines. We also develop a method for drawing a constrained guided planar spiral curve that falls within a closed boundary. The boundary is composed of straight line segments and circular arcs. Our constrained curve can easily be controlled by shape control parameter. Any change in this shape control parameter does not eect the continuity and neighbor- hood parts of the curve. There are several problems whose solution requires these types of methods. For example

Dynamics of NLS solitons described by the cubic-quintic Ginzburg-Landau equation

Abstract: The generalized moment method is applied to average the Ginzburg-Landau equation with quintic nonlinearity in the neighborhood of a soliton solution to the nonlinear Schrodinger equation. A qualitative analysis of the resulting dynamical system is presented. New soliton solutions bifurcating from a known exact soliton solution are obtained. The results of the qualitative analysis are compared with those obtained by direct numerical solution of the Ginzburg-Landau equation.

Solitary waves of nonlinear nonintegrable equations

Abstract: Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be non-perturbative, are divided in two classes. In the first class, which includes the well-known so-called truncation methods, one a priori assumes a given class of expressions (polynomials, etc.) for the unknown solution; the work involved can easily be done by hand but all solutions outside the given class are certainly missed. In the second class, instead of seeking an expression for the solution, one builds an intermediate equation with equivalent information, namely the first-order autonomous ODE satisfied by the solitary wave; in principle, no solution can be missed, but the work involved requires computer algebra. We present the application to the cubic and quintic complex one-dimensional Ginzburg-Landau equations, and to the Kuramoto-Sivashinsky equation.

Solitary waves of nonlinear nonintegrable equations

Abstract: Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations The suitable methods, which can only be nonperturbative, are classified in two classes In the first class, which includes the well known so-called truncation methods, one \textit{a priori} assumes a given class of expressions (polynomials, etc) for the unknown solution; the involved work can easily be done by hand but all solutions outside the given class are surely missed In the second class, instead of searching an expression for the solution, one builds an intermediate, equivalent information, namely the \textit{first order} autonomous ODE satisfied by the solitary wave; in principle, no solution can be missed, but the involved work requires computer algebra We present the application to the cubic and quintic complex one-dimensional Ginzburg-Landau equations, and to the Kuramoto-Sivashinsky equation

Periodic and solitary waves of the cubic quintic nonlinear Schrödinger equation

Abstract: This paper presents the possible periodic solutions and the solitons of the cubic quintic nonlinear Schrodinger equation. Corresponding to five types of different structures of the pseudo-potentials, five tyres of periodic solutions are given explicitly. Five types of solitons are also obtained explicitly from the limiting procedures of the periodic solutions. This will benefit the study of the generation of fast ions or electrons, which are produced from the soliton breaking when the plasma is irradiated a high-intensity laser pulse.

Normal integral bases for Emma Lehmer's parametric family of cyclic quintics

Abstract: Explicit normal integral bases are given for some cyclic quintic fields defined by Emma Lehmer's parametric family of quintics.

A construction of quintic rings

Abstract: We construct a discriminant-preserving map from the set of orbits in the space of quadruples of quinary alternating forms over the integers to the set of isomorphism classes of quintic rings. This map may be regarded as an analogue of the famous map from the set of equivalence classes of integral binary cubic forms to the set of isomorphism classes of cubic rings and may be expected to have similar applications. We show that the ring of integers of every quintic number field lies in the image of the map. These results have been used to establish an upper bound on the number of quintic number fields with bounded discriminant.

Topological String Partition Functions as Polynomials

Abstract: We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus.

Camera self-calibration: a new approach for solving the modulus constraint

Abstract: In this paper, the modulus constraint is used to retrieve the scale factors that are responsible for the nonlinearity of Kruppa's equations. In the case of constant intrinsic parameters, each pair of images identifies a pair of 3D points at infinity whose coordinates are expressed in terms of the scale factors we are looking for. By enforcing the coplanarity constraint on these points, a set of quintic bivariate equations is obtained for each triplet of images. Once the scale factors are calculated, the problems of retrieving the plane at infinity and solving Kruppa's equations become straightforward and linear.

A new model for the theta divisor of the cubic threefold

Abstract: In this paper we give a birational model for the theta divisor of the intermediate Jacobian of a generic cubic threefold $X$. We use the standard realization of $X$ as a conic bundle and a $4-$dimensional family of plane quartics which are totally tangent to the discriminant quintic curve of such a conic bundle structure. The additional data of an even theta characteristic on the curves in the family gives us a model for the theta divisor.

A Triangular Finite Element with First-derivative Continuity Applied to Fusion MHD Applications

Abstract: We describe properties of the reduced quintic triangular finite element. The expansion used in the element will represent a complete quartic polynomial in two dimensions, and thus the error will be of order h5 if the solution is sufficiently smooth. The quintic terms are constrained to enforce C1 continuity across element boundaries, allowing their use with partial differential equations involving derivatives up to fourth order. There are only three unknowns per node in the global problem, which leads to lower rank matrices when compared with other high-order methods with similar accuracy but lower order continuity. The integrations to form the matrix elements are all done in closed form, even for the nonlinear terms. The element is shown to be well suited for elliptic problems, anisotropic diffusion, the Grad-Shafranov-Schlter equation, and the time-dependent MHD or extended MHD equations. The element is also well suited for 3D calculations when the third (angular) dimension is represented as a Fourier series.

Fractional Branes in Landau-Ginzburg Orbifolds

Abstract: We construct fractional branes in Landau-Ginzburg orbifold categories and study their behavior under marginal closed string perturbations. This approach is shown to be more general than the rational boundary state construction. In particular we find new D-branes on the quintic -- such as a single D0-brane -- which are not restrictions of bundles on the ambient projective space. We also exhibit a family of deformations of the D0-brane in the Landau-Ginzburg category parameterized by points on the Fermat quintic.

Quantum fluctuations around bistable solitons in the cubic quintic nonlinear Schrödinger equation

Abstract: Small quantum fluctuations in solitons described by the cubic–quintic nonlinear Schrodinger equation (CQNLSE) are studied within the linear approximation. The cases of both self-defocusing and self-focusing quintic terms are considered (in the latter case, the solitons may be effectively stable, despite the possibility of collapse). The numerically implemented back-propagation method is used to calculate the optimal squeezing ratio for the quantum fluctuations versus the propagation distance. In the case of self-defocusing quintic nonlinearity, opposite signs in front of the cubic and quintic terms make the fluctuations around bistable pairs of solitons (which have different energies for the same width) totally different. The fluctuations of nonstationary Gaussian pulses in the CQNLSE model are also studied.

Critical point quantities and integrability conditions for a class of quintic systems

Abstract: For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighborhood of the origin are also given The technique employed is essentially different from usual ones The recursive formula for computation of critical point quantities is linear and then avoids complex integral operations Some results show an interesting contrast with the related results on quadratic systems

Quantum Fluctuations around Bistable Solitons in the Cubic-Quintic nonlinear Schr\"{o}dinger equation

Abstract: Small quantum fluctuations in solitons described by the cubic-quintic nonlinear Schr\"{o}dinger equation (CQNLSE) are studied with the linear approximation. The cases of both self-defocusing and self-focusing quintic term are considered (in the latter case, solitons may be effectively stable, despite the possibility of collapse). The numerically implemented back-propagation method is used to calculate the optimal squeezing ratio for the quantum fluctuations vs. the propagation distance. In the case of the self-defocusing quintic nonlinearity, opposite signs in front of the cubic and quintic terms make the fluctuations around bistable pairs of solitons (which have different energies for the same width) totally different. The fluctuations around nonstationary Gaussian pulses in the CQNLSE model are studied too.

Optimal Rational Circles of Degrees Five and Six

Abstract: This paper presents new low degree, complete Bcircles with positive weights. Speciflcally: two symmetric, quintic parametrizations | opti- mized towards arc-length parametrization in L 2 and L 1 norms | are developed and a new degree six circle with a symmetric, near arc-length parametrization is presented. Properties of the parametrizations are discussed and compared.

The Quintic Gauss Sums

Abstract: We investigate the possibility of generalization of the Cassel-McGettrick formula for the quintic Gauss sums We construct a fundamental region for the fifth cyclotomic field we describe in general the combinatoric of their geometry The formula obtained so far satisfied a recurrence relation The Euler relation is proved We show how to extract canonicaly a root of unity once we have contructed the fundamental region The numerical computation shows that a generalization of Cassels-McGettrick formula fails One should actually attempt to modify the shape of the fundamental region to see if there is a new formula We prove that there are new conjectures involving Gauss sums This is actually supported by strong computation within a certain range In the appendix we show that, there are Gauss sums which are rational intgers we explicitely give a proof and how to find them

On the lagrange resolvents of a dihedral quintic polynomial

Abstract: The cyclic quartic field generated by the fifth powers of the Lagrange resolvents of a dihedral quintic polynomial f(x) is explicitly determined in terms of a generator for the quadratic subfield of the splitting field of f(x) .