on hamiltonian stationary lagrangian spheres in non einstein kahler surfaces hamiltonian stationary lagrangian spheres in kahler einstein surfaces are minimal we prove that in the family of non einstein kahler surfaces given by the product 1 2 of two complete orientable riemannian surfaces of different constant gauss curvatures there is only a non minimal hamiltonian stationary lagrangian sphere this example defined when the surfaces 1 and 2 are spheres is unstable

an efficient wavelet preconditioner for iterative solution of three dimensional electromagnetic integral equations a wavelet based preconditioning method is proposed to facilitate the iterative solution of three dimensional 3 d electromagnetic integral equations the preconditioner is derived from the wavelet transform of the moment matrix it is based on the observation that both the moment matrix and its inverse exhibit a sparse multilevel finger structure a method based on the forbenius norm minimization is used to solve the inverse of the matrix under the multilevel finger structure numerical results on a 3 d cavity show that the iteration numbers are significantly reduced with the wavelet preconditioned system the computational cost of the preconditioner is kept under o nlogn

price dynamics of the financial markets using the stochastic differential equation for a potential double well abstract we have used the ito s stochastic differential equation for the double well with additive white noise as a mathematical model for price dynamics of the financial market we have presented a model which allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets we have obtained the mean price in terms of the parameter that represents the force of the randomness term of the model

pseudo holomorphic curves in complex grassmann manifolds it is proved that the kahler angle of the pseudo holomorphic sphere of constant curvature in complex grassmannians is constant at the same time we also prove several pinching theorems for the curvature and the kahler angle of the pseudo holomorphic spheres in complex grassmannians with non degenerate associated harmonic sequence

indication of multiscaling in the volatility return intervals of stock markets a certain trend with the mean interval we generate surrogate records using the schreiber method and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law we also find that the original and surrogate records exhibit slight tendencies for short and long due to the discreteness and finite size effects of the records respectively to avoid as possible those effects for testing the multiscaling behavior we investigate the moments in the range 10100 and find that the exponent from the power law fitting m has a narrow distribution around 0 which depends on m for the 500 stocks the distribution of for the surrogate records are very narrow and centered around 0 this suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility

constant curvature surfaces of the supersymmetric ℂpn 1 sigma model constant curvature surfaces are constructed from the finite action solutions of the supersymmetric pn 1 sigma model it is shown that there is a unique holomorphic solution which leads to constant curvature surfaces the generalized veronese curve we give a general criterion to construct non holomorphic solutions of the model we extend our analysis to general supersymmetric grassmannian models

stochastic process with multiplicative structure for the dynamic behavior of the financial market abstract a stochastic model with multiplicative noise has been proposed as a mathematical model for the prices dynamics of the financial market we have presented a model which allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to facts of the financial market we calculate the long range memory of the model and studied the behavior of the long tail distribution of the cumulative distribution of probabilities for the model with additive and multiplicative noise

a flexible and efficient higher order fe bi mlfma for scattering by a large body with deep cavities the hybrid finite element boundary integral multilevel fast multipole algorithm fe bi mlfma is applied to solve the challenge problem of scattering by a large body with deep cavities in this paper the hierarchical higher order curvilinear vector finite element hcvfe is employed to reduce the numerical dispersion error in the fem and to efficiently model the geometry of the cavity the coupling approaches are investigated at the interface between the fe region and the bi region for handling the problem of the different order basis functions and meshes used in the fe and bi region the problems encountered with the previous decomposition algorithm of fe bi mlfma are pointed out and analyzed in this paper a special algorithm of fe bi mlfma is designed based on the distinct geometry characteristics of deep cavity numerical results are presented to demonstrate the accuracy efficiency and flexibility of the higher order fe bi mlfma for scattering by a large body with big and deep cavities

the space of almost complex 2 spheres in the 6 sphere the complex dimension of the space of linearly full almost complex 2 spheres of area 4 d in the round 6 sphere is calculated to be d 8 explicit examples of these objects are constructed for every integer value of the degree d 6 d 6 7 furthermore it is shown that when d 6 this space is isomorphic to the group g2 c and when d 7 this space is empty we also show that the dimension of the space of non linearly full almost complex 2 spheres of area 4 d in the round 6 sphere is 2d 5

an efficient preconditioner for electromagnetic integral equations using predefined wavelet packet basis an approximate inverse preconditioner based on the predefined wavelet packet pwp basis is proposed for the fast iterative solution of electromagnetic integral equations the pwp basis is designed to achieve a sparse representation of the moment matrix and the preconditioner is constructed by inverting the block diagonal approximation of the pwp based moment matrix and transforming the results into the space domain numerical results show that the pwp preconditioner is effective in accelerating the convergence rate of iterative solution to moment equations it is also demonstrated that by properly designing the block diagonal matrix and computing the matrix elements the total computational complexity and memory costs for the preconditioner can be kept to o nlogn

minimal surfaces of constant curvature in ⁿ in this note we study an overdetermined system of partial differential equations whose solutions determine the minimal surfaces in s of constant gaussian curvature if the gaussian curvature is positive the solution to the global problem was found by calabi while the solution to the local problem was found by wallach the case of nonpositive gaussian curvature is more subtle and has remained open we prove that there are no minimal surfaces in sn of constant negative gaussian curvature even locally we also find all of the flat minimal surfaces in s and give necessary and sufficient conditions that a given two torus may be immersed minimally conformally and flatly into s 0 introduction in this paper we classify the connected minimal surfaces of constant gaussian curvature in the unit n sphere sn c enll for all n it is a classical fact and follows easily from the structure equations that the only examples up to rigid motion in s3 are the open subsets of the geodesic spheres with k 1 and the clifford torus with k 0 in an early paper boruvka constructed a linearly full immersion s2 c s2m for each m 0 where the induced metric had k 2 m m 1 later calabi showed that up to rigid motion these boruvka spheres were the only compact minimal surfaces with k ko 0 in s for any n wallach proved that any connected piece of minimal surface with k a positive constant in sn was a subset of a boruvka sphere kenmotsu 1976 found all of the flat minimal surfaces k 0 in s and quite recently kenmotsu 1983 showed that k ko 0 is impossible for minimal surfaces in s4 the techniques used in the above proofs range from harmonic analysis to rather involved calculations with the moving frame on the other hand in this paper we take a somewhat different point of view if m2 ds2 is a surface of constant gaussian curvature k then the minimal surfaces in s n c e n 1 of constant gaussian curvature k are given locally by smooth maps f m en lwhich satisfy three conditions first kf f 1 second af 2f a is the laplace beltrami operator of ds2 and third that f should be an isometry kdf df ds2 we study the more general class of maps f m en 1 which only satisfy the first two conditions note that this set of equations is already overdetermined by one equation received by the editors august 14 1984 1980 mathematics subject classification primary 53a10 secondary 53b25 53c40

new concentration phenomena for su 3 toda system in this paper we consider the following su 3 toda system 0 1 u1 2 2h1eu1 2h2eu2 0in b1 0 u2 2 2h2eu2 2h1eu1 0in b1 0 u1 u2 0on b1 0 where is a positive parameter which will go to zero h1 x h2 x h x is a positive smooth function and b1 0 is a unit ball in r2 in 29 the authors construct a family of solutions u1 u2 of 0 1 for h 1 such that the solutions blow up at the origin with mass 8 4 after some scaling with the limiting profile wi x i 2ewi in r2 r2 x i 2ewi where i 23 i for i 1 2 in that paper the authors ask whether there exist blow up solutions of mass 8 4 with the limiting profile w 2ew 0in r2 r2ew such that u1 is the sum of two bubbles and u2 has one bubble in this paper we prove that such solution exists

a finite element boundary integral formulation for scattering by three dimensional cavity backed apertures a novel numerical technique is proposed for the electromagnetic characterization of the scattering by a three dimensional cavity backed aperture in an infinite ground plane the technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity specifically the finite element method is used to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane unlike traditional approaches the proposed technique does not require a knowledge of the cavity s green s function and is therefore applicable to arbitrary shape depressions and material fillings furthermore the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms

convergence rate location and z2 condition for fully bubbling solutions to su n 1 toda systems abstract it is well known that the study of su n 1 toda systems is important not only to chern simons models in physics but also to the understanding of holomorphic curves harmonic sequences or harmonic maps from riemann surfaces to c p n one major goal in the study of su n 1 toda system on riemann surfaces is to completely understand the asymptotic behavior of fully bubbling solutions in this article we use a unified approach to study fully bubbling solutions to general su n 1 toda systems and we prove three major sharp estimates important for constructing bubbling solutions the closeness of blowup solutions to entire solutions the location of blowup points and a z 2 condition

a willmore functional for compact surfaces of complex projective plane where h denotes the mean curvature vector of the immersion k the sectional curvature of m restricted to and da the canonical measure of the induced metric this functional has been extensively studied when m is the euclidean space r or the sphere s or the hyperbolic space rh because w is invariant under conformal transformations of ambient space the type of problems which have been studied for this ambient space r are of a different nature on the one hand are the papers written with the object of obtaining lower bounds for the functional w given that w has 4 as an absolute minimum and is only reached by the round spheres of r willmore proposed to study this functional on tori and conjectured that 2 is the minimum value for these surfaces and it is attained only by the clifford torus this problem which still has not been resolved can be considered as the starting point of a series of important papers in which minimization

classification of conformal minimal immersions of constant curvature from s 2 to hp 2 in this paper we study geometry of conformal minimal two spheres immersed in quaternionic projective spaces we firstly use bahy el dien and wood s results to obtain some characterizations of the harmonic sequences generated by conformal minimal immersions from s 2 to the quaternionic projective space hp 2 then we give a classification theorem of linearly full totally unramified conformal minimal immersions of constant curvature from s 2 to the quaternionic projective space hp 2

analysis of transient electromagnetic scattering from overfilled cavities in this paper we consider the time domain scattering problem of a two dimensional overfilled cavity embedded in the infinite ground plane the problem is first discretized in time by the beta gamma newmark time marching scheme at each time step the variational formulation of the semidiscrete problem is derived via a nonlocal boundary condition to truncate the infinite problem domain existence and uniqueness of the variational solutions are established error analysis of the fully discrete problem is performed stability criteria of the time stepping scheme are also obtained

a moebius characterization of veronese surfaces in s n let m m be an umbilic free submanifold in s n with i and ii as the first and second fundamental forms an important moebius invariant for m m in moebius differential geometry is the so called moebius form phi defined by phi rho 2 sum i alpha h alpha i sum j ii alpha ij h alpha i ij e j log rho omega i otimes e alpha where e i is a local basis of the tangent bundle with dual basis e alpha is a local basis of the normal bundle h sum alpha h alpha e alpha is the mean curvature vector and rho sqrt m over m 1 ii hi in this paper we prove that if x s 2 to s n is an umbilics free immersion of 2 sphere with vanishing moebius form phi then there exists a moebius transformation tau s n to s n and a 2k equator s 2k subset s n with 2 le k le n 2 such that tau circ x s 2 to s 2k is the veronese surface

modeling of the financial market using the two dimensional anisotropic ising model we have used the two dimensional classical anisotropic ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market the model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets we have obtained the mean price in terms of the strong of the site anisotropy term which reinforces the sensitivity of the agent s sentiment to external news

general solutions of the supersymmetric ℂp2 sigma model and its generalisation to ℂpn 1 a new approach for the construction of finite action solutions of the supersymmetric pn 1 sigma model is presented we show that this approach produces more non holomorphic solutions than those obtained in previous approaches we study the p2 model in detail and present its solutions in an explicit form we also show how to generalise this construction to n 3

correction to the classification of the surfaces with parallel mean curvature vector in two dimensional complex space forms we give a condition under which the findings of the paper by kenmotsu and zhou it amer j math bf 122 2000 no 2 295 317 work well and determine the surfaces that were not considered before

electromagnetic scattering from three dimensional cavities via a connection scheme the electromagnetic scattering from arbitrary three dimensional cavities is presented to alleviate computational constraints for three dimensional problems a connection scheme is developed based on microwave network theory this scheme allows the cavity to be divided into sections and each section to be analyzed independently of the rest of the cavity each section of the cavity is represented by a generalized admittance matrix which if formulated via a boundary integral equation approach using the concept of input and load admittance the aperture admittance matrix of the cavity can be derived by cascading the admittance matrices of individual sections once the cavity aperture admittance matrix is obtained the aperture electric field and the backscattered field are found by the standard generalized network formulation numerical results are compared against modal solutions of regularly shaped cavities with good agreement this connection scheme leads to a reduction in computational resources especially for cavities with one dimension much larger than the other two

new blow up phenomena for su n 1 toda system abstract we consider the su n 1 toda system s u 1 2 e u 1 e u 2 e u k 0 in u 2 e u 1 2 e u 2 e u k 0 in u k e u 1 e u 2 2 e u k 0 in u 1 u 2 u k 0 on if 0 and is symmetric with respect to the origin we construct a family of solutions u 1 u k to s such that the i th component u i blows up at the origin with a mass 2 i 1 as goes to zero

classification and nondegeneracy of su n 1 toda system with singular sources we consider the following toda system open image in new window where i 1 0 is dirac measure at 0 and the coefficients a ij form the standard tri diagonal cartan matrix in this paper i we completely classify the solutions and obtain the quantization result sum j 1 n a ij int mathbb r 2 e u j dx 4 pi 2 gamma i gamma n 1 i quad forall 1 leq i leq n this generalizes the classification result by jost and wang for i 0 forall 1 leq i leq n ii we prove that if i i 1 j for all 1 i j n then any solution u i is radially symmetric w r t 0 iii we prove that the linearized equation at any solution is non degenerate these are fundamental results in order to understand the bubbling behavior of the toda system

a generalized transition matrix model for open ended cavity with complex internal structures in this paper a novel generalized transition matrix gtm algorithm is proposed to analyze the electromagnetic problems of open ended cavity structures an artificial reference surface is applied to seal the slots and or apertures to reshape the target cavity into an interior domain containing inner metallic surface and internal structures and an exterior domain containing the outer surface of the cavity special junctions at the transitional connection of the two domains are applied to guarantee the current continuity on the metallic surface based on the huygens principle an associated gtm is constructed on the reference surface and the special junctions to extract the characteristics of the interior region of the cavity the gtm is independent of the outer shape of the cavity and the exterior electromagnetic environment the computational complexity can be effectively reduced especially when the interior region is with fine structures and internal sources to investigate the feasibility and effectiveness of the proposed approach several numerical examples are presented

surfaces with parallel mean curvature vector in complex space forms we consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its 2 0 part is holomorphic when the complex dimension of the ambient space is equal to 2 we define a second quadratic form with the same property and then determine those surfaces with parallel mean curvature vector on which the 2 0 parts of both of them vanish we also provide a reduction of codimension theorem and prove a non existence result for 2 spheres with parallel mean curvature vector

a near resonance decoupling approach nrda for scattering solution of near resonant structures the generalized network formulation is applied in combination with the method of moments to calculate the electromagnetic scattering from conducting objects containing near resonant open ended cavities the presence of the cavity increases the iteration number in conjugate gradient iterations due to the near resonant modes and the multiple wave bounces inside the cavity the equivalence principle is used to separate the cavity region from the rest of the object allowing an independent solution of the cavity problem by a direct inversion algorithm using a connection scheme the solution of the cavity is then represented by a generalized admittance matrix numerical results for two dimensional 2 d composite targets show that the iteration number can be reduced significantly for objects containing long cavities this algorithm can also be applied to three dimensional problems

on conformal minimal immersions of constant curvature from s 2 to hp n we generalize here our general characterization of the harmonic sequence generated by conformal minimal immersions from s 2 to the quaternionic projective space hp n then we give a classification theorem of linearly full unramified conformal minimal immersions of constant curvature from s 2 to hp n under some conditions

submanifolds with curvature normals of constant length and the gauss map we show that a submanifold with curvature normal of constant length has constant principal curvatures under suitable global hypothesis we construct local counterexamples to show that the global hypothesis can not be dropped

the classification of the surfaces with parallel mean curvature vector in two dimensional complex space forms in this paper we find new surfaces with parallel mean curvature vectors in two dimensional complex space forms that are not of constant kahler angles and then classify all of them the surface can be isometrically deformed preserving both the length of the mean curvature vector and the kahler angle from this classification the deformations appear only when the curvature of the ambiant space is nonpositive

degree counting and shadow system for toda system of rank two one bubbling abstract we initiate the program for computing the leray schauder topological degree for toda systems of rank two this program still contains a lot of challenging problems for analysts as the first step we prove that if a sequence of solutions u 1 k u 2 k blows up then one of h j e u j k m h j e u j k d v g j 1 2 tends to a sum of dirac measures this is so called the phenomena of weak concentration our purposes in this article are i to introduce the shadow system due to the bubbling phenomena when one of parameters i crosses 4 and j 4 n where 1 i j 2 ii to show how to calculate the topological degree of toda systems by computing the topological degree of the general shadow systems iii to calculate the topological degree of the shadow system for one point blow up we believe that the degree counting formula for the shadow system would be useful in other problems

filtrations factorizations and explicit formulae for harmonic maps we use filtrations of the grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a riemann surface and so all harmonic maps from the 2 sphere to the unitary group for a general class of factorizations by unitons we show how these specialize to give explicit formulae for such harmonic maps to each of the classical compact lie groups and their inner symmetric spaces the nonlinear model of particle physics our methods also give an explicit iwasawa decomposition of the algebraic loop group

sequences of willmore surfaces in this paper we develop the theory of willmore sequences for willmore surfaces in the 4 sphere we show that under appropriate conditions this sequence has to terminate in this case the willmore surface either is the twistor projection of a holomorphic curve into mathbb c mathbb p 3 or the inversion of a minimal surface with planar ends in mathbb r 4 these results give a unified explanation of previous work on the characterization of willmore spheres and willmore tori with non trivial normal bundles by various authors

analytic aspects of the toda system i a moser trudinger inequality in this paper we analyze solutions of the open toda system and establish an optimal moser trudinger type inequality for this system let be a closed surface with area 1 and k aij n n the cartan matrix for su n 1 i e we show that has a lower bound in h1 n if and only if this inequality is optimal as a direct consequence if mj for 4 for j 1 2 n m has a minimizer u that satisfies 2001 john wiley sons inc

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

degree counting for toda system with simple singularity one point blow up abstract in this paper we study the degree counting formula of the rank two toda system with simple singular source when 1 0 4 4 8 and 2 4 n the key step is to derive the degree formula of the shadow system which arises from the bubbling solutions as 1 tends to 4 in order to compute the topological degree of the shadow system we need to find some suitable deformation during this deformation we shall deal with new difficulty arising from the phenomenon blow up does not necessarily imply concentration of mass this phenomenon occurs due to the collapsing of singularities this is a continuation of the previous work 25

quantization of curvature of harmonic two spheres in grassmann manifolds various pinching theorems for curvature of minimal two spheres in grassmann manifolds have been proved in particular we show that when the curvature is large then the minimal map from s2 into g m n must be either holomorphic or antiholomorphic also minimal two spheres of curvature k 2 in g 2 4 have been classified 0 introduction it is known that starting from a harmonic map f from a riemann surface into a complex grassmann manifold one can define sequences of harmonic maps by using the 0 transform and the 0 transform these sequences are called harmonic sequences cw when f is holomorphic the sequence generated by f via the 0 transform is called a pseudoholomorphic sequence and the corresponding maps are called pseudoholomorphic maps in 1980 a m din and w j zakrzewski dz and then in 1983 j eells and j c wood ec showed that all harmonic maps from s2 to the complex projective space cpf are in fact pseudoholomorphic recently f burstall j rawnsley and s salamon announced in brs that all stable harmonic maps from s2 into irreducible hermitian symmetric spaces are either holomorphic or antiholomorphic it is also known that when the target space is a general complex grassmann manifold holomorphic curves do not generate all harmonic maps cw ra on the other hand m rigoli showed in r that for a linearly full nonsingular holomorphic curve from s2 into cpn if its curvature k 4 n then k 4 n is constant then j bolton et al bjrw generalized this result to pseudoholomorphic maps and showed that for a linearly full isometric pseudoholomorphic map of position r from s2 into cpn if its curvature k 4 2r n r n then k 41 2r n r n is constant in this paper we prove various pinching theorems of curvature for harmonic maps and show that for any nonsingular harmonic map from s2 into a complex grassmann manifold if the curvature of its induced metric is large then received by the editors january 18 1988 and in revised form april 11 1988 1980 mathematics subject classification 1985 revision primary 53a10 53c55

rigidity of pseudo holomorphic curves of constant curvature in grassmann manifolds rigidity of minimal immersions of constant curvature in harmonic sequences generated by holomorphic curves in grassmann manifolds is studied in this paper by lifting them to holomorphic curves in certain projective spaces we prove that for such curves the curvature must be positive and that all such simply connected curves in cp are generated by veronese curves thus generalizing calabi s counterpart for holomorphic curves in cp we also classify all holomorphic curves from the riemann sphere into g 2 4 whose curvature is equal to 2 into two families which illustrates pseudo holomorphic curves of positive constant curvature in g m n are in general not unitarily equivalent constracting to the fact that generic isometric complex submanifolds in a kaehler manifold are congruent where f x dfi for j 0 1 2 and f m c7 w n are harmonic maps one defines mj x 0 if f is anti holomorphic we call fr a pseudo holomorphic curve of position r generated by when is holomorphic where is called the directrix of fr such curves with the induced metrics from the associated grassmannians form a class of minimal immersions when special ized to g l n i cp a pseudo holomorphic curve of position r is just the r th position vector of a frenet frame of a holomorphic curve projected into cp the importance of such maps comes from the fact that any har monic map from the riemann sphere or any harmonic map of nonzero degree from a torus into cp is pseudo holomorphic 7 furthermore in 6 these curves play a central role when m s defined in the sequence 0 1 are all equal and f s are orthogonal called frenet harmonic sequences for the study of

conformally parametrized surfaces associated with protect bb c p n 1 sigma models two dimensional parametrized surfaces immersed in the su n algebra are investigated the focus is on surfaces parametrized by solutions of the equations for the sigma model the lie point symmetries of the model are computed for arbitrary n the weierstrass formula for immersion is determined and an explicit formula for a moving frame on a surface is constructed this allows us to determine the structural equations and geometrical properties of surfaces in the fundamental forms gaussian and mean curvatures willmore functional and topological charge of surfaces are given explicitly in terms of any holomorphic solution of the model the approach is illustrated through several examples including surfaces immersed in low dimensional su n algebras

on spectral geometry of minimal surfaces in ⁿ by employing the standard isometric imbedding of cpn into the euclidean space a classification theorem for full minimal 2 type surfaces in cpn that are not holomorphic is given all such compact minimal surfaces are either totally real minimal surfaces in cp2 or totally real superminimal surfaces in cp3 and cp4 in the latter case they are locally unique moreover some eigenvalue inequalities for compact minimal surfaces of cpn with constant kaehler angle are shown