the fast multipole method fmm for electromagnetic scattering problems the fast multipole method fmm developed by v rokhlin 1990 to efficiently solve acoustic scattering problems is modified and adapted to the second kind integral equation formulation of electromagnetic scattering problems in two dimensions the present implementation treats the exterior dirichlet problem for two dimensional closed conducting objects of arbitrary geometry the fmm reduces the operation count for solving the second kind integral equation from o n sup 3 for gaussian elimination to o n sup 4 3 per conjugate gradient iteration where n is the number of sample points on the boundary of the scatterer a sample technique for accelerating convergence of the iterative method termed complexifying k the wavenumber is also presented this has the effect of bounding the condition number of the discrete system consequently the operation count of the entire fmm all iterations becomes o n sup 4 3 computational results for moderate values of ka where a is the characteristic size of the scatterer are given

investigation of nonplanar perfectly matched absorbers for finite element mesh truncation we present a detailed theoretical and numerical investigation of the perfectly matched layer pml concept as applied to the problem of mesh truncation in the finite element method fem we show that it is possible to extend the cartesian pml concepts involving half spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems by using the method of separation of variables it is possible to solve the boundary value problems in these geometries the analytical solutions demonstrate that under certain conditions outgoing waves are absorbed with negligible reflection and the transmitted wave is attenuated within the pml to reduce the white space in radiation or scattering problems conformal pmls are constructed via parametric mappings it is also verified that the pml concept which was originally introduced for problems governed by maxwell s equations can be extended to cases governed by the scalar helmholtz equation finally numerical results are presented to demonstrate the use of the pml in fem mesh truncation

on the positivity of the effective action in a theory of random surfaces it is shown that the functional s eta frac 1 24 pi int left frac 1 2 left nabla eta right 2 2 eta right d mu 0 defined onc functions on the two dimensional sphere satisfies the inequalitys 0 if is subject to the constraint int e eta 1 d mu 0 0 the minimums 0 is attained at the solutions of the euler lagrange equations the proof is based on a sharper version of moser trudinger s inequality due to aubin which holds under the additional constraint int e eta xd mu 0 0 this condition can always be satisfied by exploiting the invariance ofs under the conformal transformations ofs2 the result is relevant for a recently proposed formulation of a theory of random surfaces

a singular sphere covering inequality uniqueness and symmetry of solutions to singular liouville type equations we derive a singular version of the sphere covering inequality which was recently introduced in gui and moradifam invent math https doi org 10 1007 s00222 018 0820 2 2018 suitable for treating singular liouville type problems with superharmonic weights as an application we deduce new uniqueness results for solutions of the singular mean field equation both on spheres and on bounded domains as well as new self contained proofs of previously known results such as the uniqueness of spherical convex polytopes first established in luo and tian proc am math soc 116 4 1119 1129 1992 furthermore we derive new symmetry results for the spherical onsager vortex equation

a fast numerical method for electromagnetic scattering from dielectric rough surfaces in this paper we propose an efficient and accurate iterative numerical approach to analyze em scattering from 1 d dielectric rough surfaces it is based on a new splitting of the impedance matrix z to improve the asymptotic convergence rate of the resultant iterative system the structure of split matrix is then fully explored in combination with the application of an identity for inverse of block matrix to further reduce the computational and storage complexity the embedded matrix vector product is computed using the spectral acceleration technique extensive numerical simulations demonstrate a couple of appealing features of this proposed method for gaussian surface with gaussian spectrum 1 it converges faster than both forward backward method fbm and fbm with spectral acceleration fbm sa 2 for hh polarization the proposed method is about twice as fast as fbm sa for vv polarization the proposed method is better when the rms slope is not larger than 16 or interestingly when rms height is beyond 2 0 wavelengths moreover it converges for cases where fbm sa fails for both polarizations these features indicate that the proposed method can be effectively used to analyze em scattering from 1 d dielectric gaussian surface with gaussian spectrum

compact isospectral sets of surfaces on etudie des ensembles de surfaces qui sont isospectrales par rapport a l operateur de laplace beltrami

the generalized forward backward method for analyzing the scattering from targets on ocean like rough surfaces in holliday et al 1995 1996 the iterative forward backward fb method has been proposed to solve the magnetic field integral equation mfie for smooth one dimensional 1 d rough surfaces this method has proved to be very efficient converging in a very small number of iterations nevertheless this solution becomes unstable when some obstacle like a ship or a large breaking wave is included in the original problem in this paper we propose a new method the generalized forward backward gfb method to solve such kinds of complex problems the approach is formulated for the electric field integral equation efie which is solved using a hybrid combination of the conventional fb method and the method of moments mom the latter of which is only applied over a small region around the obstacle the gfb method is shown to provide accurate results while maintaining the efficiency and fast convergence of the conventional fb method some numerical results demonstrate the efficiency and accuracy of the new method even for low grazing angle scattering problems

numerical approximations to the scaled first derivatives of the solution to a two parameter singularly perturbed problem abstract a singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise uniform shishkin mesh scaled discrete derivatives with scaling only used within the layers are shown to be parameter uniformly convergent to the scaled first derivatives of the continuous solution

invariant conformal metrics on ⁿ in this paper we use the relationship between conformal metrics on the sphere and horospherically convex hypersurfaces in the hyperbolic space for giving sufficient conditions on a conformal metric to be radial under some constrain on the eigenvalues of its schouten tensor also we study conformal metrics on the sphere which are invariant by a k parameter subgroup of conformal diffeomorphisms of the sphere giving a bound on its maximum dimension moreover we classify conformal metrics on the sphere whose eigenvalues of the shouten tensor are all constant we call them isoparametric conformal metrics and we use a clas

extremals for moser inequalities this paper shows that extremals exist for four moser inequalities involving exponential integrals the results are for sobolev spaces defined on the spheres s2 and s3 on the disk d2 and on rp2 the method that carleson and chang used for the n ball with boundary value zero can be modified and applied to functions with mean value zero on these domains this approach also provides an elementary proof of the moser inequality for sn n 2 which is a special case of a result of fontana

a uniformly convergent galerkin method on a shishkin mesh for a convection diffusion problem abstract a galerkin finite element method that uses piecewise bilinears on a simple piecewise equidistant mesh is applied to a linear convection dominated convection diffusion problem in two dimensions the method is shown to be convergent uniformly in the perturbation parameter of ordern 1 ln nin a global energy norm and of ordern 1 2ln3 2 npointwise near the outflow boundary where the total number of mesh points iso n2

sharp moser trudinger inequalities for the laplacian without boundary conditions we derive a sharp moser trudinger inequality for the borderline sobolev imbedding of w2 n 2 bn into the exponential class where bn is the unit ball of rn the corresponding sharp results for the spaces w0d n d are well known for general domains and are due to moser and adams when the zero boundary condition is removed the only known results are for d 1 and are due to chang yang cianchi and leckband the proof of our result is based on a new integral representation formula for the canonical solution of the poisson equation on the ball that is the unique solution of the equation u f which is orthogonal to the harmonic functions on the ball the main technical difficulty of the paper is to establish an asymptotically sharp growth estimate for the kernel of such representation expressed in terms of its distribution function

the scalar curvature flow on s n perturbation theorem revisited for the problem of finding a geometry on s n for n 3 with a prescribed scalar curvature there is a well known result which is called the perturbation theorem it is due to chang and yang duke math j 64 27 69 1991 their key assumption is that the candidate f for the prescribed scalar curvature is sufficiently near the scalar curvature of the standard metric in the sup norm it is important to know how large that difference in sup norm can possibly be here we consider prescribing scalar curvature problem using the scalar curvature flow

application of an adams type inequality to a two chemical substances chemotaxis system abstract this paper deals with positive solutions of the fully parabolic system u t u u v in 0 1 v t v v w in 0 2 w t w w u in 0 under homogeneous neumann boundary conditions or mixed boundary conditions no flux and dirichlet conditions in a smooth bounded domain r n n 4 with positive parameters 1 2 0 and nonnegative smooth initial data u 0 v 0 w 0 in the lower dimensional case n 3 it is proved that for all reasonable initial data solutions of the system exist globally in time and remain bounded in the case n 4 it is shown that in the radially symmetric setting solutions to the neumann boundary value problem of the system exist globally in time and remain bounded if u 0 l 1 8 2 as to the mixed boundary value problem we will establish global existence and boundedness of solutions if u 0 l 1 8 2 without radial symmetry the key ingredients are a lyapunov functional and an adams type inequality a lyapunov functional of the above problems will be constructed and the constant 8 2 is deduced from the critical constant in the adams type inequality this result is regarded as a generalization of the well known 8 problem in the keller segel system to higher dimensions

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

discrete approximations of solutions and derivatives for a singularly perturbed parabolic convection diffusion equation in this paper we consider grid approximations of a boundary value problem on a segment for a singularly perturbed parabolic convection diffusion equation classical finite difference approximations on piecewise uniform meshes condensing in a neighborhood of the boundary layer are used it is necessary to find numerical approximations to both the solution and its first order derivatives with errors weakly depending on the perturbation parameter e the approximation errors in solutions and derivatives are examined in the metric which is adequate for capturing singular solutions of problems with boundary layers in this metric the errors of the solution and its derivative t u x t are determined by the absolute errors and the error in the derivative x u x t is determined by the relative error with respect to a majorant function for this derivative in the boundary layer and by the absolute error outside it in the class of meshes whose mesh size in the boundary layer does not decrease away from the boundary it is shown that there are no meshes on which the scheme converges e uniformly in the metric we establish conditions imposed on the parameters of piecewise uniform meshes under which the schemes converge in the metric almost e uniformly that is at a rate of o e vn 1 n0 1 where v 0 may be arbitrarily small n and n0 define the numbers of mesh points in x and t respectively

domain compression via anisotropic metamaterials designed by coordinate transformations we introduce a spatial coordinate transformation technique to compress the excessive white space i e free space in the computational domain of finite methods this approach is based on the form invariance property of maxwell s equations under coordinate transformations clearly maxwell s equations are still satisfied inside the transformed space but the medium turns into an anisotropic medium whose constitutive parameters are determined by the coordinate transformation the proposed technique can be employed to reduce the number of unknowns especially in high frequency applications wherein a finite method requires an electrically large computational domain after developing the analytical background of this technique we report some numerical results for finite element simulations of electromagnetic scattering problems

conformal deformation of metrics on s 2 soit d un domaine lisse de s 2 et k une fonction lisse definie sur d alors pour que le probleme aux limites de neumann u k exp 2u 1 sur d u n 0 sur d ait une solution u on a a quand aire d max x d k x 0

a new approach to sharp moser trudinger and adams type inequalities a rearrangement free argument abstract the main purpose of this paper is two fold on the one hand we will develop a new approach to establish sharp singular moser trudinger and adams type inequalities in unbounded domains of euclidean spaces without using the standard symmetrization on the other hand we will prove the sharp singular adams type inequality on high order sobolev spaces w m n m r n of arbitrary integer order m theorem 1 1 which improves the results of ruf and sani 2013 48 where sharp adams inequalities were established for even m and those of the authors lam and lu 2012 28 29 for odd m but with different and more restricted norms we first establish the sharp local singular adams inequality on domains in r n of finite measure theorem 1 4 we take a perspective that any function in the high order sobolev spaces w m n m r n can be represented as a bessel potential thus we can fully use the tools from harmonic analysis and the kernel properties of the polyharmonic operators i m 2 once we have established this sharp local adams inequality then we can adapt the rearrangement free method we will develop in this paper to derive a global sharp adams inequality from a local one our argument substantially simplifies those in ruf and sani 2013 48 and lam and lu 2012 28 29 and avoids the use of rather deep and complicated comparison principle of solutions to polyharmonic operators used in ruf and sani 2013 48 lam and lu 2012 28 29 moreover our theorem holds on sobolev spaces w n r n of any positive fractional order n theorems 1 6 and 1 7 as consequences we can also establish sharp adams inequalities with less restrictions on the sobolev norms see theorems 1 2 1 3 and 1 5 our approach is surprisingly simple and general and can be easily applied to scenarios such as riemannian and sub riemannian manifolds where symmetrization argument does not work see e g on the heisenberg group lam and lu 2012 30

non degeneracy and uniqueness of solutions to singular mean field equations on bounded domains abstract the aim of this paper is to complete the program initiated in 51 23 and then carried out by several authors concerning non degeneracy and uniqueness of solutions to mean field equations in particular we consider mean field equations with general singular data on non smooth domains the argument is based on the alexandrov bol inequality and on the eigenvalues analysis of linearized singular liouville type problems

on the symmetric scalar curvature problem on sn abstract we discuss some existence results dealing with the scalar curvature problem on s n in the presence of various symmetries

rotation hypersurfaces in spaces of constant curvature rotation hypersurfaces in spaces of constant curvature are defined and their principal curvatures are computed a local characterization of such hypersurfaces with dimensions greater than two is given in terms of principal curvatures some special cases of rotation hypersurfaces with constant mean curvature in hyperbolic space are studied in particular it is shown that the well known conjugation between the helicoid and the catenoid in euclidean three space extends naturally to hyperbolic three space h3 in the latter case catenoids are of three different types and the explicit correspondence is given it is also shown that there exists a family of simply connected complete embedded nontotally geodesic stable minimal surfaces in h3

monte carlo simulations of large scale problems of random rough surface scattering and applications to grazing incidence with the bmia canonical grid method scattering of a te incident wave from a perfectly conducting one dimensional random rough surface is studied with the banded matrix iterative approach canonical grid bmia cag method the bmia cag is an improvement over the previous bmia the key idea of bmia cag is that outside the near field interaction the rest of the interactions can be translated to a canonical grid by taylor series expansion the use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast fourier transform for nonnear field interaction the method can be used for monte carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface we illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns the method is also applied to study scattering from random rough surfaces at near grazing incidence the numerical examples illustrate the importance of using a large surface length for some backscattering problems

remesh free shape optimization by transformation optics a remesh free numerical method is developed for shape optimization problem by combining the transformation optics approach the finite element method and the genetic optimization algorithm to overcome cumbersome remeshing processes transformation media are designed within the elements where the contour of the object passes a simple rectangular mesh is used and only the material parameters of the media are redefined according to the scatterer contour that is represented by b spline curves the proposed approach is validated through benchmark inverse electromagnetic scattering problems

electromagnetic scattering from perfectly conducting rough surfaces a new full wave method a method that does not make use of the telegraphist s equations and takes into account the two dimensional roughness of the surface from the start is developed it is shown that the scattering coefficients obtained agree with those given in earlier work by e bahar 1973 1987 the method is based on reducing the three dimensional scattering problem to a two dimensional problem by expanding each rectangular component of maxwell s equations in terms of local basis functions along the perpendicular direction to the mean surface the transformed two dimensional field equations are solved using fourier transforms the full wave solutions are also compared with the first order perturbation solutions the kirchhoff type solutions and integral equation results

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

lattice electromagnetic theory from a topological viewpoint the language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice it is shown that differential forms and their discrete counterparts cochains provide a natural bridge between the continuum and the lattice versions of the theory allowing for a natural factorization of the field equations into topological field equations i e invariant under homeomorphisms and metric field equations the various potential sources of inconsistency in the discretization process are identified distinguished and discussed a rationale for a consistent extension of the lattice theory to more general situations such as to irregular lattices is considered

stochastic solutions to rough surface scattering using the finite element method we propose stochastic solutions to the scattering of electromagnetic waves from penetrable randomly rough surfaces using the vector based finite element method fem the random nature of the surface requires the computation to be performed on multiple surface instances we propose a mesh deformation scheme which allows the use of a single fem mesh for computing ensemble averaged quantities this scheme is used to perform monte carlo mc iterations which is much faster than the conventional techniques where a different mesh is utilized for each surface instance this scheme also allows for mc free formulations of the problem in the first kind we expand the solution in a stochastic basis using the concept of generalized polynomial chaos obtaining ensemble averaged quantities this results in a larger set of equations that need to be solved just once in the second kind the stochastic collocation method we run the deterministic solver at certain specified points in the random domain corresponding to the rough surface description we compare these results with those obtained by mc iterations and outline the computational costs and convergence behavior we find that stochastic methods are ideal for surfaces with large correlation lengths for other parameters the mc approach is preferable

an equation of monge ampere type in conformal geometry and four manifolds of positive ricci curvature we formulate natural conformally invariant conditions on a 4 manifold for the existence of a metric whose schouten tensor satisfies a quadratic inequality this inequality implies that the eigenvalues of the ricci tensor are positively pinched

extremal metrics of zeta function determinants on 4 manifolds in conformal geometry the sobolev inequality at a critical exponent has received much attention in particular the determination of the best constants has played a crucial role in the yamabe problem in dimension two the analogous problem deals with the moser trudinger inequality on a compact riemann surface m2 there exists a constant c c m so that f e47w2 c m if f ivw12 1 and f w 0 the connection of this inequality with geometry comes through the zeta functional determinant of the laplacian as defined by ray singer for a riemannian metric g let 0 a1 a2 be the spectrum

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

non maxwellian locally conformal pml absorbers for finite element mesh truncation we introduce the locally conformal perfectly matched layer pml approach which is an easy and straightforward pml implementation to the problem of mesh truncation in the finite element method fem this method is based on a locally defined complex coordinate transformation which has no explicit dependence on the differential geometric characteristics of the pml free space interface as a result it is possible to handle challenging pml geometries with interfaces having arbitrary curvature especially those with curvature discontinuities in order to implement this approach we also introduce the concept of complex space fem using elements with complex nodal coordinates after developing the analytical background of this method we present some numerical results to demonstrate the performance of this method in three dimensional electromagnetic scattering problems

on the best constant in the moser onofri aubin inequality let s2 be the 2 dimensional unit sphere and let j denote the nonlinear functional on the sobolev space h1 s2 defined by j alpha u frac alpha 16 pi int s 2 nabla u 2 d mu 0 frac 1 4 pi int s 2 u d mu 0 rm ln int s 2 e u frac d mu 0 4 pi where d mu 0 sin theta d theta wedge d phi onofri had established that j is non negative on h1 s2 provided 1 in this note we show that if j is restricted to those u in h 1 s 2 that satisfies the aubin condition int s 2 e u x j d mu 0 0 quad rm for all 1 leq j leq 3 then the same inequality continues to hold i e j u 0 whenever alpha geq frac 2 3 epsilon 0 for some epsilon 0 0 the question of chang yang on whether this remains true for all alpha geq frac 1 2 remains open

numerical approximation of solution derivatives in the case of singularly perturbed time dependent reaction diffusion problems numerical approximations to the solution of a linear singularly perturbed parabolic problem are generated using a classical finite difference operator on a piecewise uniform shishkin mesh first order convergence of these numerical approximations in an appropriately weighted c 1 norm is established numerical results are given to illustrate the theoretical error bounds

scalar curvature functions in a conformal class of metrics and conformal transformations on etudie le probleme de prescrire la courbure scalaire dans une classe conforme pour l action du groupe conforme on montre l universalite des conditions d integrabilite dues a j l kazdan et f w warner

a quantization property for blow up solutions of singular liouville type equations abstract motivated by the study of self dual vortices in gauge field theory cf vortices and monopoles birkhauser boston 1980 solitons in field theory and nonlinear analysis monographs in mathematics springer new york 2001 we consider a concentrating solution sequence u k satisfying u k z 2 k v k z e u k in b 1 z 2 k v k z e u k z 0 weakly in the sense of measures in b 1 where i k r k ii v k c 0 1 b 1 0 a v k b and v k a in b 1 we prove that necessarily 8 n 8 1 8 z the result is sharp as shown by explicit examples and should be compared with that obtained by li shafrir ind univ math j 43 4 1994 1255 concerning the situation where k 0 k n

a new numerical method for rough surface scattering calculations a new approach to solving the magnetic field integral equation mfie for the current induced on a infinite perfectly conducting rough surface is presented by splitting the propagator matrix into contributions from the left and from the right of the point of observation a second kind integral equation can be formed with a new born term and a new kernel following discretization of this new integral equation the unknown currents can be determined more rapidly and with significantly less storage requirements than conventional lu decomposition where the time saving factor is roughly n 3 where n is the number of current samples on the surface and the usual storage requirements associated with matrix inversion are eliminated while the new born term is usually adequate for scattered field calculations the new discretized integral equation can be iterated to amy desired accuracy with no apparent convergence problems results are presented for one dimensional rough surfaces with rms heights exceeding one wavelength and rms slopes exceeding 40 which illustrate the robustness of the new born term

monte carlo simulation of electromagnetic scattering from two dimensional random rough surfaces the fast multipole method fast fourier transform fmm fft method is developed to compute the scattering of an electromagnetic wave from a two dimensional 2 d rough surface the resulting algorithm computes a matrix vector multiply in o n log n operations this algorithm is shown to be more efficient than another o n log n algorithm the multilevel fast multipole algorithm mlfma for surfaces of small height for surfaces with larger roughness the mlfma is found to be more efficient using the mlfma monte carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2 d random rough surfaces using a workstation for the rougher surface backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient for the smoother surface the monte carlo results compare well with the results of the approximate kirchhoff theory

adams inequalities for bi laplacian and extremal functions in dimension four let be a smooth oriented bounded domain be the sobolev space and be the first eigenvalue of the bi laplacian operator 2 then for any a 0a o we have and the above supremum is infinity when a o this strengthens adams inequality in dimension 4 d adams a sharp inequality of j moser for high order derivatives ann of math 128 1988 365 398 where he proved the above inequality holds for a 0 moreover we prove that for sufficiently small a an extremal function for the above inequality exists as a special case of our results we thus show that there exists with such that this establishes the existence of an extremal function of the original adams inequality in dimension 4

a transformation media based approach for efficient monte carlo analysis of scattering from rough surfaces with objects this paper presents a computational model that utilizes transformation based metamaterials to enhance the performance of numerical modeling methods for achieving the statistical characterization of two dimensional electromagnetic scattering from objects on or above one dimensional rough sea surfaces monte carlo simulation of the rough surface scattering problem by means of differential equation based finite methods such as finite element or finite difference methods usually places a heavy burden on computational resources because at each realization of the monte carlo technique a mesh must be generated anew for each surface realization the main purpose of the proposed approach in this paper is to create a single mesh without repeating mesh generation at each step by introducing a transformation medium above the rough surface in the computational domain of the finite methods material parameters of the medium are obtained by the coordinate transformation technique which is based on the form invariance property of maxwell s equations at each realization only the material parameters are modified with respect to the geometry of surface without changing the mesh in this manner a great reduction in cpu time is achieved the proposed technique is analyzed and validated via various finite element simulations

remarks on prescribing gauss curvature we study the nonlinear partial differential equation for the problem of prescribing gauss curvature k on s 2 we give an example of a rotationally symmetric k for which the kazdan warner obstruction is satisfied but the equation has no rotationally symmetric solution on the other hand we give a simple sufficient condition for solvability of the equation when k is rotationally symmetric finally we give a sufficient condition for solvability when k is not necessarily rotationally symmetric

classification of singular radial solutions to the σk yamabe equation on annular domains the study of the kth elementary symmetric function of the weyl schouten curvature tensor of a riemannian metric the so called k curvature has produced many fruitful results in conformal geometry in recent years in these studies in conformal geometry the deforming conformal factor is considered to be a solution of a fully nonlinear elliptic pde important advances have been made in recent years in the understanding of the analytic behavior of solutions of the pde however the singular behavior of these solutions which is important in describing many important questions in conformal geometry is little understood this note classifies all possible radial solutions in particular the singular solutions of the k yamabe equation which describes conformal metrics whose k curvature equals a constant although the analysis involved is of elementary nature these results should provide useful guidance in studying the behavior of singular solutions in the general situation