covariant description of contact interfaces considering anisotropy for adhesion and friction part 1 formulation and analysis of the computational model a covariant description for contact problems including anisotropy for both adhesion and sliding domains is proposed the principle of maximum dissipation is used to obtain a computational model in the case of quasi static motion various cases including curvilinear anisotropy on arbitrary surfaces illustrating the possibility to model machined surfaces are considered the part is served to be a necessary preparation for further finite element implementations and numerical analysis

on the geometry of sasakian einstein 5 manifolds on simply connected five manifolds sasakian einstein metrics coincide with riemannian metrics admitting real killing spinors which are of great interest as models of near horizon geometry for three brane solutions in superstring theory 24 we expand on the recent work of demailly and kollar 14 and johnson and kollar 20 who give methods for constructing kahler einstein metrics on log del pezzo surfaces by a previous result of the first two authors 9 circle v bundles over log del pezzo surfaces with kahler einstein metrics have sasakian einstein metrics on the total space of the bundle here these simply connected 5 manifolds arise as links of isolated hypersurface singularities which by the well known work of smale 36 together with 11 must be diffeomorphic to s 5 l s 2 s 3 more precisely using methods from mori theory in algebraic geometry we prove the existence of 14 inequivalent sasakian einstein structures on s 2 s 3 and infinite families of such structures on l s 2 s 3 with 2 l 7 we also discuss the moduli problem for these sasakian einstein structures

constructions in sasakian geometry we first generalize the join construction described previously by the first two authors 4 for quasi regular sasakian einstein orbifolds to the general quasi regular sasakian case this allows for the further construction of specific types of sasakian structures that are preserved under the join operation such as positive negative or null sasakian structures as well as sasakian einstein structures in particular we show that there are families of sasakian einstein structures on certain 7 manifolds homeomorphic to s 2 s 5 we next show how the join construction emerges as a special case of lerman s contact fibre bundle construction 32 in particular when both the base and the fiber of the contact fiber bundle are toric we show that the construction yields a new toric sasakian manifold finally we study toric sasakian manifolds in dimension 5 and show that any simply connected compact oriented 5 manifold with vanishing torsion admits regular toric sasakian structures this is accomplished by explicitly constructing circle bundles over the equivariant blow ups of hirzebruch surfaces

integrability of two dimensional homogeneous potentials combining the extended painleve conjecture with yoshida s singularity and stability analyses 1986 it is shown that for two dimensional homogeneous potentials of degree 2m integrability restricts kowalevskaya exponents and integrability coefficients to discrete sets of values this result is made use of in the analysis of integrability of symmetric potentials with m 2 3 and 4 direct construction of additional first integrals is successful only in special cases which can be transformed to known integrable ones

the ring structure on the cohomology of coordinate subspace arrangements every simplicial complex delta subset2 n on the vertex set n 1 ldots n defines a real resp complex arrangement of coordinate subspaces in mathbb r n resp mathbb c n via the correspondence delta ni sigma mapsto rm span e i i in sigma the linear structure of the cohomology of the complement of such an arrangement is explicitly given in terms of the combinatorics of delta and its links by the goresky macpherson formula here we derive by combinatorial means the ring structure on the integral cohomology in terms of data of delta we provide a non trivial example of different cohomology rings in the real and complex case furthermore we give an example of a coordinate arrangement that yields non trivial multiplication of torsion elements

polynomial constants of motion in flat space some general results on commuting integrals for a hamiltonian system are given the question of the existence of integrals which are polynomial in the momenta is investigated and the results applied to a variety of mechanical systems

locally conformal kahler manifolds with potential a locally conformally kahler lck manifold m is one which is covered by a kahler manifold widetilde m with the deck transformation group acting conformally on widetilde m if m admits a holomorphic flow acting on widetilde m conformally it is called a vaisman manifold neither the class of lck manifolds nor that of vaisman manifolds is stable under small deformations we define a new class of lck manifolds called lck manifolds with potential which is closed under small deformations all vaisman manifolds are lck with potential we show that an lck manifold with potential admits a covering which can be compactified to a stein variety by adding one point this is used to show that any lck manifold m with potential dim m 3 can be embedded into a hopf manifold thus improving similar results for vaisman manifolds ornea and verbitsky math ann 332 121 143 2005

on the moduli space of certain smooth codimension one foliations of the 5 sphere by complex surfaces in this paper we first determine the set of all possible integrable almost cr structures on the smooth foliation of s 5 constructed in m v we give a specific concrete model of each of these structures we show that this set can be naturally identified with c c c we then adapt the classical notions of coarse and fine moduli space to the case of a foliation by complex manifolds we prove that the previous set identified with c 3 defines a coarse moduli space for the foliation of m v but that it does not have a fine moduli space finally using the same ideas we prove that the standard lawson foliation on the 5 sphere can be endowed with almost cr structures but none of these is integrable this is a foliated analogue to the examples of almost complex manifolds without complex structure

the weak painleve property as a criterion for the integrability of dynamical systems we investigate the validity of the weak painleve property as an integrability criterion we present an example of a time dependent hamiltonian system which possesses a weak painleve type expansion while presenting a chaotic behavior however this system presents also critical fixed singularities the importance of the latter as far as integrability is concerned is discussed here

quasi point separation of variables for the henon heiles system and a system with a quartic potential we examine the problem of integrability of two dimensional hamiltonian systems by means of separation of variables a systematic approach to the construction of the special non pure coordinate separation of variables for certain natural two dimensional hamiltonians is proposed

complex geometry of moment angle manifolds moment angle manifolds provide a wide class of examples of non kahler compact complex manifolds a complex moment angle manifold mathcal z is constructed via certain combinatorial data called a complete simplicial fan in the case of rational fans the manifold mathcal z is the total space of a holomorphic bundle over a toric variety with fibres compact complex tori in general a complex moment angle manifold mathcal z is equipped with a canonical holomorphic foliation mathcal f which is equivariant with respect to the mathbb c times m action examples of moment angle manifolds include hopf manifolds of vaisman type calabi eckmann manifolds and their deformations we construct transversely kahler metrics on moment angle manifolds under some restriction on the combinatorial data we prove that any kahler submanifold or more generally a fujiki class mathcal c subvariety in such a moment angle manifold is contained in a leaf of the foliation mathcal f for a generic moment angle manifold mathcal z in its combinatorial class we prove that all subvarieties are moment angle manifolds of smaller dimension and there are only finitely many of them this implies in particular that the algebraic dimension of mathcal z is zero

a new class of integrable systems we present a family of dynamical systems associated with the motion of a particle in two space dimensions these systems possess a second integral of motion quadratic in velocities apart from the hamiltonian and are thus completely integrable they were found through the derivation and subsequent resolution of the integrability condition in the form of a partial differential equation pde for the potential a most important point is that the same pde was derived through considerations on the analytic structure of the singularities of the solutions weak painleve property

optimization algorithms for the solution of the frictionless normal contact between rough surfaces this paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half plane using the boundary element method bem after recasting the resulting linear complementarity problem lcp as a convex quadratic program qp with nonnegative constraints different optimization algorithms are compared for its solution i a greedy method based on different solvers for the unconstrained linear system conjugate gradient cg gauss seidel cholesky factorization ii a constrained cg algorithm iii the alternating direction method of multipliers admm and iv the non negative least squares nnls algorithm possibly warm started by accelerated gradient projection steps or taking advantage of a loading history the latter method is two orders of magnitude faster than the greedy cg method and one order of magnitude faster than the constrained cg algorithm finally we propose another type of warm start based on a refined criterion for the identification of the initial trial contact domain that can be used in conjunction with all the previous optimization algorithms this method called cascade multi resolution cmr takes advantage of physical considerations regarding the scaling of the contact predictions by changing the surface resolution the method is very efficient and accurate when applied to real or numerically generated rough surfaces provided that their power spectral density function is of power law type as in case of self affine fractal surfaces

on the hausdorff dimension of some graphs consider the functions wb x b cn 1 bnx on 1 0n n oo where b 1 0 0 such that if b is large enough then the hausdorff dimension of the graph of wb is bounded below by 2a c ln b we also show that if a function f is convex lipschitz of order a then the graph of f has a finite measure with respect to hausdorff s measure in dimension 2 a the convex lipschitz functions of order a include zygmund s class a our analysis shows that the graph of the classical van der waerdentagaki nowhere differentiable function has a finite measure with respect to h t t in 1 t we consider the hausdorff dimension of the graphs of various continuous functions we introduce a new geometric property of a function convex lipschitz of some order and obtain an upper bound on the dimension of a graph with this property in particular our analysis includes functions of the form

on simple polytopes letp be a simpled polytope ind dimensional euclidean space mathbb e d and let p be the subalgebra of the polytope algebra generated by the classes of summands ofp it is shown that the dimensions of the weight spaces r p of p are theh numbers ofp which describe the dehn sommerville equations between the numbers of faces ofp and reflect the duality between r p and d r p moreover p admits a lefschetz decomposition under multiplication by the element of 1 p corresponding top itself which yields a proof of the necessity of mcmullen s conditions in theg theorem on thef vectors of simple polytopes the lefschetz decomposition is closely connected with the new hodge riemann minkowski quadratic inequalities between mixed volumes which generalize minkowski s second inequality also proved are analogous generalizations of the aleksandrov fenchel inequalities a striking feature is that these are obtained without using brunn minkowski theory indeed the brunn minkowski theorem without characterization of the cases of equality can be deduced from them the connexion found between p and the face ring of the dual simplicial polytopep enables this ring to be looked at in two ways and a conjectured formulation of theg theorem in terms of a gale diagram ofp is also established

on the metric structure of non kahler complex surfaces we give a characterization of a locally conformally kahler l c k metric with parallel lee form on a compact complex surface using the kodaira classification of surfaces we classify the compact complex surfaces admitting such structures this gives a classification of sasakian structures on compact three manifolds a weak version of the above mentioned characterization leads to an explicit construction of l c k metrics on all hopf surfaces we characterize the locally homogeneous l c k metrics on geometric complex surfaces and we prove that some inoue surfaces do not admit any l c k metric

statistical model of nearly complete elastic rough surface contact abstract in the area of homogeneous isotropic linear elastic rough surface normal contact many classic statistical models have been developed which are only valid in the early contact when real area of contact is infinitesimally small e g the greenwood williamson gw model in this article newly developed statistical models built under the framework of the i gw ii nayak bush and iii greenwood s simplified elliptic models extend the range of application of the classic statistical models to the case of nearly complete contact nearly complete contact is the stage when the ratio of the real area of contact to the nominal contact area approaches unity at nearly complete contact the non contact area consists of a finite number of the non contact regions over a finite nominal contact area each non contact region is treated as a mode i crack the area of each non contact region and the corresponding trapped volume within each non contact region are determined by the analytical solutions in the linear elastic fracture mechanics respectively for a certain average contact pressure not only can the real area of contact be determined by the newly developed statistical models but also the average interfacial gap rough surface is restricted to the geometrically isotropic surface i e the corresponding statistical parameters are independent of the direction of measurement relations between the average contact pressure non contact area and average interfacial gap for different combinations of statistical parameters are compared between newly developed statistical models the relations between non contact area and average contact pressure predicted by the current models are also compared with that by persson s theory of contact the analogies between the classic statistical models and the newly developed models are also explored

the homotopy types of moment angle complexes for flag complexes we study the homotopy types of moment angle complexes or equivalently of complements of coordinate subspace arrangements the overall aim is to identify the simplicial complexes k for which the corresponding moment angle complex z k has the homotopy type of a wedge of spheres or a connected sum of sphere products when k is flag we identify in algebraic and combinatorial terms those k for which z k is homotopy equivalent to a wedge of spheres and give a combinatorial formula for the number of spheres in the wedge this extends results of berglund and jollenbeck on golod rings and homotopy theoretical results of the first and third authors we also establish a connection between minimally non golod rings and moment angle complexes z k which are homotopy equivalent to a connected sum of sphere products we go on to show that for any flag complex k the loop space of z k is homotopy equivalent to a product of spheres and loops on spheres when localised rationally or at any prime not equal to 2

a stochastic model of rough surfaces for finite element contact analysis abstract this paper is concerned with the development of mathematical models for the normal and tangential stiffness of rough flat surfaces a detailed statistical analysis of a rough surface is performed in terms of peak distribution and the distribution of curvature at the peaks a random surface model of elasto plastically yielding asperities with a gaussian height distribution combined with mechanical description of a single peak based on hertz theory coupled with the mindlin friction theory is investigated the stochastic model is included in an incremetal finite element procedure to make the two dimensional contact problem solution possible the influence of the standard deviation of the height asperities on the values of both the tangential and normal stiffness at the joint interface has been found significant it is an important factor when determining the overall behaviour of the fixed flat joint the standard deviation of curvatures has been found to have a secondary effect only

non integrable systems with algebraic singularities in complex time dynamical arguments are presented which suggest that there are non integrable systems without clustering of singularities without infinite singularities or singularities with an infinite number of branches in the complex t plane several examples with only algebraic singularities are studied for which strong numerical evidence is presented for non integrability and infinitely sheeted solutions weak painleve potentials are also analysed from this point of view and all integrable cases are found to possess only finitely sheeted solutions

similarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure some modern scaling and fractal approaches to the characterization of surface roughness are under consideration a new mathematical model of a multilevel profile suitable for flexible simulation of roughness is presented as a development from these approaches the iterative construction of the model is described it is shown that the profile is a hierarchical structure with self affine and fractal features its geometrical properties are studied both analytically and numerically and some of them are proved to be of the renormalization type the profile contour length can be finite or infinite depending on the chosen values of the structural parameters some characteristics including the bearing curve and the upper volume function of the profile and the corresponding prestructures are calculated

painleve analysis yoshida s theorems and direct methods in the search for integrable hamiltonians treating as an example two dimensional similarity invariant hamiltonians with polynomial velocity dependent potentials the authors show how painleve analysis yoshida s theorems and direct methods can be combined in the search for integrable hamiltonians new integrable systems are found one of which has a polynomial second invariant of fifth order in the momenta most of the necessary calculations have been performed by applying various reduce packages developed for that purpose

linearization on a submanifold of integrable hamiltonians with polynomials potentials abstract following a method proposed by j weiss we linearize the integrable hamiltonians with quartic potentials as well as the remaining integrable cubic potentials a non generic solution is obtained in each case we explain this phenomenon in terms of a constraint submanifold over which the solution of the system is in fact linearizable we show that the linearization approach can depending on the particular case lead to generic solutions non generic ones or even to no solutions at all

kuranishi type moduli spaces for proper cr submersions fibering over the circle kuranishi s fundamental result 1962 associates to any compact complex manifold x 0 sub a finite dimensional analytic space which has to be thought of as a local moduli space of complex structures close to x 0 sub in this paper we give an analogous statement for levi flat cr manifolds fibering properly over the circle by describing explicitely an infinite dimensional kuranishi type local moduli space of levi flat cr structures we interpret this result in terms of kodaira spencer deformation theory making clear the likenesses as well as the differences with the classical case the article ends with applications and examples

integrability of hamiltonians with third and fourth degree polynomial potentials the weak painleve property as a criterion of integrability is applied to the case of simple hamiltonians describing the motion of a particle in two dimensional polynomial potentials of degree three and four this allows a complete identification of all the integrable cases of cubic potentials in the case of quartic potentials although our results are not exhaustive some new integrable cases are discovered in both cases the integrability is explicited by a direct calculation of the second integral of motion of the system

adhesive contact of the weierstrass profile the weierstrass series was considered in ciavarella et al ciavarella et al 2000 proc r soc lond a 456 387405 doi 10 1098 rspa 2000 0522 to describe a linear contact problem between a ri

scaling range and cutoffs in empirical fractals fractal structures appear in a vast range of physical systems a literature survey including all experimental papers on fractals which appeared in the six physical review journals a char21 e and letters during the 1990s shows that experimental reports of fractal behavior are typically based on a scaling range ensuremath delta that spans only 0 5 char21 2 decades this range is limited by upper and lower cutoffs either because further data are not accessible or due to crossover bends focusing on spatial fractals a classification is proposed into a aggregation b porous media c surfaces and fronts d fracture and e critical phenomena most of these systems except for class e involve processes far from thermal equilibrium the fact that for self similar fractals in contrast to the self affine fractals of class c there are hardly any exceptions to the finding of ensuremath delta l 2 decades raises the possibility that the cutoffs are due to intrinsic properties of the measured systems rather than the specific experimental conditions and apparatus to examine the origin of the limited range we focus on a class of aggregation systems in these systems a molecular beam is deposited on a surface giving rise to nucleation and growth of diffusion limited aggregation like clusters scaling arguments are used to show that the required duration of the deposition experiment increases exponentially with ensuremath delta furthermore using realistic parameters for surfaces such as al 111 it is shown that these considerations limit the range of fractal behavior to less than two decades in agreement with the experimental findings it is conjectured that related kinetic mechanisms that limit the scaling range are common in other nonequilibrium processes that generate spatial fractals

explicit integrability for hamiltonian systems and the painleve conjecture we analyze a class of hamiltonian systems in two dimensions for which we proved that a second constant of motion exists it is shown that using the two first integrals the equations of motion can be written in a form which allows their integration by quadratures an analysis of the equations of motion in this reduced form establishes the behavior of the solutions in the complex time plane it is shown explicitly that the systems belonging to this class possess the weak painleve property i e their solutions in complex time can present singularities of a specific algebraic type

integrability of toda lattice by generalized variational symmetry approach a systematic method of finding nontrivial generalized variational symmetries are presented herein and the corresponding first integrals for nonlinear dynamical system with two degrees of freedom are derived then a method is applied to a toda lattice given by the potential v ex y c1e2y c2ey c3e 2x c4 e x where c1 c2 c3 and c4 are parameters the symmetries and constants of motion are presented explicitly

directional rates of change under spatial process models spatial process models are now widely used for inference in many areas of application in such contexts interest is often in the rate of change of a spatial surface at a given location in a given direction examples include temperature or rainfall gradients in meteorology pollution gradients for environmental data and surface roughness assessment for digital elevation models because the spatial surface is viewed as a random realization all such rates of change are random as well we formalize the notions of directional finite difference processes and directional derivative processes building upon the concept of mean square differentiability as developed by stein and banerjee and gelfand we obtain complete distribution theory results under the assumptions of a stationary gaussian process model either for the data or for spatial random effects we present inference under a bayesian framework which in this setting presents several advantages finally we illustrate our methodology with a simulated dat

finite element analysis of contact between elastic self affine surfaces finite element methods are used to study nonadhesive frictionless contact between elastic solids with self affine surfaces we find that the total contact area rises linearly with the load at small loads the mean pressure in the contact regions is independent of load and proportional to the root mean square slope of the surface the constant of proportionality is nearly independent of the poisson ratio and roughness exponent and lies between previous analytic predictions the contact morphology is also analyzed connected contact regions have a fractal area and perimeter the probability of finding a cluster of area a c drops as a tau c where tau increases with a decrease in roughness exponent the distribution of pressures shows an exponential tail that is also found in many jammed systems these results are contrasted to simpler models and experiments

a new geometric construction of compact complex manifolds in any dimension we consider holomorphic linear foliations of dimension m of mathbb c n with n 2m fulfilling a so called weak hyperbolicity condition and equip the projectivization of the leaf space for the foliation restricted to an adequate open dense subset with a structure of compact complex manifold of dimension n m 1 we show that except for the limit case n 2m 1 where we obtain any complex torus of any dimension this construction gives non symplectic manifolds including the previous examples of hopf calabi eckmann haefliger linear case loeb nicolau linear case and lopez de medrano verjovsky we study some properties of these manifolds that is to say meromorphic functions holomorphic vector fields forms and submanifolds for each manifold we construct an analytic space of deformations of dimension m n m 1 and show that under some additional conditions it is universal lastly we give explicit examples of new compact complex manifolds in particular of connected sums of products of spheres and show the existence of a momentum like map which classifies these manifolds up to diffeomorphism

the generalized cattaneo partial slip plane contact problem i theory the cattaneo problem is considered for a general plane contact between elastically similar materials i e a monotonically increasing tangential load starting from zero with normal loading held fixed instead of the classical argument on the displacement field in the stick zone of cattaneo solution we attack the problem implicitly from the governing integral equations in the stick zones after discussing and solving the full stick case we move to the more realistic for finite friction case of partial slip we show that upon isolating the effect of full sliding the equalities and inequalities governing the corrective solution for the corrective shearing tractions in the stick zone are exactly the same as those governing the solution of the normal contact problem with a lower load but the same rotation as the actual one this analogy permits us to deduce several general properties and gives a general procedures for solving partial slip cattaneo problems as frictionless normal indentation ones therefore the general solutions for single multiple and periodic contacts is given a comprehensive set of explicit results is given in the part ii of the paper

the transverse dynamics of a holomorphic flow on considere un champ vectoriel polynomial homogene p z dans c n 1 les solutions du systeme d equations differentielles dz i dt p i z t c i 0 n feuillette c n 1 par des courbes holomorphes ayant des singularites le long du lieu commun p i z 0 on definit la notion de dynamique transverse du feuilletage

fractal models of elastic perfectly plastic contact of rough surfaces based on the cantor set abstract the objective of this study was to formulate discrete and continuous models to describe the elastic perfectly plastic deformation of two rough surfaces in contact the two surfaces in contact are assumed to exhibit fractal behavior and are modeled as an effective fractal surface compressed into a smooth rigid substrate the rough self affine fractal structure of the effective surface is approximated using a cantor set representation both of the proposed models admit analytical solution for the cases when the plastic deformation is volume conserving or not results are presented that illustrate the effects that volume conservation and initial surface structure have on the elastic perfectly plastic deformation process the results from the continuous model are compared with the results obtained from the discrete model and also with existing experimental load displacement results for the deformation of a ground steel surface

iterated function systems and the global construction of fractals iterated function systems i f ss are introduced as a unified way of generating a broad class of fractals these fractals are often attractors for i f ss and occur as the supports of probability measures associated with functional equations the existence of certain p balanced measures for i f ss is established and these measures are uniquely characterized for hyperbolic i f ss the hausdorff besicovitch dimension for some attrac tors of hyperbolic i f ss is estimated with the aid of p balanced measures what appears to be the broadest framework for the exactly computable moment theory of p balanced measures that of linear i f ss and of probabilistic mixtures of iterated riemann surfaces is presented this extensively generalizes earlier work on orthogonal polynomials on julia sets an example is given of fractal reconstruction with the use of linear i f ss and moment theory

darboux points and integrability of hamiltonian systems with homogeneous polynomial potential in this paper we study the integrability of natural hamiltonian systems with a homogeneous polynomial potential the strongest necessary conditions for their integrability in the liouville sense have been obtained by a study of the differential galois group of variational equations along straight line solutions these particular solutions can be viewed as points of a projective space of dimension smaller by one than the number of degrees of freedom we call them darboux points we analyze in detail the case of two degrees of freedom we show that except for a radial potential the number of darboux points is finite and it is not greater than the degree of the potential moreover we analyze cases when the number of darboux points is smaller than maximal for two degrees of freedom the above mentioned necessary condition for integrability can be expressed in terms of one nontrivial eigenvalue of the hessian of potential calculated at a darboux point we prove that for a given potential these nontrivial eigenvalues calculated for all darboux points cannot be arbitrary because they satisfy a certain relation which we give in an explicit form we use this fact to strengthen maximally the necessary conditions for integrability and we show that in a generic case for a given degree of the potential there is only a finite number of potentials which satisfy these conditions we also describe the nongeneric cases as an example we give a full list of potentials of degree four satisfying these conditions then investigating the differential galois group of higher order variational equations we prove that except for one discrete family among these potentials only those which are already known to be integrable are integrable we check that a finite number of potentials from the exceptional discrete family are not integrable and we conjecture that all of them are not integrable

on the fractal dimension of self affine profiles one dimensional profiles f x can be characterized by a minkowski bouligand dimension d and by a scale dependent generalized roughness w f epsilon this roughness can be defined as the dispersion around a chosen fit to f x in an epsilon scale it is shown that d limepsilon to 0 2 in w f epsilon in epsilon holds for profiles nowhere differentiable this establishes a close connection between the roughness and the fractal dimension and proves that d 2 h for self affine profiles h is the roughness or hurst exponent two numerical algorithms based on the roughness one around the local average f x epsilon usual roughness and the other around the local rms straight line a generalized roughness are discussed the estimates of d for standard self affine profiles are reliable and robust especially for the last method

periodic orbits and nonintegrability of generalized classical yang mills hamiltonian systems the averaging theory of first order is applied to study a generalized yang mills system with two parameters two main results are proved first we provide sufficient conditions on the two parameters of the generalized system to guarantee the existence of continuous families of isolated periodic orbits parameterized by the energy and these families are given up to first order in a small parameter second we prove that for the nonintegrable classical yang mills hamiltonian systems in the sense of liouville arnold which have the isolated periodic orbits found with averaging theory cannot exist in any second first integral of class c1 this is important because most of the results about integrability deals with analytic or meromorphic integrals of motion

an integrable three particle system a study of the existence of some integrable systems with nonlinear constants of motion is presented using the approach of the theory of generalized dynamical or hidden symmetries two lagrangians are considered both obtained by modifying the toda lagrangian first a two particle system is studied and then the results are generalized to a three particle system it is shown that in both cases the lagrangians possess nonlinear constants of motion in involution and thus they are integrable

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

analytic structure of the henon heiles hamiltonian in integrable and nonintegrable regimes the solutions of the henon heiles hamiltonian are investigated in the complex time plane the use of the painleve property i e the property that the only movable singularities exhibited by the solution are poles enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes these boundaries have a remarkable self similar structure whose form changes as a function of the nonlinear coupling

finiteness and tenseness theorems for riemannian foliations we prove a finiteness theorem for the spectral sequence e i d i associated to a riemannian foliation inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i on a compact manifold m and to a flat vector bundle e over m with flat connection using this result we prove that every riemannian foliation on a compact manifold is tense in the sense of f w kamber and ph tondeur foliations and metrics progr math vol 32 1983 pp 103 152 we also show that the main tautness theorems for riemannian foliations on compact manifolds which were proved by several authors are immediate consequences of our results

conductance of rough random profiles abstract recently the real contact area and the compliance and electrical resistance for a rough surface defined with a weierstrass series have been studied under the assumption that superposed self affine sine waves had well separated wavelengths extending the celebrated procedures pioneered by archard archard j f 1957 elastic deformation and the laws of friction proc r soc lond a 243 190 205 here more realistic fractal rough surface profiles are considered by using the weierstrass series with random phases and with much lower separation of the various scales using a full or a hybrid numerical analytical technique a non linear layer algorithm is developed which is a very efficient approximate tool to study this problem avoiding the need for averaging over various realizations of profiles with random phases the multiscale problem is solved by a cascade of 2 scales problems each of which is solved with a few elements for an imposed contact area deriving load as a function of indentation and the conductance by differentiation using barber s analogy theorem dimensionless results for the conductance as a function of applied pressures show that the conductance seems to be close to a power law at low loads and is nearly linear at intermediate loads following the normalized single sinusoidal case except at the origin at high loads the conductance becomes strongly dependent on fractal dimension because of weak dependence on the contribution of small wavelength scales higher order terms in the series since roughness tends to be squeezed out the conductance tends to increase more than linearly more so the smaller is the fractal dimension however another limit could be found in terms of the finite size of the specimen which may suggest reaching a finite limit the resulting curves could then be sigmoidal as confirmed by qualitative comparisons with experiments in the literature

the loop space homotopy type of simply connected four manifolds and their generalizations abstract we determine loop space decompositions of simply connected four manifolds n 1 connected 2n dimensional manifolds provided n 4 8 and connected sums of products of two spheres these are obtained as special cases of a more general loop space decomposition of certain torsion free cw complexes with well behaved skeleta and some poincare duality features

singular point analysis and integrals of motion for coupled nonlinear schrodinger equations for a system of two coupled nonlinear schrodinger equations and the corresponding madelung fluid equations we calculate the similarity transformation and reductions to ordinary differential equations the symmetries can be used to classify several types of solutions besides a system of coupled painleve ii equations we obtain a two dimensional quartic hamiltonian system using noether s theorem and performing a painleve test we identify those parameters which lead to regular motion on tori using the results of the p test we obtain heretofore undiscovered integrals of motion for the madelung fluid by direct calculations investigating the dynamics of the system for parameters that are different from those obtained by the painleve test we calculate numerically the surface of section kam tori and study the transition into chaotic behaviour

holomorphic foliations in ruled surfaces we analyse the universal families of holomorphic foliations with singularities in a ruled surface in terms of chern classes we determine the general and the special families we also classify all nonsingular foliations a holomorphic foliation with singularities by curves in a complex manifold m may be defined locally as the integral curves of a nonidentically zero holomorphic vector field and globally by a holomorphic bundle map from a line bundle on m to the tangent bundle of m x l tm uniquely defined up to multiplication by a never vanishing holomorphic function the set of all holomorphic foliations by curves in a compact manifold m has a natural structure of a complex analytic variety usually with infinitely many connected components and in case m is a hodge manifold then each connected component is compact 5 the objective of this paper is to describe these components for the case of a ruled surface s we organise the components according to the chern classes of the defining bundle l and we determine those elements in h 2 s z that appear as chern classes of l using the notion of an ample direction b or of the ample cone in h 2 s z we observe a generic behaviour of the components 2m m for m large enough and a special behaviour for m small the pattern observed resembles the pattern obtained in the theory of special divisors on a riemann surface 7 we also determine all nonsingular foliations in ruled surfaces and give topological and analytic descriptions of them we finish by determining which foliations in ruled surfaces accept a change of complex structure on the leaves keeping the transversal structure fixed 6 the paper is organised as follows in 1 we describe the results of ruled surfaces i e holomorphic cpl bundles over a riemann surface b that we will need in 2 we will obtain restrictions on the chern classes c l e h 2 s z of holomorphic foliations x l ts and describe the nonsingular foliations if the genus g of b is distinct from 1 in 3 we analyse the case g 1 in 4 we describe the components as well as the subvariety of that parametrizes foliations that have an algebraic leaf of fixed fundamental class finally in 5 we apply the variational method of 6 to the ruled surface case received by the editors october 15 1987 1980 mathematics subject classification 1985 revision primary 58f18 14j26 supported by conacyt and university of warwick 1989 american mathematical society 0002 9947 89 1 00 25 per page

integrable hamiltonian systems with velocity dependent potentials the integrability of a two dimensional hamiltonian in which the potential depends explicitly on the momenta is investigated hamiltonians of this kind are encountered in the description of the motion of a particle in a magnetic field two integrable classes of potentials are identified and the second integral of motion is constructed for each of them the singularity analysis of the equations of motion is also performed confirming once more the relation between the weak painleve property and integrability

on the number of singularities in meromorphic foliations on compact complex surfaces here we study meromorphic foliations with singularities on a smooth compact complex surface aim study the locations of the singularities using vector bundle techniques and techniques introduced in the cohomological study of projective geometry roughly speaking a meromorphic foliation with singularities on a complex connected manifold s is described by a subsheaf f of the tangent bundle ts with f closed under lie brackets see for instance gl g2 g3 g4 g5 gk gm or for the case dim 5 2 here in 1 8 1 the singularities of the foliations are the points of s at which f is not a subbundle of ts with this definition the singularities may occur only in codimension at least 2 but a meromorphic foliation without singularities is not a holomorphic foliation in the classical sense note that any rank one subsheaf of ts is involutive and it is contained in a line bundle contained in ts in general not as subbundle thus a rank one meromorphic foliation g with singularities on s is given by a line bundle m on s and a nonzero map m ts which induces an inclusion as sheaves of m in ts up to a scalar factor of course one imposes that s o has no hypersurface as component i e that m is a saturated subsheaf of ts equivalent g is given by m and s e h s ts m with s 0 up to a scalar factor the singularities of g are the zero locus s o of s such a foliation is called also a foliation by curves thus for fixed m e pic s we are looking at a linear problem many papers are concerned with this case see e g g2 g3 g4 gk from different points of view and with several different kinds of problems in mind when dim 5 2 as always in this paper every foliation is a foliation by curves for the case dim 5 2 relevant references are among others g2 and g3 from now on we assume dim 5 2 it happens very seldom that s has a meromorphic foliation without singularities by definition this happens if and only if ts is an extension of two line bundles here we are interested essentially on the possible location for various m e pic is of the singularities associated to some s e h s ts m very often we will be interested in a general such s the main problems considered here are a given a zero dimensional scheme z c s find if there is seh s ts m 5 0

a list of all integrable two dimensional homogeneous polynomial potentials with a polynomial integral of order at most four in the momenta we searched for integrable two dimensional homogeneous polynomial potentials with a polynomial first integral by using the so called direct method of searching for first integrals we proved that there exist no polynomial first integrals which are genuinely cubic or quartic in the momenta if the degree of homogeneous polynomial potentials is greater than four

fractal dimensions and singularities of the weierstrass type functions a new type of fractal measures k s 1 s 2 defined on the subsets of the graph of a continuous function is introduced the k dimension defined by this measure is closer to the hausdorff dimension than the other fractal dimensions in recent literatures for the weierstrass type functions defined by w x 0 i g i x where 1 0 1 and g is an almost periodic lipschitz function of order greater than it is shown that the k dimension of the graph of w equals to 2 this conclusion is also equivalent to certain rate of the local oscillation of the function some problems on the knot points and the nondifferentiability of w are also discussed

real quadrics in cn complex manifolds and convex polytopes in this paper we investigate the topology of a class of non kahler compact complex manifolds generalizing that of hopf and calabi eckmann manifolds these manifolds are diffeomorphic to special systems of real quadrics cn which are invariant with respect to the natural action of the real torus s1 n onto cn the quotient space is a simple convex polytope the problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes we prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich we also resolve an associated wall crossing problem by introducing holomorphic equivariant elementary surgeries related to some transformations of the simple convex polytope finally as a nice consequence we obtain that affine non kahler compact complex manifolds can have arbitrary amount of torsion in their homology groups contrasting with the kahler situation

fractal analysis of surface roughness by using spatial data summary we develop fractal methodology for data taking the form of surfaces an advantage of fractal analysis is that it partitions roughness characteristics of a surface into a scale free component fractal dimension and properties that depend purely on scale particular emphasis is given to anisotropy where we show that for many surfaces the fractal dimension of line transects across a surface must either be constant in every direction or be constant in each direction except one this virtual direction invariance of fractal dimension provides another canonical feature of fractal analysis complementing its scale invariance properties and enhancing its attractiveness as a method for summarizing properties of roughness the dependence of roughness on direction may be explained in terms of scale rather than dimension and can vary with orientation scale may be described by a smooth periodic function and may be estimated nonparametrically our results and techniques are applied to analyse data on the surfaces of soil and plastic food wrapping for the soil data interest centres on the effect of surface roughness on retention of rain water and data are recorded as a series of digital images over time our analysis captures the way in which both the fractal dimension and the scale change with rainfall or equivalently with time the food wrapping data are on a much finer scale than the soil data and are particularly anisotropic the analysis allows us to determine the manufacturing process which produces the smoothest wrapping with least tendency for micro organisms to adhere

linear elastic contact of the weierstrass profile a contact problem is considered in which an elastic half plane is pressed against a rigid fractally rough surface whose profile is defined by a weierstrass series it is shown that no applied mean pressure is sufficiently large to ensure full contact and indeed there are not even any contact areas of finite dimension the contact area consists of a set of fractal character for all values of the geometric and loading parameters a solution for the partial contact of a sinusoidal surface is used to develop a relation between the contact pressure distribution at scale n 1 and that at scale n recursive numerical integration of this relation yields the contact area as a function of scale an analytical solution to the same problem appropriate at large n is constructed following a technique due to archard this is found to give a very good approximation to the numerical results even at small n except for cases where the dimensionless applied load is large the contact area is found to decrease continuously with n tending to a power law behaviour at large n which corresponds to a limiting fractal dimension of 2 d where d is the fractal dimension of the surface profile however it is not a simple fractal in the sense that it deviates from the power law form at low n at which there is also a dependence on the applied load contact segment lengths become smaller at small scales but an appropriately normalized size distribution tends to a limiting function at large n the authors dedicate this paper to the memory of dr j f archard 1918 1989

complex manifolds with maximal torus actions we say that an effective action of a compact torus g on a connected smooth manifold m is maximal if there exists a point x m such that dimg dimgx dimm in this talk we give a one to one correspondence between the family of connected closed complex manifolds with maximal torus actions and the family of certain combinatorial objects which is a generalization of the correspondence between complete nonsingular toric varieties and complete nonsingular fans research institute for mathematical science kyoto university e mail address ishida kurims kyoto u ac jp date june 16 2014 1

a new efficient numerical method for contact mechanics of rough surfaces abstract in this work a numerical method has been developed to investigate the adhesionless contact mechanics between rough surfaces to solve the elastic problem a boundary elements approach is used with self equilibrated square elements the domain of integration is discretized developing an intelligent adaptive mesh and obtaining a considerable memory saving the numerical convergence of the method has been verified by comparing the results with the hertzian solution and by checking the stress probability distribution at the contact interface the methodology has been then utilized to analyse the contact between an elastic flat substrate and a periodic numerically generated self affine fractal rigid surface the fractal surface has been generated by employing spectral methods the results of our investigation supports the findings of some analytical theories persson 2001 and numerical findings yang et al 2006 hyun et al 2004 carbone and bottiglione 2008 campana and muser 2007 in terms of linearity between contact area and load and stress probability distributions

the equation on a positive current we study the induced equation on a positive current in a complex manifold we extend the l 2 estimates for the equation to harmonic currents of bidimension 1 1 satisfying a frobenius type condition we also show that the l 2 estimates are satisfied for the equation on a positive closed current of bidegree 1 1 on a pseudoconvex domain in n

incipient sliding of rough surfaces in contact a multiscale numerical analysis in this paper the cattaneo theory of frictional contact is extended to elastic half spaces in contact through rough disordered interfaces the discrete version of the cattaneo theorem is provided and represents the basis of a multiscale numerical contact algorithm mathematical surfaces with imposed roughness as well as experimentally digitised ones are analysed by means of a numerical method the evolution of the contact domain at different resolution is investigated roughness of the interfaces provides lacunarity of the contact domains whose fractal dimension is always smaller than 2 0 when a tangential force is applied the extent of the stick area decreases in the same way as the contact area develops with increasing pressure and the slip area is found to be proportional to the tangential force as predicted by cattaneo theory the evolution of the shear centroid as well as the amount of dissipated energy up to full sliding are provided finally it is shown that at a sufficient level of discretization the distribution of contact pressures is multifractal

centennial history of hilbert s 16th problem the second part of hilbert s 16th problem deals with polynomial differential equations in the plane it remains unsolved even for quadratic polynomials there were several attempts to solve it that failed yet the problem inspired significant progress in the geometric theory of planar differential equations as well as bifurcation theory normal forms foliations and some topics in algebraic geometry the dramatic history of the problem as well as related developments are presented below 1 the problem and its counterparts what may be said about the number and location of limit cycles of a planar polynomial vector field of degree n the limit cycle is an isolated closed orbit of a vector field this second part of hilbert s 16th problem appears to be one of the most persistent in the famous hilbert list h second only to the riemann function conjecture traditionally hilbert s question is split into three each one requiring a stronger answer problem 1 is it true that a planar polynomial vector field has but a finite number of limit cycles problem 2 is it true that the number of limit cycles of a planar polynomial vector field is bounded by a constant depending on the degree of the polynomials only the bound on the number of limit cycles in problem 2 is denoted by h n and known as the hilbert number linear vector fields have no limit cycles hence h 1 0 it is still unknown whether or not h 2 exists problem 3 give an upper bound for h n a solution to any of these problems implies a solution for the previous ones only the first problem is solved now the positive answer was established in e92 i91 there are analytic counterparts of problems 1 and 2 received by the editors december 2001 2000 mathematics subject classification primary 34cxx 34mxx 37f75

using green s function molecular dynamics to rationalize the success of asperity models when describing the contact between self affine surfaces we use green s function molecular dynamics to evaluate the effectiveness of asperity models when describing the contact mechanics of elastic solids with self affine surfaces surfaces are created with the help of a fourier filtering algorithm and the interactions between the solids are modeled via hard wall potentials we illustrate how the real area of contact a real is formed by a set of contact clusters two different regimes are identified when the normal force per cluster l c is plotted as a function of its area a c small clusters satisfy a hertzian type law l c approximately a c 32 while large clusters display a linear l c approximately a c behavior it is shown how the area a c where the crossover between the two regimes takes place depends only on the roughness at the smallest length scale if the longitudinal dimension of the surface remains unaltered moreover our results display a distribution of cluster sizes p a c remaining nearly constant for areas smaller than a c while showing power law decay above such a critical value furthermore we found the heights of the contacting atoms to be normally distributed with width inversely proportional to the surface roughness

non kahler manifolds and git quotients bosio generalized the construction by lopez de medrano verjovsky meersseman lvm of a family of non algebraic compact complex manifolds of any dimension we describe how to construct the generalized family from certain geometric invariant theory git quotients we show that bosio s generalization parallels exactly the extension from mumford s git to the more general git developed by bialynicki birula and wi cicka this point of view yields new results on the geometry of lvm and bosio s manifolds

painleve conjecture revisited the discovery of new integrable two dimensional hamiltonian systems is reported the analytic structure of the solutions makes necessary the generalization of the painlev e conjecture a widely used integrability criterion such a generalization is presented which the authors believe should replace the usual conjecture for two dimensional hamiltonian systems it is indeed compatible with all the systems already found and in addition leads to still new integrable cases

configuration spaces and polyhedral products abstract this paper aims to find the most general combinatorial conditions under which a moment angle complex d 2 s 1 k is a co h space thus splitting unstably in terms of its full subcomplexes in this way we study to which extent the conjecture holds that a moment angle complex over a golod simplicial complex is a co h space our main tool is a certain generalisation of the theory of labelled configuration spaces

a unified theory of surface roughness the properties of the peaks and summits of a rough surface are predicted on the assumption that the surface is two dimensional random noise the important result is that in non dimensional form the answers depend only to a minor degree on the parameters describing the surface or on the sampling interval used on the other hand the absolute values are strongly dependent on the sampling interval experimental results on a real surface agree remarkably well with the predictions