slanted vector fields for jet spaces low pole order frames of slanted vector fields are constructed on the space of vertical k jets of the universal family of complete intersections in mathbb p n and adapting the arguments low pole order frames of slanted vector fields are also constructed on the space of vertical logarithmic k jets along the universal family of projective hypersurfaces in mathbb p n with several irreducible smooth components both the pole order here 5k 2 and the determination of the locus where the global generation statement fails are improved compared to the literature previously k 2 2k thanks to three new ingredients we reformulate the problem in terms of some adjoint action we introduce a new formalism of geometric jet coordinates and then we construct what we call building block vector fields making the problem for arbitrary jet order k geqslant 1 into a very analog of the much easier case where k 0 i e where no jet coordinates are needed

integral points divisibility between values of polynomials and entire curves on surfaces abstract we prove some new degeneracy results for integral points and entire curves on surfaces in particular we provide the first examples to our knowledge of a simply connected smooth variety whose sets of integral points are never zariski dense some of our results are connected with divisibility problems i e the problem of describing the integral points in the plane where the values of some given polynomials in two variables divide the values of other given polynomials

nilpotent and polycyclic by finite maximal subgroups of skew linear groups abstract let d be an infinite division ring n a natural number and n a subnormal subgroup of gl n d such that n 1 or the center of d contains at least five elements this paper contains two main results in the first one we prove that each nilpotent maximal subgroup of n is abelian this generalizes the result in ebrahimian 2004 3 which asserts that each maximal subgroup of gl n d is abelian and a result in ramezan nassab and kiani 2013 12 in the second one we show that a maximal subgroup of gl n d cannot be polycyclic by finite

holomorphic curves in surfaces of general type this note answers some questions on holomorphic curves and their distribution in an algebraic surface of positive index more specifically we exploit the existence of natural negatively curved pseudo finsler metrics on a surface s of general type whose chern numbers satisfy c 2 1 2c2 to show that a holomorphic map of a riemann surface to s whose image is not in any rational or elliptic curve must satisfy a distance decreasing property with respect to these metrics we show as a consequence that such a map extends over isolated punctures so assuming that the riemann surface is obtained from a compact one of genus q by removing a finite number of points then the map is actually algebraic and defines a compact holomorphic curve in s furthermore the degree of the curve with respect to a fixed polarization is shown to be bounded above by a multiple of q 1 irrespective of the map

defect relations for holomorphic maps between spaces of different dimensions there is now a rather rich theory of defect relations for holomorphic maps between spaces of equal dimension developed by nevanlinna stoll griffiths and many other people however for the case of maps between spaces of unequal dimension essentially there is only the theory developed by weyl weyl and ahlfors when the target space is the complex projective space and their theory is built on the projective linear structure of the projective space a partial list of references for these results is given at the end of this paper in this paper we derive a defect relation for holomorphic maps between spaces of different dimensions where the target space can be an arbitrary compact complex algebraic manifold since the special case of maps from c to a compact complex manifold of complex dimension two contains already the methods and techniques needed for the general case in order to avoid unnecessarily complicated notations and to make the arguments more easily understood we give complete details only for this special case and indicate the easy modifications needed for the general case besides the usual techniques in value distribution theory of using the poincar6 lelong formula the calculus lemma of estimating the integrand by its integral and the concavity of logarithm a new key point in our argument is to introduce a meromorphic connection so that the second fundamental form of a divisor with respect to the connection is zero more precisely for the case of a meromorphic map f from c to a compact kihler surface m to consider the defect for a nonsingular zero set of a holomorphic section s of a positive holomorphic line bundle l we introduce a meromorphic connection i v form with the following two properties i for some hermitian holomorphic line bundle f over m and some holomorphic section 0 of f

compact kahler manifolds with nonpositive bisectional curvature in this article we prove that for any compact kahler manifold mn with real analytic metric and nonpositive bisectional curvature there exists a finite cover m of m such that m is a holomorphic and metric fiber bundle over a compact kahler manifold n with nonpositive bisectional curvature and c1 n 0 and the fiber is a flat complex torus this partially confirms a conjecture of yau

maximal subgroups of sln d abstract given a non commutative f central division ring d n a subnormal subgroup of g l n d and m a non abelian maximal subgroup of n if m is a non abelian soluble maximal subgroup of n then n 1 and d is cyclic of prime degree p with a maximal cyclic subfield k f such that the groups g a l k f and m k m are isomorphic furthermore for any x m k we have x p f and d f m i 1 p k x i

a collocation method for the gurtin maccamy equation with finite life span a collocation method along the characteristics for a stiff problem arising from population dynamics is proposed and analyzed it is a fourth order implicit runge kutta method of two stage to the integration of the ode along the characteristics whose collocation points are zeros of the linearly transformed legendre monic polynomial nonnegativity of the numerical solutions is shown the stability of the method is discussed it is proven that the scheme is convergent at a fourth order rate in the maximum norm several numerical examples are presented

locally soluble by locally finite maximal subgroups of gln d abstract let d be a non commutative division ring and m a maximal subgroup of gl n d n 2 this paper continues the ongoing effort to show that the structure of maximal subgroups of gl n d is similar in some sense to the structure of gl n d it is known that every locally soluble normal subgroup of gl n d is abelian here among other results we prove that if either i d is finite dimensional over its center or ii the center of d contains at least five elements and m is soluble by finite or iii char d 0 and m is locally soluble by finite then every locally soluble normal subgroup of m is abelian

finitely generated subnormal subgroups of gln d are central abstract let d be an infinite division algebra of finite dimension over its center assume that n is a subnormal subgroup of gln d with n 1 it is shown that if n is finitely generated then n is central

pluri canonical divisors on kahler manifolds soit p x m une application reguliere propre de varietes complexes a fibres connexes de dimension k o est un point de m on suppose que p 1 0 x 0 est dans la classe 7b c soit m un entier positif et on suppose le diviseur d une section non nulle dans h 0 x 0 xd 0 k m est lisse alors il y a un voisinage analytique u de o dans m tel que p l p 1 z p l x 0 pour l 1 m et pour tout z dans u

effective algebraic degeneracy we show that for every smooth projective hypersurface x n 1 of degree d and of arbitrary dimension n 2 if x is generic then there exists a proper algebraic subvariety y x such that every nonconstant entire holomorphic curve f x has image f which lies in y as soon as its degree satisfies the effective lower bound d geqslant 2 n 5

approximating the survival probability in finite life span population models abstract we consider the numerical approximation of the survival probability in the case of an unbounded mortality rate related to a finite life span in age structured population models our numerical approach is based on the approximation of the integral that characterizes this probability function by means of an appropriate quadrature rule we demonstrate the convergence of this approximation assuming suitable conditions in relation with the unbounded mortality rate that will be reasonable in the real applications of this model the numerical experiments carried out with typical mortality rates corroborate the interest of this method

age time continuous galerkin methods for a model of population dynamics continuous galerkin finite element methods in the age time domain are proposed to approximate the solution to the model of population dynamics with unbounded mortality coefficient function stability of the method is established and a priori l 2 error estimates are obtained treatment of the nonlocal boundary condition is straightforward in this framework the approximate solution is computed strip by strip marching in time some numerical examples are presented

hyperbolicity of generic surfaces of high degree in projective 3 space the main goal of this work is to prove that a very generic surface of degree at least 21 in complex projective 3 dimensional space is hyperbolic in the sense of kobayashi this means that every entire holomorphic map f inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i x to the surface is constant in 1970 kobayashi conjectured more generally that a very generic hypersurface of sufficiently high degree in projective space is hyperbolic our technique follows the stream of ideas initiated by green and griffiths in 1979 which consists of considering jet differentials and their associated base loci however a key ingredient is the use of a different kind of jet bundle namely the semple jet bundles previously studied by the first named author the base locus calculation is achieved through a sequence of riemann roch formulas combined with a suitable generic vanishing theorem for order 2 jets our method covers the case of surfaces of general type with picard group inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i and 13 12 2 c 2 1 9 c 2 0 where 2 is the 2 jet threshold bounded below by 1 6 for surfaces in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i 3 the final conclusion is obtained by using recent results of mcquillan on holomorphic foliations

on the complement of a generic curve in the projective plane let c be a very generic smooth curve of degree d in the complex projective plane in this paper we show that for any curve d in the projective plane that does not contain c the set c d contains at least d 2 distinct points moreover this bound is sharp when d 3 our motivation for the study of this problem comes from the problem of hyperbolicity of the complement of a plane curve as an application of our result we give another proof of the following fact if c is a very generic smooth curve of degree d 5 in the complex projective plane then the intersection of the complement of c in the projective plane with any plane curve d which does not contain c is hyperbolic

a remark on the codimension of the green griffiths locus of generic projective hypersurfaces of high degree we show that for every smooth generic projective hypersurface x in p n 1 there exists a proper subvariety y in x of codimension at least 2 such that for every non constant holomorphic map f c x one has f c is contained in y provided that the degree of x is greater than 2 n 5 in particular we obtain an affirmative confirmation of the kobayashi conjecture for threefolds in p 4

discontinuous continuous galerkin methods for a structured model of a biological system a hybrid discontinuous continuous galerkin finite element method is proposed to approximate the solution to a class of composite hyperbolic parabolic pdes which arises in the study of biological systems we employ a discontinuous galerkin finite element technique for the numerical approximation of the linear hyperbolic transport part of the pde posed in an age time domain while we approximate the second order elliptic operator using a standard conforming finite element method the strong stability is established and a priori l 2 l 2 error estimates are obtained the finite elements in the age time domain are constructed in such a manner that the discontinuous galerkin method is applied over a triangulation in an explicit fashion from triangle to triangle the methods are effective in the sense that age and time steppings are easily adaptive and the computations are readily parallelizable no restriction is imposed on the time step in connection with the mesh size in the space the approximate solution is computed slap by slap marching in time some numerical examples are presented

numerical methods for the lotka mckendrick s equation the lotka mckendrick s model is a well known model which describes the evolution in time of the age structure of a population in this paper we consider this linear model and discuss a range of methods for its numerical solution we take advantage of different analytical approaches to the system to design different numerical methods and compare them with already existing algorithms in particular we set up some algorithms inspired by the approach based on volterra integral equations and we also consider a direct approach based on the nonlinear system that describes the evolution of the age profile of the population

on the approximation of the lotka mckendrick equation with finite life span abstract we consider the linear lotka mckendrick equation and discuss in detail how to solve the problem of the breakdown of the usual finite difference methods when the mortality is unbounded usual error bounds require some derivative of the mortality rate to be bounded across all ages our approach works for a model class of mortality rates and we show that not all methods are compatible with any mortality function

defects for ample divisors of abelian varieties schwarz lemma and hyperbolic hypersurfaces of low degrees we prove that the defect vanishes for a holomorphic map f from the affine complex line to an abelian variety a and for an ample divisor d in a the proof uses the translational invariance of the zariski closure of the k jet space of the image of f and the theorem of riemann roch to construct a nonidentically zero meromorphic k jet differential whose pole divisor is dominated by a divisor equivalent to pd and which vanishes along the k jet space of d to order q with p q smaller than a prescribed small positive number then estimates involving the theta function with divisor d and the logarithmic derivative lemma are used we also prove a pointwise schwarz lemma which gives the vanishing of the pullback by a holomorphic map from the affine complex line to a compact complex manifold of a holomorphic jet differential vanishing on an ample divisor this pointwise schwarz lemma is a slight modification of a statement whose proof green and griffiths sketched in their alternative treatment of bloch s theorem on entire curves in abelian varieties the log pole case of the pointwise schwarz lemma is also given we construct examples of hyperbolic hypersurface whose degree is only 16 times the square of its dimension

vector fields on the total space of hypersurfaces in the projective space and hyperbolicity the results we obtain in this article concern the hyperbolicity of very generic hypersurfaces in the 3 dimensional projective space we show that the kobayashi conjecture is true in this setting as long as the degree of the hypersurface is greater than 18

on the logarithmic kobayashi conjecture we study the hyperbolicity of the log variety pn x where x is a very general hypersurface of degree d 2n 1 which is the bound predicted by the kobayashi conjecture using a positivity result for the sheaf of twisted logarithmic vector fields which may be of independent interest we show that any log subvariety of pn x is of log general type give a new proof of the algebraic hyperbolicity of pn x and exclude the existence of maximal rank families of entire curves in the complement of the universal degree d hypersurface moreover we prove that as in the compact case the algebraic hyperbolicity of a log variety is a necessary condition for the metric one

nilpotent maximal subgroups of gln d abstract in s akbari j algebra 217 1999 422 433 it has been conjectured that if d is a noncommutative division ring then d contains no nilpotent maximal subgroup in connection with this conjecture we show that if gln d contains a nilpotent maximal subgroup say m then m is abelian provided d is infinite this extends one of the main results appeared in s akbari j algebra 259 2003 201 225 theorem 4

a numerical method for nonlinear age structured population models with finite maximum age abstract we propose a new numerical method for the approximation of solutions to a non autonomous form of the classical gurtin maccamy population model with a mortality rate that is the sum of an intrinsic age dependent rate that becomes unbounded as the age approaches its maximum value plus a non local non autonomous bounded rate that depends on some weighted population size we prove that our new quadrature based method converges to second order and we show the results of several numerical simulations

on the brody hyperbolicity of moduli spaces for canonically polarized manifolds we show that the moduli stack mh of canonically polarized complex manifolds with hilbert polynomial h is brody hyperbolic hence if mh denotes the corresponding coarse moduli scheme and if u mh is a quasi finite morphism induced by a family then there are no nonconstant holomorphic maps c u

on the hyperbolicity of the complements of curves in algebraic surfaces the three component case the paper is a contribution to the conjecture of kobayashi that the complement of a generic curve in the projective plane is hyperbolic provided the degree is at least five previously the authors treated the cases of two quadrics and a line and three quadrics the main results are let c be the union of three curves in p 2 whose degrees are at least two one of which is at least three then for generic such configurations the complement of c is hyperbolic and hyperbolically embedded the same statement holds for complements of curves in generic hypersurfaces x of degree at least five and curves which are intersections of x with hypersurfaces of degree at least five furthermore results are shown for curves on surfaces with picard number one

maximal subgroups of gln d abstract in this paper we study the structure of locally solvable solvable locally nilpotent and nilpotent maximal subgroups of skew linear groups in s akbari et al j algebra 217 1999 422 433 it has been conjectured that if d is a division ring and m a nilpotent maximal subgroup of d then d is commutative in connection with this conjecture we show that if f m f contains an algebraic element over f then m is an abelian group also we show that c c j is a solvable maximal subgroup of real quaternions and so give a counterexample to conjecture 3 of s akbari et al j algebra 217 1999 422 433 which states that if d is a division ring and m a solvable maximal subgroup of d then d is commutative also we completely determine the structure of division rings with a non abelian algebraic locally solvable maximal subgroup which gives a full solution to both cases given in theorem 8 of s akbari et al j algebra 217 1999 422 433 ultimately we extend our results to the general skew linear groups

high order discontinuous galerkin methods for a class of transport equations with structured populations in this paper we analyze a discontinuous galerkin finite element method for approximating solutions to transport equations with certain nonlinearities we consider models for age structured populations allowing for a nonlinear removal rate with non local boundary conditions on the in flow boundary the method employs a stabilizing term over the interior edges allowing for convergence in a stronger than usual norm we establish convergence rates for general higher order basis functions and provide numerical examples consistent with this result