generalizations of siegel s and picard s theorems we prove new theorems that are higher dimensional generalizations of the classical theorems of siegel on integral points on affine curves and of picard on holomorphic maps from c to affine curves these include results on integral points over varying number fields of bounded degree and results on kobayashi hyperbolicity we give a number of new conjectures describing from our point of view how we expect siegel s and picard s theorems to optimally generalize to higher dimensions in this article we prove new theorems that are higher dimensional generaliza tions of the classical theorems of siegel on integral points on affine curves and of picard on holomorphic maps from c to affine curves in section 2 we will give the statements of siegel s and picard s theorems and we will recall how these two theorems from such seemingly different areas of mathematics are related we will then proceed to give a number of new conjectures describing from our point of view how we expect siegel s and picard s theorems to optimally generalize to higher dimensions these include conjectures on integral points over varying number fields of bounded degree and conjectures addressing hyperbolic questions these conjectures appear to be fundamentally new we will then summarize our progress on these conjectures we have been able to get results in all dimensions with best possible results in many cases for surfaces

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

holomorphic curves into algebraic varieties intersecting divisors in subgeneral position recently there are many developments on the second main theorem for holomorphic curves into algebraic varieties intersecting divisors in general position or subgeneral position in this paper we refine the concept of subgeneral position by introducing the notion of the index of subgeneral position with this new notion we give some surprising improvement of the previous known second main theorem type results moreover via the analogue between nevanlinna theory and diophantine approximation the corresponding schmidt s subspace type theorems are also established in the final section

sur la non densite des points entiers we give non density results for integral points on affine varieties inthe spirit of lang vojta conjecture in particular let x be a projective variety of dimension d 2 over a number field k resp over c let h be the sum of 2d properly intersecting ample divisors on x we show that any set of quasi integral points resp any integral curve on x h is not zariski dense resume on donne des resultats de non densite pour les points entiers sur des varietes affines dans l esprit de la conjecture de lang vojta en particulier soit x une variete pro jective de dimension d 2 sur un corps de nombres k resp sur c soit h la somme de 2d diviseurs amples sur x qui se coupent proprement on montre que tout ensemble de points quasi entiers resp toute courbe entiere sur x h est non zariski dense

two point constitutive equations and integration algorithms for isotropic hardening rate independent elastoplastic materials in large deformation this paper presents alternative forms of hyperelastic plastic constitutive equations and their integration algorithms for isotropic hardening materials at large strain which are established in two point tensor field namely between the first piola kirchhoff stress tensor and deformation gradient the eigenvalue problems for symmetric and non symmetric tensors are applied to kinematics of multiplicative plasticity which imply the transformation relationships of eigenvectors in current intermediate and initial configurations based on the principle of plastic maximum dissipation the two point hyperelastic stress strain relationships and the evolution equations are achieved in which it is considered that the plastic spin vanishes for isotropic plasticity on the computational side the exponential algorithm is used to integrate the plastic evolution equation the return mapping procedure in principal axes with respect to logarithmic elastic strain possesses the same structure as infinitesimal deformation theory then the theory of derivatives of non symmetric tensor functions is applied to derive the two point closed form consistent tangent modulus which is useful for newton s iterative solution of boundary value problem finally the numerical simulation illustrates the application of the proposed formulations

tackling an mcdm problem with the help of some results from fuzzy set theory abstract the problem to be addressed and tackled in this paper arose as a byproduct from some efforts at solving problems involving multiple goals by linking linear and goal programming models the critical issue was that some forms for interdependence among the goals could not be handled in the programming models here we will deal with a set of goals with realistic counterparts in a finnish plywood industry in which a subset of the goals are i conflicting another subset ii unilaterally supporting and a third subset iii mutually supporting it is furthermore observed that the elements of a studied set of goals may be partly independent and partly interdependent which makes the context a fullfledged mcdm problem it is tackled with a technique which is based on the theory of fuzzy sets the conceptual framework for fuzzy decisions and the algorithms developed for fuzzy mathematical programming the resulting fuzzy multiobjective programming model is simplified and tested with the help of a fairly complex numerical example

a defect relation for holomorphic curves intersecting hypersurfaces in 1933 h cartan proved a defect relation q j 1 f h j n 1 for a linearly nondegenerate holomorphic curve f inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i and hyperplanes h j 1 j q in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i in general position this paper extends it to holomorphic curves intersecting hypersurfaces in 1979 b shiffman conjectured that if f inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i is an algebraically non degenerate holomorphic map and d 1 d q are hypersurfaces in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i in general position then q j 1 f d j n 1 this paper proves this conjecture

on a general thue s equation we analyze the integral points on varieties defined by one equation of the form f 1 f r g where the f i g are polynomials in n variables with algebraic coefficients and g has small degree we shall use a method that we recently introduced in the context of siegel s theorem for integral points on curves classical very particular instances of our equations arise e g in a well known corollary of roth s theorem the case n 2 f i linear forms deg g r 2 and with the norm form equations treated by w m schmidt here we shall prove thm 1 that the integral points are not zariski dense provided deg f i n max deg f i deg g and provided the f i g satisfy certain mild assumptions which are generically verified our conclusions also cover certain complete intersection subvarieties of our hypersurface thm 2 finally we shall prove thm 3 an analogue of the schmidt s subspace theorem for arbitrary polynomials in place of linear forms

holomorphic curves and integral points off divisors we deal with the distributions of holomorphic curves and integral points off divisors we will simultaneously prove an optimal dimension estimate from above of a subvariety w off a divisor d which contains a zariski dense entire holomorphic curve or a zariski dense d integral point set provided that in the latter case everything is defined over a number field then if the number of components of d is large the estimate leads to the constancy of such a holomorphic curve or the finiteness of such an integral point set at the beginning we extend logarithmic bloch ochiai s theorem to the kahler case

aspiration profile preserving compromising within a multicriterial conflict zone abstract the multicriterial compromise problem is tackled by a fuzzy linear programming construct based on given aspirations the aspiration vector is interpreted as a managerially relevant profile in objective space the key issue is to find an efficient compromise which corresponds to the aspiration profile as closely as possible

profit apportionment in concerns with mutual ownership an application of fuzzy inequalities abstract this study focuses on the profit apportionment problem in concerns with mutual ownership between the concern members the analysis draws upon the following results 1 i weil s matrix algebraic formula for profit apportionment 2 ii wallin s fuzzy linear programming model 3 iii ramik and rimanek s model for transforming fuzzy inequalities into ordinary crisp inequalities the study extends the sensitivity analysis presented by wallin through incorporating imprecise profit aspirations and trade off intervals in the problem formulation due to weil s formula the approach is applicable to large scale concern structures the fuzzy lp framework provides one approach to expressing subjective imprecision in the aspirations of the decision maker with obvious relevance for concern management

algebraic hyperbolicity of ramified covers of mathbb g 2_m and integrap points on affine subsets of mathbb p _2 let x be a smooth affine surface x to mathbb g 2 m be a finite morphism we study the affine curves on x with bounded genus and number of points at infinity obtaining bounds for their degree in terms of euler characteristic a typical example where these bounds hold is represented by the complement of a three component curve in the projective plane of total degree at least 4 the corresponding results may be interpreted as bounding the height of integral points on x over a function field in the language of diophantine equations our results may be rephrased in terms of bounding the height of the solutions of f u v y 0 with u v y over a function field u v s units it turns out that all of this contain some cases of a strong version of a conjecture of vojta over function fields in the split case moreover our method would apply also to the nonsplit case we remark that special cases of our results in the holomorphic context were studied by m green already in the seventies and recently in greater generality by noguchi winkelmann and yamanoi however the algebraic context was left open and seems not to fall in the existing techniques

on cartan s theorem and cartan s conjecture we give a mild generalization of cartan s theorem on value distribution for a holomorphic curve in projective space relative to hyperplanes this generalization is used to complete the proof of the following theorem claimed in an earlier paper by the author given hyperplanes in projective space in general position there exists a finite union of proper linear subspaces such that all holomorphic curves not contained in that union even linearly degenerate curves satisfy the inequality of cartan s theorem except for the ramification term in addition it is shown how these methods can lead to a shorter proof of nochka s theorem on cartan s conjecture and in the number field case how nochka s theorem gives a short proof of wirsing s theorem on approximation of algebraic numbers by algebraic numbers of bounded degree