a system of matrix equations and a linear matrix equation over arbitrary regular rings with identity abstract in this paper we consider the classical system of matrix equations a 1 xb 1 c 1 a 2 xb 2 c 2 over r an arbitrary regular ring with identity necessary and sufficient conditions for the existence and the expression of the general solution to the system are derived as an application the linear matrix equation axb cyd e over r is considered

generalization of roth s solvability criteria to systems of matrix equations w e roth 1952 proved that the matrix equation ax xb c has a solution if and only if the matrices graphics and graphics are similar a dmytryshyn and b kagstrom 2015 extended roth s c

the solution of the equation ax x b 0 abstract we describe how to find the general solution of the matrix equation ax x b 0 where a c m n and b c n m are arbitrary matrices x c n m is the unknown and x denotes either the transpose or the conjugate transpose of x we first show that the solution can be obtained in terms of the kronecker canonical form of the matrix pencil a b and the two nonsingular matrices which transform this pencil into its kronecker canonical form we also give a complete description of the solution provided that these two matrices and the kronecker canonical form of a b are known as a consequence we determine the dimension of the solution space of the equation in terms of the sizes of the blocks appearing in the kronecker canonical form of a b the general solution of the homogeneous equation ax x b 0 is essential to finding the general solution of ax x b c which is related to palindromic eigenvalue problems that have attracted considerable attention recently

consistency of a pair of generalized sylvester equations a necessary and sufficient condition is given for the existence of a simultaneous solution of a pair of generalized sylvester equations an auxiliary result deals with constant solutions of sylvester equations with polynomial matrices

some subclasses of analytic functions involving the generalized noor integral operator abstract in this paper we define the generalized noor integral operator i p n a b c by using convolution by applying this operator we introduce some subclasses k p n a 1 b c a b kk p n a b c a b and s p n a b c a b of analytic functions and study their subordinate relations inclusion relations the integral operator the sufficient conditions for a function to be in the class s p n a b c and the radius problems

gromov witten invariants in algebraic geometry gromov witten invariants for arbitrary non singular projective vari eties and arbitrary genus are constructed using the techniques from k behrend b fantechi the intrinsic normal cone

consistency for bi skew symmetric solutions to systems of generalized sylvester equations over a finite central algebra let be a finite dimensional central algebra with an involutorial antiautomorphism and char 2 n n be the set of all n n matrices over a aij n n is called bisymmetric if aij an i 1 n j 1 aji and biskewsymmetric if aij an i 1 n j 1 aji the following systems of generalized sylvester equations over a1x yb1 c1 i asx ybs cs a1xb1 c1xd1 e1 ii asxbs csxds es are considered necessary and sufficient conditions are given for the existence of constant solutions with bi skew symmetric constrains to i and ii as a particular case auxiliary results dealing with the system of sylvester equations are also presented

the noor integral and strongly starlike functions abstract let a denote the class of analytic functions f z defined in the unit disc satisfying the condition f 0 f 0 1 0 we introduce some new subclasses of strongly starlike functions defined by the noor integral and study their properties

quivers and matrix equations abstract we discuss methods for solving some familiar matrix equations the methods were derived from the theory of quivers a powerful tool in the representation theory of algebras it is not necessary that the reader understand quivers but we include a brief explanation for those who may be interested

the noor integral operator and strongly close to convex functions the purpose of the present paper is to introduce some new subclasses of strongly close to convex functions defined by using the noor integral operator and study their inclusion relationships with the integral preserving properties our results include several previous known results as special cases

a recurrent neural network for solving sylvester equation with time varying coefficients presents a recurrent neural network for solving the sylvester equation with time varying coefficient matrices the recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time varying solution of a given sylvester equation theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network simulation results of time varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network

some classes of analytic functions involving noor integral operator the object of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions defined by using the noor integral operator the integral preserving properties in connection with the operator are also considered relevant connections of the results presented here with those obtained in earlier works are pointed out

weak approximation for isotrivial families we study weak approximation for isotrivial families of rationally connected varieties over a smooth projective curve in the case where the family is formed by taking a quotient of a cyclic group action we find a necessary and sufficient condition for weak approximation to hold in most other cases there is also a sufficient condition we also check that this condition is satisfied for all smooth fano hypersurfaces in projective spaces

singular foliations with trivial canonical class this paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds

solvability conditions and general solution for mixed sylvester equations in this paper we give some necessary and sufficient solvability conditions for the mixed sylvester matrix equations and parameterize general solution when it is solvable moreover we investigate the maximal and minimal ranks of the general solution and maximal and minimal ranks and inertias of hermitian part of solution respectively

stability of quaternionic linear systems the main goal of this paper is to characterize stability and bounded input bounded output bibo stability of quaternionic dynamical systems after defining the quaternion skew field algebraic properties of quaternionic polynomials such as divisibility and coprimeness are investigated having established these results the smith and the smith mcmillan forms of quaternionic matrices are introduced and studied finally all the tools that were developed are used to analyze stability of quaternionic linear systems in a behavioral framework

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial

the grothendieck ring of varieties and piecewise isomorphisms let k0 var k be the grothendieck ring of algebraic varieties over a field k l et x y be two algebraic varieties over k which are piecewise isomorphic i e x and y admit finite partitions x1 xn y1 yn into locally closed subvarieties such that xi is iso morphic to yi for all i n then x y in k0 var k larsen and lunts ask whether the converse is true for characteristic zero and algebraically closedfield k we answer positively this question when dim x 1o rx is a smooth connected projective surface or if x contains only finitely many rational curves

hermitian metrics of positive holomorphic sectional curvature on fibrations the main result of this note essentially is that if the base and fibers of a compact fibration carry hermitian metrics of positive holomorphic sectional curvature then so does the total space of the fibration the proof is based on the use of a warped product metric as in the work by cheung in case of negative holomorphic sectional curvature but differs in certain key aspects e g in that it does not use the subadditivity property for holomorphic sectional curvature due to grauert reckziegel and wu

simultaneous decomposition of quaternion matrices involving ź hermicity with applications let r and h m n stand respectively for the real number field and the set of all m n matrices over the real quaternion algebra h a 0 a 1 i a 2 j a 3 k i 2 j 2 k 2 ijk 1 a 0 a 1 a 2 a 3 r for i j k a real quaternion matrix a h n n is said to be hermitian if a a where a a and a stands for the conjugate transpose of a arising in widely linear modeling we present a simultaneous decomposition for a set of nine real quaternion matrices involving hermicity with compatible sizes a i h p i t i b i h p i t i 1 and c i h p i p i where ci are hermitian matrices i 1 2 3 as applications of the simultaneous decomposition we give necessary and sufficient conditions for the existence of an hermitian solution to the system of coupled real quaternion matrix equations a i x i a i b i x i 1 b i c i i 1 2 3 and provide an expression of the general hermitian solutions to this system moreover we derive the rank bounds of the general hermitian solutions to the above mentioned system using ranks of the given matrices ai bi and ci as well as the block matrices formed by them finally some numerical examples are given to illustrate the results of this paper

torsion cohomology classes and algebraic cycles on complex projective manifolds abstract atiyah and hirzebruch gave examples of even degree torsion classes in the singular cohomology of a smooth complex projective manifold which are not poincare dual to an algebraic cycle we notice that the order of these classes must be small compared to the dimension of the manifold however building upon a construction of kollar one can provide such examples with arbitrary high prime order the dimension being fixed this method also provides examples of torsion algebraic cycles which are non trivial in the griffiths group and lie in a arbitrary high level of the h saito filtration on chow groups

a simultaneous decomposition for seven matrices with applications abstract let h m n be the set of all m n matrices over the quaternion algebra h in this paper we construct a simultaneous decomposition for seven matrices with compatible sizes a h m n b h m p 1 c h m p 2 d h m p 3 e h q 1 n f h q 2 n and g h q 3 n as applications of the simultaneous matrix decomposition we give some solvability conditions general solutions as well as the range of ranks of the general solutions to the following two generalized sylvester matrix equations b x e c y f d z g a and b x w e c y f d z g a where a b c d e f and g are given quaternion matrices moreover we provide some numerical examples to illustrate the results of this paper

mathbb a 1 connected varieties of rank one over nonclosed fields in this paper we prove two results regarding the arithmetics of separably mathbb a 1 connected varieties of rank one first we prove that over a large field there is an mathbb a 1 curve through any rational point of the boundary if the boundary divisor is smooth and separably rationally connected secondly we generalize a theorem of hassett tschinkel for the zariski density of integral points over function fields of curves

a pencil of enriques surfaces with non algebraic integral hodge classes we prove that there exists a pencil of enriques surfaces defined over mathbb q with non algebraic integral hodge classes of non torsion type this gives the first example of a threefold with the trivial chow group of zero cycles on which the integral hodge conjecture fails as an application we construct a fourfold which gives the negative answer to a classical question of murre on the universality of the abel jacobi maps in codimension three

rational curves in holomorphic symplectic varieties and gromov witten invariants abstract we use gromov witten theory to study rational curves in holomorphic symplectic varieties we present a numerical criterion for the existence of uniruled divisors swept out by rational curves in the primitive curve class of a very general holomorphic symplectic variety of k 3 n type we also classify all rational curves in the primitive curve class of the fano variety of lines in a very general cubic 4 fold and prove the irreducibility of the corresponding moduli space our proofs rely on gromov witten calculations by the first author and in the fano case on a geometric construction of voisin in the fano case a second proof via classical geometry is sketched

a system of real quaternion matrix equations with applications abstract let h be the real quaternion algebra and h n m denote the set of all n m matrices over h let p h n n and q h m m be involutions i e p 2 i q 2 i a matrix a h n m is said to be p q symmetric if a paq this paper studies the system of linear real quaternion matrix equations a 1 x 1 c 1 x 1 b 1 c 2 a 2 x 2 c 3 x 2 b 2 c 4 a 3 x 1 b 3 a 4 x 2 b 4 c c we present some necessary and sufficient conditions for the existence of a solution to this system and give an expression of the general solution to the system when the solvability conditions are satisfied as applications we discuss the necessary and sufficient conditions for the system a a x c a xb b c b a c xb c c c to have a p q symmetric solution we also show an expression of the p q symmetric solution to the system when the solvability conditions are met moreover we provide an algorithm and a numerical example to illustrate our results the findings of this paper extend some known results in the literature

a system of quaternary coupled sylvester type real quaternion matrix equations abstract in this paper we establish some necessary and sufficient solvability conditions for a system of quaternary coupled sylvester type real quaternion matrix equations in terms of ranks and generalized inverses of matrices an expression of the general solution to this system is given when it is solvable also a numerical example is presented to illustrate the main result of this paper the findings of this paper widely generalize the known results in the literature the main results are also valid over the real number field and the complex number field

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

simultaneous solutions of matrix equations and simultaneous equivalence of matrices given matrices ai bi and ci i i of corresponding dimensions over a field f we prove that i if aiciobi are simultaneously similar to aioobi then there exists a simultaneous solution x to the matrix sylvester equations aix xbi ci and ii if aiciobi are simultaneously equivalent to aioobi then there exist simultaneous solutions x y to the matrix equations aix ybi ci we also show that analogous results hold for mixed pairs of matrix sylvester equations a1x1 yb1 c1 a2x2 yb2 c2 and for generalized stein equations x ayb c

weak approximation over function fields of curves over large or finite fields let k k c be the function field of a curve over a field k and let x be a smooth projective separably rationally connected k variety with x k neq emptyset under the assumption that x admits a smooth projective model pi mathcal x to c we prove the following weak approximation results 1 if k is a large field then x k is zariski dense 2 if k is an infinite algebraic extension of a finite field then x satisfies weak approximation at places of good reduction 3 if k is a nonarchimedean local field and r equivalence is trivial on one of the fibers mathcal x p over points of good reduction then there is a zariski dense subset w subseteq c k such that x satisfies weak approximation at places in w as applications of the methods we also obtain the following results over a finite field k 4 if k 10 then for a smooth cubic hypersurface x k the specialization map x k longrightarrow prod p in p mathcal x p kappa p at finitely many points of good reduction is surjective 5 if mathrm char k neq 2 3 and k 47 then a smooth cubic surface x over k satisfies weak approximation at any given place of good reduction

two sided coupled generalized sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices abstract in this paper we investigate and analyze in detail the structure and properties of a simultaneous decomposition for fifteen matrices a i c p i t i b i c s i q i c i c p i t i 1 d i c s i 1 q i and e i c p i q i i 1 2 3 we show that from this simultaneous decomposition we can derive some necessary and sufficient conditions for the existence of a solution to the system of two sided coupled generalized sylvester matrix equations with four unknowns a i x i b i c i x i 1 d i e i i 1 2 3 apart from proving an expression for the general solutions to this system we derive the range of ranks of these solutions using the ranks of the given matrices a i b i c i d i and e i we provide some numerical examples to illustrate our results moreover we present a similar approach to consider the simultaneous decomposition for 5k matrices and the system of k two sided coupled generalized sylvester matrix equations with k 1 unknowns a i x i b i c i x i 1 d i e i i 1 k k 4 the main results are also valid over the real number field and the real quaternion algebra

constrained two sided coupled sylvester type quaternion matrix equations abstract in this paper we consider the solvability of a system of constrained two sided coupled generalized sylvester quaternion matrix equations some necessary and sufficient conditions for the existence of solutions to this system are derived in terms of the ranks and the generalized inverses of the coefficient matrices moreover we find an expression of the general solution to this system when the solvability conditions are satisfied finally a numerical example is presented to illustrate our results

the quaternion lms algorithm for adaptive filtering of hypercomplex processes the quaternion least mean square qlms algorithm is introduced for adaptive filtering of three and four dimensional processes such as those observed in atmospheric modeling wind vector fields these processes exhibit complex nonlinear dynamics and coupling between the dimensions which make their component wise processing by multiple univariate lms bivariate complex lms clms or multichannel lms mlms algorithms inadequate the qlms accounts for these problems naturally as it is derived directly in the quaternion domain the analysis shows that qlms operates inherently based on the so called ldquoaugmentedrdquo statistics that is both the covariance e xx h and pseudocovariance e xx t of the tap input vector x are taken into account in addition the operation in the quaternion domain facilitates fusion of heterogeneous data sources for instance the three vector dimensions of the wind field and air temperature simulations on both benchmark and real world data support the approach

on certain classes of analytic functions defined by noor integral operator abstract integral operator introduced by noor is defined by using convolution let fn z z 1 z n 1 n n0 and let f be analytic in the unit disc e then inf f 1 n f where fn f 1 n z 1 z using this operator certain classes of analytic functions related with the classes of functions with bounded boundary rotation and bounded boundary radius rotation are defined and studied in detail some basic properties rate of growth of coefficients and a radius problem are investigated it is shown that these classes are closed under convolution with convex functions most of the results are best possible in some sense

right eigenvalue equation in quaternionic quantum mechanics we study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n dimensional quaternionic vector spaces for quaternionic linear operators the eigenvalue spectrum consists of n complex values for these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations our discussion is also extended to complex linear operators whose spectrum is characterized by 2n complex eigenvalues we show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products finally we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution

roth s solvability criteria for the matrix equations ax xˆb c and x axˆb c over the skew field of quaternions with an involutive automorphism q qˆ abstract the matrix equation a x x b c has a solution if and only if the matrices a c 0 b and a 0 0 b are similar this criterion was proved over a field by w e roth 1952 and over the skew field of quaternions by huang liping 1996 h k wimmer 1988 proved that the matrix equation x a x b c over a field has a solution if and only if the matrices a c 0 i and i 0 0 b are simultaneously equivalent to a 0 0 i and i 0 0 b we extend these criteria to the matrix equations a x x b c and x a x b c over the skew field of quaternions with a fixed involutive automorphism q q

properties of close to convexity preserved by some integral operators let c s and k be the classes of univalent functions defined in e z z 1 which are convex of order starlike of order and close to convex of order type let f z 1 z1 1 z0z1x 2 f z dz 0 1 we discuss the properties of the function f when this function f belongs to the class k and its various subclasses

potentially non klt locus and its applications we introduce the notion of potentially klt pairs for normal projective varieties with pseudoeffective anticanonical divisor the potentially non klt locus is a subset of x which is birationally transformed precisely into the non klt locus on a k x minimal model of x we prove basic properties of potentially non klt locus in comparison with those of classical non klt locus as applications we give a new characterization of varieties of fano type and we also improve results on the rational connectedness of uniruled varieties with pseudoeffective anticanonical divisor

quaternions and matrices of quaternions abstract we give a brief survey on quaternions and matrices of quaternions present new proofs for certain known results and discuss the quaternionic analogues of complex matrices the methods of converting a quaternion matrix to a pair of complex matrices and homotopy theory are emphasized

local global principle for 0 cycles on fibrations over rationally connected bases abstract we study the brauer manin obstruction to the hasse principle and to weak approximation for 0 cycles on algebraic varieties that possess a fibration structure the issue is to establish the exactness of a local to global sequence e of chow groups of 0 cycles recently harpaz and wittenberg proved the exactness of e for rationally connected fibrations whose smooth fibres verify the exactness of e and whose base is either the projective space or a curve verifying the exactness of e in the present paper we prove the exactness of e for fibrations whose bases are ch telet surfaces or smooth proper models of homogeneous spaces of connected linear algebraic groups with connected stabilizers we require that either the fibration is valuatively split in codimension 1 and most closed fibres satisfy weak approximation for 0 cycles or the generic fibre has a 0 cycle of degree 1 and e is exact for most fibres

families of rationally connected varieties recall that a proper variety x is said to be rationally connected if two general points p q x are contained in the image of a map g p x this is clearly a birationally invariant property when x is smooth this turns out to be equivalent to the a priori weaker condition that two general points can be joined by a chain of rational curves and also to the a priori stronger condition that for any finite subset x there is a map g p x whose image contains and such that gtx is an ample bundle

on the fibration method for zero cycles and rational points conjectures on the existence of zero cycles on arbitrary smooth projective varieties over number elds were proposed by colliot th el ene sansuc kato and saito in the 1980 s we prove that these conjectures are compatible with brations for brations into rationally connected varieties over a curve in particular they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers we prove the analogous result for rational points conditionally on a conjecture on locally split values of polynomials which a recent work of matthiesen establishes in the case of linear polynomials over the rationals

generalized schur methods with condition estimators for solving the generalized sylvester equation stable algorithms are presented for solving the generalized sylvester equation they are based on orthogonal equivalence transformations of the original problem perturbation theory and rounding error analysis are included condition estimators dif sup 1 estimators are developed which when substituted into derived error bounds give accuracy estimates of a computed solution results from numerical experiments on well conditioned and ill conditioned problems are reported

inclusion properties of a subclass of analytic functions defined by an integral operator involving the gauss hypergeometric function abstract in the present paper we introduce and investigate a new subclass of analytic functions in the open unit disk u which is defined by the convolution f 1 f z where f z 1 z 2 f 1 a b c z z z 2 f 1 a b c z z u 0 several interesting properties including for example integral preserving properties of this analytic function class are also considered

output feedback eigenstructure assignment using two sylvester equations the eigenstructure assignment problem with output feedback is studied for systems satisfying the condition p m n the main tool used is the concept of c a b invariance and two coupled sylvester equations the solution of which leads to the computation of an output stabilizing feedback a computationally efficient algorithm for the solution of these two coupled equations which leads to the computation of a desired output feedback is presented

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

on integral operators abstract let fn z z 1 z n 1 n no and f 1 n be defined such that f n f 1 n z 1 z where denotes convolution hadamard product let f be analytic in the unit disc e we define a new operator inf f 1 n f which is analogous to one defined by ruscheweyh using this operator the classes m n are defined a function f analytic in e is in m n if and only if inf is close to convex the properties of f m n are discussed in some detail it is shown that m n m n 1 for n no and for n 0 1 m n consists entirely of univalent functions closure properties of some integral operators defined on m n are also given

bloch s conjecture for catanese and barlow surfaces catanese surfaces are regular surfaces of general type with pg 0 they specialize to double covers of barlow surfaces we prove that the ch0 group of a catanese surface is equal to z which implies the same result for the barlow surfaces

solution to generalized sylvester matrix equations an explicit solution to the generalized sylvester matrix equation ax by exf is established this solution is expressed in terms of the r controllability matrix of e a b a generalized symmetric operator matrix and an observability matrix moreover based on this solution solutions to some other matrix equations are also derived the results may provide great convenience for the analysis and synthesis problems related to these equations

integral operators defined by convolution with hypergeometric functions we define an integral operator on the class a of analytic functions in the unit disc involving gauss hypergeometric functions and introduce certain new subclasses of a using this operator some inclusion results a covering theorem radius problems and several other interesting properties of these classes are studied

solutions to matrix equations x axb cy r and x axb cy r abstract the present work proposed an alternative approach to find the closed form solutions of the nonhomogeneous yakubovich matrix equation x a x b c y r based on the derived closed form solution to the nonhomogeneous yakubovich matrix equation the solutions to the nonhomogeneous yakubovich quaternion j conjugate matrix equation x a x b c y r are obtained by the use of the real representation of a quaternion matrix the existing complex representation method requires the coefficient matrix a to be a block diagonal matrix over complex field in contrast in this publication we allow a quaternion matrix of any dimension as an application eigenstructure assignment problem for descriptor linear systems is considered

on subordinations for certain analytic functions associated with noor integral operator by making use of the method of differential subordination we investigate several interesting properties of the noor integral operator

comments on the quaternion lms algorithm for adaptive filtering of hypercomplex processes in a previous paper took et al proposed a quaternion least mean square algorithm for adaptive filters the gradients can be obtained in two different solutions from the same cost function the derivation of the gradient is incorrect because the quaternion product is non commutative we study the quaternion gradient update rules and derive the right quaternion gradient the obtained gradient in the correction has only one solution

systems of coupled generalized sylvester matrix equations this paper studies some systems of coupled generalized sylvester matrix equations we present some necessary and sufficient conditions for the solvability to these systems we give the expressions of the general solutions to the systems when their solvability conditions are satisfied

log fano varieties over function fields of curves consider a smooth log fano variety over the function field of a curve suppose that the boundary has positive normal bundle choose an integral model over the curve then integral points are zariski dense after removing an explicit finite set of points on the base curve